U.S. patent application number 17/582587 was filed with the patent office on 2022-09-29 for automotive radar device.
The applicant listed for this patent is UHNDER, INC.. Invention is credited to Murtaza Ali, Stephen William Alland, Jean Pierre Bordes, Vasco Caldeira, Curtis Davis, Paul W. Dent, Aria Eshraghi, Marius Goldenberg, Monier Maher, Frederick Rush, Suleyman Gokhun Tanyer.
Application Number | 20220308160 17/582587 |
Document ID | / |
Family ID | 1000006434070 |
Filed Date | 2022-09-29 |
United States Patent
Application |
20220308160 |
Kind Code |
A1 |
Dent; Paul W. ; et
al. |
September 29, 2022 |
AUTOMOTIVE RADAR DEVICE
Abstract
An automotive radar using combinations of the techniques of
alternating transmit-receive bursts of digitally frequency
modulated millimeter wave carriers; sparse MIMO antenna arrays with
sidelobe-suppressive coarse and fine beamforming; frequency
hopping; range-walking-compensated Doppler analysis and successive,
and subtractive target detection in signal strength order.
Inventors: |
Dent; Paul W.; (Pittsboro,
NC) ; Tanyer; Suleyman Gokhun; (Victoria, CA)
; Ali; Murtaza; (Cedar Park, TX) ; Rush;
Frederick; (Auburn, AL) ; Maher; Monier; (St.
Louis, MO) ; Eshraghi; Aria; (Austin, TX) ;
Bordes; Jean Pierre; (St. Charles, MO) ; Goldenberg;
Marius; (Austin, TX) ; Caldeira; Vasco; (Sao
Domingos de Rana, PT) ; Alland; Stephen William;
(Newbury Park, CA) ; Davis; Curtis; (St. Louis,
MO) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
UHNDER, INC. |
Austin |
TX |
US |
|
|
Family ID: |
1000006434070 |
Appl. No.: |
17/582587 |
Filed: |
January 24, 2022 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
63140567 |
Jan 22, 2021 |
|
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G01S 7/354 20130101;
G01S 7/0232 20210501; G01S 13/931 20130101; G01S 7/0234 20210501;
G01S 7/358 20210501; G01S 7/0236 20210501; G01S 7/0231
20210501 |
International
Class: |
G01S 7/02 20060101
G01S007/02; G01S 7/35 20060101 G01S007/35 |
Claims
1. An radar sensing system comprising: a transmitter configured to
transmit radio signals; a dual-polarized receiver configured to
receive radio signals of two polarizations that include (i) the
transmitted radio signals transmitted by the transmitter and
reflected from objects in an environment, and (ii) other radio
signals that include radio signals transmitted by at least one
other radar sensing system; wherein the dual-polarized receiver is
configured to process the received radio signals of both
polarizations and to segregate wanted targets from interference by
using polarization differences.
2. The radar sensing system of claim 1, wherein the dual-polarized
receiver is configured to segregate received signals by direction
of arrival and adapted to perform said segregation by polarization
differences separately for each direction of arrival.
3. The radar sensing system of claim 1 further comprising a receive
antenna array communicatively coupled to coarse beamforming to
perform the segregation by direction of arrival.
4. The radar sensing system of claim 1, wherein the dual-polarized
receiver is configured to separate received signals into spectral
components, and further configured to perform the segregation by
polarization differences separately for each spectral
component.
5. The radar sensing system of claim 1, wherein the dual-polarized
receiver is configured to separate receive signals into spectral
components and further into directions of arrival for each spectral
component and configured to apply the segregation by polarization
differences separately for each combination of a spectral component
and a direction of arrival.
6. The radar sensing system of claim 1, wherein the transmitter is
configured for installation and use on a vehicle, and wherein the
dual-polarized receiver is configured for installation and use on
the vehicle.
7. A radar sensing system comprising: a transmitter configured to
transmit radio signals; a receiver configured to receive radio
signals that include (i) the transmitted radio signals transmitted
by the transmitter and reflected from objects in an environment;
wherein the receiver is configured to reduce interference to wanted
signals by separating received signals by any combination of the
domains of polarization, direction of arrival and frequency
components using reversible transforms, further configured to null
or deemphasize separated components deemed to contain interference
and then to recombine the remaining separated components using
reverse transforms for further processing to detect radar
targets.
8. The radar sensing system of claim 7, wherein the transmitter and
receiver are configured to transmit and receive alternately in
bursts, wherein the separation of received signals in multiple
domains with interference reduction per separated component being
adapted on a per burst basis.
9. The radar sensing system of claim 7 comprising a plurality of
transmitters and a plurality of receivers, wherein the plurality of
receivers are configured to reduce interference to other
non-collaborating radars of the same or different design, wherein
each transmitter of the plurality of transmitters is configured to
transmit the combination of a coded transmitter signal unique to
each transmitter and a nulling signal.
10. The radar sensing system of claim 9 further comprising a first
calculating unit configured to estimate composite interference from
the transmitters that would be received at a number of desired null
positions, and a second calculating unit configured to calculate,
based the estimated interference signals, the nulling signals to be
combined with each transmitter's uniquely coded signal so that the
composite interference received in each of the null directions is
nominally zero.
11. The radar sensing system of claim 9 comprising a receive
antenna array communicatively coupled to each receiver of the
plurality of receivers, wherein the plurality of receivers are each
configured to process the received signals to combine the received
signals from the antenna array to produce receive nulls in specific
directions from which interference may be received.
12. The radar sensing system of claim 11, wherein each of the
plurality of receivers is configured to downconvert the received
radio signals.
13. The radar sensing system of claim 7, wherein the transmitter is
configured for installation and use on a vehicle, and wherein the
receiver is configured for installation and use on the vehicle.
14. An automotive radar device adapted to operate in a MIMO mode,
comprising: a plurality of transmitters communicatively coupled to
associated transmit antennas and configured to transmit a sequence
of I,Q samples generated by a transmit modulation generator, the
sequence of I,Q samples for each transmitter having one or more
different distinguishing features; a plurality of receivers
communicatively coupled to associated receive antennas and
configured to receive radio signals that include transmitted radio
signals transmitted by the transmitters and reflected from objects
in an environment; a virtual receiver (VRX) processing module
configured to correlate each of the receive signals with each of
the transmitter I,Q sequences to produce a plurality of VRX signals
for each of a number of delays between the transmitter IQ signals
and the receive signals; each VRX signal having apparently been
received from a virtual antenna having coordinates equal to the sum
of the underlying transmit antenna coordinates and the underlying
receive antenna coordinates, the virtual antennas forming a virtual
antenna array (VRX array); a Doppler processing module configured
to process each of the VRX signals as it changes from time to time
to determine for each of the VRXs and each delay a number of
Doppler frequency amplitudes; and a digital beamforming module
configured to jointly process the VRX signals corresponding to the
same Doppler frequency and delay to further segregate signals by
angle of arrival, wherein digital beamforming module is configured
to reduce the sidelobes of the VRX array when the VRX array is a
sparse array.
15. The automotive radar of claim 14 in which the sequences of IQ
samples transmitted by the transmitters represent a signal
modulated with a digital code, wherein the code bits are different
for each transmitter.
16. The automotive radar of claim 14 in which the sequences of IQ
samples transmitted by the transmitters represent a signal offset
in frequency by a frequency hopping offset valid for a burst time
period and varying between different burst time periods.
17. The automotive radar of claim 14, wherein the transmitters are
configured for installation and use on a vehicle, and wherein the
receivers are configured for installation and use on the vehicle.
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] The present application claims the filing benefits of U.S.
provisional application, Ser. No. 63/140,567, filed Jan. 22, 2021,
which is hereby incorporated by reference herein in its
entirety.
FIELD OF THE INVENTION
[0002] The present invention is directed to radar systems, and more
particularly to radar systems for vehicles and robotics.
BACKGROUND OF THE INVENTION
[0003] The use of radar to determine range, velocity, and angle
(elevation or azimuth or both) of objects in an environment is
important in a number of applications including automotive radar
and gesture detection. Radar systems typically transmit a radio
frequency (RF) signal and listen for the reflection of the radio
signal from objects in the environment. The FCC and other
International Frequency Allocation Organizations have opened up
frequency bands in the millimeter wave region for consumer
radar-based devices. For example, frequencies in the 70-80 GHz
region may be used for medium-range automotive driver-assistance
radar and frequencies in the 61-61.5-GHz region may be used for
short-range indoor sensors such as motion sensors or people
counters and security devices.
[0004] A radar system estimates the location of objects, also
called targets, in the environment by correlating the transmitted
radio signal with delayed echoes of the transmitted signal
reflected from said objects and received at the radar receivers. A
radar system can also estimate the relative velocity of the target
by the Doppler shift of its echoes. A radar system with multiple
transmitters and multiple receivers can also determine the angular
position of a target. Depending on antenna scanning and/or the
number of antenna/receiver channels and their geometry, different
angles (e.g., azimuth or elevation) can be determined.
[0005] Radars as mentioned above may use any one of a number of
transmit waveforms and transmit-receive formats. For example, FMCW
chirp radars may be used where the transmitter transmits a swept
frequency and the receiver simultaneously receives a frequency
different than the momentary transmit frequency according to the
echo delay. The beat frequency between the received signal and the
transmit signal then yields the delay of the target echo.
[0006] Another technique is digital FMCW or PMCW, in which a
carrier is frequency- (or phase-)modulated with a digital code
using, for example, Gaussian Minimum Shift Keying (GMSK) or Offset
Quadrature Phase Shift Keying (OQPSK). The received echoes are
correlated with the code to determine the echo amplitudes at
different delays. Digital FMCW radar lends itself to be constructed
in a MIMO variant in which multiple transmitters transmitting
multiple codes are received by multiple receivers that each
correlate with all codes. The advantage of the MIMO digital FMCW
radar is that the angular resolution is that of a virtual antenna
array having an equivalent number of elements equal to the product
of the number of transmitters and the number of receivers, termed a
virtual antenna array, with associated virtual receivers
(VRXs).
[0007] Digital FMCW MIMO radar techniques are described in commonly
owned U.S. Pat. Nos. 9,989,627; 9,945,935; 9,846,228; and
9,791,551, which are all hereby incorporated by reference herein in
their entireties.
[0008] In the digital FMCW case, the receiver operates during the
transmit time and requires sophisticated means to null-out own
transmitter interference. Self-interference or spillover
cancellation increases in complexity when the number of MIMO
transmitters and receivers increases; therefore, methods are sought
to reduce both complexity and power consumption, for which
Pulse-Digital MIMO Radar may be used, wherein the transmitter
transmits for a short time to fill the go-return pipe for the
longest range, followed by a receive period to receive the echoes.
The alternating transmit/receive format then repeats.
[0009] In both FMCW and Pulse FMCW, the range resolution is related
to the instantaneous bandwidth and the angular resolution is
related to the size of the antenna array. If the antenna array
achieves high angular resolution by means of large aperture using
virtual antenna element spacings of more than a quarter wavelength
(or half wavelength, depending on the convention), grating lobes
appear, which can be mistaken for false targets. There is therefore
a need to improve both range and angular resolution over the limits
set by prior art technology while avoiding confusion by grating
lobes.
[0010] There is also a need to consider potential mutual
interference between multiple radars operating independently in the
same frequency band within range of each other and to devise
techniques for mitigation of mutual interference between different,
non-collaborating radars.
SUMMARY OF THE INVENTION
[0011] An exemplary automotive radar comprises an array of transmit
antennas and receive antennas connected to a signal processing
circuit. In one implementation the antenna arrays may be linear
(1-dimensional) arrays to provide radar target resolution only in
Azimuth or Elevation while in other implementations the antenna
arrays may be two-dimensional and provide target resolution in both
Azimuth and Elevation simultaneously.
[0012] An exemplary radar device embodiment includes any
combination of advanced features including use of sparse arrays
with novel, sidelobe-reduction beamforming techniques; dual
polarization for interference mitigation; transmit or receiver
null-steering, or both, to improve mutual interference and
frequency hopping for increasing range resolution and improved
mutual interference characteristics by clash detection.
[0013] Each transmit array antenna is connected to an associated
transmitter and each receive array antenna is connected to an
associated receiver, each receiver comprising low-noise
amplification, down-conversion to the quadrature (I,Q) baseband
using I-Q mixers driven by a common local oscillator, baseband
filtering as necessary, programmable gain adjustment as necessary
and Digital to Analog (D-to-A) conversion at a sampling rate
adequate to capture all spectral components of interest. All of the
above signal processing elements are part of the signal processing
circuit which may comprise one or more integrated circuit
chips.
[0014] After D-to-A conversion, each receiver's processing
correlates its received signal samples with digital values
representing each transmitter's modulation to produce a number of
correlations corresponding to different echo delays, there being
one such set for each receiver-transmitter combination, in total a
number of sets of range correlations equal to the product of the
number of transmit antennas with the number of receive antennas and
the number of transmitter bursts correlated at successive times.
Like correlations obtained at successive times are combined using
all postulates of Doppler shift to produce complex values in
range-Doppler bins for each VRX. Beamforming over the VRXs then
takes place for each range-Doppler bin.
[0015] A transmit signal echoed from a reflecting object and
received and correlated by a receiver results in a digitized radar
echo signal that is the same as would have been produced by a
transmit and receive antenna co-located at coordinates which are
the mean of the actual transmit and receive antenna coordinates.
Such signals, called virtual receiver (VRX) signals, are further
combined according to delay and Doppler shift to resolve targets in
the four dimensions of azimuth, elevation, range and Doppler.
[0016] When the convention for VRX antenna positions is that they
are deemed to be located at the mean of the associated physical
transmitter and receiver antenna coordinates, a spacing of VRX
antennas equal to a quarter wavelength produces a beam pattern
which can be scanned over +/-90 degrees, that is, a hemisphere,
without grating lobes appearing. An alternative convention is that
the VRX antennas are deemed to be located at the sum of the
associated TX and RX coordinates, in which case the grating
lobe-free spacing is a half wavelength.
[0017] When a grating-lobe-free antenna spacing is used, the total
antenna aperture is limited by the number of VRXs, that is, by the
total acceptable radar complexity. For a given maximum complexity,
therefore, the angular resolution can be increased by using wider
VRX antenna spacings and tolerating grating lobes. Special
techniques are described herein to render grating lobes benign in
order to facilitate the use of wider VRX spacings for greater
angular resolution.
[0018] Range resolution is limited by the bandwidth used. The
instantaneous bandwidth is limited by the ability of A-to-D
converters to digitize the receiver output. Herein, techniques
using burst-to-burst frequency hopping are described to improve the
range resolution by combining correlations from a number of
instantaneously narrow-band signals that can be digitized by
available A-to-D technology, thereby achieving a range resolution
commensurate with the whole frequency-hop span.
[0019] To improve the angular resolution for a given processing
complexity according to one aspect of this invention, the transmit
and receive antenna arrays are configured such that the
corresponding VRX coordinates are spread in the Azimuthal and
Elevation directions in order to mimic a much larger antenna
aperture, and the spreading is deliberately irregular in order to
minimize sidelobes and grating lobes. Co-filed and commonly owned
patent application Ser. No. 17/582,437, entitled "Sparse Antenna
Arrays for Automotive Radar," describes how sparse arrays are
constructed to give minimum sidelobe levels, and is hereby
incorporated by reference herein in its entirety.
[0020] The VRX coordinates may lie on regularly spaced grid points
such as a quarter-wave-spaced grid, but not all grid points are
necessarily populated with an associated VRX. Such an array is
called a "sparse array" and the following steps may be used to
reduce and tolerate the array pattern sidelobes that are produced
by a sparse array:
[0021] (1). Differential beamforming may be used wherein, after
resolving VRX signals by range and Doppler shift, products of
signals corresponding to the same range and Doppler shift from
different VRXs are multiplied (one being complex-conjugated) to
form Dyads, also called differential virtual receiver signals (DVRX
signals), and the Dyads are weighted and combined using different
direction-related phase shifts to produce a set of beam signals.
Targets appear as strong beam signals at particular azimuths and
elevations when VRX signals resolved into the correct range and
Doppler bins for that target are used to form the DVRX signals.
[0022] The product of one VRX signal with the conjugate of another
gives a Dyad containing a target echo phase related to the
difference in the coordinates of the two VRXs. Such a signal can be
regarded as having arisen from a differential virtual receiver or
DVRX with the difference coordinates. The exemplary antenna array
structure used for differential beamforming ensures that DVRX
coordinates are as far as possible unique with as few as possible
coincidences and well spread to give a desired differential antenna
pattern and angular resolution. In differential beamforming, the
loss which would normally be expected in multiplying two noisy
signals together is compensated by the fact that the number of
DVRXs combined is nearly equal to the square of the number of VRXs.
In an exemplary system of 16 transmitters and 16 receivers, the
number of VRXs is 256 and the number DVRXs may be a little less
than 256.sup.2 or 65,536.
[0023] (2). Differential beamforming as described in (1) is
equivalent to and may be performed by N instances of VRX
beamforming where N is the number of VRXs and where the VRX signals
are weighted by a different weighting function for each of the N
VRX beamformings, the moduli-squared of the results of the
different VRX beamformings then being further weighted and combined
to produce a differentially beamformed result. Note that the
magnitude of the further weightings can be absorbed into the
different weighting functions, but not their signs, which would be
lost in the modulus-squaring operation.
[0024] According to an aspect of the exemplary differential
beamforming embodiment, the different weighting functions may be
Eigenvectors of the N.times.N matrix which contains the weightings
of the Dyads and the further weightings are the associated
Eigenvalues. In another aspect of the present embodiment,
recognizing that the virtual location of a DVRX corresponding to
the product of a VRX signal with itself conjugated is (0,0) and
that that location is populated N times, those Dyad weights may be
reduced by the factor N in the matrix to give equal weighting to
DVRX locations. More generally, if any DVRX location is repeated,
the corresponding Dyad weights in the N.times.N matrix may be
reduced by dividing by the number of repeats to produce uniform
weighting of each DVRX location. Other than uniform location
weighting may also be contrived if beneficial in reducing
sidelobes. The net result is that the N.times.N matrix so contrived
will have distinct Eigenvectors and Eigenvalues that can be
precomputed and embedded in the design of an exemplary
embodiment.
[0025] (3). Simplified differential beamforming may be performed,
which is a version of (2) above in which fewer than N, for example
two, VRX beamformings are performed using different VRX signal
weighting functions and the results combined. In the reduced case
of only two VRX beamformings using weighting functions denoted
herein by Gplus and Gminus, the weighting functions may be scaled
so that the moduli-squared or just the moduli of their results can
be directly subtracted with no further weighting. Note that
according to another aspect of the present embodiment, it was found
that subtracting the moduli of the Gplus-weighted VRX beamforming
and the moduli of the Gminus-weighted VRX beamforming can produce
lower worst-case sidelobes than subtracting the moduli-squared,
because the difference in the moduli is converted to decibels by a
20 Log.sub.10(x) operation in contrast to the 10 Log.sub.10(x)
function for the difference in the moduli squared. In another
exemplary variant, two or more beamformings are performed using
different weighting functions and the minimum of corresponding
beams taken. The weighting functions are chosen to give identical
main lobe gain but produce different lobes, and the minimum
sidelobe level for each direction is thus obtained.
[0026] (4). In (3) above, the weighting functions Gplus and Gminus
are no longer necessarily constrained to be the Eigenvectors of any
matrix, but may be optimized by any suitable optimization technique
such as Monte Carlo, or the method of steepest descent using
gradients, to produce the most desirable antenna pattern, typically
that with the lowest worst case sidelobes.
[0027] The resolution of VRX signals into different range and
Doppler bins is carried out before beamforming, and then any of the
above beamforming methods may be applied to any or all
range-Doppler bins to resolve targets in each range-Doppler bin by
boresight.
[0028] Resolution by range is performed by correlating a segment of
received VRX signal samples with the corresponding segment of
transmitted signal samples to obtain a complex number for each
delay between the transmit samples and the received samples. The
transmitted signal is modulated with binary bits using a form of
OQPSK, preferably raised cosine binary FM as described in commonly
owned U.S. Pat. No. 10,191,142 and entitled "Digital frequency
modulated continuous wave radar using handcrafted constant envelope
modulation," which is hereby incorporated by reference herein in
its entirety.
[0029] Complex correlation results are then obtained for different
numbers of bits delay between the transmitted signal samples and
the received VRX signal samples, and possibly for fractional bit
delays by correlating with several sample-shifts per bit.
[0030] The Doppler frequency resolution is of the order of the
reciprocal of the total time over which such segments are
collected, called the scan time. Doppler analysis may comprise
performing a Fourier transform, such as an FFT, across a set of
like-range correlation results calculated from bursts transmitted
at successive times.
[0031] Doppler shift is caused by target velocity (.times.2) which
equals rate of change of go-and-return range. When the Doppler
frequency is high due to a high target velocity relative to the
radar, a target echo may not be in the same range bin over the
entire time period over which burst segments are collected for
Doppler analysis, a phenomenon called "range walking" which blurs
both Doppler and range resolution. A special Doppler analysis is
described in which the range-walking is predicted based on each
Doppler shift being analyzed, so that Doppler analysis takes place
over a sliding set of range bins to compensate for range walking
for each Doppler shift independently. The sliding between range
bins is preferably done by interpolating between adjacent range
bins to obtain smooth sliding, or alternatively by jumping to an
adjacent bin when it is predicted to have become the principal one
that would contain the target echo. The need for compensation for
range-walking during Doppler analysis may be reduced by
systematically phase-retarding the frequency reference used for
transmit signal generation (for a forward looking radar with
positive forward velocity) and phase-advancing the frequency
reference used for receive local oscillator generation and
sampling. This is termed "removing eigenvelocity" such that the
Doppler shift depends only on the target velocity and not the
target-to-radar relative velocity. Thus, a speedometer signal may
be input to the radar to facilitate such eigenvelocity
compensation.
[0032] Because range resolution is related to bandwidth, the
resolution may be improved by causing the signal to probe a wide
range of frequencies during each scan time. This may be done by
frequency hopping between different transmit/receive periods.
Frequency hopping is carried out either by digitally applying phase
ramps to the transmit signal, or by taking a time-out to change the
synthesizer frequency and then resuming the alternating
transmit/receive format, or a combination of both. When frequency
shifts are performed by digital phase ramping, the transmit and
receive sample rates are high enough to represent both the bit
modulation and the frequency shift, so there are many samples per
bit. Range correlations are performed for each transmit/receive
period in sample shifts of this elevated sample rate, thus
obtaining range correlations in finer delay steps than one bit and
combined from one Tx/Rx period to another so as to obtain a range
resolution inversely proportional to the total bandwidth over which
hopping occurs. Moreover, a Doppler resolution is obtained in
frequency steps that are the reciprocal of the total time spanned
by the frequency hop pattern, called the scan time.
[0033] Transmit bursts are filled by modulating the RF carrier with
a digital code. The code should be such as to minimize
cross-correlation between different range correlations and between
different transmitter codes. It is described how this achieved by
selecting bits from an M-sequence to fill the bursts with code
modulation. The bits may be selected from time-offset parts of the
M-sequence according to the frequency hop deviation from a mean
frequency, irrespective of the order in which the hops are
transmitted. Different transmitters use the same M-sequence with
greater time offsets so that no two range correlations for any
transmitter are performed with the same shift of the M-sequence.
Such linking of code-offset to frequency offset is found to reduce
unwanted range-to-range or Doppler-to-Doppler cross
correlations.
[0034] When hopping is carried out by a combination of digital
phase ramping for smaller frequency offsets combined with
synthesizer side-stepping for larger offsets, the sample rate
increase is only commensurate with the instantaneous transmitted
bandwidth, that is with the digital ramping part of the frequency
hopping. However, to get the advantage of the full hop-bandwidth,
samples are required at a rate commensurate with the full
bandwidth. In this case, the receive sample stream may be upsampled
using FFT interpolation as part of the range correlation operation,
which uses cyclic convolution. Finally, having obtained a set of
range correlations and carried out a range-walking-compensated
Doppler analysis to obtain a set of VRX signals per range and per
Doppler, beamforming is carried out over the set of VRX signals
obtained for each range-Doppler combination to determine the
strongest signal azimuth and elevation using coarse beamforming,
and further refines the angular position of the strongest signal
so-determined by examining a region around the coarse position
using fine-resolution beamforming.
[0035] Using the refined angular position and the determined signal
complex amplitude, the illumination of the VRXs that gave rise to
that target signal is determined and subtracted, where prestored
calibration values for the phase and amplitude mismatch of the VRXs
in different directions may be employed, as well as potential
modeling of the effects of null-steering. The calibration-corrected
VRX values for the strongest target are subtracted from the actual
VRX values and thus remove both the strongest signal and any
sidelobes thereof. Beamforming is then repeated on the residual VRX
signals to determine the second strongest signal, and so forth to
discover all targets of interest for the given range/Doppler bin.
The processing of a given range-Doppler bin is terminated by a STOP
criterion which determines when residuals of subtraction no longer
reliably indicate the presence of even weaker targets than those
already found. The processing is repeated in principle for all
range/Doppler combinations, but processing may be curtailed by
sparsification, which can use the history of previous scans to
indicate where targets of interest lie and do not lie. Successive
subtraction is also curtailed as mentioned above by implementing a
stop test to determine if residual signals are real, noise, or
artefacts.
[0036] All of the above processing may be carried out using
dual-polarization receive antennas and duplicated processing chains
up to a point in the chain where interference can be discriminated
from wanted signals by polarization and partly or completely
eliminated thereby. The wanted signal polarization is assumed to be
the same as that transmitted (or opposite hand, if circular).
Typically, 45-degree linear polarization has the advantage that an
oncoming interfering radar of the same type will be
cross-polarized. Circular polarization has the advantage that an
oncoming radar of the same type will have the same polarization as
that transmitted while wanted target echoes have the opposite
polarization to that transmitted. Since polarization is not
accurately maintained when reflected from an irregular object,
there is still a gain to be had in adaptive polarization
processing.
[0037] A dual-polarization receive antenna can comprise co-located
crossed dipoles. Alternatively, the crossed dipoles can be in
offset locations, thus giving rise to different VRX arrays for the
two polarizations. The advantage of that is that the polarization
of grating lobes is different than the polarization of the main
lobe, thus providing extra grating lobe suppression.
[0038] To improve the mutual interference characteristics between
different radars in different vehicles beyond that achievable by
different codes, polarizations and frequency hop patterns, the
radar transmit antennas may be driven in such a way as to produce
zero illumination (nulls) in specified directions. Since the
transmitters do not transmit the same code, a novel method to
achieve such nulls is described whereby the signal that would be
received at a specified position is calculated and then the
negative of it is transmitted in a narrow beam focused on that
position using the same transmitters and antennas. The receive
antennas can also be phased so as to produce nulls in specified
directions. The effect of transmit or receiver nulling or both is
modelled in the signal processing when a detected target signal is
subtracted from the receive signals to reveal a weaker target. The
position distortion of a target lying near a null may also be
modelled and corrected.
[0039] Embodiments of the present invention thus provide for a
radar system that provides for greater immunity to interference
from other radar systems, particularly from chirp radars. Exemplary
embodiments also provide "good citizen" measures that help to
reduce interference that might be caused to other radar
systems.
[0040] An exemplary radar system providing the benefits of the
preceding paragraph includes dual polarization receive channels in
the expectation that interference will be a different polarization
than the desired radio signals transmitted by own transmitters and
reflected from targets in the environment. The polarization of
interference can, in one implementation, be determined in a quiet
period of own radar and thereafter used to adapt the receive
antenna polarization to minimize the ratio of unwanted to wanted
signals. The radar system also provides improved signal handling
dynamic range to avoid receive channels saturating at the A-to-D
converter stage before the radio signal has reached the digital
signal processing domain. Signals that are digitized and recorded
in memory can be processed "offline," that is retrospectively, in
different ways or even in time-reversed sample order to best detect
wanted targets amid interference.
[0041] In an aspect of the present invention, an exemplary radar
system embodiment includes a transmit pipeline that includes a
plurality of transmitters. The radar system also includes a receive
pipeline that includes a plurality of receivers. The transmitters
are configured to transmit radio signals. The receivers are
configured to receive radio signals that include the transmitted
radio signals transmitted by the transmitters and reflected from
objects in the environment. The receive pipeline is configured to
provide interference immunity from interfering radio signals
transmitted by other radar systems.
[0042] In an aspect of the present invention, the interfering radar
systems may be chirp radars.
[0043] In another aspect of the present invention, the transmit
pipeline and/or the receive pipeline is configured to avoid
transmitting radio signals that interfere with the other radar
systems.
[0044] In a further aspect of the present invention, the receive
pipeline comprises exemplary dual polarization receive channels.
The interfering radio signals are a different polarization than the
radio signals transmitted by the transmitters and reflected from
targets in the environment.
[0045] In yet another aspect of the present invention, the receive
pipeline is configured to provide improved signal handling dynamic
range to avoid receive channels saturating at the A-to-D converter
stage before the radio signal has reached the digital signal
processing domain.
[0046] In another aspect of the invention, Doppler analysis is
performed by a method that compensates for range-walking.
[0047] In yet another aspect of the invention, fine range
resolution is achieved by using a total bandwidth during a radar
scan time comprising many alternating transmit-receive burst
periods by changing the frequency used for a burst period either by
digital phase-ramping or by side-stepping a frequency synthesizer
that generates the transmit/receive center frequencies.
[0048] In another aspect of the invention, eigenvelocity may be
removed by reducing the transmit frequency reference and increasing
the receive frequency reference according to the radar's own
forward speed, or vice versa for a rear-looking radar.
[0049] All information determined by the radar regarding range,
azimuth, elevation and Doppler of target objects is output to a
higher level of processing which may track targets from scan to
scan and provide collision avoidance warnings or actions.
[0050] These and other objects, advantages, purposes and features
of the present invention will become apparent upon review of the
following specification in conjunction with the drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
[0051] The patent or application file contains at least one drawing
executed in color. Copies of this patent or patent application
publication with color drawing(s) will be provided by the Office
upon request and payment of the necessary fee.
[0052] FIG. 1 is a plan view of an automobile equipped with a radar
system in accordance with an embodiment of the present
invention;
[0053] FIG. 2A and FIG. 2B are block diagrams of radar systems in
accordance with an embodiment of the present invention;
[0054] FIG. 3 is a block diagram illustrating a radar with a
plurality of receivers and a plurality of transmitters (MIMO radar)
in accordance with an embodiment of the present invention;
[0055] FIG. 4 is a block diagram of an exemplary dual-polarized
MIMO radar system with dual polarization receive channels in
accordance with an embodiment of the present invention;
[0056] FIG. 5 illustrates the basic principle of transmit
nulling;
[0057] FIG. 6 illustrates a method of creating one or more transmit
nulls in accordance with an embodiment of the present
invention;
[0058] FIG. 7 illustrates the matrix expressions for a more general
nulling method in accordance with an embodiment the present
invention;
[0059] FIG. 8 illustrates the simplified matrix equation for
forming an exemplary two nulls;
[0060] FIG. 9 illustrates an exemplary method for simplifying
null-forming to look-up table operations in accordance with an
embodiment of the present invention;
[0061] FIG. 10 is a diagram of an exemplary illumination pattern of
code 1 caused by placing null in the center in accordance with an
embodiment of the present invention;
[0062] FIG. 11 is a diagram of an exemplary non-uniformity of
illumination by code 2 due to placing a null in the center in
accordance with an embodiment of the present invention;
[0063] FIG. 12 is a diagram of an exemplary sum of powers of all
codes over the field off view in accordance with an embodiment of
the present invention;
[0064] FIG. 13 is a diagram of an exemplary pulse mode signal
format in accordance with an embodiment of the present
invention;
[0065] FIG. 14 illustrates an exemplary placement of M-sequence
bits in accordance with an embodiment of the present invention;
[0066] FIG. 15 is a diagram of an exemplary range-to-range
cross-correlation from a strong target at medium range to all other
ranges in accordance with an embodiment of the present
invention;
[0067] FIG. 16 is a diagram of an illustration of an exemplary
zero-padded cyclic convolution in accordance with an embodiment of
the present invention;
[0068] FIG. 17 is a block diagram of one transmitter and one
receiver in accordance with an embodiment of the present
invention;
[0069] FIG. 18 is a diagram illustrating the need to use an (N+1)th
M-sequence bit to randomize the last phase in accordance with an
embodiment of the present invention;
[0070] FIG. 19 is a diagram illustrating the principle of
range-walking compensated Doppler analysis in accordance with an
embodiment of the present invention;
[0071] FIG. 20 is a diagram of an exemplary simulation of actual
range-walking at 10 MPH in accordance with an embodiment of the
present invention;
[0072] FIG. 21 is a diagram of an exemplary simulation of
range-walking at 50 MPH in accordance with an embodiment of the
present invention;
[0073] FIG. 22 is a diagram of an exemplary heat map for no
range-walking compensation at 250 MPH in accordance with an
embodiment of the present invention;
[0074] FIG. 23 is a diagram of an exemplary heat map for
compensated range-walking at 250 MPH in accordance with an
embodiment of the present invention;
[0075] FIG. 24 is a diagram illustrating close-in ACF of pure
frequency hopped CW in accordance with an embodiment of the present
invention;
[0076] FIG. 24A is a diagram illustrating an exemplary pure FH
autocorrelation function in steps of one sample in accordance with
an embodiment of the present invention;
[0077] FIG. 25 is a diagram illustrating full ACF of pure
frequency-hopped CW in accordance with an embodiment of the present
invention;
[0078] FIG. 26 is a diagram illustrating full and close-in ACF of
FHCW with corrected DC term in accordance with an embodiment of the
present invention;
[0079] FIG. 27 is a diagram illustrating an exemplary
video-filtered FHCW autocorrelation function in accordance with an
embodiment of the present invention;
[0080] FIG. 28 is a diagram of close-in effect of video filtering
in accordance with an embodiment of the present invention;
[0081] FIG. 28A is a diagram of an exemplary autocorrelation
function of code alone at 256 bits per burst in accordance with an
embodiment of the present invention;
[0082] FIG. 28B is a diagram illustrating narrowing of the ACF peak
for code+FH and increasing hop bandwidth in accordance with an
embodiment of the present invention;
[0083] FIG. 29 is a diagram illustrating range-to-range
autocorrelation for FH plus code modulation in accordance with an
embodiment of the present invention;
[0084] FIG. 30 is a diagram illustrating an improvement in
range-range cross-correlation by linking burst code rotation to hop
frequency in accordance with an embodiment of the present
invention;
[0085] FIG. 31 is a diagram illustrating MLS shift spacing of 2
between successive burst bits in accordance with an embodiment of
the present invention;
[0086] FIG. 32 is a diagram illustrating range-walking compensated
range-Doppler resolution of a 50 MPH target at 50 meters in
accordance with an embodiment of the present invention;
[0087] FIG. 33 is a diagram illustrating an exemplary effect on
target visibility with 50% erased hops in accordance with an
embodiment of the present invention;
[0088] FIG. 34 is a diagram illustrating an exemplary effect of 70%
erased hops in accordance with an embodiment of the present
invention;
[0089] FIG. 35 is a diagram illustrating an exemplary effect of 85%
erased hops in accordance with an embodiment of the present
invention;
[0090] FIG. 36 is a diagram illustrating an exemplary geometry for
antenna array analysis in accordance with an embodiment of the
present invention;
[0091] FIG. 37 is a diagram illustrating exemplary physical and
non-physical beam locations in accordance with an embodiment of the
present invention;
[0092] FIG. 38 is a diagram illustrating an exemplary VRX array
formed from a Tx and an Rx array in accordance with an embodiment
of the present invention;
[0093] FIG. 39 is a diagram illustrating actual Tx and Rx locations
in accordance with an embodiment of the present invention;
[0094] FIG. 40 is a diagram illustrating an exemplary full F.O.V
pattern of the array of FIG. 38 in accordance with an embodiment of
the present invention;
[0095] FIG. 41 is a diagram illustrating an exemplary beam pattern
restricted to physical coordinates in accordance with an embodiment
of the present invention;
[0096] FIG. 42 is a diagram illustrating an exemplary beam pattern
restricted to +/-7.5 degrees of elevation in accordance with an
embodiment of the present invention;
[0097] FIG. 43 is a diagram illustrating exemplary sidelobes of an
off-center, also demonstrating distortion when using equal angular
increments instead of equal increments in (u,v) space in accordance
with an embodiment of the present invention;
[0098] FIG. 44 is a diagram illustrating an exemplary beam pattern
of a cluster of four strong targets using the array of FIG. 38;
[0099] FIG. 45 is a diagram illustrating an exemplary beam pattern
of the cluster of 4 strong targets using a DVRX array in accordance
with an embodiment of the present invention;
[0100] FIG. 46 is a diagram illustrating an exemplary optimized
sparse array in accordance with an embodiment of the present
invention;
[0101] FIG. 47 is a diagram illustrating an exemplary pattern of
the array of FIG. 46 with uniform weighting;
[0102] FIG. 48 is a diagram illustrating the Bplus beam with Gplus
weighting of the array of FIG. 46;
[0103] FIG. 49 is a diagram illustrating the B-minus beam with
Gminus weighting of the array of FIG. 46;
[0104] FIG. 50 is a diagram illustrating the beam produced by 20
Log.sub.10(.parallel.bplus|-|bminus.parallel.) in accordance with
an embodiment of the present invention;
[0105] FIG. 51 is a diagram illustrating an exemplary keep-out area
around the main lobe during sidelobe minimization in accordance
with an embodiment of the present invention;
[0106] FIG. 52 is a diagram of the steps to a method for Monte
Carlo MINIMAX sidelobe minimization in accordance with an
embodiment of the present invention;
[0107] FIG. 53 is a diagram of the steps to another method for
Monte Carlo MINIMAX algorithm in accordance with an embodiment of
the present invention;
[0108] FIG. 54 is a diagram of an exemplary register structure for
computing on-the-fly the square of a bit serially presented binary
number in accordance with an embodiment of the present
invention;
[0109] FIG. 55 is a diagram illustrating how residual subtraction
errors arise from position determination errors in accordance with
an embodiment of the present invention;
[0110] FIG. 56 is a diagram illustrating residuals of FIG. 42 due
to position quantizing error;
[0111] FIG. 57 is a diagram illustrating apparent versus actual
target position as a target moves through a transmit null in
accordance with an embodiment of the present invention;
[0112] FIG. 58 is a diagram illustrating an exemplary close-in look
at target position error near a transmit null in accordance with an
embodiment of the present invention;
[0113] FIG. 59 is a diagram illustrating an exemplary close-in
position error due to a receive null in accordance with an
embodiment of the present invention;
[0114] FIG. 60 is a diagram illustrating a comparison of real and
apparent position near both transmit and receive nulls in
accordance with an embodiment of the present invention;
[0115] FIG. 61 illustrates position distortion due to nulling not
evident on the macro scale in accordance with an embodiment of the
present invention;
[0116] FIG. 62 illustrates an exemplary process for compensating
for nulling during subtraction in accordance with an embodiment of
the present invention;
[0117] FIG. 63 illustrates exemplary position estimation errors due
to target proximity in accordance with an embodiment of the present
invention; and
[0118] FIG. 64 illustrates exemplary steps to a method for
combining multiple beamformings.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0119] Referring to the drawings and the illustrative embodiments
depicted herein, wherein numbered elements in the following written
description correspond to like-numbered elements in the figures, a
radar system provides for greater immunity to interference from
other radar systems, particularly chirp radars. The exemplary radar
system also provides "good citizen" measures that help to reduce
interference that might be caused to other radar systems. The radar
system will include exemplary dual polarization receive channels in
the expectation that interference will be a different polarization
than the desired radio signals transmitted by own transmitters and
reflected from targets in the environment. The radar system also
provides improved signal handling dynamic range to avoid receive
channels saturating at the A-to-D converter stage before the radio
signal has reached the digital signal processing domain.
[0120] FIG. 1 illustrates an exemplary radar system 100 configured
for use in a vehicle 150. In an aspect of the present invention, a
vehicle 150 may be an automobile, truck, or bus, etc. The radar
system 100 may utilize multiple radar systems (e.g., 104a-104d)
embedded in the vehicle 150 (see FIG. 1). Each of these radar
systems may employ multiple transmitters, receivers, and antennas
(see FIG. 3). These signals are reflected from objects (also known
as targets) in the environment and received by one or more
receivers of the radar system. A transmitter-receiver pair is
called a virtual radar (or sometimes a virtual receiver). As
illustrated in FIG. 1, the radar system 100 may comprise one or
more transmitters and one or more receivers (104a-104d) for a
plurality of virtual radars. Other configurations are also
possible. FIG. 1 illustrates the receivers/transmitters 104a-104d
placed to acquire and provide data for object detection and
adaptive cruise control.
[0121] As illustrated in FIG. 1, a controller 102 receives and then
analyzes position information received from the receivers 104a-104d
and forwards processed information (e.g., position information) to,
for example, an indicator 106 or other similar devices, as well as
to other automotive systems. The radar system 100 (providing such
object detection and adaptive cruise control or the like) may be
part of an Advanced Driver Assistance System (ADAS) for the
automobile 150.
[0122] An exemplary radar system operates by transmitting one or
more signals from one or more transmitters and then listening for
reflections of those signals from objects in the environment by one
or more receivers. By comparing the transmitted signals and the
received signals, estimates of the range, velocity, and angle
(azimuth and/or elevation) of the objects can be estimated.
[0123] There are several ways to implement a radar system. One way,
illustrated in FIG. 2A, uses a single antenna 202 for transmitting
and receiving. The antenna 202 is connected to a duplexer 204 that
routes the appropriate signal from the antenna 202 to a receiver
208 or routes the signal from a transmitter 206 to the antenna 202.
A control processor 210 controls the operation of the transmitter
206 and the receiver 208 and estimates the range and velocity of
objects in the environment. A second way to implement a radar
system is shown in FIG. 2B. In this system, there are separate
antennas for transmitting (202A) and receiving (202B). A control
processor 210 performs the same basic functions as in FIG. 2A. In
each case, there may be a display 212 to visualize the location of
objects in the environment.
[0124] A radar system with multiple antennas, multiple
transmitters, and multiple receivers is shown in FIG. 3. Using
multiple antennas 302, 304 allows an exemplary radar system 300 to
determine the angle (azimuth or elevation or both) of targets in
the environment. Depending on the geometry of the antenna system,
different angles (e.g., azimuth or elevation) can be
determined.
[0125] The radar system 300 may be connected to a network via an
Ethernet connection or other types of network connections 314, such
as, for example, CAN-FD and FlexRay. The radar system 300 may also
have memory (310, 312) to store software used for processing the
signals in order to determine range, velocity, and location of
objects. Memory 310, 312 may also be used to store information
about targets in the environment. There may also be processing
capability contained in the ASIC 316 apart from the transmitters
203 and receivers 204.
[0126] The description herein includes an exemplary radar system in
which there are NT transmitters and NR receivers. Each transmitter
transmits a different code and each receiver correlates with each
transmitter code to produce NT.times.NR virtual radar signals, one
for each transmitter-receiver pair. For example, a radar system
with eight transmitters and eight receivers will have 64 pairs or
64 virtual radars (with 64 virtual receivers). When three
transmitters (Tx1, Tx2, Tx3) generate signals that are being
received by three receivers (Rx1, Rx2, Rx3), each of the receivers
is receiving the transmission from each of the transmitters
reflected by objects in the environment. Each receiver can attempt
to determine the range and Doppler of objects by correlating with
delayed replicas of the signal from each of the transmitters. The
physical receivers may then be "divided" into three separate
virtual receivers, each virtual receiver correlating with delay
replicas of one of the transmitted signals.
[0127] There are several different types of signals that
transmitters in radar systems employ. A radar system may transmit a
pulsed signal or a continuous signal. In a pulsed radar system, the
signal is transmitted for a short time and then no signal is
transmitted. This is repeated over and over for a length of time
termed the scan time. The processor collects and processes
everything received over the scan time which is chosen to be long
enough to receive enough target energy to detect reliably and to be
able to resolve Doppler with fine precision. A typical scan time
range is between 10 ms and 30 ms. A typical transmit burst length
is 2 .mu.s and is followed by a 2 .mu.s receive period. There are
thus an exemplary 4,095 transmit/receive periods in a typical 16 ms
scan time. Shifts of a 4,095-bit M sequence may thus be used to
fill the 4,095 transmit bursts with digital code modulation.
[0128] When the signal is not being transmitted, the receiver
listens for echoes or reflections from objects in the environment.
In some radars a single antenna is used for both the transmitter
and receiver and the radar transmits on the antenna and then
listens to the received signal on the same antenna. This process is
then repeated.
[0129] In a continuous wave radar system, the signal is
continuously transmitted. There may be an antenna for transmitting
and a separate antenna for receiving.
[0130] Another classification of radar systems is in the modulation
of the signal being transmitted. A first type of continuous wave
radar signal is known as a frequency modulated continuous wave
(FMCW) radar signal. In an FMCW radar system, the transmitted
signal is a continuous sinusoidal signal with a varying frequency.
By measuring a time difference between when a certain frequency was
transmitted and when the received signal contained that frequency,
the range to an object can be determined. By measuring several
different time differences between a transmitted signal and a
received signal, velocity information can be obtained. If the
frequency changes smoothly in a ramp fashion, the radar may be
known as a chirp radar.
[0131] A second type of continuous wave signal used in radar
systems is known as a phase modulated continuous wave (PMCW) radar
signal. In a PMCW radar system, the transmitted signal from a
single transmitter is a continuous sinusoidal signal in which the
phase of the sinusoidal signal varies. Typically, the phase during
a given time period (called a chip period or chip duration) is one
of a finite number of possible phases. The spreading code could be
a binary code (e.g., +1 or -1). A spreading code consisting of a
sequence of chips, (e.g., +1, +1, -1, +1, -1 . . . ) is mapped
(e.g., +1->0, -1-->1) into a sequence of phases (e.g., 0, 0,
90, 0, 270 . . . ) that is used to modulate a carrier signal to
generate the radio frequency (RF) signal. The spreading code could
be a periodic sequence or could be a pseudo-random sequence with a
very large period, so it appears to be a nearly random sequence.
Herein, a particular choice of spreading code is shown to provide
advantages, namely, successive bits of an M-sequence equal in
length to the number of transmit bursts in the scan period are
placed as the first bit of each successive burst and then a shift
of them M-sequence is placed as the second bit of each burst and so
on until the burst if filled with a desired number of bits. The
resulting signal has a bandwidth that is proportional to the rate
at which the phases change, called the chip rate, which is the
inverse of the chip duration=1/T. By comparing the return signal to
the transmitted signal, the receiver can determine the range and
the velocity of reflected objects.
[0132] In one implementation, a burst of transmit signal (e.g., a
PMCW signal) is transmitted over a short time period (e.g., 1
microsecond) and then turned off for a similar time period. The
receiver is only turned on during the time period where the
transmitter is turned off. In this approach, reflections of the
transmitted signal from very close targets will only comprise the
last few bits transmitted because the receiver is not active during
a large fraction of the time when the reflected signals are being
received. However, since nearby objects produce strong reflected
signals, enough energy is received in those few bits per burst to
detect them. Thus, it is desirable that the first received bit, and
being the last bit transmitted and reflected from the nearest
object, collected one from each burst in the scan, should as far as
possible be orthogonal to the set of second receive bits collected
over the scan and representing the second nearest reflecting
object. The latter is the purpose of using M-sequences spread over
the scan, which will be described in greater detail in the
following paragraphs.
[0133] The radar sensing system of the present invention may
utilize aspects of the radar systems described in U.S. Pat. Nos.
10,261,179; 9,971,020; 9,954,955; 9,945,935; 9,869,762; 9,846,228;
9,806,914; 9,791,564; 9,791,551; 9,772,397; 9,753,121; 9,599,702;
9,575,160, and/or 9,689,967, and/or U.S. Publication Nos.
2018/0231656, 2018/0231652, 2018/0231636, and 2017/0309997, and/or
U.S. provisional applications, Ser. No. 62/486,732, filed Apr. 18,
2017, Ser. No. 62/528,789, filed Jul. 5, 2017, Ser. No. 62/573,880,
filed Oct. 18, 2017, Ser. No. 62/598,563, filed Dec. 14, 2017, Ser.
No. 62/623,092, filed Jan. 29, 2018, and/or Ser. No. 62/659,204,
filed Apr. 18, 2018, which are all hereby incorporated by reference
herein in their entireties.
[0134] Digital frequency modulated continuous wave (FMCW) and phase
modulated continuous wave (PMCW) are techniques in which a carrier
signal is frequency or phase modulated, respectively, with digital
codes using, for example, GMSK. Digital FMCW radar lends itself to
be constructed in a MIMO variant in which multiple transmitters
transmitting multiple codes are received by multiple receivers that
decode all codes, as mentioned above. The advantage of the MIMO
digital FMCW radar is that the angular resolution is that of a
virtual antenna array having an equivalent number of elements equal
to the product of the number of transmitters and the number of
receivers. Digital FMCW MIMO radar techniques are described in U.S.
Pat. Nos. 9,989,627; 9,945,935; 9,846,228; and 9,791,551, which are
all hereby incorporated by reference herein in their
entireties.
[0135] FIG. 4 is a block diagram of an exemplary radar system that
provides for greater immunity to interference from other radar
systems, particularly chirp radars. The exemplary radar system also
provides "good citizen" measures that help to reduce interference
that might be caused to other radar systems. The radar system can
include dual polarization receive channels 400 in the expectation
that interference will be a different polarization than the desired
radio signals transmitted by own transmitters and reflected from
targets in the environment. The radar system also provides improved
signal handling dynamic range to avoid receive channels saturating
at the A-to-D converter stage 470 before the radio signal has
reached the digital signal processing domain 480, 550.
[0136] As illustrated in FIG. 4, the exemplary radar system
improves the dynamic range up to and including the A-to-D
converters 470 by using the results of digital radar signal
analysis to date from the digital signal processing domain 550 in a
digital signal prediction step 540 to construct a digital
prediction of the receiver channel signals to be received at a
future time, probably 1 .mu.s into the future. The dynamic range
can be improved by D-to-A converting the predictions into the
analog domain using, for example, only coarse D-to-A converters 460
and to then subtract the analog interference prediction signals
from the corresponding receive channel signals in a summing or
subtracting junction 450, such that the residual signals presented
to the A-to-D converters 470 are of a reduced amplitude but still
filling the dynamic range of converters 470. Thus, the total
dynamic range for signal handling is equal to the dynamic range of
converters 470 enhanced by the amount by which interference
subtraction lowered the residuals. One way to think of it is that
coarse D-to-As 460 might slice off the top 4 bits of signal dynamic
range leaving the bottom 6 bits only to be converted by converters
470, and thereby achieving the equivalent of a 10-bit
conversion.
[0137] In order to achieve the accuracy of, for example, a 10-bit
conversion, the amount of interference subtracted in the analog
domain has to be added back in in interference re-adder 480 with
high accuracy. The method envisaged to do this is that each level
(perhaps 16 to 64 levels) of each of the coarse D-to-A converters
460 will have an auto-learned digital word to describe it which
will be adaptively learned to a high accuracy so that when that
level is subtracted in the analog domain in unit 450 an accurate
digital value will be added back in the digital interference
re-addition unit 480.
[0138] After the A-to-D converters 470 of limited word length, the
digital signal processing thereafter can have whatever word length
is needed to avoid digital saturation. The analog interference
subtraction should occur as early as possible in the analog path.
In one exemplary embodiment, the analog interference subtraction is
performed after down-conversion to the (1,0) baseband, as
subtraction is more complex and more power consuming if the
predictions are mixed up to 80 GHz for subtraction in the RF
domain; and moreover, that has been found to a give a significant
noise factor degradation.
[0139] For dual-polarization receivers, the balanced
dual-polarization antenna (V,H) connection can comprise four
ball-bonds in a square. When arranged in the above way, the signals
are nominally spatially orthogonal and any residual coupling
between them is unimportant given that the dual polarization
antenna may be crossed-dipoles for example.
[0140] With the availability of the dual-polarization signals from
NR receivers and both polarizations, the digital radar signal
analysis can comprise, as described in the incorporated patents, of
an FFT-based scheme for burst-by-burst correlation of the received
signal in each channel with the known transmitter codes. If this is
done, note that transmitting GMSK (or UMSK as defined in the
incorporated patents) using the GSM-type 90-degree per bit
pre-rotation coding reduces the correlation to correlating a
complex received signal with a real template, rather than a full
complex correlation. There might however be even faster and less
power consuming correlation methods that need no multiplies, which
can be used when the same received signal is to be correlated with
many binary codes (many shifts of many different codes is a large
number of binary correlations). These are based on the fact that
the number of possible bit patterns of finite length, such as 8, is
256 times however many codes are correlated with, and since the
same 256-bit patterns will reoccur many times in many codes, 8
signal samples need be combined only once in all 256 ways, and by
doing it in Gray code order, only one new addition is required for
each combination. The latter alone is an 8:1 speed up and is
disclosed in expired U.S. Pat. No. 5,931,893 entitled "Efficient
Correlation over a Sliding Window." Other correlation methods are
described herein when the correlation is performed using multiple
samples per bit in frequency hopping systems to obtain finer ranger
resolution.
[0141] There is an advantage in the per-pulse FFT correlation
method. That is, when the signal is temporarily available in the
frequency domain, narrow-band interference stands out and can be
clipped, nulled or otherwise mitigated.
[0142] An advance on interference nulling in the spectral domain
only is to perform a rough beamforming over all antenna channels
for each FFT component. A rough beamforming over, for example, 16
receive channels can be a 16-point FFT. Whatever is used, it should
be an easily invertible, information lossless transform, but not
necessarily an orthogonal transform like the FFT. The combination
of a 256-pt FFT for correlation with a 16-pt FFT over corresponding
spectral components of the 256-pt FFT is in fact a 256.times.16 2-D
FFT, which is a 2,048 pt Walsh-Fourier transform. The difference
between a 2,048 pt Fourier transform and a Walsh-Fourier transform
is that the former has twiddles at each stage while the latter
omits twiddles between certain stages corresponding to the "Walsh"
part. So, there are no twiddles between the 256 pt correlation FFT
and the 16 pt beamforming FFT.
[0143] After a rough beamforming of each FFT component, the signal
is in the 3D domain of spectrum and space. Nulling out big
components at particular frequencies and particular spatial
directions removes less of the wanted signal energy, thus causing
less loss of wanted target detection sensitivity and producing
fewer artefacts. Moreover, the directions from which other-radar
interference is received are likely to be long-term and thus carry
over from one burst to another. Likewise, in a dual-polarized
radar, the principal interference polarization can be determined
per frequency and coarse direction and is likely to be stable for
at a least a few 1 .mu.s bursts. Therefore, the directions and
polarizations to de-weight can be determined per spectral
component, resulting in substantial interference mitigation with
little loss of wanted signal. This technique of nulling components
of a 2,3 or even 4-dimensional transform) over different domains
(e.g. frequency, azimuth, elevation and polarization) can be
considered to be a further generalization of the technique
described in expired U.S. Pat. No. 5,831,977, entitled "Subtractive
CDMA system with simultaneous subtraction in code space and
direction-of-arrival space." The advantage of nulling in a multiple
domain transform space is that a smaller fraction of the total
transform components is deleted to reduce interference and thus
there is less wanted signal distortion upon returning to the
original domains with an inverse transform.
[0144] Thus, the addition of polarization as an additional domain
(even though the order of its transform is only 2) provides another
dimension in which to segregate interference. Since the
polarization of other radar interference is also likely to be
long-term stable, it can be determined solidly and then the
following algorithm can be used to annul it to great advantage even
though the polarization domain has only two points:
[0145] For each spatio-spectral component to be cleaned up, form
.alpha.V+.beta.H where V and H are the horizontal and vertical
components (or other cross-polarized components such as +/-45),
such that the resulting polarization, which is determined by the
ratio of .alpha. to .beta., is orthogonal to the interferer's
polarization, but the scaling of .alpha. and .beta. is chosen to
leave the signal component unattenuated; at least within reason--if
the polarizations of the signal and interferer were close, .alpha.
and .beta. would become large, magnifying noise, so there is in
that case a compromise between noise magnification and signal loss
that is known from many other similar problems.
[0146] So, using all 4 domains--spectral, 2 spatial and
polarization, substantial reduction of interference from other
radars can already be obtained at the per-burst stage. Note that it
is also known to divide a burst into a smaller number of periods
corresponding to, for example, 256 samples, a convenient FFT size,
which is then called a "pulse," a burst comprising several such
pulses. Interference excision in the 4 domains can occur on a
per-pulse basis, and then, while still in the transform domain, the
results are combined and subjected to a single inverse transform.
It is possible that only a single polarization, the above weighted
combination of V and H, need be passed on to be accumulated over
all pulses and processed further in Doppler analysis and eventual
beamforming, thus restricting the extra complexity of dual
polarization to the early stages of processing. Inverting the rough
beamforming needs to be done only once on the accumulated pulse
transforms and likewise the inverse 256-point FFT, the outputs of
which are signals segregated by range.
[0147] The additional complexity introduced for
spatio-spectral-polarization interference nulling is thus a
doubling of the number of correlation FFTs to be performed, as
there is one for each polarization. This is needed on the
assumption that different interferers in different parts of the
spectrum or lying in different directions might have different
polarizations, so even though their polarizations may be known in
advance, if they are not the same, polarization combination cannot
be done ahead of the FFT and rough beamforming FFT; rather, the
interferers have to be separated by spectrum and direction in order
to apply a polarization nulling adapted to each one.
[0148] In the exemplary embodiment illustrated in FIG. 4, the rough
beamforming FFTs include 256 16-point beamforming FFTs after
sixteen 16.times.16 point (256 point performed base 16) correlation
FFTs, assuming 16 receivers, one FFT per RX (and per TX). This is
less than a 50% increase in processing, as the 256-point FFT has
twiddles between its two stages of 16 pt FFTs, while no twiddles
are needed between the 256-point FFTs and the rough beamforming
FFTs. Because of the large number of base-16 FFTs used, an
optimized 16-point hardware implementation is used, based on known
techniques to reduce multiplications, such as, the Winograd method,
or using base-4 decomposition with the Gauss method for complex
multiplication with the twiddling constants. Note that Gauss
complex multiplication requires 5 adds and 3 multiplies compared to
the usual 2 adds and 4 multiples when both complex numbers are
arbitrary but reduces to three adds and 3 multiplies when one of
the complex numbers is always the same, as is the case with
twiddling constants.
[0149] Thus, one exemplary embodiment disclosed herein includes an
exemplary radar system that provides for greater immunity to
interference from other radar systems, particularly from chirp
radars. The exemplary radar system also provides "good citizen"
measures that help to reduce interference that might be caused to
other radar systems. A first technique disclosed to achieve the
latter is the use of transmit nulling to place nulls in the
direction of other oncoming radars such that they are not
illuminated by our radar's transmissions.
[0150] Since the MIMO radar transmits different uncorrelated codes
from each transmitter, there is no way that they alone form a beam
or a null. However, given the direction of an oncoming radar, the
composite signal that an object in that direction would receive
from our own transmitters can be calculated by applying the
conjugate of the phase factors that are used to form receive beams
in that direction, and which are likely already available for the
latter requirement and possibly already stored in a look-up table
for many thousands of different directions to avoid real-time
sine/cosine calculations. Moreover, the phases received from the
interfering radar can be determined by correlating the received
interference as between the receive antennas and, using transmit
and receive antenna calibration information, the transmit phases
necessary to place nulling beam on the same location can be
determined. Having determined the composite signal that would be
received at the oncoming radar, a novel transmit nulling technique
comprises adding the negative of it, properly phased, to all
transmitters so as to form a beam pointed only at the oncoming
radar and which will thus null out all of our radar's transmissions
only at that point, leaving wanted targets in different locations
more or less still illuminated. Since each transmitter is now
transmitting the sum of two signals, its normal code plus the
nulling signal, it has to be a linear transmitter even if the code
modulation alone is constant-envelope. However, the linearity
requirement is not excessive if seeking only of the order of 15-20
dB of interference mitigation. Typically, the transmitter would be
backed off 5 dB from saturation and the resulting efficiency loss
is tolerated while interference mitigation operation is active.
[0151] FIG. 6 shows a method of creating a null to all transmitters
in a given direction. Codes 1 to 16 for transmission by respective
transmitters enter at the bottom to 16-point FFT 1303. The output
of FFT 1303 is a set of signals in "Beam-space," that, each signal
represents what will be transmitted using a specific antenna beam
pattern. In this case, the antenna patterns are only narrow beams
if the transmitting antennas are regularly spaced. If the
transmitters are not regularly spaced, a different transformation
from code domain to beam domain than an FFT would have to be used,
as will be described below.
[0152] Assuming for now that "beam domain" comprises a number of
different narrow beam directions, to prevent illumination of
targets in that direction that beam signal is set to null before
using IFFT 1302 to transform back from beam domain to antenna
signal domain. The signal outputs of IFFT 1302 are then D-to-A
converted and up-converted to the transmit frequency and amplified
to a transmit power level in modulators and PAs 1301, and then
transmitted from respective antennas 1300.
[0153] As pointed out above, this method must be modified if the
transmit antenna spacings are not regular, as an FFT/IFFT does not
then provide good beamforming. For clarity, the matrix formulation
of a more general method is illustrated as FIG. 7. FIG. 7
illustrates the transformation from code domain to beam domain by
premultiplying a vector of code bits (top right) with a
signal-to-beam domain transforming matrix (such as an FFT in the
regular spaced antenna case), followed by setting certain beams to
zero (the zeros in the diagonal matrix) and then transforming back
to signal/antenna domain with another matrix multiplication on the
left hand side, such as an FFT for regular spaced antennas, is
equivalent to the lower matrix equation in which the FFT and IFFT
matrices have disappeared. Instead, it is only necessary to
calculate matrices U,V, which comprise each only as many rows or
columns as the number of nulls desired, UV times the code vector
forming what has to be subtracted from the set of transmissions to
created nulls in one, two or more directions.
[0154] FIG. 8 illustrates the basic equation for creating an
exemplary two nulls. With C being the column vector of code bits, a
new column vector is formed by multiplying C by UV, where U is a
2.times.N matrix (N=16, the number of codes and transmit antennas
in the cases exemplified here) depending on the desired null
directions and V is an N.times.2 matrix also depending on the
desired null directions. U calculates what would be received at the
null locations and V determines how to form beams to transmit the
negatives of the latter to those two locations. Nominally U and V
are conjugate transposes of each other if the different null
directions are uncorrelated. The term used for U and V is "steering
vectors" as they phase the antennas to steer a beam in a particular
direction. Otherwise, U is V# multiplied by the inverse of the
steering vector cross-correlation matrix, which is L.times.L, where
L is the number of nulls to be created. How the above produces a
null may be understood as follows:
[0155] If U.sub.L.times.N is the collection of L steering vectors
from the N transmit antennas to the L desired null directions and
C.sub.N.times.1 is a vector of code bits, then what would be
received at the L null locations is given by U.sub.L.times.N
C.sub.N.times.1, which is an L.times.1.column vector.
[0156] Now multiply that by V.sub.N.times.L and subtract from the
code vector to obtain [I.sub.N.times.N-V.sub.N.times.L
U.sub.L.times.N]]C.sub.N.times.1.
[0157] Now when that is transmitted, what is received in the null
directions is U.sub.L.times.N[I.sub.N.times.N-V.sub.N.times.L
U.sub.L.times.N]]C.sub.N.times.1=[U.sub.L.times.N-U.sub.L.times.N
V.sub.N.times.L U.sub.L.times.N]]C.sub.N.times.1.
[0158] Now letting V.sub.N.times.L=U*.sub.N.times.L
[U*.sub.N.times.L U.sub.L.times.N].sup.-1, the above becomes
[U.sub.L.times.N-U.sub.L.times.N U*.sub.N.times.L [U*.sub.N.times.L
U.sub.L.times.N].sup.-1 U.sub.L.times.N]]C.sub.N.times.1.ident.0 as
the inverse matrix cancels with U.sub.L.times.N U*.sub.N.times.L
leaving[U.sub.L.times.N-U.sub.L.times.N]] which is zero.
[0159] However, what is received in any collection of directions U'
that are not the null directions is
[U'.sub.L.times.N-U'.sub.L.times.N U*.sub.N.times.L
[U*.sub.N.times.L U.sub.L.times.N].sup.-1
U.sub.L.times.N]]C.sub.N.times.1.
[0160] Now U'.sub.L.times.N U*.sub.N.times.L [U*.sub.N.times.L
U.sub.L.times.N].sup.-1 does not cancel to unity.
[0161] It may be noted that, for orthogonal null directions, the
inverse matrix [U*.sub.N.times.L U.sub.L.times.N].sup.-1 is a
diagonal matrix of values 1/N, ( 1/16 here), which provides the
necessary scaling for the nulling beam to be of unity gain. In
general this matrix provides the correct scaling to generate deep
nulls where desired.
[0162] The oncoming radars receive phased combinations of our
transmitted codes given by VC. The result is a new column vector
that depends on the code bits and the null directions.
[0163] FIG. 5 shows the straightforward principle of transmit
nulling. Code streams numbered Code 0 to Code F destined to be
transmitted by the corresponding transmitters enter at the left.
The code streams pass straight across to subtractors 1203-1 to
1203-16 where the nulling signal is subtracted. The null signal is
generated by first multiplying the Code bits by V in multipliers
1200-1 to 1200-16 and summing junction 1201 (for a single row V
corresponding to one null) and then multiplying the sum value by U
in multipliers 1202-1 to 1202-16 to phase them in order to create a
narrow beam for transmitting the nulling signal. All arithmetic
operations are complex. Note that a scaling of 1/N i.e., 1/16 shall
take place somewhere in this sequence to ensure that the net gain
of the nulling beam is only unity. This arises by reference to the
above matrix mathematics. The nulling signal thus properly phased
for each antenna is then subtracted from the code signals to be
transmitted, an operation which assumes that the transmit chain
thereafter is linear and thus able to transmit the now non-constant
envelope signals without excessive distortion. A 5 dB PA back-off
suffices when looking for modest null depths of the order to 15 to
20 dB.
[0164] Since the code bits are only +1 or -1, this suggests a way
of precomputing the signals to be transmitted and storing them in a
look up table for use as long as the null directions are constant,
maybe for hundreds of transmit bursts i.e. 100's of microseconds
during which time an oncoming radar will hardly have changed
bearing. Note that, given linear transmitters, there is no reason
not to use a linear modulation such as OQPSK. For OQPSK, only the
output of FIG. 5 needs to be computed at one sample per bit and
then linearly filter the outputs by upsampling FIR filters to
produce multiple samples per bit of smooth, spectrally controlled
waveforms. Since there are only 16 code bits input at any one time,
there can only be 65,536 possible sets of output values to the
modulators. Since 65,536 is a large number, FIG. 9 shows how to do
this in two chunks of 8 to reduce total look up table size by a
factor of 128.
[0165] Referring to FIG. 9, a first look-up table 1205 has inputs
of one bit of each of codes 1 to 8. Since there are only 8 binary
bits, there can only be a total of 256 possible outputs. The output
for each of the 16 transmitters is precomputed for each of those
256-bit combinations based on the desired null directions and
stored in the 4,000-word look-up table 1205. The table 1205 is then
valid for as long as the null directions are not changed. The
angular position of an oncoming radar does not change in the 4
.mu.s period of a transmit-receive cycle, therefore the table, once
precomputed, may be used for all bits of many successive transmit
receive bursts. Table 1206 is likewise precomputed for code inputs
9 to 16. The method of precomputation is to apply phase shifts (the
rows or steering vectors of matrix V) to the codes depending on the
distance differences from each associated transmit antenna along
the null line to a target, adding up the results to determine the
values for multiplication by matrix U and then subtracting the
resulting vector from the code vector. The two look-up tables 1205
and 1206 are thus different because the distance differences along
the sightline of the nulls to the targets are different for
transmitters 1 to 8, which transmit codes 1 to 8, as compared to
transmitters 9 to 16, which transmit codes 9 to 16.
[0166] FIG. 10 illustrates a radar image as an exemplary heat map
showing the extremely sharp null produced for a single null case.
The heat map represents signal strength over a 2D field of view
comprising +/-90 degrees of Azimuth and +/-7.12 degrees
approximately of elevation, which is sufficient for automotive
radar. The radar image shows the ripple in illumination strength,
mapped to color, over the whole field of view for one transmitter,
with a sharp notch at the null location being evident. The light
green color indicates an average illumination level, and the yellow
spots indicate a lower-than-average illumination by up to perhaps
10 dB in places, according to the color scale on the right. FIG. 11
illustrates the same phenomenon for code 2. It may be seen that the
ripple pattern is completely different. Over the 16 codes, the
total illumination power is thus more uniform, as shown in FIG. 12,
as the loss of illumination at certain points with one code does
not coincide with a loss for another code, except at the one place
in the center where they all exhibit a sharp null. The effect of
nulling on the radar display of target positions will be shown in
more detail after explaining the method of beamforming.
[0167] The receive antennas may also be combined in null processing
to reduce received interference from oncoming radars of the same or
different type. Since interference does not separate by range or
Doppler, receive nulling is performed before range or Doppler
computations. In one implementation, the receiver A-to-D outputs
are captured during a period that own transmitters are silent. Such
periods may occur for other reasons such as synthesizer
sidestepping in frequency hopping modes. The D-to-A outputs are
then processed to determine the principal directions (and
polarizations, if dual polarization receivers are used) from which
interference is being received. If receiver channel amplitude
differences have been calibrated out, this analysis yields an
interference phase for each channel. This is used to construct U,V
vectors in the same way as for transmit nulling, that is, a narrow
beam is formed focused on the interference by multiplying the
receiver signals with vectors that are the conjugate of the
received phases (receive steering vectors) and then an appropriate
amount ( 1/16 here) is subtracted from each of the receive antenna
signals before performing range correlation and Doppler
processing.
[0168] FIG. 13 illustrates an exemplary transmit-receive format
used in pulse mode digital FM radar. The square wave represents the
transmitter ON when the square wave is high and OFF when the square
wave is low. The Tx OFF period is the receiver ON period. IQ
samples representing digital bits are modulated on to the transmit
carrier for each burst. Bit 2000-1 is the last bit transmitted, and
thus, the first bit received from the nearest target reflecting the
first transmit burst. B it 2000-2 is likewise the last bit
transmitted of the second burst and received reflected form the
same target, and so on. Knowing what was transmitted, the receiver
processing correlates all of these first received samples with the
known transmission to determine the strength of the nearest echoing
object.
[0169] Bit 2001-1 is the second to last bit transmitted in the
first burst and is received overlapping bit 2000-1 from a target
1-bit time of go-return delay further away. Likewise bit 2001-2 is
received from that second nearest target as an echo of the second
last transmitted bit of the burst. It is desirable that, when the
receiver correlates received samples 2000-1 . . . 2000-n over the
whole scan that the correlation with bits 2001-1 . . . 2001-n over
the whole scan should as far possible be zero. This is achieved by
choosing bits 2000-1 to 2000-n to be a first shift of an M-sequence
and bits 2001-1 . . . 2001-n to be a second shift of the same
M-sequence, as it is known that maximum correlation between
different shifts of an M sequence is -1/M. Therefore, the number of
bursts n over which correlation is performed, also called the scan
period, is chosen to be the length of an M-sequence, for example
4,095. For 2 .mu.s Tx and 2 .mu.s Rx, the TX/RX period is 4 us and
the scan period is 4,095.times.4 us or approximately 16 ms.
[0170] Doppler shift due to a moving target causes the phase of
like bits in successive received bursts such as 2000-1, 2001-1 . .
. 200n-1 to rotate systematically. Thus, the samples are derotated
by amounts corresponding to hypothesized Doppler shifts before
accumulating across the scan, thereby obtaining range correlations
for a complete set of Doppler hypotheses. The results form a 2D
data set called the range-Doppler bins. For later echoes that
provide two or more receivable bits during the receive period, the
correlation of those bits can be accumulated over a burst without
relative Doppler phase untwisting as the Doppler phase rotation
during a 2 .mu.s burst can be neglected. Thus, partial correlations
are first obtained over one burst at a time, corresponding to the
first received bit (2000-1) for the earliest echo, the sum of the
first and second received bits (2000-1 plus 2001-1) for the second
earliest echo, and so forth, where "correlation" implies that the
known bit polarities of the M-sequence are removed before
accumulation to ensure that all contributions for a valid target
echo are additive. Then the partial correlations from different
bursts are combined with all possible Doppler phase untwistings to
fill the range-Doppler bins. The operation as just described can be
performed by subjecting the partial correlations to a DFT or a FFT,
which can employ a weighting function to reduce sidelobes. However,
for high Dopplers, the signal echo does not appear in the same
range bin across the whole scan, a phenomenon called
"range-walking" for which compensation techniques will be
disclosed.
[0171] FIG. 14 illustrates in more detail an exemplary placement of
M-sequence bits b.sub.1, b.sub.2 . . . b.sub.n-1, b.sub.n. If
b.sub.n is the last bit transmitted in burst 1, then choose
b.sub.n-1 to be the last bit transmitted in burst 2, b.sub.n-2 to
be the last bit transmitted in burst 3, and so forth. That way the
earliest bits received across all bursts of the scan will form a
complete sequence (reversed) of b.sub.n b.sub.n-1 . . . b.sub.2
b.sub.1.
[0172] The second to last bits transmitted shall be chosen to be a
different shift of the same code, for example, the (cyclically)
adjacent shift b.sub.n-1 . . . b.sub.2 b.sub.1 b.sub.n and so
forth. It may seem that the burst contents then just shift through
the code from burst to burst. It will be shown later that choosing
adjacent bits in the burst to be non-adjacent shifts of the code
can reduce residual range-to-range correlations when using
frequency hopping. Without frequency hopping however, the
range-to-range unwanted cross correlation properties of the
M-sequence placed as in FIG. 14 are very good, ranging from -72 dB
to -88 dB as shown in FIG. 15, which was computed for 4,096 bits
per burst, and thus the whole M-sequence was used (rotated) in
every burst.
[0173] Since it is also necessary to keep the 16 transmitter
signals as far as possible orthogonal, this can be done either by
reducing the number of bits per burst to say 256, which only uses
1/16th of the available code shifts, leaving the rest for the other
transmitters, or else by differentiating the different transmitters
by inverting their burst signals using an assigned Walsh code per
transmitter. Inverting a burst transmission does not change the
correlation of a transmitter signal with an echo of itself, and
therefore, does not destroy the good autocorrelation properties of
the M-sequence, but renders different transmitters orthogonal or
near-orthogonal to each other. Instead of different Walsh codes,
different shifts of a different M=4,095 sequence, of which there
are several, could be used to impose an overall burst sign
change.
[0174] In an initial simulation it was noticed that transmitter to
transmitter correlations were higher than expected, this was found
to be because the last bit transmitted, due to filter tails, has a
waveform that merges into a bit beyond the last bit which was
always the same polarity. The phase at the end of the last bit was
therefore always the same. Since this is the first sample received,
the first samples received were the same for all transmitters and
this correlation dies out only slowly when using a low bitrate and
many samples per bit, such as, 16 bits sampled at 256 samples per
bit. FIG. 18 illustrates that in fact a 16-bit burst needs to use
17 M-sequence bits so that the 17 phases including the start and
end phases are all code-dependent and therefore uncorrelated as
between transmitters. Thus, the method of generating samples is to
use a start phase of 0 or 180 in dependence of a 17th (or N+1 th)
code bit and to then rotate the phase according to the 16 (or N)
bits in the burst, at 256 (or 4,096/N) samples per bit. The above
keeps the number of samples transmitted at 4,096, however many bits
N there are in a burst, but this is not obligatory, and other
numbers of samples can be used. Moreover, this waveform is then
inserted into the burst in time-reversed order so that the first
phase (0 or 180) becomes the last phase transmitted and thus the
first sample received. This eliminated the unexpectedly high
inter-transmitter correlations.
[0175] Partial range correlations may be computed per bit or per
sample. Thus, a burst may contain 256 bits represented by 16
samples per bit and correlation may be performed for each of the
4,096 samples received over the 2 .mu.s receive period. The partial
correlations are computed for each burst as follows:
[0176] For the earliest sample received after the end of the
transmit burst, the partial correlation is that sample times the
conjugate of the last transmitter sample.
[0177] The next partial correlation is the product of the first
sample received with the conjugate of the second last transmitted
sample plus the second sample received times the conjugate of the
last transmitted sample, and so forth as shown in FIG. 16 which
illustrates zero-padded cyclic convolution.
[0178] In FIG. 16, the received samples numbered S1 to Sn clockwise
are disposed around the right half of the outer circle while the
left half is filled with zeros. The transmitted samples T1 to Tn
are disposed clockwise around the left half of the inner circle
while the right half is filled with zeros. In this state, there is
a zero in the transmit sample circle apposing every received sample
and a zero in the outer circle apposing every transmit sample;
thus, multiplying apposite pairs and adding would give zero in this
state. Now either the inner circle is rotated clockwise, or the
outer circle is rotated counterclockwise, bringing S1 into
apposition with Tn. Now S1 multiplies the conjugate of Tn, giving
S1.T*.sub.n while all other pairs give zero. This is the required
first correlation. Further relative rotations of one circle
relative to the other, with multiplication of the value in the
outer circle by the conjugate of the value in the inner circle and
adding, produces successively:
[0179] S1.T*.sub.n
[0180] S1.T*.sub.n-1+S2.T*.sub.n
[0181] S1.T.*.sub.n-2++S3.T*.sub.n and so forth, which are the
desired burst-wise partial correlations.
[0182] It is well known that cyclic convolution of two sequences
can be efficiently performed by multiplying the FFT of one sequence
by the conjugate of the FFT of the other and then inverse
Fast-Fourier Transforming the result.
[0183] In the case of FIG. 16, the two sequences to be convolved
are the received sample sequence padded out with as many zeros as
transmit samples to be correlated and the transmit sequence padded
out with as many zeros as received samples to be correlated. The
maximum number of transmit and receive samples currently envisaged
is 4,096, therefore size 8,192 FFTs would be used.
[0184] The 4,096 samples could represent 256 bits at 16 samples per
bit, 128 bits at 32 samples per bit, all the way down to, for
example, 16 bits at 256 samples per bit or even one bit at 4,096
samples. The number of samples and bits is merely exemplary and is
related to the desired granularity of range. For example,
correlating with 4,096 samples that span a 2 .mu.s period gives a
range granularity of:
0.5*3e8.times.2e-6/4,096 meters=7.3 centimeters or 3''
approximately.
[0185] The range resolution however is not the same as the
granularity of calculation but depends on the sharpness of the
autocorrelation function of the transmitted signal, which is the
Fourier Transform of its power spectrum. When the number of bits
per burst is small, the bandwidth is narrow, and the range
resolution is much coarser than the granularity of calculation by a
factor of approximately the number of samples per bit. Such
oversampling of the range however may be useful if an algorithm is
used to search for the correlation peak, which would occur after
beamforming to raise the signal to noise ratio.
[0186] Frequency hopping from burst to burst is a way for spanning
more bandwidth over the scan than the bandwidth used by one burst.
It is also a way of dodging interference from other,
non-collaborating radars. For example, if the burst format is 16
bits sampled at 256 samples per bit, giving 4,096 I,Q values
modulated on to the 80 GHz carrier per burst, the I,Q values can be
digitally phase-rotated in a phase ramp to digitally create a
frequency offset. The phase ramp considered is an integral number m
of 2.pi. rotations over the burst. The phase rotation per sample is
thus 2 m.pi./4,096. Rotations of more than 180 degrees per sample
would alias to rotations of less than 180 degrees in the opposite
direction and moreover rotations of that magnitude would cause
diametric signal transitions in the I/O plane, which are
problematic in systems endeavoring to use nearly constant-envelope
transmissions. Therefore, to stay well away from that region, the
maximum rotation per sample allowed is 90 degrees per sample, so
the value of m ranges from -512 to +512 maximum.
[0187] With digital phase rotation as a way of frequency hopping,
the receiver might need to A-to-D convert the received signal at
4,096 complex samples per burst despite the fundamental bandwidth
of the signal being much lower, were it not for the frequency
offset. In one implementation, a similar phase ramp can be applied
to the receive local oscillator to remove the phase ramp and center
the received signal in a narrower bandwidth, allowing some analog
narrowband filtering and thus a lower A-to-D conversion rate. Note
that the response time of any narrowband analog filtering may
result in a delay after the transmitter stops before received
signals can be discerned. This ring-down time limitation on minimum
range can be alleviated by blanking the filter's poles until after
transmission stops e.g., by turning on a shorting MOSFET across
capacitors. It can also be alleviated by at least partially
restricting the signal bandwidth with digital filters that process
the signal in time-reversed sample order. Nevertheless, the impulse
of the analog filter must be allowed to build up before any signal
is available at full amplitude, limiting the observation of very
small delays.
[0188] If the A-to-D conversion rate is less than the 4,096 samples
per burst proposed for convolution, the collected samples must be
upsampled to that number. For example, if there are 32 bits per
burst and the receiver samples the signal at 8 samples per bit to
obtain 256 samples, then the 256 samples must be upsampled 16:1 to
obtain 4,096 samples and the samples of each burst so upsampled
shall correctly represent their frequency offsets from the
mean.
[0189] The ideal interpolator for frequency limited signal samples
is to perform a Fourier Transform on the samples and to then
perform an inverse transform using a higher order Transform, with
the higher order input frequency amplitudes set to zero, to obtain
a greater number of output samples than input samples that are
still spectrally contained to the spectrum of the original input.
Thus, performing a 256-point FFT on 256 samples and plugging the
256-point spectrum into an 8,192 point transform along with 7,936
zeros and inverse Fourier transforming the 8,192-point array, will
perfectly upsample the 256 samples to 8,192 samples. Moreover, by
plugging the 256 frequency samples into the 8,192-point transform
off-center, the desired frequency offset of the burst from the mean
frequency of the scan is correctly modelled. It was explained above
that the highest offset frequency considered is a phase ramp slope
of +/-512 times 211 per 2 .mu.s period. The frequency step size is
211 per 2 .mu.s period, which is 500 KHz. The frequency step size
of an 8,192-point transform having a time span of 2 .mu.s is also
500 KHz. If frequency index 4,097 corresponds to zero frequency
(DC) in the 8,192 point transform and frequency point 129 of the
256 point transform likewise corresponds to zero frequency, then
inserting frequency point 129 from the 256 point transform into
point 4,097 of the 8,192 point transform corresponds to zero
frequency offset of the burst. If however, the burst phase ramp is
m times 211 over the 2 .mu.s period, corresponding to m.times.500
KHz offset, the frequency index 129 of the 256 point transform
shall be inserted into frequency point 4,097+m of the 8,192 point
transform, with other points likewise shifted, and zeros inserted
elsewhere.
[0190] Since an 8,192-point transform is required for cyclic
convolution, there is no need to perform an inverse transform at
this stage; rather, the 8,192 point transform is multiplied by the
conjugate of the Fourier transform of the 4,096 transmitted IQ
samples padded with 4,096 zeros, and then the inverse transform is
performed to obtain the desired set of partial correlations. If the
transmitted waveform was generated with fewer than 4,096 IQ points,
then it too may be upsampled using the same technique. If the
transmit waveform was generated without digital ramping but
frequency offset by modulating the local oscillator phase, then it
too may have its frequency offset represented by plugging its
smaller transform with the correct offset into the larger
8,292-point transform. In such cases it may be noted that effort
can be saved by avoiding multiplies or adds with zero in any of the
transform operations.
[0191] The above method is illustrated in the block diagram of FIG.
17.
[0192] Referring to FIG. 17, IQ samples corresponding to code bits
to be transmitted, generated at several samples per bit, are
streamed into the transmit I,Q modulator. The samples are also
required in parallel for range correlation. It is not material
whether samples are first assembled in transmit I,Q buffer memory
3000 and then streamed out at a given clock rate, or whether they
are generated at a given clock rate on-the-fly and simultaneously
collected in buffer memory 3000.
[0193] The I-sample stream enters I D-to-A converter 3000-A and the
Q-samples enter Q D-to-A convertor 3000-B. The analog output
signals from the D-to-A convertors are low-pass filtered in filters
3001-A and 3001-B. It is common for the digital samples to have
been generated in a way that already controls the main part of the
spectrum of the modulation so that low-pass filters 3001-A and B
can be relatively wide, just to remove sampling frequency
components and beyond. These filters are often known as "roofing
filters".
[0194] The now smooth analog IQ signals are applied to balanced
modulators 3002-A and 3002-B along with Cosine and Sine carrier
signals at the final radar frequency in the 80 GHz region. The
balanced modulators can be Gilbert cells using MOSFETs fabricated
in a 28 nM silicon process, or smaller.
[0195] Summing junction 3003 sums the balanced mixer outputs and
feeds them to power amplifier 3004 and hence to antenna 3005.
[0196] The frequency of the cosine and sine carriers is a center
frequency f plus an offset mdf in this method of frequency hopping.
In this method, the transmit sample rate, D-to-A convertors and
low-pass filters need only have a bandwidth commensurate with the
modulation bitrate, and not commensurate with the wider bandwidth
of the modulation plus frequency offset mdf. However, note the
caution expressed above with regard to the minimum range of targets
that can be detected due to longer filter impulse response times in
either the transmitter, the receiver or both.
[0197] After the transmitted signal is reflected from target 3011
and received at receive antenna 3006, it is amplified in low noise
amplifier 3007 and down-converted in balanced mixers 3008-A, 3008-B
against 80 GHz cosine and sine carriers to obtain analog (baseband)
I,Q signals. It is assumed that the cosine and sine carriers are at
the exact same frequency f+mdf as in the case of the transmitter,
so that the receiver is centered on the transmit frequency; but
this is not imperative. If there is a difference in the transmit
and receive local oscillators such that the receiver is not
centered on the transmit frequency, it would be necessary to
increase the bandwidth of low pass filters 3009-A and B and to
increase the sample rate of A-to-D converters 3010-A and B to
accommodate the modulation bandwidth plus the transmit-receive
frequency offset. bin the case of a forward-looking radar, the
transmit frequency may be slightly lowered by the one-way Doppler
and the receive center frequency slightly raised by the one-way
Doppler due to the radar's own speed, such that reflections from
static objects are received with no Doppler shift. Small offsets,
such as might be used as mentioned above to remove eigenvelocity,
can be ignored.
[0198] The transmit and receive frequency offsets can be produced
by digitally phase rotating the local oscillators, using balanced
mixers in a single-sideband upconvertor configuration, or
alternatively can be produced by synthesizer sidestepping. For the
latter, a time-out of perhaps 4 to 8 .mu.s must be taken to give
the synthesizer time to settle after a frequency change, so this
would not be the preferred method to change frequency between every
burst, but rather would be used a few times per scan, that is once
every 100 or so bursts.
[0199] After low pass filtering the received analog I,Q signals in
filters 3009-A,B, they are A-to-D converted in 3010-A and B and the
results collected in receive buffer memory 3100. Again, note that,
if filters 3009-A and B and the sample rate of converters 3010A and
B are too restrictive, the attendant long impulse response means
that the receiver signal will not be fully developed in time to
respond to very short delay echoes from very nearby targets.
Methods to minimize this effect by receiver blanking during the
transmit period and time-reverse processing were mentioned
above.
[0200] Because narrowband filters are desirable to suppress
other-radar interference, it is conceivable to have a
dual-bandwidth receiver whereby the analog IQ signals are sampled
in a wide bandwidth using a high A-to-D rate for an initial part of
the receive period where early target echoes would be found and
simultaneously low pass filtered by narrower band filters 3009A,B
and A-to-D converted at a slower rate for sampling later echoes.
Since both early and late processing would simply be different
instances of the processing described herein, they will not be
described separately.
[0201] Assuming that the receiver is centered on the transmitter
frequency, and that the number of receive samples N1/2 collected
over a burst in receive buffer memory 3100 is the same as the
number of transmit IQ samples N1/2 collected in transmit buffer
memory 3000, then it is desired to perform the zero-padded cyclic
convolution of one with the other. Thus, the N1/2 samples of each
are zero-padded to N1 samples and subjected to N1-point FFTs 3101
and 3102. The conjugate of the transmit sample FFT values are then
multiplied point-by-point with corresponding values of the receive
FFT in multiplier 3103. The result is N1 values, which if inverse
transformed, would represent partial range correlations without
regard to frequency offset. These cannot be accumulated with
partial correlations from other bursts using different frequency
offsets because frequency change completely alters the phase of an
echo due to there being thousands of wavelengths distance to the
target and back. To accumulate partial correlations from different
bursts therefore, the FFT of their correlations from multiplier
3103 must be frequency shifted according to the frequency offset
used and inserted into 8192-point IFFT buffer 3104 with the correct
offset m from center. The spectral center or "DC" has been defined
above as frequency index 4097 in the 8,192-point buffer and the
corresponding DC term of the N1 transform is therefore placed into
8,192-point buffer position 4097+m. As explained above, m ranges
from -512 to +512 as an exemplary number. Therefore, the N1
frequency points from multiplier 3103 are inserted into N1
positions of the 8192 point buffer centered on position 4097+m
which can range between a center of 4097-512 to 4097+512.
[0202] In principle, it is possible to accumulate sets of N1 values
additively from different bursts in an 8,192-point buffer before
performing an inverse 8,192-point FFT. However, this would only
yield range correlations for zero-Doppler targets.
[0203] To accumulate range correlations across different bursts
taking account of the phase rotations due to different Dopplers,
the range correlations have to be accumulated in many different
ways corresponding to all Dopplers of interest. The number of
Doppler frequencies that can be resolved is equal to the number of
bursts in the scan, for example 4,095. Therefore, ultimately the
number of range-doppler bins that will be populated is
(4,095).sup.2 or over 16 million. It is likely that previous scans
would be used to indicate a much-reduced subset of interest in
order to save memory and processing, a process known as
"sparsification."
[0204] An alternative method of frequency hopping does not
necessarily involve changing the local oscillator frequencies by
applying a phase ramp thereto, but rather by applying a phase ramp
digitally to the transmit IQ samples, which implies that the sample
rate is large enough to represent both modulation and the largest
frequency offset. In this case the receiver can be of either type
but may also not choose to change its local oscillator frequency
but simply use a bandwidth and A-to-D convertor rate that is large
enough to represent both modulation and the largest frequency
offset. It is clear that hybrids of both methods could also be
used, where smaller frequency offsets are applied by digital phase
ramping and larger offsets are applied by local oscillator
frequency changes by either phase ramping or synthesizer
side-stepping.
[0205] Due to the need to accumulate range correlations over many
bursts taking account of different Dopplers, the contents of
8,192-point buffer 3104 are IFFTed for every burst to obtain
partial range correlations rather than the Fourier transform
thereof. These are held in a 2D memory with dimensions (range,time)
where time refers to the time of the burst in which the range
correlations were collected. This memory is in principle of size
(rounded up) 4096.times.4096 or 16 megawords complex per VRX. This
memory can be an external cache, as specific memory technologies
are more cost efficient than combining bulk memory with custom
processing. Alternatively, a smaller memory of sparsified
range-time bins can be used. In this case the record in the memory
comprises the range index, the burst number or time index and a
complex correlation value.
[0206] The data from cache may be read back for Doppler analysis
where an analysis for each range point is performed along the time
axis with phase twists corresponding to different Dopplers.
[0207] The issue of range-walking has already been mentioned above,
whereby a high-speed and thus high-Doppler target may not lie in
the same range bin across the whole scan. If no attempt is made to
deal with that, a blurring of both range and Doppler resolution
results. However, because Doppler shift is rate of change of range,
when an analysis is being performed to compute the correlation for
a specific Doppler assumption, it can be exactly predicted how the
target will move from one range to another, and thus the track
through the range-time bins along which values are accumulated can
shift range at the predicted times to follow the signal as it
"walks" through successive range bins over the scan.
[0208] FIG. 19 illustrates the principle of range-walking
compensated Doppler analysis. The range-time bins obtained by
burst-wise partial correlations as just described are illustrated
by a grid of points, each being a memory location holding a complex
number. The different rows represent ranges spaced by the range
resolution of about 7.3 cm or 3'' while the different columns
represent burst times 4 .mu.s apart. A zero Doppler correlation
starts at a given range hypothesis on the left and accumulates
values along a horizontal line without changing range, as indicated
by the RED track. There are such horizontal tracks starting at
every possible range on the left and ending at the same range on
the right.
[0209] A medium speed Doppler correlation starts at a given point
on the left, but knowing that, for the hypothesized speed/Doppler
the target will get systematically nearer over the scan, the track
moves up to a one-bin shorter range periodically at predicted
times, as illustrated by the BLUE track. There is one such BLUE
track starting at every possible range on the left. Alternatively,
the range walking correlation can be usefully performed backwards.
Starting at a given point on the right, accumulation of complex
values occurs from right to left with the range increasing as the
target gets further way at older times, (if it is oncoming, or the
range reduces for older times if it is a receding target), the
complex values being phase-un-twisted before accumulation based on
the hypothesized Doppler shift. There is one such track for every
terminal range on the right, and the advantage is target parameters
related to the last range rather than an out-of-date range are
successively obtained.
[0210] A high-speed, high-Doppler target has its Doppler
accumulation track changing likewise through the grid, but shifting
range more often, as illustrated by the PURPLE track.
[0211] A computer simulation can be performed in the absence of
noise to observe the range-walking effect. In practice, a real
radar may not have a sufficient signal-to-noise ratio before
beamforming over all VRXs to display the effect satisfactorily. In
the absence of noise, a simulation can produce a heat map
corresponding to the grid of FIG. 19 in which color represents the
magnitude of the complex value in the range-Doppler bin, as shown
in FIGS. 20 and 21.
[0212] The axes of FIG. 20 are switched as compared to FIG. 19,
with time (in bursts) running vertically and range running
horizontally. Each row represents partial range correlation
magnitude encoded to color according to the color scale on the
right. Note that the picture has been increased in brightness by
doubling the dB values so as better to see sidelobes that are many
dB down.
[0213] The target amplitude is unity, which is color white. It may
be seen that the white stripe migrates to one range bin shorter
from the beginning of the scan at the bottom to the end of the scan
at the top. The range bin sizes in this simulation were 0.5 ns
delay apart, corresponding to one of the 4,086 burst samples and
corresponding to about 6'' in go-return-distance or 3'' in range.
That this is indeed commensurate with the speed may be seen as
follows:
10 MPH=10.times.63360 inches/hour=10.times.63360/3600=176 inches
per second. The scan period is 4095.times.4 .mu.s=0.01638
seconds.
[0214] Change in range over the scan is 176.times.0.01638=2.88
inches which is approximately one range bin.
[0215] Thus, with range resolution as fine as 3'', since
range-walking starts to be significant already at only 10 MPH,
range-walking compensation is highly desirable.
[0216] FIG. 21 shows the range-walking that occurs at 50 MPH. At
five times the speed of FIG. 20, it can be seen that the target
echo does indeed migrate 5 times over the scan to progressively
shorter-range bins.
[0217] After Doppler analysis, the cache memory holds range-Doppler
bin values which replace the range-time bin values. Simulation in
the absence of noise can also produce 2D heat maps with
range-Doppler axes instead of the range-time axes of FIGS. 19,20
and 21. The most dramatic illustration of the benefits of
range-walking compensated Doppler analysis is obtained by comparing
range-Doppler heat maps for a 250 MPH relative target speed
computed with and without range-walking compensation.
[0218] FIG. 22 shows the section of the total range-Doppler heat
map containing a target initially at 250 m and approaching at 250
MPH uncompensated Doppler analysis results in blurring of the
target echo energy in both range and Doppler over several hundred
range Doppler bins with the result that the signal in each is 24 dB
lower than the correct total echo energy.
[0219] In FIG. 23, range-walking compensation is used, and the
energy has been compressed to a group of about four bins of the
order of 3 to 6 dB down, which in fact could be due to the target
straddling two discrete range and Doppler bins rather than being a
processing loss.
[0220] The preferred method of compensation is to interpolate
smoothly between range bins rather than the abrupt switching
illustrated in FIG. 19. When a target straddles two range bins, the
correlation in each is given by the +/- half-bin edge-loss of the
autocorrelation function of the modulation, which is about -3 dB.
Interpolation would therefore make a weighted sum of the two range
bin values with weights of 1/ 2 (-3 dB) and would produce a net
contribution of 1.2 from each range bin and thus a net of unity,
which is the true target amplitude. Obvious functions to use for
interpolation are thus sine and cosine functions which take on
values of 1/ 2 at 45 degrees. We thus form: Interpolated
value=Cos(.theta.) BIN(k)+Sin(.theta.) BIN(k+1) where .theta.=0 for
range bin k, 90 degree for range bin k+1 and 45 degrees half-way
between the two bins. When the target reaches the center of range
bin k+1, replace k by k+1, k+1 by k+2, and reset the angle .theta.
to zero so that interpolation now begins between bin (k+1) and bin
k+2. This was the algorithm used for the range-walking compensation
of FIG. 23. The value of 8 is calculated such that it changes by 90
degrees in the time it takes the target to move one range bin,
which can be calculated exactly for each Doppler assumption being
tested.
[0221] It was mentioned above that an extra (N+1).sup.th M-sequence
bit is needed to fill bursts with N bits and keep different ones of
the radar's transmitter signals orthogonal over the scan. This is
true even if there are zero bits per scan, that is, the burst is
filled with CW. The extra bit is used to determine whether the CW
signal is one way up or the other way up as between different
transmitters. The extra bit can form an M-sequence over the scan
and a different shift of the M-sequence used for different
transmitters, thereby ensuring near-orthogonality. Thus, a pure
frequency hopping system with no burst code modulation can be
envisaged. Each burst generates a phase ramping of the carrier
signal corresponding to a chosen frequency offset. The ramping is
preferably a phase change of an integral number of 2.pi. radians
over the burst, but not more than +90 degrees per sample. Each
transmitter preferably uses the same frequency at the same time
when the objective is to keep the momentary frequency occupancy
over the burst low so as not to interfere with other radars except
in the case of a random frequency clash. Thus, each transmitter
uses the same phase-ramped signal but inverted or not inverted
according to its assigned M-sequence bit for that burst. The
correlation of a received echo signal with a transmit signal yields
a VRX signal phase that depends on the frequency used for the
burst. When the phase ramp changes the transmitter phase by 2 m.pi.
over a 2 .mu.s burst the frequency offset produced is m.times.500
KHz. Thus, the hop-set comprises frequencies spaced by 500 KHz. If
the frequencies are used in order, increasing by 500 KHz each
burst, the VRX phase produced will increase by an increment each
time also. This systematic phase increase is removed when
burst-wise correlations are accumulated according to the block
diagram of FIG. 17. The correlation of one transmitter with the
echo of another transmitter will not however accumulate coherently
but will yield a result which is the sum of the M-sequence bits
time a progressive phase twist, which is in fact a Fourier
component of the M-sequence. Since M-sequences have a flat
spectrum, the energy in this component is 1/M, which is 1/4,095,
but only the square root of that in voltage terms. Thus, while the
correlation of different M sequences is -1/M in voltage terms,
which is -72 dB for M=4,095, it is only -36 dB in the case of an
energy suppression of 1/M. Thus, a cross-correlation between
different transmitters of -36 dB is expected.
[0222] If however, the hop-frequencies are not used in order lowest
to highest, the resulting phase twist of the VRX signal form an
order-scrambled Fourier sequence. The correlation of the scrambled
Fourier sequence with the M-sequence is the same as a Fourier
component of a scrambled M sequence which could be higher than 1/M.
Therefore, in order to preserve the -36 dB cross-correlation
between different transmitters, the order of use of M-sequence bits
to differentiate them is tied to the order of use of frequencies in
the hop set.
[0223] The main lobe of the autocorrelation function of pure
frequency-hopped CW as described above is shown in FIG. 24 on a
linear scale. It looks like and can be mathematically shown to be
the sin(x)/x function.
[0224] FIG. 24A shows the function when computed by simulation of
the radar, which is now quantized in steps of one sample.
[0225] The sidebands of a sine(x)/x) function do not fall off very
quickly, as can be seen in FIG. 25 which shows the full
autocorrelation function, falling to -66 dB at the extremes.
[0226] In calculating FIG. 25, hop frequency signals on either side
of zero, which are respectively Exp(-jwt) and Exp(+jwt) were
combined to Cos (wt). It was realized that this gave them a weight
of 0.5 while the DC term, that has no negative partner, remained
with a weight of 1, causing a DC bias. Giving the DC term also a
weight of 0.5 made the simulated hopping spectrum flat, as
intended, improving the ultimate skirts of the autocorrelation
function to -72 dB as shown in FIG. 26, which also shows the main
lobe on a dB scale.
[0227] When a function shown on for example a `scope or spectrum
analyzer has wild ripples or noise, sometimes called "grass"
because of the traditional green `scope trace, a video filter is
sometimes used on the `scope signal to smooth out the ripples. It
would indeed be possible to run a short FIR filter across the range
correlations and it was determined that an appropriate filter would
be: 0.5Z+1+0.5Z.sup.-1.
[0228] The effect of this "video filtering" is shown in FIG. 27 to
have taken the skirts down to -120 dB. FIG. 28 shows that the
effect on the main lobe of the video filtering is to broaden it
somewhat, corresponding to an increase in range resolution from 3''
to about 6''.
[0229] Another way to reduce the skirts without broadening the main
lobe is to add code bits within the bursts, that is to use an "N"
greater than 0 and in the region 16 to 256, always with the
(N=1).sup.th bit for reasons previously described. The effect of
placing code bits in the burst would be expected to produce an
autocorrelation function which was the product of the pure FHCW
autocorrelation function and the code autocorrelation function,
which is much wider. The width of the FHCW main lobe is
approximately one sample while the width of the code
autocorrelation is roughly one bit, so its autocorrelation function
is wider by a factor equal to the number of samples per bit. FIG.
28A shows the autocorrelation function of code alone, with no
frequency hopping, and FIG. 28B shows the shape of the correlation
peak for code and FH combined as the total hop bandwidth is
increased, eventually having the shape of FIG. 24A at maximum hop
bandwidth.
[0230] Yet another way to lower the autocorrelation skirts is to
employ a weighting function across the different frequency points
correlated. Rather than deweight different bursts, which weakens
their contribution to defeating noise, certain frequencies can be
emphasized more than others by including them twice or more in the
total number of hop frequencies.
[0231] Frequency hopping worsens the code autocorrelation function
for range-to-range cross-correlations from sidelobes of magnitude
1/M (-72 dB) to 1/ M as previously explained. The resulting
range-range cross-correlation function is shown in FIG. 29. FIG. 29
shows the peak correlation of a target at 150 m and the sidebands
thereof extending down to zero range at left, where they are about
-36 dB mean, and extending up to 300 m range at right, where the
cross-correlation improves to -55 dB mean because the burstwise
partial correlations are based on more bits. FIG. 29 was simulated
without linking burst bit content to hop frequency. FIG. 30 shows
the improvement at longer ranges of linking burst bit content to
hop frequency.
[0232] There was a hint that the phenomenon seen in FIG. 30 was
dependent on the selection of M-sequence shifts to place in
successive burst bits. FIG. 14 illustrated the selection of
adjacent M-sequence shifts for adjacent bits in the burst.
Experiments were then carried out using different selections of the
spacing of M-sequence shifts to place in adjacent burst bits.
Different selections resulted in different cross-correlation
functions when the bit content was still linked to hop frequency,
and a spacing of 2 appeared to give useful results for all main
lobe ranges. FIG. 31 illustrates the function for a target main
lobe at 50 meters. Thus, the burst content of a burst may be
b.sub.1 b.sub.3 b.sub.5 . . . b.sub.2N-1 for one hop frequency and
b.sub.3 b.sub.5 b.sub.7 . . . b.sub.2N+1 for the adjacent hop
frequency, irrespective of the burst/time at which it is
transmitted. Bit content is thus linked to hop frequency rather
than burst order in the scan. Note that because 4,095 is odd, a bit
spacing that is not a factor of 4,095 will eventually wraparound
and use all 4,095 bits in 4,095 bursts.
[0233] Much experimentation with different shift spacings and
M-sequences remains, to determine if further improvements are
possible, which can be performed by a person skilled in the art
based on the teachings above.
[0234] It has thus been described how range correlations can be
performed with arbitrary IQ sample content in bursts, ranging from
pure FHCW ramps to mixed FH and code modulation and eventually to
pure code with no FH. It has been described also how the partial
correlations are combined by FFT or preferably range-walking
compensated analysis to separate targets by Doppler shift. It is
appropriate to mention at this point that, to avoid confusion
between the phase changes of burst correlations caused by hopping
to systematic phase changes caused by Doppler, the phase changes
due to the hopping frequency pattern should be as unlike the
systematic phase ramps of a Fourier sequence as possible. One type
of frequency hopping would be adaptive avoidance of interfering
radars. In that case, a running metric can be kept of the
resemblance to a Fourier sequence and priority given dynamically to
frequency choices for subsequent bursts that decreased the
resemblance.
[0235] Frequency hopping has the desirable characteristic that,
unlike CDMA, the interference to or from other devices is related
to the probability of a clash and not very dependent on the
strength of the interference. The latter is called the "near-far"
tolerance, which is much better for FH than CDMA. Moreover,
damaging clashes can be detected by a sudden increase in signal
level, and excised from subsequent processing.
[0236] FIG. 32 shows the range-Doppler resolution for a 50 MPH
target at 50 meters range using Range-walking compensation with no
frequency hopping interference. The wanted target is the white
square which corresponds to zero dB amplitude.
[0237] FIG. 33 illustrates the effect of 50% erased hops. When 50%
of interfered hops are excised from the processing, the result is
scaled up 2:1 to compensate, so the wanted target amplitude remains
unchanged. It can be seen that surrounding range Doppler bins
increase in level but the wanted target is still clearly visible.
FIGS. 34 and 35 show the same effect with 70% and 85% erasures
respectively, indicating that frequency-hopping is very tolerant of
interference as regards being able to detect the strongest signal.
It will be explained during the following discussion on beamforming
that it is only necessary to be able to detect the strongest
signal, and then subtracting it out removes all of the energy that
it also created in other range-Doppler bins due to imperfectly
orthogonal cross-correlation or frequency hop erasures. Moreover,
FIGS. 33, 34, and 35 are for one VRX, before beamforming, and it is
not known if the unwanted energy in other range-Doppler bins will
even form a beam.
[0238] Once a set of complex numbers is achieved for all VRXs for
the same range and Doppler, beamforming over the VRXs can be
carried out to separate targets also by Azimuth and elevation. The
beamforming algorithms to be described are independent and agnostic
of which of the above methods is used to produce a set of
range-Doppler bins per VRX.
[0239] Beamforming will be described in terms of: [0240] The
geometry, coordinate system and mathematics involved; [0241]
construction of sparse arrays with low grating lobes; [0242]
sidelobe-reduction beamforming algorithms; and [0243] the on-chip
beamforming engine.
[0244] FIG. 36 shows the geometry of a planar antenna array
receiving signals from a target located at a boresight with azimuth
angle AZ or .theta. and elevation angle Elev or .phi..
[0245] Letting .theta. be the Azimuth angle of a target at distance
R.
[0246] Letting .phi. be the Elevation angle of the target.
[0247] Then the target's coordinates are X=R
cos(.phi.)sin(.theta.); Y=R sin(.phi.); Z=R
cos(.phi.)cos(.theta.).
[0248] The plane of the array is the X,Y plane with Z=o. Consider
an antenna in the plane of the array located at (x,y,0). The
distance from the antenna to the target is: d= (R
cos(.phi.)sin(.theta.)-x).sup.2+(R sin(.phi.)-y).sup.2+(R
cos(.phi.)cos(.theta.)).sup.2.
d= R.sup.2-2R(x cos(.phi.)sin(.theta.)+y
sin(.phi.))+x.sup.2+y.sup.2
d=R 1-2(x cos(.phi.)sin(.theta.)+y
sin(.phi.))/R+(x.sup.2+y.sup.2)/R.sup.2
[0249] which for large R compared to (x,y) is
R(1-(x cos(.phi.)sin(.theta.)+y sin(.phi.))/R)=R-x
cos(.phi.)sin(.theta.)-y sin(.phi.).
[0250] The amount R is common all antennas so does not affect
relative path distance and so can be dropped.
[0251] The path phase shift factor between target and the antenna
at (x,y,0) is therefore:
Exp[-jK(x cos(.phi.)sin(.theta.)+y sin(.phi.)
[0252] where K is the "wave number"=2O/.lamda..
[0253] Phase factor=Exp[-jKx cos(.phi.)sin(.theta.)]Exp[-jKy
sin(.phi.)].
[0254] Thus, the phase factor is the product of two-phase factors,
one depending only on the antenna's x-coordinate in the array and
the other depending only on the antenna's y coordinate in the
array. The first is the same for all antennas with the same x
coordinate and the second factor is the same for all antennas with
the same y coordinate.
[0255] In a MIMO radar, N.sub.rx receivers have coordinates
{x.sub.rx(i),y.sub.rx(i)}, i=1:N.sub.rx and N.sub.tx transmitters
have coordinates {x.sub.tx(j),y.sub.tx(j)}, j=1:N.sub.tx. The total
phase factor for sum of the go and return distances is the product
of the phase factors for each of the go and return distances, that
is:
e.sup.-jKxrx(i)cos(.phi.)sin(.theta.)e.sup.-jKyrx(i)sin(.phi.)e.sup.-jKx-
tx(j)cos(.phi.)sin(.theta.)e.sup.-jKytx(j)sin(.phi.);
which can also be written as:
e.sup.-jK[xrx(i)+xtx(j)]
cos(.phi.)sin(.theta.)e.sup.-jK[yrx(i)+ytx(j)]sin(.phi.).
[0256] Using the convention that the virtual radar location is the
sum of the Tx and Rx coordinates therefore, the location
[0257] [(x.sub.rx (i)+x.sub.tx (j)), (y.sub.rx (i)+y.sub.tx(j))] is
the virtual radar location which can be renamed
[X.sub.vrx(1),Y.sub.vrx(1)].
[0258] Therefore, given the virtual radar antenna locations and the
target azimuth .theta. and elevation .phi. the received signal
phases at the virtual antennas can be calculated.
[0259] Unshaped beamforming comprises multiplying each signal that
is received by receiver(i) from transmitter(j) by the conjugate of
the above factor (just dropping the minus sign) and summing over i
and j so as to phase them all together, producing a beam that is
probing for a target in the direction (.theta., .phi.).
[0260] Traditional radar rotated the antenna mechanically to
produce beams in different directions at successive times. When an
antenna array is used and the signals are captured digitally, they
can be processed in different ways to form beams in all directions
simultaneously.
[0261] It is advantageous to compute beams in equal increments of
variables u=cos(.phi.)sin(.theta.) and v=sin(.phi.) rather than in
equal increments of .theta. and .phi..
[0262] The above phase factor can then be written:
e.sup.-jK[Xvrxu+Yvrxv].
[0263] Xvrxu+Yvrxv is the dot product of the antenna location
coordinates with the sightline direction cosines (u,v) and
represents the antenna vector offset from array center resolved in
the sightline direction, which is the relevant distance that causes
relative phase shifts between antennas.
[0264] The maximum possible value of u=cos(.phi.)sin(.theta.) is
.+-.1 and likewise the maximum possible value of v=sin(.phi.) is
.+-.1. Therefore, the range .+-.1 may be divided into 2Naz equal
steps of 1/Naz and u is allowed to range from an integral number of
steps Iaz=-Naz steps to Iaz=+Naz steps to cover -90 to +90 degrees
of azimuth. The same steps could be used for Elevation, but
typically only a smaller range of elevation is of interest in
automotive radar, so v only ranges from an integral number of steps
Iel=-Nel steps to Iel=+Nel steps where Nel<<Naz.
[0265] Beamforming is also simplified if the VRX locations are all
on a regular grid, even when the grid points are sparsely
populated, and if the grid spacing is a multiple of some integral
fraction of a wavelength. For example, if the grid spacing is
.lamda./16, then the VRX locations can be expressed as (Ix,Iy)
.lamda./16.
[0266] The phase-retarding distance then becomes:
Xvrxu+Yvrxv=.lamda.(IxIaz+IyIel)/(16Naz).
[0267] Then multiplying by the wavenumber K=2.pi./.lamda., obtain
the phase retard:
2.pi.(IxIaz+IyIel)/(16Naz).
[0268] Letting .omega.=-2.pi./(16Naz), the phase factor then
becomes:
.omega..sup.|IxIaz+IyIel|16Naz.
[0269] The integer IxIaz+IyIel may be reduced modulo 16Naz as
additional factors of 2.pi. do not change the complex exponential
value. Thus, only 16Naz values arise which could be stored in a
lookup table addressed by |IxIaz+IyIel|16Naz.
[0270] Beamforming comprises calculating the 2D array of complex
numbers B(Iaz, Iel) for all Iaz and Iel of interest as shown by the
following pseudocode:
[0271] FOR Iaz=-Naz to +Naz
[0272] FOR Iel=-Nel to +Nel
[0273] B(Iaz,Iel)=0
[0274] FOR Ivrx=1 TO Nvrx
[0275] k=|Ix(Ivrx)Iaz+Iy(Ivrx)Iel|16Naz
[0276] BEAM((Iaz,Iel)=B(Iaz,Iel)+VRX(Ivrx).omega..sup.k
[0277] Next Ivrx
[0278] Next Iel
[0279] Next Iaz
[0280] The above pseudocode accumulates, for each beam azimuth and
elevation direction, all Nvrx VRX signal values numbered VRX(1)
VRX(Nvrx), phase-twisted by a power k of w that is proportional to
the quantized antenna location vector (Ix(Ivrx), Iy(Ivrx) in the
plane of the array resolved in the direction given by the azimuth
and elevation variables u and v quantized to Iaz,Iel steps of
1/Naz.
[0281] The above is an efficient method for computer simulations,
but a much more efficient hardware implementation has been devised
for chip implementation.
[0282] The variable u=cos(.phi.)sin(.theta.) is allowed to range
from -1 to +1 to cover the azimuth range -90<.theta.<+90, but
u can only have a magnitude of 1 at .theta.=+90 when elevation
.phi.=0. FIG. 37 illustrates that not all beams computed as above
thus necessarily represent physical directions. The number of
meaningless values computed however is negligible when the range of
interest of elevation is only say +/-7.12 degrees.
[0283] In FIG. 37, the outer square represents the range u=.+-.1,
v=.+-.1, but only the grey circle contains physical positions. The
grey circle is in fact the hemisphere in front of the radar, which
is its entire field-of-view. (u,v) values between the grey circle
and the outer square are not physical locations. The green area
represents a restricted range of elevation that is of interest for
automotive radar. If beamforming is performed over a rectangle
encompassing the green area, only a few locations at the edges will
be non-physical beam locations and thus the wasted effort in
computing them is small.
[0284] When the antenna array to be subjected to beamforming is a
linear array of regularly spaced antennas with no gaps, beamforming
can be efficiently performed with a 1-dimensional FFT. The beams
span exactly .+-.90 degrees when the antenna spacing is .lamda./2.
If the antenna spacing less than .lamda./2, some of the beams so
computed will represent non-physical locations; when the antenna
spacing is greater than .lamda./2, the beams will span less than
.+-.90 degrees, but objects beyond that span and up to 90 degrees
away will exhibit a phase change between antenna elements greater
than 180 degrees which cannot be distinguished from a phase change
of between 0 and -180 degrees. The object will thus be aliased to a
"grating lobe" on the other side of the scan.
[0285] Regularly spaced arrays on a rectangular grid with every
grid point occupied can also be efficiently beamformed with a 2D
FFT. If the number of rows is N1 and the number columns is N2, then
beamforming comprises performing N2-point FFTs along rows followed
by N1-point FFTs along columns of the first FFT output values. The
behavior with different antenna spacings is the same as for the 1D
case but in each dimension separately.
[0286] If antenna spacings are not regular, but irrational values,
then beamforming is performed by multiplying the antennas signals
with a matrix of steering vectors, the elements of which are
ExpjKX.sup.(vrxu+Yvrxv) as shown above, which phases however are
not now integer multiples of a basic phase shift unit, and so the
beamforming cannot done fast with an FFT.
[0287] If the antenna spacings lie on a regular rectangular grid,
but not every grid point is populated, the array is termed a
"sparse array." Beamforming can be carried out using a 2D FFT, but
the sizes of the FFTs have to equal the total number of grid points
spanned by the array in each dimension, which can be much greater
than the number of antennas elements of the sparse array. The use
of FFTs in that case could involve more computation than treating
the array as an irrationally-spaced array. In either case, when a
sparse array is beamformed, sidelobes/grating lobes arise due to
the missing grid points cause different beams to no longer be
orthogonal.
[0288] In a MIMO radar, the VRX array to be beamformed arises from
a conjunction of the transmit and receive antenna arrays. Each pair
comprising a transmitter and a receiver gives rise to a VRX at
coordinates which are the sum of the transmitter and receiver
coordinates. FIG. 38 shows one such VRX array that arises from the
transmitter and receiver array below it. The lower part of FIG. 38
shows an array of 16 transmitter locations indicated by red X's and
16 receiver locations indicated by white O's. The virtual antenna
locations (VRXs) are computed by forming all 256 possible sums of
the coordinates of a Tx antenna with the coordinates of an RX
antenna. The Tx and Rx antennas were located on a nominally
.lamda./2 grid, but not every point is populated. The actual
positions of the antennas are given in units of .lamda. in FIG. 39.
The effect of some antennas being on odd multiples of .lamda./2 and
some on even multiples of .lamda./2 results in a set of 256 VRXs
show at the top that are located on a grid with horizontal spacing
.lamda./2 but vertical spacing 3.lamda.. The VRXs exhibit 8
antennas on each of 32, 3.lamda.-shaped horizontal lines and
various numbers of antennas have one of 106 .lamda./2 spaced
horizontal coordinates, of which 6 are unpopulated.
[0289] Placing a unit amplitude target signal at 0 degrees
elevation and azimuth, the resultant beamforming of the array of
FIG. 38 is shown in FIG. 40 over the entire hemispherical field of
view, that is with u and v each varying over the range .+-.1. FIG.
41 shows the range corresponding only to physical locations. It is
oval merely because of the aspect ratio of the page. The wanted
target is the green spot in the center of the image, having an even
smaller white spot in its center corresponding to unit amplitude.
All similar green spots, particularly those above and below,
represent unwanted grating lobes or aliasing. The aliasing in the
vertical dimension is due to the 3.lamda. vertical antenna spacing.
The number of elevation points computed (.+-.Nel) is +32 steps of
1/256 in v, so the maximum value of sin(.phi.) is 1/8th. Thus,
.phi. ranges over +/-7.18 degrees. This can be tolerated because
the F,O,V of interest is only about .+-.7 degrees in the elevation
direction.
[0290] FIG. 42 shows the picture restricted to +7.12 degrees of
elevation. Targets above and below are attenuated by choosing the
antenna element vertical patterns to be narrow in the vertical
plane but yet wide in the horizontal plane. One type of antenna
element used to achieve this is a waveguide slot array. It can be
seen that there are many sidelobes that are only of the order of -6
dB relative to the wanted main lobe in the center and the worst
grating lobes are those at +/-90 degrees just above and below the
horizontal plane.
[0291] An interesting feature of computing beams in u,v space is
that the image is doubly periodic. That is, if the wanted signal is
shifted to the left, the entire image of FIG. 40 shifts to the left
and sidelobes that were in non-physical positions now shift into
physical positions. Likewise, the entire image of FIG. 40 shifts up
or down cyclically upon shifting the wanted target up or down.in
elevation. Thus, the sidelobes at +/-90 degrees cannot be ignored
as with non-central targets they move well into the wanted F.O.V.
FIG. 43 shows the shifting of the sidelobes into the main F.O.V.
FIG. 43 was also computed in equal increments of azimuth and
elevation angle instead of equal increments of u and v, in order to
show the stretching distortion, the edges due to the non-linear
cosine and sine functions. Thus, it is only when using (u,v)
coordinates that image merely shifts cyclically when the target
changes position.
[0292] Sidelobes are proportional in amplitude to the target signal
from which they derive; therefore, a method of preventing sidelobes
from being mistaken for false targets was developed, based on
identifying through beamforming the strongest echo, and then
subtracting it, which also removes its sidelobes, revealing weaker
targets beneath. The second strongest target is then identified and
subtracted, and so forth. Before describing successive subtraction
in signal strength order in more detail however, steps taken to
reduce sidelobes of a sparse array will be described.
[0293] Co-filed and commonly owned patent application Ser. No.
17/582,437, entitled "Sparse Antenna arrays for Automotive Radar,"
described a systematic way to arrive at Tx and Rx arrays that will
produce a VRX array having the lowest possible sidelobes. This
application was incorporated by reference above in its entirety.
The inventive sparse arrays are based on the realization that every
pair of antennas produces a main lobe, which when the antennas are
all properly phased is in the same place for all pairs but produces
sidelobes in different angular positions depending on the vector
joining the two antenna locations. Thus, if different pairs of
antennas have vectors joining them that are all different, in both
length and direction, they will not produce sidelobes in the same
place that are additive, but rather the sidelobe energy will be
more evenly spread over the F.OV. The optimum design of sparse
arrays to achieve the above has a strong synergy with the theory of
differential arrays.
[0294] Beamforming of an array can be expressed in matrix/vector
form as follows:
[0295] Using the definition of variables as in the mathematics
above, to form a beam in direction (Iaz, Iel) with VRX antennas
having locations in the plane of the array given by Ix(Ivrx),
Iy(Ivrx) where Ivrx is the index of the VRX, each VRX signal is
phase-untwisted by multiplying it by .omega..sup.k
[0296] where k=|Ix(Ivrx)Iaz+Iy(Ivrx)Iel|.sub.16Naz.
[0297] Placing the 256 values of .omega..sup.k, one for each VRX,
in a row vector V, and placing the 256 VRX signal values in a
column vector S, the complex value B of a beam in the direction
with indices Iaz, Iel is B=VS.
[0298] If row vectors for each beam direction are arranged under
each other to form a matrix [V] of size (2Naz+1)(2Nel+1).times.256,
then the beam values are given by the (2Naz+1)(2Nel+1)-element
column vector B=[V]S.
[0299] It would be normal to enquire which of the computed beams
was the strongest, in other words, the magnitude of the beams is of
primary interest and not their phase, which depends on the
arbitrary reflection coefficient of the target object. Whether the
beams are compared in magnitude |B|, magnitude squared |B|.sup.2 or
in dBs as 20 Log.sub.10|B| or 10 Log.sub.10(|B|.sup.2) is
immaterial.
[0300] The magnitude squared of a single beam B=VS is given by:
[0301] B*B=S.sup.#[V.sup.#V]S, where # means conjugate transpose.
This is the sum of each VRX signal value times the conjugate of
another weighted by a phase factor V that is a complex exponential
of the difference in phases between them due to the conjugation of
one of the V's; namely elements of [V.sup.#V] are of the form
.omega..sup.|Ix(Ivrx1)Iaz+Iy(Ivrx1)Iel-Ix(Ivrx2)Iaz-Iy(Ivrx2)Iel|16Naz
or
.omega..sup.|{Ix(Ivrx1)-Ix(Ivrx2)}Iaz+{Iy(Ivrx1)-Iy(Ivrx2}Ie1)Iel|16Naz.
[0302] That is, it looks like beamforming with antennas, the
coordinates of which are the difference {Ix(Ivrx1)-Ix(Ivrx2)},
{Iy(Ivrx1)-Iy(Ivrx2} between pairs of antenna coordinates for Ivrx1
and Ivrx2. These are called "differential VRXs" or DVRXs. If there
are 256 VRXs, then there are 256.sup.2 DVRXs, but they are not
necessarily all in distinct virtual locations. Obviously, there are
256 DVRXs at location (0,0), corresponding to the 256 times Ivrx1
and Ivrx2.are the same VRX, and there may be others that accidently
have the same location.
[0303] Due to the periodicity of the beamformed pattern in (u,v)
coordinates, it is only necessary to consider the sidelobe pattern
for a target located at (0,0). The pattern for any other target
position is the same, merely shifted cyclically in (u,v) space,
while maintaining the same separations and amplitudes of sidelobes
relative to the main beam. Thus to form any beam, the phase factors
are first applied to each VRX (i.e., form R=SV element by element
without implied summation, R now being a column vector of the same
size as S and V as indicated by the overlining, and then these may
be summed with weights equal to 1 to give the magnitude square of
the beam, that is:
[0304] |B|.sup.2=R.sup.# [1] R, where [1] is a matrix with unity in
every position. Calculating the above for every beam produces a set
of differentially-beamformed beams which, however, is exactly the
same as normal beamforming followed by taking the modulus squared
of the beams.
[0305] Because there are repeated locations among the DVRXs, flat
weighting of the DVRXs all with 1 is not flat location weighting.
Because all DVRXs corresponding to the diagonal of the matrix [1]
have the same location, that location is 256:1 overpopulated.
Therefore, the diagonal of the matrix can be reduced by a factor
256, and any other elements in the matrix corresponding to
duplicated VRX positions can be divided by the number of times the
position is duplicated in order to produce flat location
weighting.
[0306] FIG. 44 shows the radar image of a cluster of four strong
nearby targets formed with the VRX array of FIG. 38. FIG. 45 shows
the same cluster of targets imaged with the DVRX array form with
the VRXs of FIG. 38, after position-weight flattening. It is
evident that there is an improvement in the discrimination between
nearby targets, and in sidelobe level reduction.
[0307] The DVRX array formed by the VRX array of FIG. 38 had many
repeated locations and this is considered a waste of antenna
resources. To avoid duplicated locations and obtain the greatest
number of distinct DVRX locations, it is desired that the vector
differences in distances between every pair of VRXs should be as
far as possible distinct. This is the problem for which a method of
solution is developed in the above-incorporated Sparse MIMO arrays
patent application.
[0308] The expression B=R.sup.# [1] R above can be factorized by
noting that any matrix [G] can be expressed as [E][.LAMBDA.][E]
.sup.T where [E] is the matrix of Eigenvectors of [G] and
[.LAMBDA.] is a diagonal matrix of its eigenvalues. Since:
[0309] Therefore, B=R.sup.#[1] R=R.sup.#[E][.LAMBDA.][E].sup.T
R=B.sup.#[.LAMBDA.]B where the vector B is obtained by beamforming
R with the Eigenvector matrix [E] of the matrix of all 1's,
[1].
[0310] The magnitude squared of each of the beamformings with
different eigenvectors are then weighted with the corresponding
diagonal elements of [.LAMBDA.] and added. However, a matrix of 1's
having all the rows the same has rank of only 1 and therefore only
one non-zero eigenvalue exists equal to 1/256, the corresponding
eigenvector of which is all 1's. Therefore, only one beamforming is
necessary, the magnitude of which will be the desired answer.
[0311] However, after position weight-flattening, the matrix [1] is
no longer all 1's and has different eigenvalues, half of which are
positive and the other half negative. Differential beamforming then
amounts to performing 256 beamforming, each with different
eigenvector, and adding or subtracting the results according to the
sign and weight of the corresponding diagonal element of
[.LAMBDA.].
[0312] Unfortunately, full differential beamforming done any way is
256 times more onerous than regular beamforming, which is
prohibitive. After experimenting by using only the largest positive
eigenvalue and the largest negative eigenvalue, it was realized
that the two beamforming weights were no longer constrained to be
Eigenvectors of anything, and the corresponding eigenvalues could
be premultiplied into the weight vectors. Therefore, two length 256
weight vectors, called Gplus and Gminus were defined, and their
values sought that would give the most desirable beam patterns,
defined as unity gain to the wanted target and minimum worst case
sidelobe level. In one implementation, a first beamforming would
form for every direction, Bplus=GplusR and a second beamforming
would form Bplus=GminusR and then the magnitude squared of the beam
would be given by |Bplus|.sup.2-|Bminus|.sup.2. Moreover, the sum
of the Gplus values is constrained to be unity so as to give unity
gain to the wanted signal when all VRXs add in phase, and for the
same reason the sum of the Gminus is constrained to be zero, so
that it is does detract from the wanted signal amplitude. The above
expression would be converted to an amplitude in dBs by:
10 Log.sub.10(.parallel.Bplus|.sup.2-|Bminus|.sup.2|) The
additional modulus brackets .parallel. ensures that
|Bplus|.sup.2-|Bminus|.sup.2. is always rendered positive within
the log function. The expectation is that an optimum choice of
Gplus and Gminus will result in the sidelobes of Bplus and Bminus
canceling without affecting the wanted signal amplitude.
[0313] If indeed the sidelobes of Bplus and Bminus could be similar
in amplitude after squaring, a further thought was that they might
also be similar in amplitude before squaring, so that the
expression .parallel.Bplus|-|Bminus.parallel. could be equally
valid, but with the advantage that it converts to dBs by
20 Log 10.parallel.Bplus|-|Bminus.parallel..
[0314] Addings or subtracting the results of two or more
beamformings is not the only conceivable way of combining different
beamformings to reduce sidelobe levels from a sparse antenna array.
Another conceivable method is to perform several beamformings using
different weighting functions, each constrained to give unity gain
in the wanted direction, and then to determine the minimum response
in each direction. Since the different have unity gain to the
wanted target, all of the beams will have equal response to the
target but will exhibit sidelobes of different amplitude and/or in
different places. Therefore, taking the minimum across all does not
reduce the wanted signal response but retains the lowest sidelobe
of all in each direction.
[0315] The general principle of combining multiple beamformings is
shown in FIG. 64. At step 6402, the set of VRX values corresponding
to a given range and Doppler is phased using a steering vector to
produce a main beam in the direction given by the steering vector.
At step 6404, the VRX signals are weighted by different weighting
functions and combined to produce multiple candidate beam
amplitudes. At step 6406, the beam amplitudes are computed on any
monotonic scale that preserved relative magnitude, such a amplitude
squared, modulus or decibels, under the assumption that minimum
sidelobe amplitude is the goal. At step 6408, the different
beamformings are combined, for example by retaining at step 6510
that which gave the minimum amplitude, or by adding some and
subtracting others in a predetermined way such as the
|Bplus|-|Bminus| combination described in this application.
[0316] While some analytic methods were found for minimizing the
sum of sidelobe levels, minimizing the worst sidelobe level (a
MINIMAX problem) is too non-linear for analytic solution.
Therefore, a Monte Carlo search was used for optimum weighting
functions Gplus and Gminus, for which several significant program
acceleration algorithms were found.
[0317] The Monte Carlo search for best for a best length 256 Gplus
and best length 256 Gminus is a 512-variable optimizing problem.
The figure of demerit to be minimized is the sidelobe of greatest
amplitude anywhere in the F.OV. excluding a keep-out area around
the main lobe. As there are (2Naz+1)(2Nel)+1) beams to consider,
where Naz=256 and Nel=32, this amounts to 33,345 beams to consider
at each iteration, less the keep-out area. The keep-out area was
tailored to mask the main lone and consisted of an ellipse of
principal radii 15 steps in the u direction and 6 steps in the v
direction. Within this ellipse, values are set to zero after
beamforming as indicated by the black hole in FIG. 51.
[0318] The first acceleration algorithm noted that, if a new
modified Gplus,Gminus pair does not reduce the beam that was
previously the largest, then the solution can be rejected based on
recalculating only that beam. Thus a new beamforming is only
carried out after finding a new Gplus,Gminus that reduces the
previous worst case beam, as shown in the flow chart of FIG.
52.
[0319] Referring to the flow chart of FIG. 52, at step 5202, the
MINIMAX value is set to something large such as 1.0e16 and Gplus
and Gminus are set to initial values such as all Gplus values equal
1/256 and all Gminus values are zero. At step 5204, an initial
beamforming is done with the initial Gplus, Gminus and the worst
case sidelobe amplitude is found in step 5206. At step 5208, the
largest sidelobe just found is compared with MINIMAX and if it is
greater, the algorithm proceeds to step 5210, where previous values
of Gplus and Gminus are retained, and then proceeds to step 5214;
else, if the worst case sidelobe is an improvement over the current
MINIMAX value, the algorithm proceeds to step 5212 where the Gplus,
Gminus values are saved as the best so far, MINIMAX is set equal to
the new, lower worst-case sidelobe level and the index of the worst
case beam is saved. Then the algorithm proceeds to step 5214.
[0320] At step 5214, Gplus and Gminus are randomly perturbed,
keeping the sum of the Gplus equal to 1 and the sum of Gminus equal
to zero. This can be done by forming the sum of Gminus values after
perturbation and subtracting 1/256th of the sum from each. In the
Gplus case, form the sum and subtract 1/256th of the difference
between the sum and unity from all; alternatively, divide by the
sum.
[0321] At step 5216, only the beam that was previously the worst
case, the indices of which were saved in step 5212, is recomputed
with the new Gplus, Gminus values, and the amplitude compared with
the previous worst case at step 5218. If it is worst, the new
Gplus, Gminus are rejected and a return to step 5210 takes place,
otherwise proceed to step 5220. Steps 5220, 5222, 5224, 5226, and
5228 comprise a loop to recalculate all beam values, monitoring at
step the loop 5224 whether any beam is worse than the previous
worst sidelobe. If any beam is worse, then a return is made to step
5210, otherwise if all beams are recalculated without a return to
step 5210, a new better solution has been found and a return is
made to step 5212 to save it as the current best.
[0322] FIG. 53 shows an even faster Monte Cralo MINIMAX algorithm.
Steps 5302 and 5304 perform an initial beamforming with initial
Gplus,Gminus values as in FIG. 52. At step 5306 however, the
sidelobes are sorted in amplitude order highest to lowest.
Actually, no value is moved during the sort; rather, a linked list
is developed where an initial address provides the index of the
largest sidelobe, and a linked list value addressed by the same
index gives the index of the next largest value. It was found that,
because two linked lists can be merged in place, the usual split,
recur and merge sort algorithm can be performed in-place in a time
O(n Log(n)).
[0323] The purpose of the sort is the expectation that testing
beams with a new Gplus, Gminus value is likely to reject a worse
solution more rapidly if the previously strongest beams are tested
first. Thus, steps 5312 to 5320 are analogous to the loop of steps
5220 to 5228 in FIG. 52 except that the beams are rested in sorted
order. If the loop gets all the way through without rejecting the
solution with a return to step 5308, then at step 5322 the new
improved values are saved and a return is made to step 5306 to
resort the newly computed beam values.
[0324] The algorithm of FIG. 53 was found to reject bad solutions
in orders of magnitude fewer than 33,345 beam calculations. Only if
the search gets through testing all 33,345 beams without finding
one that is stronger than the previous worst case sidelobe is a new
solution found and retained, and now a complete set of new sidelobe
values has just been calculated and is resorted. Thus 33,345 beams
are only calculated whenever a new improved solution is found.
[0325] The improved VRX array produced by the incorporated and
co-filed Sparse MIMO arrays application is shown in FIG. 46. Only
the vertical grid lines are shown, as the number of different
vertical coordinates is now too numerous to show a horizontal line
for each. Both the Tx and Rx arrays as well as the resulting VRX
array now look more random and less systematic in pattern, which is
exactly what was determined to be desirable for minimizing
sidelobes.
[0326] The sidelobe pattern of the array of FIG. 46 using standard
VRX (sum-array) beamforming with flat weighting is shown in FIG.
47. By comparing with the sidelobe pattern of FIG. 38, it is
evident that the worst case sidelobes have been much reduced, and
in particular, the largest ones that were at .+-.90 degrees have
vanished. This array is a good starting point for now applying the
Gplus/Gminus beamforming derived above from simplifying
differential beamforming.
[0327] FIG. 48 shows the beam Bplus found by using the weighting
function Gplus alone, as determined by Monte-Carlo optimization. It
seems mainly to have reduced the sidelobe levels to the immediate
upper right and lower left of the main beam, which were the largest
for this array.
[0328] FIG. 49 shows the beam pattern Bminus produced by
beamforming with weights Gminus alone. It may be remarked that
there is very small null dead center over the main beam so that the
Bminus beam does not dilute the wanted signal amplitude when
subtracted. It may also be remarked that the two yellow sidelobes
to the immediate upper right and lower left of center are also
present in the Gminus beam, and thus we hope for cancellation.
[0329] FIG. 50 shows the beam pattern by using
.parallel.Bplus|-|Bminus.parallel. which is converted to dB by a 20
Log.sub.10 operation. It is possible that optimization has caused
the sidelobes of Bminus to substantially cancel the sidelobes of
Bplus with the result that the worst case sidelobe achieved is
-24.18 dB relative to the main lobe. At this level, it no longer
threatens to confuse the determination of the strongest signal even
when there are many signals in the F.O.V., each producing sidelobes
that may combine constructively or destructively depending on the
relative phase of target echoes, which are continuously
changing.
[0330] "Contrast" in a radar refers to the ability to detect weak
targets in the presence of strong targets. The method developed to
improve contract here comprises detecting the strongest target by
beamforming a given set of VRX signals for a given range-Doppler
bin, subtracting its contribution to the VRX signals, and then
beamforming again with the strongest target signal gone to detect
the second strongest target, and forth. The basic method of
subtracting a target signal from the VRX signals is to weight the
steering vector for the index of the strongest beam with the
determined complex amplitude of the strongest beam and subtract it.
Subtraction of the target signal in principle eliminates all
sidelobes that it produces also. The ultimately achievable contract
depends on how accurate the subtraction of the strongest signal can
be. Limiting factors to accuracy are:
[0331] (i) Quantization of the target position in (u,v) space.
[0332] (ii) Position and amplitude corruption due to another strong
nearby overlapping target.
[0333] (iii) VRX antenna and processing channel mismatches that are
not modeled in the subtracted steering vector; particularly
mismatches that depend on the antenna look-angle, i.e. on
(u,v).
[0334] (iv) Position distortion caused by the use of transmit or
receive nulling.
[0335] Noise is not so much of an issue in causing subtraction
errors, because the error is only of the order of the noise level.
Only weak signals will have significant noise-induced subtraction
errors, but their importance is diminished in proportion to the
signal strength.
[0336] The above limitations will be addressed one by one with
explanation of the steps that can be taken to minimize the
errors.
[0337] Quantization of the target position estimate arises due to
computing beams only at a limited number of equal steps of (u,v).
If steps of u,v are such that several beams are computed within the
-3 dB beamwidth of the array, the beams are said to be spatially
oversampling. With a modest amount of oversampling, such as between
2:1 and 3:1 the target position may be determined more accurately
by interpolation between adjacent beam values. However, given the
extremely large number of beamformings that have to be done, the
consequent short time available for each, and consideration of how
to design chip hardware for parallel processing, a different method
called "zoom beamforming" has been developed which seems more
practical in the circumstances. Zoom beamforming comprises
utilizing the cyclic shift properties of (U,V) space to shift the
radar image such that the strongest identified target appears at
(u,v)=(0,0), and then to perform a zoomed-in beamforming around a
small area centered on (0,0) with much finer steps. The target is
centered on (0,0) by multiplying the VRX values by the steering
vector used for its beam, thus removing the VRX phases such that a
new beamforming on the shifted VRX values will find the target with
a zero-phase steering vector, which corresponds to (u,v)=(0,0). The
new beamforming is performed with steering vectors computed in very
much finer steps of (U,V) for example, 256 steps of u and 32 steps
of v but with the step size reduced by a factor 8.
[0338] To prepare for zoom beamforming, the value of w defined
above by:
[0339] 4.omega.=-271(16Naz) is precomputed and stored in even finer
steps such as given by .omega.=-2.pi.(128Naz), where only every 8th
value is used in normal beamforming, but every value is used in
fine beamforming. Thus, if NAZ=256, a table of 32,768 values of
.omega. is precomputed and stored, at least for a software
implementation such as would be used for simulation.
[0340] Commonly owned U.S. patent application Ser. No. 17/582,359,
entitled "N-point Complex Fourier Transform Structure having only
2N Real Multiplies, and other Matrix Multiply Operations,"
describes a fully parallel engine that can be constructed on a
silicon chip to perform all operations in parallel related to
multiplication of a complex vector by a complex matrix, the
elements which are complex exponentials. In the beamforming
application, the matrix is indeed a matrix of steering vectors
which are complex exponentials of antenna phases needed to create
beams in each desired direction in (u,v) space. This application is
hereby incorporated by reference herein in its entirety. In the
Application, it is described how in parallel to compute the product
of an 8,192.times.256 complex matrix with a 256-element complex
vector to obtain an 8192 complex result in as little as 2 ns. In
this application, the 256-element vector is the set of 256 VRX
signal values corresponding to one range-Doppler bin. The complex
matrix is a set of 8129, 256-element steering vectors, each element
which is the complex exponential of a phase. The beamforming engine
starts by using serial arithmetic to stream the 256 VRX values
through a serial adder tree that computes all 256 possible
combinations of 8 VRX signals at a time, where a combination
comprises either adding a VRX signal to the combination or not, a
binary choice. It is shown in the incorporated application how this
may be done with one serial adder per desired combination by
computing them in Grey-Code order whereby only one of said binary
choices is changed from one combination to another. There are 32
such adder trees to deal with all 256 VRX signals, each producing a
digital result serially on 256 serial lines, a total of 8192 serial
lines.
[0341] The 8129.times.256 complex matrix comprises cosines and
sines which range from -1 to +1. To eliminate minuses, 1 is added
to all cosine or sine components and then the result divided by two
so that every real and imaginary part lies between 0 and 1. This is
equivalent to adding a matrix of all 1's to the real parts and
likewise to the imaginary parts, and to compensate for that in the
final product, the sum of all real parts of the VRX vector must be
subtracted from the real part of every result and the sum of the
imaginary parts of the VRX vector must be subtracted from the
imaginary part of the result, which is done on-the-fly in parallel
using single-bit serial adders.
[0342] The binary bit pattern of each now always positive matrix
value is now examined and a row of bits of like significance
through the matrix shall multiply the VRX vector. Taking 8 bits a
time, the result of multiply that with 8 VRX values is already
available on one of the 8,192 serial lines formed with binary
choices corresponding to whether a VRX value is added or not that
matched the 8-bit pattern. Thus, a serial adder is placed on the
crossover of the appropriate serial line to pick up that partial
product and connect it to the partial products selected by the
other 31 groups of 8 matrix row bits.
[0343] After performing the above for each row of matrix bits of
different significance the results must be added with a shift
corresponding to the matrix bit place significance. Where this
scheme achieves it efficiency over conventional matrix-vector
multiplication is by delaying combining the partial products from
each multiplication, combining partial products of the same
significance form each multiplication, and delaying combining
partial products of different significance until the end. The
latter step, equivalent to a shift and add multiplication, means
that in effect the matrix-vector multiplication is performed using
only one multiplication per output value.
[0344] Having obtained 8,182 output values, that with the largest
magnitude must be identified, which requires forming the sum of the
squares of the real and imaginary parts of each value. To do this,
a serial squaring circuit may be used as shown in FIG. 54.
[0345] Suppose we have the square of an X received bit serially up
to bit i so far, in other words
S.sub.i=X.sup.2.sub.i=(a.sub.i,a.sub.i-1 . . .
a.sub.2,a.sub.1).sup.2.
To account for place significance, the convention for where the
binary points are is:
[0346] Xi is less than 1, i.e. it is 0. a.sub.ia.sub.i-1 . . .
a.sub.2,a.sub.1.
Since the square of something less than 1 is less than 1 too, and
has twice as many bits,
[0347] S.sub.i=0. s.sub.2i s.sub.2i-1 . . . s.sub.2 s.sub.1
Now we receive bit a.sub.i+1 and we want to update to S.sub.i+1 The
update is:
X.sub.i+1=1/2X.sub.i+1/2a.sub.i+1.
e.g. if a.sub.i+1=1, X.sub.i+1=0. 1 a.sub.ia.sub.i-1 . . .
a.sub.2a.sub.1
[0348] or if a.sub.i+1=0, X.sub.i+1=0. 0 a.sub.ia.sub.i-1 . . .
a.sub.2a.sub.1
S.sub.i+1=1/4Si+1/4a.sub.i+1+1/2a.sub.i+1X.sub.i,
which means: [0349] Step1: Shift right a.sub.i+1 one place into
both Si and X.sub.i to get X.sub.i+1 and 1/2 Si+1/2 a.sub.i+1.
[0350] Step2: If a.sub.i+1=1, add X.sub.i to the above and shift
right again.
[0351] The above is performed by the register structure of FIG.
54.
[0352] There is at the top a 16-bit register (4000) to receive X
serially, LSB first. Below that is the same register, just showing
the contents after the new bit a.sub.i+1 is shifted in. At the
bottom there a 32-bit register (4001) to receive S, the square of
X. The register above that is the same register just showing the
new bit a.sub.i+1 shifted in. Between the two is a 16-bit adder
(4002) that adds the old X to the shifted S. There may be a carry,
which goes into the MSB of the square register (4001). The result
is shifted back into the square register to be the updated square.
Although this could all be done in one clock cycle per bit in
principle, because the S-register is updated twice per new bit
input, it may have to run at half speed. However, of the 32 clock
cycles needed to square a 16 bit value, there is a 16-clock overlap
with the beamformer so the squarer adds only 16 more clock
cycles.
EXAMPLE
[0353] Suppose we have received 111 so far so Xi=0.111 "7"
[0354] and Si will be 0.110001 "49"
Now we receive another "1": Shift it into both:
TABLE-US-00001 X -> 0.1111 "15" S -> 0.1110001 add original X
0.111 1.1100001 Shift right 1 0.11100001 "225"
The procedure works for 1's complement negative numbers with a
small error: We get the square of X+1 instead e.g. the square of
-1
[0355] 1111111111111111 is 0000000000000000 (zero instead of
1).
This error is likely tolerable given that we only want to identify
the strongest target, and even the second strongest will suffices
if it is as close as 1 LSB.
[0356] The method can be extended to the sum of squares as
follows:
[0357] Let X be received bit serially LSB first as a1,a2,a3, etc.,
and suppose bit as has already been processed. Likewise, Y is
received bit serially as b1, b2, b3, etc., and b.sub.i has already
been processed.
[0358] Let Si be X.sup.2+Y.sup.2 up to the ith bits a.sub.i and
b.sub.i Then:
X i + 1 = 1 / 2 .times. a i + 1 + 1 / 2 .times. X i ##EQU00001## Y
i + 1 = 1 / 2 .times. b i + 1 + 1 / 2 .times. Y i ##EQU00001.2## S
i + 1 = 1 / 4 .times. S i + 1 / 4 .times. a i + 1 + 1 / 4 .times. b
i + 1 + 1 / 2 .times. a i + 1 .times. X i + 1 / 2 .times. b i + 1 +
Y i = 1 / 4 .times. S i + 1 / 4 .times. a i + 1 .times. X i + 1 / 4
.times. b i + 1 .times. Y i + 1 / 4 .times. a i + 1 .times. X i + 1
+ 1 / 4 .times. b i + 1 .times. Y i + 1 ##EQU00001.3##
This translates to the following sequence: Since the sum of two
squares, each being less than 1, can be greater than 1, Si now has
one bit extra (carry bit) to the left of the binary point. Clock1:
Load a.sub.i+1 into the carry bit of the X.sub.i register; Load
b.sub.i+1 into the carry bit of the Y.sub.i register; Apply
a.sub.i+1 .AND. X.sub.i to a first input of a 3-way adder; Apply
b.sub.i+1 .AND. Y.sub.i to a second input of the 3-way adder with
S.sub.i being the 3rd input, the adder having 2 carries Shift right
Xi,Yi and Si, clocking the adder output, including both carries
into Si plus its extra carry bit. Let the adder ripple through
again, now adding Xi and Yi to the Si register and generating up to
2 carries. Clock 2: Shift the adder output right into Si plus its
carry bit to get the answer s.ssssss . . . s which will be 33 bits
long if X and Y were each 16 bits long. Suppose we have received 3
bits so far, with
TABLE-US-00002 Xi = 0.111 7 Yi = 0.101 5 Si = 1.001010 25 + 49 =
74
Suppose now the next bits a4 and b4 of X and Y are both 1
TABLE-US-00003 Xi -> 1.111 Yi -> 1.101 Si 1.001010 old Xi
+.111 old Yi +.101 10.101010 Shift right into S 1.010101 Shift Xi
to get X.sub.i+1 0.1111 15 Shift Yi to get Y.sub.i+1 0.1101 13 Sum
11.0001010 Shift right to get S.sub.i+1 1.10001010 225 + 169 =
394
Doing the sum of squares simultaneously thus only needs a single
output register and effectively both squares are computed and added
in parallel.
[0359] Having obtained the squared magnitudes of each beam, it is
desired to know which is the largest. For this purpose, the square
registers are read out MSB first into a magnitude comparator. A
magnitude comparator determines which value presented serially MSB
first is the first to be binary 1 while the other is binary 0. This
is described in expired patent U.S. Pat. No. 5,187,675, and
entitled "Maximum Search Circuit," which is hereby incorporated by
reference herein. The circuit also includes traceback to yield the
index of the value, which was the largest, as required for the
current application. This circuit may also be adapted to output the
complex value of largest magnitude, by propagating the complex
values that were deemed to give the largest sum of squares at each
comparison through the tree to the comparator tree output.
According to the index, the un-weighted VRX signals are then
multiplied by an associated steering vector to shift the radar
image to centralize the largest target on (u,v)=(0,0). The
centralized VRX values are then applied to the fine beamformer
which is constructed similarly to the coarse beamformer but using
steering vectors that are in much finer angular steps, and there
are not so many of them. The fine beamformer therefore occupies
only a fraction of the chip area taken by the coarse beamformer and
operates in parallel to fine beamform the previously found target
in a range-Doppler bin while the coarse beamformer is working on a
different set of VRX values corresponding to a different
range-Doppler bin. The fine-beamformer operates on VRX values that
are not weighted by Gplus or Gminus, but rather shifted by the
centralization operation.
[0360] The centralization operation requires multiplication of the
256 complex element VRX signal set with a 256-element complex
steering vector. For this purpose, a fully parallel set of 256
complex multipliers is made available and used for various
purposes, including multiplying the VRX signals with the
256-element (real) vectors Gplus and Gminus prior to application
serially to the beamforming.
[0361] The beamformer shall actually beamform the VRX signals using
Gplus weights and again using Gminus weights in separate operations
and subtract the magnitude of one from the other. This requires a
square root operation to be performed after the sum of squares
operation. It is well known how to perform a square root operation
on a binary value to yield a binary word of half the length in
bits. Therefore, although the sum of squares operations doubles the
word length, the square root operation halves it again. The square
root circuit operates on serial data most significant bit first, as
does the magnitude comparator, therefore registers are needed to
store sum-of-square values in order to reverse the direction from
LSB first to MSB first.
[0362] The square root operation is needed only every two coarse
beamformings. The various operations of weighting with Gplus or
Gminus, coarse beamforming, squaring, square-rooting,
centralization and fine beamforming may be overlapped as between
different VRX sets and pipelined so as maximize throughput.
[0363] The output for fine beamforming is a refined position index
of the strongest target and its complex echo value made with
unweighted data. The fine steering vector for the refined position
is obtained for example from a look up table. The fine steering
vector is modified by combining it with any amount of nulling
signal that was added to each transmitter to model the transmit
codes combined with nulling signals that were transmitted, if
nulling is in use, and then the phase and amplitude of each VRX
component is adjusted by calibration factors that were
predetermined during radar calibration to model uncorrected VRX
phase and amplitude mismatches. The calibration of a radar
determines calibration factors for each Tx and Tx averaged over all
(U,V) and are combined to produce an average VRX calibration
factor. These calibration factors are removed early in the
processing chain, at least before coarse beamforming.
[0364] Now that the position of a target is known, the residual
calibration factors for VRXs for the particular (u,v) sector in
which the target lies can be applied to the steering vector to
obtain the most accurate representation of what was transmitted.
Then the steering vector, so modified by nulling signals and
sector-wise VRX calibration is multiplied by the determined complex
echo amplitude and subtracted from the VRX signals applied to the
fine beamformer to subtract the just-found target's contribution as
accurate as possible, and with it, all sidelobes and grating lobes
of sparse beamforming.
[0365] An alternative is to apply the residual VRX calibration
factors, that depend of the (u,v) of the target found from coarse
beamforming, to the unweighted VRX values prior to fine
beamforming; however, they must still be applied also to the
steering vector for the fine position found from fine beamforming
in determining the subtraction signal.
[0366] As a result of pipelining, it is possible that a first stage
of subtraction is done for all range-Doppler bins of interest
leaving in them modified sets of VRX signals with the strongest
signal now gone. The set, or a further sparsification thereof, is
then passed through the entire chain again to determine and
subtract second-strongest targets, and so forth until all targets
of significance have been located in the four dimensions of range,
Doppler, azimuth and elevation.
[0367] The importance of obtaining fine positions for accurate
subtraction is illustrated with the aid of FIG. 55. In FIG. 55, the
black curve (1) is the true, unquantized target beam shape. The
vertical red lines (3) represent the angle to which the target's
beam peak can be quantized. The true peak (2) lies midway between
two quantizing levels and is quantized to the nearest quantizing
level (4). The subtraction signal beam shape is indicated by dotted
line (5) which is misaligned with the true target beam shape due to
the position quantizing error. Thus, it is too high on the left,
giving to error (6) and too low on the right, but matches quite
well in the middle. Therefore, subtraction will subtract out the
center of the beam but leave two residual errors on either side of
the beam. This can clearly be seen from FIG. 56. FIG. 56 is derived
from FIG. 42 by localizing and subtracting the strong target at the
center. It can be seen that the sidelobe background has been
reduced substantially, but the target has left two residuals of
subtraction on either side of its true location, and faint pairs of
residuals of other sidelobes that were likewise imperfectly
subtracted may be seen.
[0368] Although it was mentioned that, if transmit nulling is used,
the actual subtracted signal should include the nulling signal
combined with the transmitter signals, there is still a potential
position error caused when a wanted target is close to a null. A
simulation has determined the position error versus proximity of
the target to a null and true and apparent position are compared in
FIG. 57 versus target-to-null spacing. It can be seen that the
apparent target position displays a kink as the target passes
through the null. The kink is shown magnified in FIG. 58. The
apparent target position tends to come to a halt on one side of the
null and the rapidly jump to the other side as the target emerges
from the null. It is straightforward to model this, however, when
the return actually passes through the null, given that it now has
the same range, Doppler and bearing as the oncoming radar that the
null is aimed to protect, it may be assumed that it IS the oncoming
radar and thus has coordinates equal to the null. Moreover, the
echo is so attenuated when the target is very close to null it is
unlikely to be high up on the strong targets to be subtracted.
[0369] FIG. 59 illustrates that exactly the same distortion arises
from creating a receive null to protect our radar from oncoming
interfering radars.
[0370] FIG. 60 illustrates the effect of both a receive and
transmit null in the same location. The only difference between a
transmit or receive null alone is that the kink is a little
sharper.
[0371] FIG. 61 illustrates that the kink is not at all noticeable
on the macro scale of (u=-1 to +1 corresponding to azimuth -90 to
+90 degrees and beam index 0 to 1024 which is used on the vertical
scale. The target is at u=0, azimuth=0 and beam index 511.
[0372] FIG. 62 shows more detail of the arrangement for
compensating the subtraction signal for nulling. A nulling
arrangement (5000) as previously described illuminated the
environment except for a selected null position. A receive
processing chain (5003) as previously described receives, down
converts, correlates, Doppler analyzes and beamforms the echo
signals received. After beamforming determines the fine target
position, the steering vector corresponding to that position and
weighted with the determined complex target amplitude synthesizes
the VRX signal for which the target is responsible in unit 5001,
without taking the null into account. The nulling subtracted in the
transmitter (5000) is then also subtracted from the synthesized VRX
signal in unit 5002 before subtraction from the received VRX
signal, the residual then being fed back into the beamformer (at
some later stage due to the pipelining mentioned above) to remove
the just-detected target.
[0373] Another mechanism for target position error is when two
targets are so close that their beams partially overlap. At some
point it would be expected that a radar might interpret two very
close targets of equal amplitude as a single target midway between
the two. FIG. 63 shows the apparent positions estimated for two
equal and out-of-phase targets as one passes through the other.
There is not much distortion until they are within about -0.65
degrees of each other, which is of the order of 1/4 of the -3 dB
beamwidth. Because the targets are nominally equal, one may be
detected first and subtracted before detecting the other, or vice
versa. They were interpreted to be a single target only at complete
coincidence. The effect varies significantly with relative phase
amplitude, but it can be deduced, given two apparent target
positions (u1,v1) and (u2,v2) and their measured apparent complex
signal strengths, that the actual positions are different than
(u1,v1) and (u2,v2) by amounts along the line joining (u1,v1) and
(u2, v2) depending on the complex amplitude ration. Therefore, it
is proposed to coarsely quantize the amplitude ratio, maybe in dB
and radians, and to address a look-up table with (u1-v1,u2-v2) and
the coarsely quantized amplitude ration to determine position and
amplitude corrections to be applied to compensate. This table would
be assembled by simulation and built into an integrated circuit in
the product.
[0374] Because subtraction residuals may be larger than a weak
target, they can be detected as false targets and subtracted before
the weak target's turn to be the strongest beam. As it can be
difficult to discriminate between such a false target and a weak
target close to a strong target, it is desirable to reduce these
residuals.
[0375] A method of reducing residuals caused by two or more nearby
signals causing amplitude, phase and position estimation error is
multipass subtraction, after subtracting a second strong target,
the amount subtracted for a first strong target is added back and
its position and complex amplitude estimated again, now with the
second target gone. After subtracting the new estimate, the amount
of second target subtracted can be added back and it re-estimated
again. Such backtracking can be done to any depth for which
computational resources suffice. Ultimately "joint detection" of
multiple targets comprises finding the smallest number of target
positions and amplitudes that jointly explain the received VRX
signals to an accuracy approaching the noise level. Joint detection
is computationally burdensome and can be done in increasing stages,
where the strongest first detected, subtracted and second strongest
signal identified. Then, using those clues as an initial starting
point, a joint detection iteration optimizes their two amplitudes
and positions to minimize the residual energy when they are
subtracted. Then a third signal is identified, and so forth. By
simulation it was verified that iterative multipass subtraction
converged to the joint-detection result. Joint detection may be
simplified by noting that, given a hypothesis of target positions,
their amplitudes that minimize the residual can be analytically
determined and substituted to obtain the lowest possible residual
for those target amplitudes. The positions are then searched by any
means, such as Monte-Carlo or steepest descent method using
gradients, to obtain the optimum positions.
[0376] Accordingly, an exemplary radar system includes any
combination of advanced features including use of sparse arrays
with sidelobe-reduction beamforming techniques; dual polarization
for interference mitigation; transmit or receiver null-steering, or
both, to improve mutual interference and frequency hopping for
increasing range resolution, and improved mutual interference
characteristics by clash detection.
[0377] Changes and modifications in the specifically-described
embodiments may be carried out without departing from the
principles of the present invention, which is intended to be
limited only by the scope of the appended claims as interpreted
according to the principles of patent law including the doctrine of
equivalents.
* * * * *