U.S. patent application number 09/730316 was filed with the patent office on 2001-05-03 for method and apparatus for acquiring wide-band pseudorandom noise encoded waveforms.
This patent application is currently assigned to DATA FUSION CORPORATION. Invention is credited to Kober, Wolfgang, Thomas, John K..
Application Number | 20010000660 09/730316 |
Document ID | / |
Family ID | 27368991 |
Filed Date | 2001-05-03 |
United States Patent
Application |
20010000660 |
Kind Code |
A1 |
Kober, Wolfgang ; et
al. |
May 3, 2001 |
Method and apparatus for acquiring wide-band pseudorandom noise
encoded waveforms
Abstract
The method and apparatus of the present invention is directed to
architectures for signal processing, such as for performing
analog-to-digital and digital-to-analog conversions, in which the
source signal is decomposed into subband signals by an analysis
filter, processed, and the processed subband signals combined to
form a reconstructed signal that is representative of the source
signal.
Inventors: |
Kober, Wolfgang; (Aurora,
CO) ; Thomas, John K.; (Erie, CO) |
Correspondence
Address: |
Douglas W. Swartz
SHERIDAN ROSS P.C.
Suite 1200
1560 Broadway
Denver
CO
80202-5141
US
|
Assignee: |
DATA FUSION CORPORATION
|
Family ID: |
27368991 |
Appl. No.: |
09/730316 |
Filed: |
December 4, 2000 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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09730316 |
Dec 4, 2000 |
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09137383 |
Aug 20, 1998 |
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60087036 |
May 28, 1998 |
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60056455 |
Aug 21, 1997 |
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60056228 |
Aug 21, 1997 |
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Current U.S.
Class: |
341/6 |
Current CPC
Class: |
G01S 1/045 20130101;
H03M 1/121 20130101; G01S 7/285 20130101; G01S 7/021 20130101 |
Class at
Publication: |
341/6 |
International
Class: |
H03M 001/22 |
Claims
What is claimed is:
1. A method for acquiring a signal having a bandwidth, comprising:
decomposing the signal into a plurality of signal segments, each
signal segment having a signal segment bandwidth that is less than
the signal bandwidth; processing each of the signal segments to
form a plurality of processed signal segments; and combining the
processed signal segments into a composite signal wherein the
signal is one of analog or digital and the composite signal is the
other one of analog or digital.
2. The method of claim 1, wherein the processing step includes
performing analog-to-digital conversion of each of the signal
segments.
3. The method of claim 1, wherein the processing step includes
performing digital-to-analog conversion of each of the signal
segments.
4. The method of claim 1, wherein the processing step includes
removing a noise component from each of the signal segments to form
a corresponding plurality of noise reduced signal segments and
thereafter converting each of the noise reduced signal segments
from one of analog or digital format to the other of analog or
digital format.
5. The method of claim 1, wherein in the processing step each of
the signal segments is processed separately.
6. The method of claim 1, wherein the composite signal has the same
bandwidth as the signal bandwidth.
7. The method of claim 1, wherein the composite signal is a time
delayed replica of the signal.
8. The method of claim 1, wherein the signal has a bandwidth of at
least about 1 GHz.
9. The method of claim 1, wherein the sum of the plurality of
signal bandwidths is equivalent to the signal bandwidth.
10. The method of claim 1, wherein the signal is in one of analog
or digital format and the composite signal is in the other of
analog or digital format.
11. The method of claim 1, wherein the processing step comprises:
assigning boundary values to a plurality of bins; sampling a signal
segment to provide a sampled value corresponding to the sampled
portion of the signal segment; comparing the sampled value with
assigned boundary values for each of the plurality of bins;
selecting an appropriate bin for the sampled portion of the signal
segment; thereafter reassigning new boundary values to at least a
portion of the plurality of bins; and repeating the assigning,
sampling, comparing and selecting steps.
12. The method of claim 1, wherein the processing step comprises:
correlating the plurality of signal segments with a corresponding
plurality of replicated signal segments to provide a corresponding
plurality of correlation functions.
13. The method of claim 12, wherein the processing step comprises:
determining an amplitude, time delay, and phase delay for at least
a portion of a plurality of peaks defined by the plurality of
correlation functions and realigning and scaling at least a portion
of the signal defined by the signal segments based on one or more
of the amplitude, time delay, and phase delay for the at least a
portion of the plurality of peaks.
14. An apparatus for acquiring a signal having a signal bandwidth,
comprising: means for receiving a signal in the form pseudorandom
or random waveform having a signal bandwidth; means for decomposing
the signal into a plurality of signal segments, each signal segment
having a signal segment bandwidth that is less than the signal
bandwidth; means for processing each of the signal segments to form
a plurality of processed signal segments; and means for combining
the processed signal segments into a composite signal wherein the
signal is one of analog or digital and the composite signal is the
other one of analog or digital.
15. The apparatus of claim 14, wherein the means for processing
includes means for performing analog-to-digital conversion of each
of the signal segments.
16. The apparatus of claim 14, wherein the means for processing
includes means for performing digital-to-analog conversion of each
of the signal segments.
17. The apparatus of claim 14, wherein the means for decomposing is
a plurality of low pass filters.
18. The apparatus of claim 14, wherein the means for decomposing
includes a plurality of analysis filters and the means for
combining includes a plurality of synthesis filters.
19. The apparatus of claim 14, wherein the means for combining is a
perfect reconstruction filter bank.
20. The apparatus of claim 14, wherein the means for processing
includes at least one of a plurality of analog-to-digital
converters and a plurality of digital-to-analog converters.
21. The apparatus of claim 14, wherein the means for processing
includes a noise rejecting quantizer.
22. A method for reducing noise in a signal having a bandwidth,
comprising: decomposing the signal into a plurality of signal
segments, each signal segment having a bandwidth that is less than
the bandwidth of the signal and removing a noise component from
each of the signal segments to form a corresponding plurality of
processed signal segments.
23. The method of claim 22, further comprising: combining each of
the processed signal segments to form a composite signal.
24. The method of claim 23, wherein the composite signal has the
same bandwidth as the signal.
25. A system for reducing noise in a signal having a bandwidth,
comprising: means for decomposing the signal into a plurality of
signal segments, each signal segment having a bandwidth that is
less than the bandwidth of the signal and means for removing a
noise component from each of the signal segments to form a
corresponding plurality of processed signal segments.
26. The system of claim 25, further comprising: means for combining
each of the processed signal segments to form a composite
signal.
27. The system of claim 26, wherein the composite signal has the
same bandwidth as the signal.
28. A method for combining a plurality of signal segments having a
signal bandwidth, to form a composite signal having a composite
bandwidth, the frequency band of the composite signal including
each of the signal segments, the method comprising: performing
synthesis filtering on each of the plurality of signal segments to
form the composite signal.
29. The method of claim 28, further comprising: emitting the
plurality of signal segments from a plurality of signal sources and
receiving each of the plurality of signal segments using a
corresponding plurality of signal receptors.
30. The method of claim 28, further comprising: converting each of
the signal segments from an analog format to a digital format.
31. A system for assembling a plurality of signal segments, each
having a signal bandwidth to form a composite signal having a
composite bandwidth that includes the frequency range of each of
the signal segments, the system comprising: means for performing
synthesis filtering on each of the plurality of signal segments to
form the composite signal.
32. The system of claim 31, further comprising: means for emitting
the plurality of signal segments from a plurality of signal sources
and means for receiving each of the plurality of signal
segments.
33. The system of claim 31, further comprising: means for
converting each of the signal segments from an analog format to a
digital format.
34. The system of claim 31, further comprising: a plurality of
analysis filters to decompose a source signal into a plurality of
decomposed signal segments; a plurality of digital-to-analog
conversion devices for converting the plurality of decomposed
signal segments from digital into analog format to form a
corresponding plurality of analog signal segments; a plurality of
amplifiers to form a corresponding plurality of signal segments; a
plurality of signal emitters for emitting the plurality of signal
segments; and a plurality of receptors for receiving the plurality
of signal segments.
35. The system of claim 31, further comprising: a plurality of
analysis filters to decompose a source signal into a plurality of
decomposed signal segments; a plurality of amplifiers to amplify
the decomposed signal segments to form a corresponding plurality of
signal segments; a plurality of signal emitters for emitting the
plurality of signal segments; and a plurality of receptors for
receiving the plurality of signal segments.
36. The system of claim 31, further comprising: a plurality of
receptors for receiving a plurality of analog signal segments; a
plurality of analog-to-digital converters to convert the plurality
of analog signal segments into the plurality of signal
segments.
37. A method for processing an analog signal having a bandwidth,
comprising: decomposing the analog signal into a plurality of
analog signal segments, each analog signal segment having a signal
segment bandwidth that is less than the signal bandwidth and
processing each of the analog signal segments to form a plurality
of processed analog signal segments; and combining the processed
analog signal segments into a composite signal.
Description
1. The present application claims priority from U.S. Provisional
Application Ser. Nos. 60/087,036 filed May 28, 1998; 60/056,455
filed Aug. 21, 1997; and 60/056,228 filed Aug. 21, 1997, all of
which are incorporated herein by this reference.
FIELD OF THE INVENTION
2. The present invention relates generally to a method and
apparatus for acquiring wide-band random and pseudorandom noise
encoded waveforms and specifically to a method and apparatus for
acquiring wide-band signals, including deterministic signals,
random signals and pseudorandom noise encoded waveforms that
divides the waveform into a plurality of subbands prior to signal
processing thereof.
BACKGROUND
3. Analog-to-digital converters are devices that convert real world
analog signals into a digital representation or code which a
computer can thereafter analyze and manipulate. Analog signals
represent information by means of continuously variable physical
quantities while digital signals represent information by means of
differing discrete physical property states. Converters divide the
full range of the analog signal into a finite number of levels,
called quantization levels, and assigns to each level a digital
code. The total number of quantization levels used by the converter
is an indication of its fidelity and is measured in terms of bits.
For example, an 8-bit converter uses 2.sup.8 or 256 levels, while a
16-bit converter uses 2.sup.16 or 65536 levels.
4. During the conversion process, the converter determines the
quantization level that is closest to the amplitude of the analog
signal at that time and outputs the digital code that represents
the selected quantization level. The rate at which the output is
created indicates the speed of the converter and is measured in
terms of samples per second (sps) or frequency in Hertz (Hz). As
will be appreciated, a larger number of bits and therefore
quantization levels equates into a finer representation of the
analog signal.
5. In designing an analog-to-digital converter, there are a number
of considerations. In many applications for example it is desirable
that the converter has not only a high rate of speed but also a
large number of quantization levels or a high degree of fidelity.
Such converters are difficult to build and therefore tend to be
highly complex and very expensive. The key reason is that
conversion errors and the consequential device layout constraints
for reducing such errors, both of which can be ignored at slow
speeds, can become significant at high speeds. As a result, in
existing converters, high fidelity and high speed are commonly
mutually exclusive; that is, the higher the converter speed the
lower the converter fidelity and vice versa.
SUMMARY OF THE INVENTION
6. It is an object of the present invention to provide an
analog-to-digital converter that has a high fidelity and a high
speed. Related objectives are to provide such an analog-to-digital
converter that is relatively simple and inexpensive.
7. The present invention is directed to a method and apparatus for
processing signals, particularly wide-band signals, including
deterministic signals, random signals, and signals defined by
pseudorandom waveforms with a relatively high degree of fidelity
and efficiency at a high speed and at a low cost. The invention is
particularly useful for processing wideband signal, including
signals defined by broadband signals (i.e., signals having a
bandwidth of preferably more than about 1 kHz and more preferably
more than about 1 GHz).
8. The signal can be in any suitable form such as electromagnetic
radiation, acoustic, electrical and optical.
9. In one embodiment, the method includes the following steps:
10. (a) decomposing the analog or digital signal into a plurality
of signal segments (i.e., subband signals), each signal segment
having a signal segment bandwidth that is less than the signal
bandwidth;
11. (b) processing each of the signal segments to form a plurality
of processed signal segments; and
12. (c) combining the processed signal segments into a composite
signal that is digital when the signal is analog and analog when
the signal is digital. As will be appreciated, the sum of the
plurality of signal bandwidths is approximately equivalent to the
signal bandwidth. The means for processing the signal segments can
include any number of operations, including filtering,
analog-to-digital or digital-to-analog conversion, signal
modulation and/or demodulation, object tracking, RAKE processing,
beamforming, null steering, correlation, interference-suppression
and matched subspace filtering.
13. In a particularly preferred application, the signal processing
step (b) includes either analog-to-digital or digital-to-analog
conversions. The use of signal segments rather than the entire
signal for such conversions permits the use of a lower sampling
rate to retain substantially all of the information present in the
source signal. According to the Bandpass Sampling Theorem, the
sampling frequency of the source signal should be at least twice
the bandwidth of the source signal to maintain a high fidelity. The
ability to use a lower sampling frequency for each of the signal
segments while maintaining a high fidelity permits the use of a
converter for each signal segment that is operating at a relatively
slow rate. Accordingly, a plurality of relatively inexpensive and
simple converters operating at relatively slow rates can be
utilized to achieve the same rate of conversion as a single
relatively high speed converter converting the entire signal with
little, if any, compromise in fidelity.
14. The means for decomposing the signal into a number of signal
segments and the means for combining the processed signal segments
to form the composite signal can include any number of suitable
signal decomposing or combining devices (e.g., filters, analog
circuitry, computer software, digital circuitry and optical
filters). Preferably, a plurality or bank of analog or digital
analysis filters is used to perform signal decomposition and a
plurality or bank of analog or digital synthesis filters is used to
perform signal reconstruction. The analysis and synthesis filters
can be implemented in any number of ways depending upon the type of
signal to be filtered. Filtration can be by, for example, analog,
digital, acoustic, and optical filtering methods. By way of
example, the filters can be designed as simple delays or very
sophisticated filters with complex amplitude and phase
responses.
15. In a preferred configuration, a plurality or bank of analysis
and/or synthesis filters, preferably designed for perfect
reconstruction, is used to process the signal segments. As will be
appreciated perfect reconstruction occurs when the composite
signal, or output of the synthesis filter bank, is simply a delayed
version of the source signal.
16. In one configuration, the analysis filters and synthesis
filters are represented in a special form known as the Polyphase
representation. In this form, Noble identities are can be used to
losslessly move the decimators to the left of the analysis filters
and the interpolators to the right of the synthesis filters.
17. In another configuration, noise components in each of the
signal segments can be removed prior to signal analysis or
conversion in the processing step. The removal of noise prior to
analog-to-digital conversion can provide significant additional
reductions in computational requirements.
18. In yet another configuration, a coded signal is acquired
rapidly using the above-referenced invention. In the processing
step, the signal segments are correlated with a corresponding
plurality of replicated signals to provide a corresponding
plurality of correlation functions defining a plurality of peaks;
an amplitude, time delay, and phase delay are determined for at
least a portion of the plurality of peaks; and at least a portion
of the signal defined by the signal segments is realigned and
scaled based on one or more of the amplitude, time delay, and phase
delay for each of the plurality of peaks.
19. In another embodiment, a method is provided for reducing noise
in a signal expressed by a random or pseudorandom waveform. The
method includes the steps of decomposing the signal into a
plurality of signal segments and removing a noise component from
each of the signal segments to form a corresponding plurality of
processed signal segments. The means for decomposing the signal can
be any of the devices noted above, and the means for removing the
noise component includes a noise reducing quantizer, noise filters
and rank reduction. Signal reconstruction may or may not be used to
process further the processed signal segments. This embodiment is
particularly useful in acquiring analog signals.
20. In yet a further embodiment, a method is provided for combining
a plurality of signal segments (which may or may not be produced by
analysis filters). In the method, synthesis filtering is performed
on each of the plurality of signal segments. The means for
performing synthesis filtering can be any of the devices noted
above.
21. A number of differing system configurations can incorporate the
synthesis filtering means in this embodiment of the invention. For
example, a system can include, in addition to the synthesis
filtering means, means for emitting the plurality of signal
segments from a plurality of signal sources (e.g., antennas); means
for receiving each of the plurality of signal segments (e.g.,
antennas); and means for converting each of the signal segments
from analog format to digital format (e.g., analog-to-digital
converter).
22. In another configuration, the system includes: a plurality of
analysis filters to decompose a source signal into a plurality of
decomposed signal segments; a plurality of digital-to-analog
conversion devices for converting the plurality of decomposed
signal segments from digital into analog format to form a
corresponding plurality of analog signal segments; a plurality of
amplifiers to form a corresponding plurality of signal segments; a
plurality of signal emitters for emitting the plurality of signal
segments; and a plurality of receptors for receiving the plurality
of signal segments.
23. In yet another configuration, the system includes: a plurality
of analysis filters to decompose a source signal into a plurality
of decomposed signal segments; a plurality of amplifiers to amplify
the decomposed signal segments to form a corresponding plurality of
signal segments; a plurality of signal emitters for emitting the
plurality of signal segments; and a plurality of receptors for
receiving the plurality of signal segments.
24. In another embodiment, a method is provided in which digital
signals are decomposed, processed, and then recombined. Signal
processing can include signal correlation (e.g., signal modulation
or demodulation), and oblique projection filtration (e.g., as
described in copending U.S. Patent Application Ser. No. 08/916,884
filed Aug. 22, 1997, entitled "RAKE Receiver For Spread Spectrum
Signal Demodulation," which is incorporated herein fully by
reference).
BRIEF DESCRIPTION OF THE DRAWINGS
25. FIG. 1 depicts a first embodiment of the present invention;
26. FIG. 2 depicts an analog signal;
27. FIG. 3 depicts the analog signal of FIG. 2 divided up into a
plurality of signal segments;
28. FIG. 4 depicts the first embodiment including decimation;
29. FIGS. 5A and 5B depict noble identities;
30. FIG. 6 depicts a polyphase filter representation;
31. FIG. 7 depicts a polyphase filter representation with noble
identities;
32. FIG. 8 depicts another embodiment of the present invention;
33. FIG. 9 depicts the quantization process of the quantizers in
FIG. 8;
34. FIG. 10 depicts a subband digital transmitter;
35. FIG. 11 depicts a subband analog transmitter;
36. FIG. 12 depicts a subband receiver;
37. FIG. 13 depicts rank reduction for noise filtering;
38. FIG. 14 depicts another embodiment of the present
invention;
39. FIG. 15 depicts another embodiment of the present
invention;
40. FIG. 16 depicts RAKE processing;
41. FIG. 17 depicts a multiplexed radar transmitter
architecture;
42. FIG. 18 depicts a radar receiver architecture;
43. FIG. 19 depicts a digital communications example of a
recursive, adaptive Wiener filter;
44. FIG. 20 depicts an alternative RAKE processing methodology;
and
45. FIG. 21 depicts a least squares, multiple input multiple output
filter design problem.
DETAILED DESCRIPTION
46. Referring to FIG. 1, an embodiment of the present invention is
illustrated. As can be seen from FIGS. 1 and 2, a wideband,
pseudorandom or random signal 40 (shown in FIG. 2) is passed to a
bank or plurality of analysis filters 44a-n. The signal 40 has a
frequency band or domain, F.sub.s, having frequency bounds,
f.sub.o, (lower) and f.sub.n, (upper), and therefore a bandwidth of
f.sub.o-f.sub.n (FIG. 2). The bandwidth commonly is at least about
1 kHz, more commonly at least about 1 GHz. Each of the analysis
filters 44a-n pass only a portion of the frequency band of the
signal to form a plurality of subband signals 48a-n, or time
frequency components, characterized by discrete portions of the
frequency band, F.sub.s, of the signal 40 (FIG. 3). As will be
appreciated, the summation of the individual frequency bandwidths
of all of the subband signals 48a-n is substantially the same as
the bandwidth of the signal 40 (FIG. 3). The various subband
signals 48a-n are processed 52a-n independently as described below
to form a corresponding plurality of processed signal segments
56a-n. The processed signal segments 56a-n are passed to a bank or
plurality of synthesis filters 60a-n and combined to form a
composite signal 64. Generally, the signal 40 is analog or digital
and, when the signal 40 is analog, the composite signal 64 is
digital, and, when the signal 40 is digital, the composite signal
64 is analog.
47. The analysis and synthesis filters 44a-n and 60a-n can be in
any of a number of configurations provided that the filters pass
only discrete, or at most only slightly overlapping, portions of
the frequency domain of the signal 40. It is preferred that the
frequency bands of the subband signals overlap as little as
possible. Preferably, no more than about 5% and more preferably no
more than about 1% of the frequency bands of adjacent subband
signals overlap.
48. The filters can be analog or digital depending on the type of
signal 40 or the processed signal segments 56a-n. Examples of
suitable analog analysis and synthesis filters include a suitably
configured bandpass filter formed by one or more low pass filters,
one or more high pass filters, a combination of band reject and low
pass filters, a combination of band reject and high pass filters,
or one or more band reject filters. Digital analysis and synthesis
filters are typically defined by software architecture that
provides the desired filter response.
49. In a preferred configuration shown in FIG. 4, the signal 40 is
decomposed by the analysis filter bank 46 (which includes analog or
digital analysis filters Hk(z) 44a-n) into subband signals which
are each sampled by a downsampler 64a-n performing an M-fold
decimation (i.e., taking every M.sup.th sample), and the sampled
subband signals are further sampled after signal processing by an
up-sampler 68a-n (and/or expander (which fills in L-1 zeros in
between each sample)) and the further sampled subband signals are
combined by a synthesis filter bank 62 (that includes analog or
digital synthesis filters Gk(z) 60a-n). The sampled subband
signals, denoted by x.sub.0(n), x.sub.1(n), . . . x.sub.m-1(n), are
the outputs of the N-band analysis filter bank and the inputs to
the N-band synthesis filter bank. As a result of decimation, the
subband signals are 1/N the rate of the input rate of the signal
40.
50. Preferably, the analysis and synthesis filters are perfect
reconstruction filters such that the composite signal 64 is a
delayed version of the signal 40 (i.e., y(n)=u(n-L) where y(n) is
the composite signal, u(n) is the signal, and L is time of delay).
Using perfect reconstruction filters, the subband signals 48a-n can
be downsampled without any loss in fidelity of the output signal.
This downsampling is permissible because the subband signals are of
narrow bandwidth and the consequence of the downsampling is that
any processing application 52a-n that is embedded in the subbands
can run at significantly reduced rates.
51. As will be appreciated, a perfect reconstruction filter system
can be formed by a number of different methods, including
quadrature mirror filter techniques. A preferred technique for
designing a filter bank is known as a least squares multiple input
multiple output filter design notation. According to this
technique, which is illustrated in FIG. 21, a rational transfer
matrix defining one of the filter banks is known, i.e., either H(z)
or G.sup.T(z), along with a rational transfer matrix F(z) defining
the ideal output of the filter banks. Assuming that H(z) and F(z)
are the known rational transfer matrices, the unknown rational
transfer matrix, G.sup.T(z), is determined by the following
equation:
G.sup.T(z)=[F(z) U.sup.T(Z.sup.-1)]+H.sub.0.sup.-1(Z)
52. where
53. H(z)=H.sub.0(z)U(z); [H.sub.0(z) is the minimum phase
equivalent of H(z)]
54. U(z)U.sup.T(z.sup.-1)=I; Paraunitary
55. [F(z)U(z.sup.-1)].sub.x: Causal part of
F(z)U.sup.T(z.sup.-1)
56. As will be appreciated if G.sup.T(z) were known and H(z) were
unkown, then the equation would be solved for H(z) rather than
G.sup.T(z), and G.sup.T(z) would be decomposed into the
following:
G.sup.T(z)=G.sub.o.sup.T(z)U(z)
57. where
58. G.sub.o.sup.T(z) is the minimum phase equivalent of
G.sup.T(z).
59. In a preferred embodiment, the rational transfer matrices of
the analysis and/or synthesis filters are mathematically expressed
in a polyphase filter representation. Exemplary equations defining
the decomposition of the signal 40 by the analysis filters 44a-n
include the following: 1 H ( z ) = l = 0 M - 1 z 1 E l ( z M )
60. where
61. M is the number of subbands (which is the same as the number of
analysis filters in the analysis filter bank; l is the subband
designation); 2 E l ( z M ) = n = - .infin. .infin. e l ( n ) z - n
e l ( n ) = h ( M n + l ) , 0 l M - 1
62. (known as a Type 1 polyphase filter representation) and 3 H ( z
) = l = 0 M - 1 z - ( M - 1 - l ) R l ( z u )
63. where
R.sub.l(z.sup.M)=E.sub.M-1-l(z)
64. (known as Type 2 polyphase filter representation). As will be
appreciated, other techniques exist for expressing a rational
transfer matrix defining a filter system including impluse response
and filter description.
65. Noble identities can be used to losslessly move the decimators
to the left of the analysis filters and the L-fold up-sampler
and/or expander to the right of the synthesis filters. In this
manner, the analysis and synthesis filters operate on lower rate
data, thereby realizing significant computational savings. The
noble identities include:
66. Identity I: Decimation by M followed by filtering defined by
the mathematical function H(z) is equivalent to filtering by
H(z.sup.M) followed by decimation by M (FIG. 5A).
67. Identity II: Filtering by G(z) followed by an upsampling by L
is equivalent to upsampling by L followed by filtering by
G(z.sup.L) (FIG. 5B).
68. By way of example, assume H(z) defines an order N finite
impulse response (FIR) digital analysis filter with impulse
response h(n), M=2, u(n) is the source signal and X(n) is the
subband signal. Using the type 1 polyphase representation above,
H(z) is decomposed to yield the following:
H(z)=H.sub.o(z.sup.2)+H.sub.1(z.sup.2)
69. Based on the foregoing, FIG. 6 is a polyphase representation
based implementation of H(z) without noble identities and FIG. 7 is
a polyphase representation-based implementation of the analysis
filters H(z) using noble identities to move the decimators ahead of
the analysis filters. In this configuration, H.sub.o(z.sup.2) and
H.sub.1(z.sup.2) are FIR filters of order n.sub.o+1 and n.sub.1+1,
where N=n.sub.o+n.sub.1+1. H.sub.o(z.sup.2) and H.sub.1(z.sup.2)
operate at half the rate as compared to H(z) and therefore have two
units of time in which to perform all the necessary computations,
and the components are continually active (i.e., there are no
resting times). Accordingly, there is an M-fold reduction in the
number of multiplications and additions per unit of time when using
both polyphase representation and the noble identities to implement
an M-fold decimation filter.
70. Subband signal processing can take a variety of forms. In one
embodiment shown in FIG. 8 which depicts a receiver and antenna
architecture, the source signal 40 and subband signals 48a-n are in
analog form and a plurality of quantizers or analog-to-digital
converters are used to convert the subband signals 48a-n to digital
form before further processing 82 (e.g., correlation for encoded
subband signals, subband signal digital beamforming in multiple
antenna systems, etc.) and/or synthesis of the digital subband
signals 78a-n is performed. As noted above, the subband signals
48a-n are preferably sampled by each of the decimators or
downsamplers 64a-n at a rate of at least about twice the bandwidth
of the corresponding subband signal 48a-n to maintain fidelity. As
shown in FIG. 9, each quantizer, or analog-to-digital converter,
74a-n determines the digital word or representation 90a-n that
corresponds to the bin 86a-n having boundaries capturing the
amplitude of the analog subband signal at that time and outputs the
digital word or representation that represents the selected
quantization level assigned to the respective bin. The digital
subband signals 78a-n are converted 94a-n from radio frequency (RF)
to base band frequency and optionally subjected to further signal
processing 60. The processed subband signals 98 are formed into a
digital composite signal 102 by the synthesis filter bank 60.
71. To provide increased accuracy, noise rejecting quantizers can
be utilized as the quantizers 74a-n. As will be appreciated, a
noise rejecting quantizer assigns more bits to the portions of the
subband signal having less noise (and therefore more signal) and
fewer bits to the noisy portion. This selective assignment is
accomplished by adaptively moving the bin boundaries so as to
narrow the bin width (thereby increasing quantization fidelity. An
example of a design equation for a Lloyd-Max noise rejecting
quantizer is as follows: 4 t k = x k - 1 + x k 2 + 2 ( x k ) - 2 (
x k - 1 ) 2 ( x k - x k - 1 ) ; x k = e k - 1 2 2 ( x k ) x k
72. where:
73. x is the signal to be quantized;
74. N is the number of quantization levels;
75. k is signal identifier;
76. .sigma. is the noise covariance.
77. The mean squared quantization error (MSE) .xi..sup.2 is as
follows: 5 2 = E ( x - x ^ ) 2 = E x 2 + k = 0 N - 1 [ 2 ( x k ) +
x k 2 - 2 x k e k ] P k
78. where:
79. {x.sub.k}.sub.o.sup.N-1 are the representation points;
80. {c.sub.k}.sub.o.sup.N-1 are the quantization bins;
81. {t.sub.k}.sub.o.sup.N-1 are the bin thresholds;
82. f.sub.y(y) is the probability density function of y;
83. y=x+n, where x is the signal component and n the noise
component; 6 e k = E x | y C k ] = 1 / P k t k t k + 1 E [ x | y =
] fy ( ) ; and P k = P [ y C k ] = t k t k + 1 fy ( )
84. The LM equations require that the bin thresholds be equidistant
from the representation points and that each representation point
be the conditional mean of x in the corresponding quantization bin.
As will be appreciated, a Lloyd-Max (LM) quantizer substantially
minimizes the mean squared error between the discrete approximation
of the signal and its continuous representation.
85. The noise covariance, .delta., can be estimated by linear mean
squared error estimation techniques. Linear mean squared error
estimates are characterized by the following equation:
{circumflex over (X)}=Ty=R.sub.xyR.sub.yy.sup.-1y
86. where T is the Wiener filter, R.sub.xy is the cross covariance
between x and y and R.sub.yy is the covariance of y.
87. R.sub.xy and R.sub.yy are unknown and require estimation. A
number of techniques can be used to estimate R.sub.xy and R.sub.yy,
including an adaptive Wiener filter (e.g., using the linear mean
squared algorithm), direct estimation, sample matrix inversion and
a recursive, adaptive Wiener filter, with a recursive, adaptive
Wiener filter being more preferred.
88. The recursive, adaptive Wiener filter is explained in Thomas,
J. K., Canonical Correlations and Adaptive Subspace Filtering, Ph.D
Dissertation, University of Colorado Boulder, Department of
Electrical and Compute Engineering, pp.1-110, June 1996. which is
incorporated herein by reference in its entirety. In a recursive,
adaptive Wiener filter assume {circumflex over (T)}.sub.M denotes
the filter when M measurements of X and Y are used. Then
{circumflex over (T)}.sub.M is the adaptive Wiener filter
T.sub.M=X.sub.MY.sub.M*(Y.sub.MY.sub.M*).sup.-1={circumflex over
(R)}.sub.xy{circumflex over (R)}.sub.yy.sup.-1,
X.sub.M=[x.sub.1x.sub.2 . . . x.sub.M]; X.sub.M=[x.sub.Mx]
Y.sub.M=[y.sub.1y.sup.2 . . . y.sub.M]; Y.sub.M=[y.sub.My]
89. If another measurement of x and y is taken, and one more column
is added to X.sub.M and Y.sub.M to build {circumflex over
(T)}.sub.M-1:
{circumflex over (T)}.sub.M+1=X.sub.MY.sub.M*{circumflex over
(R)}.sub.M+1.sup.-1+xy*{circumflex over (R)}.sub.M-1.sup.-1
90. The estimate of .sub.M+1 is {circumflex over (X)}.sub.M+1
{circumflex over (X)}.sub.M+1={circumflex over
(T)}.sub.M+1Y.sub.M+1
91. Using the estimate of X.sub.M+1, one can read off {circumflex
over (x)}.sub.M+1, which is the estimate of x: 7 x ^ M + 1 = 1 1 +
r 2 x ~ M + r 2 1 + r 2
92. where
93. r.sup.2=y*{circumflex over (R)}.sub.M.sup.-1y and {tilde over
(x)}.sub.M+1={circumflex over (T)}.sub.My.
94. Based on the above, when one observes y, the best estimate of
the unknown x is {tilde over (x)}, with corresponding estimation
error {tilde over (E)}.sub.M+1 and covariance {tilde over
(Q)}.sub.M+1. If the unknown x becomes available after a delay,
then {tilde over (x)}.sub.M+1 can be updated to {circumflex over
(x)}.sub.M+1 with error covariance {tilde over (E)}.sub.M+1 and
covariance {tilde over (Q)}.sub.M+1. The two covariances are
related by the following formula: 8 Q ~ M + 1 = Q ^ M + 1 + r 2 1 +
r 2 x x *
95. By way of example and as illustrated in FIG. 19, consider a
digital communication application in which the modulation scheme
involves transmitting x.sub.0 and x.sub.1 when bits 0 and 1 are to
be sent. During the setup of the communication link, the
transmitter sends a known bit sequence across the unknown channel.
Let X.sub.M be the matrix of signals that correspond to the known
bit sequence. The receiver observes Y.sub.M, which is the channel
filtered and noise corrupted version of X.sub.M. Since the receiver
knows the bit pattern, and therefore X.sub.M, it is able to build
{circumflex over (T)}.sub.M. Therefore we refer to X.sub.M and
Y.sub.M as the training set.
96. Once the communication link is established, the transmitter
sends a signal x, which corresponds to a data bit. The receiver
observes the corresponding y and uses it to estimate x using
{circumflex over (T)}.sub.M:
{tilde over (x)}={circumflex over (T)}.sub.My
97. The receiver determines r.sup.2, cos.sup.2.theta. and
sin.sup.2.theta..
98. When cos.sup.2.theta. is approximately equal to 1, {tilde over
(x)} is deemed to be a good estimate of x and is used to decide if
a 1 or 0 was sent. If, however, cos.sup.2.theta.<<1, then the
estimate {tilde over (x)} is scaled by cos.sup.2.theta., as
required by equation 14, before it is used to decide if a 1 or 0
was sent. Once the decision of 1 or 0 is made, the true x is known
and can be used to build {tilde over (x)} as required by equation
14 above and as illustrated in FIG. 19. The x and y are also added
to the training set to update {circumflex over (T)}.sub.M.
99. In another embodiment, the source signal 40 is digital and the
analysis filters are therefore digital, signal processing is
performed by a digital-to-analog converter, and the synthesis
filters are analog. FIG. 10 depicts a subband digital transmitter
according to this embodiment. The signal 100 is in digital format
and is transmitted to a bank of analysis filters 104a-n to form a
plurality of digital subband signals 108a-n; the digital subband
signals 108a-n are processed by digital-to-analog converters 112a-n
to form analog subband signals 116a-n; the analog subband signals
116a-n are amplified by amplifiers 120a-n to form amplified subband
signals 124a-n; and the amplified subband signals 124a-n
transmitted via antennas 128a-n.
100. In another embodiment shown in FIG. 11, a subband analog
transmitter is depicted where the signal 140 is analog and not
digital. The signal 140 is decomposed into a plurality of analog
subband signals 144a-n by analog analysis filters 148a-n and the
analog subband signals 144a-n amplified by amplifiers 152a-n, and
the amplified subband signals transmitted by antennas 156a-n.
101. In yet another embodiment shown in FIG. 12, a subband receiver
is depicted that is compatible with the subband analog transmitter
of FIG. 11. Referring to FIG. 12, a plurality of subband signals
160a-n are received by a plurality of antennas 164a-n, the received
subband signals 168a-n down converted from radio frequency to
baseband frequency by down converters 172a-n; the down converted
subband signals 176a-n which are in analog form are converted by
quantizers 180a-n from analog to digital format; and the digital
subband signals 184a-n combined by synthesis filters 188a-n to form
the digital composite signal 192.
102. In any of the above-described transmitter or receiver
embodiments, when the subband signals are encoded waveforms such as
Code Division Multiple Access (CDMA) or precision P(Y) GPS code
signals, the subband signals can be encoded or decoded to realize
computational savings. In a receiver, for example, the subband
signals are correlated with a replica of the transmitted signal
prior to detection. The correlation process can be performed before
or after synthesis filtering or before conversion to digital (and
therefore in analog) or after conversion to digital (and therefore
in digital). The approach is particularly useful for the rapid,
direct acquisition of wideband pseudorandom noise encoded
waveforms, like CDMA type signals and the P(Y) GPS code, in a
manner that is robust with respect to multipath effects and
wide-band noise. Because the M-subband signals have narrow
bandwidths and therefore can be searched at slower rates,
correlation of the subband signals rather than the signal or the
composite signal can be performed with over an M-fold reduction in
computation and therefore reduce the individual component cost.
103. To provide further reductions in computational requirements,
the number of subbands requiring correlation at any trial time and
Doppler frequency can be reduced. The pseudorandom nature of the
coded signals implies that a coded signal will only lie in certain
known subbands at any given time. According to the rank-reduction
principle and as illustrated by FIG. 13, subbands 200a-j outside of
the subbands 204a-j containing the coded signal can be eliminated
to reduce the effects of wide-band noise in the acquisition and/or
tracking of pseudorandom signals. This is accomplished by
eliminating any subband in which the noise component exceeds the
signal component (i.e., the SNR is less than 1). Such an
elimination increases the bias squared, which is the power of the
signal components that are eliminated, while drastically decreasing
the variance, which is the power of the noise that was eliminated.
In this manner, the mean squared error between the computed
correlation function and the noise-free version of the correlation
function is significantly reduced.
104. As shown in FIG. 14 to perform the correlation in the subband
signals in GPS, CDMA, and other pseudorandom or random waveform
applications, the replicated code 208 from the code generator 212
must be passed through an analysis filter bank 216 that is
identical to the analysis filter bank 220 used to decompose the
signal 224. Because the correlation must be performed for different
segments of the replicated code 208, each indexed by some start
time, this decomposition is necessary for all trial segments of the
replicated code 208. A plurality of subband correlators 228a-n
receive both the subband signals 232a-n and the replicated subband
signals 236a-n and generate a plurality of subband correlation
signals 240a-n. The subband correlation signals 240a-n are provided
by the following equation: 9 q m , n ( i ) ( j ) = k = 1 N x m ( k
+ j ) p n ( i ) ( k )
105. where:
106. q(k) is the subband correlation signal;
107. p.sub.n.sup.(i)(k) is the component of the i.sup.th trial
segment of the P(Y) code in the n.sup.th subband;
108. x.sub.m(k) is the component of the measurement that lies in
the m.sup.th subband;
109. N is the number of samples over which the correlation is
performed.
110. The subband correlation signals 240a-n are upsampled and
interpolated by the synthesis filters 244a-n and then squared and
combined. The resulting composite signal 248 is the correlation
function that can be further processed and detected.
111. After the subband correlation signals 240a-n are generated,
the signals, for example, can be processed by a RAKE processor,
which is commonly a maximal SNR combiner, to align in both time and
phase multipath signals before detection and thereby provide
improved signal-to-noise ratios and detection performance. As will
be appreciated, a signal can be fragmented and arrive at a receiver
via multiple paths (i.e., multipath signals) due to reflections
from other objects, particularly in urban areas. The formation of a
number of multipath signals from a source signal can degrade the
correlation peaks, which contributes to the degradation of the
detections. The RAKE processor determines the time and phase delays
of these multipath signals by searching for correlation peaks in
the correlation function and identifying the time and phase delays
for each of the peaks. The RAKE processor then uses the time and
phase delay estimates to realign the multipath signals so that they
can add constructively and enhance the correlation peaks. The peak
enhancement improves detection because of the increase in
signal-to-noise ratio.
112. FIG. 15 depicts an embodiment of a signal processing
architecture incorporating these features. Referring to FIG. 11,
the signals 300 are received by one or more antennas 304, down
converted by a down converter 308 to intermediate frequency,
filtered by one or more filters 312, and passed through an
analog-to-digital converter 316 to form a digital signal 320. The
digital signal 320 is passed through an analysis filter bank 324 to
generate a plurality of subband signals 328a-n, and the subband
signals 328a-n to a plurality of subband correlators 332a-n as
noted above to form a plurality of subband correlation signals
336a-n. The subband correlation signals 336a-n are passed to a
synthesis filter bank 340 to form a correlation function 344
corresponding to the signal 300. The correlation function 344 is
passed to a pre-detector 348 to determine an estimated transmit
time and frequency and an amplitude and delay for each of the
correlation peaks. The estimated transmit time and frequency 352
are provided to a code generator 356 and the amplitude and time
delay 360 associated with each correlation peak are provided to the
RAKE processor 364. The code generator 356 determines a replicated
code 368 corresponding to the signal 300 based on the estimated
trial time and frequency. Using the correlation peak amplitudes and
time and/or phase delays, the RAKE processor 364, as shown in FIG.
16, shifts the input sequence y(k) by the amounts of the multipath
time and/or phase delays and then weights each shifted version by
the amplitude of the peak of the correlation function corresponding
to that peak to form a RAKED signal 372 (denoted by y.sub.R(k)).
The RAKED sequence is commonly defined by the following
mathematical equation: 10 y R ( k ) = 1 i = 1 p A i i = 1 p A i - j
i y ( k + t i )
113. where:
114. p is the number of multipath signals (and therefore number of
peaks);
115. A.sub.i is the amplitude of the i.sup.th peak;
116. t.sub.i is the time delay of the i.sup.th peak;
117. .phi. is the phase delay of the i.sup.th peak;
118. y(k) is the input sequence into the code correlator.
119. The RAKED signal 372 and the replicated code 368 are
correlated in a correlator 376 to provide the actual transmit time
and frequency 380 which are then used by detector 384 to detect the
signal.
120. There are a number of variations of the above-desc system. The
variations are useful in specific applicat such as GPS, CDMA, and
radar.
121. In one variation of the system of FIG. 15 that i depicted in
FIGS. 17-18, multiplexed radar transmitte receiver architectures
are depicted. The radar signals 400a-n are a number of coded
waveforms that operate in separate, contiguous subbands (referred
to as "radar su signals"). As shown in FIG. 17, the radar signals
40 are simultaneously transmitted by a plurality of transmitters
404a-n that each include a plurality of analysis filters (not
shown) to form the various radar subband signals 400a-n. Referring
to FIG. 18, the va radar subband signals 400a-n are received by a
signal receptor 410 and passed through a plurality of bandpass
filters 414a-n. A bandpass filter 414a-n having unique bandpass
characteristics corresponds to each of the radar subband signals.
The various filtered subband signals 416a-n are sampled by a
plurality of decimators 422a-n and quantized by a plurality of
quantizers 426a-n to form digital subband signals 430a-n. The
digital subband signals 430a-n are analyzed by a plurality of
detectors 434a-n to form a corresponding plurality of detected
signals 438a-n. The detectors 434a-n use a differently coded
waveform for each of the transmitted radar subband signals 400a-n
so that the subband radar signals can be individually separated
upon reception. As noted above in FIGS. 14-15, the coded radar
waveform is decomposed by a plurality of analysis filters (not
shown) that are identical to the analysis filters in the receiver
to provide replicated subband signals to the detectors 434a-n. Each
detector 434a-n correlates a radar subband signal 430a-n with its
corresponding replicated subband signal to form a plurality of
corresponding detected signals 438a-n. The detected signals 438a-n
are analyzed by a synthesis filter bank 412a-n to form a composite
radar signal 446.
122. In a variation of the system of FIG. 15, a bank of analysis
filters and synthesis filters can be implemented both directly
before and after the correlation step (not shown) to provide the
above-noted reductions in computational requirements.
123. In another variation of the system of FIG. 15, the analysis
filters can be relocated before the analog-to-digital converter 316
to form the subband signals before as opposed to after
conversion.
124. In another variation shown of the system of FIG. 15 that is
depicted in FIG. 20, the RAKE processor 364 can account for the
relative delays in antenna outputs of the signal 300 (which is a
function of the arrangement of the antennas as well as the angular
location of the signal source) by summing the antenna outputs
without compensating for the relative output delays. The
correlation process may result in N.times.p peaks, where N is the
number of antenna outputs and p is the number of multipath induced
peaks. The Np peaks are then used to realign and scale the input
data before summation. The RAKE 364 in effect has performed the
phase-delay compensation usually done in beam-steering. The
advantages of this approach compared to conventional beam steering
techniques include that it is independent of antenna array
geometries and steering vectors, it does not require iterative
searches for directions as in LMS and its variants, and it is
computationally very efficient. This approach is discussed in
detail in copending application having Ser. No. 08/916,884, and
filed on Aug. 21, 1997.
125. While various embodiments of the present invention have been
described in detail, it is apparent that modifications and
adaptations of those embodiments will occur to those skilled in the
art. However, it is to be expressly understood that such
modifications and adaptations are within the scope of the present
invention, as set forth in the following claims.
* * * * *