U.S. patent application number 12/478564 was filed with the patent office on 2010-09-09 for channel extrapolation from one frequency and time to another.
Invention is credited to Paul Wilkinson Dent.
Application Number | 20100226448 12/478564 |
Document ID | / |
Family ID | 42678236 |
Filed Date | 2010-09-09 |
United States Patent
Application |
20100226448 |
Kind Code |
A1 |
Dent; Paul Wilkinson |
September 9, 2010 |
CHANNEL EXTRAPOLATION FROM ONE FREQUENCY AND TIME TO ANOTHER
Abstract
An improved channel estimation technique is provided herein that
determines accurate scatterer parameters for the scattering objects
in the wireless channel, and extrapolates the scatterer parameters
in both time and frequency to characterize the scattering objects
for a different time and a different frequency. In one embodiment,
a wireless device determines scatterer parameters that
characterizes the scattering objects of a reception channel, and
extrapolates the scatterer parameters in both time and frequency to
predict the scatterer parameters for a future time and frequency,
e.g., a future transmission time and frequency.
Inventors: |
Dent; Paul Wilkinson;
(Pittsboro, NC) |
Correspondence
Address: |
ERICSSON INC.
6300 LEGACY DRIVE, M/S EVR 1-C-11
PLANO
TX
75024
US
|
Family ID: |
42678236 |
Appl. No.: |
12/478564 |
Filed: |
June 4, 2009 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
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61157615 |
Mar 5, 2009 |
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|
Current U.S.
Class: |
375/260 ;
455/67.11 |
Current CPC
Class: |
H04L 27/2647 20130101;
H04L 25/0242 20130101; H04L 27/2626 20130101; H04L 27/2634
20130101; H04L 25/0202 20130101 |
Class at
Publication: |
375/260 ;
455/67.11 |
International
Class: |
H04L 27/28 20060101
H04L027/28; H04B 17/00 20060101 H04B017/00 |
Claims
1. A method implemented by a wireless device of characterizing a
wireless communication channel, the method comprising: determining
a first set of scatterer parameters based on signal samples
received by a wireless receiver via a first communication channel
associated with a first frequency and a first time, wherein the
first set of scatterer parameters comprises a set of scattering
coefficients for each of a plurality of path delays, and wherein
each scattering coefficient corresponds to a scattering object; and
determining a second set of scatterer parameters for a second
communication channel associated with a second frequency and a
second time by calculating extrapolated scattering coefficients for
the second set of scatterer parameters based on the first set of
scatterer parameters, the first and second frequencies, and the
first and second times.
2. The method of claim 1 wherein the first communication channel
corresponds to an uplink communication channel associated with an
uplink frequency and an uplink time, and wherein the second
communication channel corresponds to a downlink communication
channel associated with a downlink frequency and a downlink
time.
3. The method of claim 1 wherein the first communication channel
corresponds to a reception communication channel associated with a
reception frequency and a reception time, and wherein the second
communication channel corresponds to a transmission communication
channel associated with a transmission frequency and a transmission
time.
4. The method of claim 1 further comprising determining
extrapolated channel estimates for the second communication channel
based on the second set of scatterer parameters.
5. The method of claim 4 further comprising using the extrapolated
channel estimates to pre-process transmission signals to reduce
interference at one receiver from transmitted signals intended for
another receiver.
6. The method of claim 1 further comprising determining a matrix of
complex delay coefficients based on the plurality of signal samples
received via the first communication channel over an evaluation
period, wherein different rows of said delay coefficient matrix
correspond to different time intervals within the evaluation period
and wherein different columns of said delay coefficient matrix
correspond to different path delays, and wherein determining
individual sets of scattering coefficients for individual path
delays in the first set of scatterer parameters comprises applying
a time-to-frequency transform to individual columns of the delay
coefficient matrix.
7. The method of claim 6 wherein the signal samples comprise OFDM
signal samples, wherein the evaluation period comprises a plurality
of OFDM symbol periods, and wherein different rows of said delay
coefficient matrix correspond to different OFDM symbol periods.
8. The method of claim 6 wherein applying the time-to-frequency
transform to individual columns of the delay coefficient matrix
comprises applying a Prony algorithm to individual columns of the
delay coefficient matrix.
9. The method of claim 1 wherein calculating the extrapolated
scattering coefficients for the second set of scatterer parameters
comprises: rotating a phase of the scattering coefficients of the
first set of scatterer parameters based on a frequency difference
between the first and second frequencies to obtain rotated
scattering coefficients; and rotating a phase of the rotated
scattering coefficients based on a time difference between the
first and second times to obtain the extrapolated scattering
coefficients for the second set of scatterer parameters.
10. The method of claim 9 wherein each scattering coefficient in
the first set of scatterer parameters is associated with a Doppler
frequency, the method further comprising scaling the Doppler
frequencies in the first set of scatterer parameters based on a
ratio between the first and second frequencies to obtain a Doppler
frequency for each scattering coefficient in the second set of
scatterer parameters.
11. The method of claim 1 wherein each scattering coefficient in
the first set of scatterer parameters is associated with a rate of
change of delay, and wherein calculating the extrapolated
scattering coefficients comprises: calculating extrapolated path
delays for the second set of scatterer parameters based on the path
delays of the first set of scatterer parameters and the rate of
change of delay; and calculating the extrapolated scattering
coefficients based on the extrapolated path delays and the second
frequency.
12. The method of claim 11 wherein calculating the extrapolated
scattering coefficients based on the extrapolated path delays and
the second frequency comprises: determining reflection coefficients
for the first set of scatterer parameters based on the path delays
and scattering coefficients of the first set of scatterer
parameters and the first frequency; and rotating a phase of the
reflection coefficients based on the extrapolated path delays and
the second frequency to calculate the extrapolated scattering
coefficients.
13. The method of claim 1 wherein the receiver comprises a
plurality of antenna elements, the method further comprising
calculating a phase progression across the antenna elements based
on the first and second frequencies to determine different
transmission signal directions corresponding to different
scattering objects.
14. A wireless device configured to characterize a wireless
communication channel, the wireless device comprising: a first
processing element configured to determine a first set of scatterer
parameters based on signal samples received by a wireless receiver
via a first communication channel associated with a first frequency
and a first time, wherein the first set of scatterer parameters
comprises a set of scattering coefficients for each of a plurality
of path delays, and wherein each scattering coefficient corresponds
to a scattering object; and a second processing element configured
to determine a second set of scatterer parameters for a second
communication channel associated with a second frequency and a
second time by calculating extrapolated scattering coefficients for
the second set of scatterer parameters based on the first set of
scatterer parameters, the first and second frequencies, and the
first and second times.
15. The wireless device of claim 14 wherein the first communication
channel corresponds to an uplink communication channel associated
with an uplink frequency and an uplink time, and wherein the second
communication channel corresponds to a downlink communication
channel associated with a downlink frequency and a downlink
time.
16. The wireless device of claim 14 wherein the first communication
channel corresponds to a reception communication channel associated
with a reception frequency and a reception time, and wherein the
second communication channel corresponds to a transmission
communication channel associated with a transmission frequency and
a transmission time.
17. The wireless device of claim 14 wherein the second processing
element is further configured to determine extrapolated channel
estimates for the second communication channel based on the second
set of scatterer parameters.
18. The wireless device of claim 17 wherein the second processing
element is further configured to use the extrapolated channel
estimates to pre-process transmission signals to reduce
interference at one receiver from transmitted signals intended for
another receiver.
19. The wireless device of claim 14 wherein the first processing
element is further configured to determine a matrix of complex
delay coefficients based on the plurality of signal samples
received via the first communication channel over an evaluation
period, wherein different rows of said delay coefficient matrix
correspond to different time intervals within the evaluation period
and wherein different columns of said delay coefficient matrix
correspond to different path delays, and to determine individual
sets of scattering coefficients for individual path delays in the
first set of scatterer parameters by applying a time-to-frequency
transform to individual columns of the delay coefficient
matrix.
20. The wireless device of claim 19 wherein the signal samples
comprise OFDM signal samples, wherein the evaluation period
comprises a plurality of OFDM symbol periods, and wherein different
rows of said delay coefficient matrix correspond to different OFDM
symbol periods.
21. The wireless device of claim 19 wherein the first processing
element is configured to apply the time-to-frequency transform to
individual columns of the delay coefficient matrix by applying a
Prony algorithm to individual columns of the delay coefficient
matrix.
22. The wireless device of claim 14 wherein the second processing
element is configured to calculate the extrapolated scattering
coefficients for the second set of scatterer parameters by: rotate
a phase of the scattering coefficients of the first set of
scatterer parameters based on a frequency difference between the
first and second frequencies to obtain rotated scattering
coefficients; and rotate a phase of the rotated scattering
coefficients based on a time difference between the first and
second times to obtain the extrapolated scattering coefficients for
the second set of scatterer parameters.
23. The wireless device of claim 22 wherein each scattering
coefficient in the first set of scatterer parameters is associated
with a Doppler frequency, wherein the second processing element is
further configured to scale the Doppler frequencies in the first
set of scatterer parameters based on a ratio between the first and
second frequencies to obtain a Doppler frequency for each
scattering coefficient in the second set of scatterer
parameters.
24. The wireless device of claim 14 wherein each scattering
coefficient in the first set of scatterer parameters is associated
with a rate of change of delay, and wherein the second processing
element is configured to calculate the extrapolated scattering
coefficients by: calculating extrapolated path delays for the
second set of scatterer parameters based on the path delays of the
first set of scatterer parameters and the rate of change of delay;
and calculating the extrapolated scattering coefficients based on
the extrapolated path delays and the second frequency.
25. The wireless device of claim 24 wherein the second processing
element is configured to calculate the extrapolated scattering
coefficients based on the extrapolated path delays and the second
frequency by: determining reflection coefficients for the first set
of scatterer parameters based on the path delays and scattering
coefficients of the first set of scatterer parameters and the first
frequency; and rotating a phase of the reflection coefficients
based on the extrapolated path delays and the second frequency to
calculate the extrapolated scattering coefficients.
26. The wireless device of claim 14 wherein the receiver comprises
a plurality of antenna elements, wherein the second processing
element is further configured to calculate a phase progression
across the antenna elements based on the first and second
frequencies to determine different transmission signal directions
corresponding to different scattering objects.
Description
[0001] This application claims priority to U.S. Provisional Patent
Application 61/157,615 filed Apr. 28, 2009, which is incorporated
herein by reference.
BACKGROUND
[0002] In a wireless communication system, a transmitted signal
reflects off objects (e.g. buildings, hills, etc.) in the
environment, referred to herein as scattering objects. The
reflections arrive at a receiver from different directions and with
different delays. The reflections or multi-paths can be
characterized by a path delay and a complex delay coefficient. The
complex delay coefficients show fast temporal variation due to the
mobility of the vehicle while the path delays are relatively
constant over a large number of OFDM symbol periods.
[0003] Channel estimation is the process of characterizing the
effect of the radio channel on the transmitted signal. Channel
estimates approximating the effect of the channel on the
transmitted signal may be used for interference cancellation,
diversity combining, ML detection, and other purposes. Many channel
estimation techniques in common use do not produce sufficiently
accurate estimates of the channel for use by higher order
modulations. Further, it is difficult to predict how the channel
will change due to the mobility of the vehicle. Therefore, there is
a need for new channel estimation techniques that will produce more
accurate channel estimates for higher order modulation and enable
prediction of the channel from current channel estimates.
SUMMARY
[0004] The present invention provides an improved channel
estimation technique that determines accurate scatterer parameters
for the scattering objects in the wireless channel, and
extrapolates the scatterer parameters in both time and frequency to
characterize the scattering objects for a different time and a
different frequency. For example, the present invention may
determine scatterer parameters that characterizes the scattering
objects of a reception channel, and extrapolates the scatterer
parameters in both time and frequency to predict the scatterer
parameters for a future time and frequency, e.g., a future
transmission time and frequency. Thus, one benefit of the present
invention is its ability to accurately characterize a transmission
channel based on information obtained for a reception channel.
[0005] In one exemplary embodiment, a processor in a transceiver
determines a first set of scatterer parameters based on signal
samples received via a first communication channel associated with
a first frequency and a first time. The first set of scatterer
parameters comprises a set of scattering coefficients for each of a
plurality of scattering objects, where each scattering object has
an associated path delay and a rate of change of path delay, or
equivalently, Doppler shift. For example, the processor may
determine the first set of scatterer parameters using the method
provided by co-pending application Ser. No. 12/478473 and/or
co-pending application Ser. No. 12/478520, which are both
incorporated herein by reference. The processor then determines a
second set of scatterer parameters for a second communication
channel associated with a second frequency and a second time. The
processor determines the second set of scatterer parameters by
calculating extrapolated scattering coefficients for the second set
of scatterer parameters based on the first set of scatterer
parameters, the first and second frequencies, and the first and
second times. The processor may use the resulting second set of
scatterer parameters to characterize the second communication
channel, e.g., to determine channel estimates for the second
communication channel.
[0006] In one exemplary embodiment referred to herein as the
Continuous Transform approach, the processor calculates the
extrapolated scattering coefficients by rotating the phase of the
scattering coefficients in the first set of scatterer parameters
based on a frequency difference between the first and second
frequencies and a time difference between the first and second
times. In another exemplary embodiment referred to herein as the
Kalman approach, each scattering coefficient in the first set of
scatterer parameters is associated with a rate of change of delay.
The processor calculates the extrapolated scattering coefficients
based on the second frequency and extrapolated path delays
calculated for the second set of scatter parameters based on the
rate of change of delay and the path delays of the first set of
scatterer parameters.
BRIEF DESCRIPTION OF THE DRAWINGS
[0007] FIG. 1 shows the relationship between different scattering
objects and different path delays relative to a transmitter and
receiver in a wireless system.
[0008] FIG. 2 shows exemplary Doppler frequency vectors associated
with the scattering objects relative to the receiver at a
particular instant of time.
[0009] FIG. 3 shows one exemplary process for calculating
extrapolated scatterer parameters for a transmission channel.
[0010] FIG. 4 shows one exemplary Continuous Transform process for
calculating extrapolated scatterer parameters for a transmission
channel.
[0011] FIG. 5 shows one exemplary Kalman process for calculating
extrapolated scatterer parameters for a transmission channel.
[0012] FIG. 6 shows an exemplary transmitter.
[0013] FIG. 7 shows an exemplary receiver according to an exemplary
embodiment of the present invention.
[0014] FIG. 8 shows measured channel impulse responses obtained
from field test data.
[0015] FIG. 9 maps the intensity of signal rays in the
Doppler-delay domain.
[0016] FIG. 10 shows an exemplary method for determining path
delays and the corresponding Doppler parameters according to the
present invention.
[0017] FIGS. 11A and 11B show details for implementing the
transform methods of FIG. 7.
[0018] FIG. 12 shows the change in .theta. due to time delay
differences.
[0019] FIG. 13 shows one integrated Doppler process for tracking
scatterer parameters according to one exemplary embodiment of the
present invention.
[0020] FIG. 14 shows extrapolating delay slopes from one frequency
band to another.
[0021] FIG. 15 shows one exemplary process for calculating
extrapolated scatterer parameters for a multiple antenna element
device.
[0022] FIG. 16 shows another exemplary process for calculating
extrapolated scatterer parameters for a multiple antenna element
device.
DETAILED DESCRIPTION
[0023] Transmitted signals traveling through wireless communication
channels typically encounter several scattering objects, e.g.,
buildings, mountains, trees, etc., before reaching a receiver. As
used herein, the term "scattering object" refers to both single
scattering objects and clusters of scattering objects that are too
close to separate. Each scattering object reflects the transmitted
signal along a different propagation path. The receiver relies on
accurate channel estimates to process the received signal. Channel
estimation is the process of characterizing the effect of these
scattering objects on the transmitted signal. Channel estimates
typically used by receivers can include complex coefficients of the
channel impulse response at a number of equally-spaced delays,
e.g., equally-spaced chip delays in a CDMA (Code Division Multiple
Access) system, as well as complex coefficients indicative of the
channel frequency response at a number of equally-spaced
frequencies, e.g., equally-spaced subcarrier frequencies in an OFDM
(Orthogonal Frequency Division Multiplex) system. The receiver may
use channel estimates approximating the effect of the channel on
the transmitted signal for interference cancellation, diversity
combining, ML detection, and other purposes.
[0024] Accurate channel estimation relies on the accurate
characterization of the scattering objects within the channel. In
order to characterize the scattering objects, the receiver
determines the path delays, complex delay coefficients, and Doppler
or rate-of-change of delay parameters corresponding to the
scattering objects. Ideally, each scattering object in the
multi-path channel corresponds to a different path delay. However,
there are scenarios where different scattering objects cause
reflected signals to have the same path delay even though the
reflected signals traverse different paths. For example, FIG. 1
shows a plurality of ellipses surrounding a transmitter 12 and a
receiver 14, where the transmitter 12 and receiver 14 mark the foci
of the ellipses, where a scattering object 10 falls on one of the
ellipses, and where different ellipses correspond to different path
delays. Thus, the paths of different scattering objects 10
positioned along the same ellipse have the same path delay, while
the paths of different scattering objects 10 positioned along
different ellipses have different path delays. For example,
scattering objects 10a, 10b both fall on ellipse 2, while
scattering object 10c falls on ellipse 1. Thus, the path delay
associated with path 18c differs from the path delay associated
with path 18a or path 18b, where path 18a and path 18b both have
the same path delay. Because scattering objects 10a and 10b apply
the same path delay to a transmitted signal, receiver 14 cannot use
path delay alone to distinguish scattering object 10a associated
with path 18a from scattering object 10b associated path 18b.
[0025] Because path delay alone cannot be used to characterize the
scattering objects 10, the receiver 14 may use another
characterizing parameter, such as a Doppler parameter, to further
characterize and distinguish the different scattering objects 10.
For example, objects 10 with the same delay at different angular
positions on the same delay-ellipse exhibit different Doppler
shifts for moving a transmitter 12 and/or receiver 14. Thus,
receiver 14 may determine the Doppler shift (or the equivalent rate
of change of delay) to further distinguish between scattering
objects 10 having identical path delays. FIG. 2 shows an example of
the different Doppler frequency vectors associated with the
scattering objects relative to a moving receiver 14 at a particular
instant of time. By determining how the Doppler effect changes the
complex delay coefficients over time, e.g., over multiple OFDM
symbol periods, receiver 14 may distinguish different paths 18
having the same path delay but caused by different scattering
objects 10. U.S. patent application Ser. No. 12/478473 and U.S.
application Ser. No. 12/478520 to current applicants, which are
both incorporated by reference herein, describe methods for
accurately characterizing and tracking the scattering coefficients
for different scattering objects to improve the accuracy of
estimating channel impulse responses.
[0026] Generally, receivers rely on the channel estimates to
accurately process (e.g., decode/demodulate) received signals. If
the transmitter also had a reliable characterization of the
transmission channel, the transmitter could use such channel
information to improve the reliability of communications between
the transmitter and receiver. However, errors in the reception
channel estimates coupled with the differences between transmission
and reception channels, e.g., different transmission and reception
times, different transmission and reception frequencies, etc.,
generally cause transmission channel estimates derived from
reception channel estimates to be prohibitively inaccurate, and
therefore, useless.
[0027] The present invention provides a method for accurately
characterizing a transmission channel based on information obtained
for a reception channel. FIG. 3 shows one exemplary method 50 for
characterizing a transmission channel. A wireless device determines
a first set of scatterer parameters for a reception channel based
on received signal samples associated with a reception frequency
and time (block 52). The first set of scatterer parameters
comprises a set of scattering coefficients for each of a plurality
of path delays, where each scattering coefficient corresponds to a
scattering object. The device then determines a second set of
scatterer parameters for a transmission channel associated with a
transmission frequency and time by calculating extrapolated
scattering coefficients for the second set of scatterer parameters
based on the first set of scatterer parameters, the reception and
transmission frequencies, and the reception and transmission times
(block 54).
[0028] The following describes the invention in terms of reception
and transmission channels. It will be appreciated, however, that
the present invention generally applies to communication channels
associated with different communication times and frequencies. It
will further be appreciated that the present invention does not
require the use of all reception channel scattering coefficients.
Instead, in determining the scatterer parameters for the
transmission channel, the processor may only use some of the
reception channel scattering coefficients. The remaining reception
channel scattering coefficients may be discarded or used as
transmission channel scattering coefficients.
[0029] In one exemplary embodiment, referred to herein as the
Continuous Transform embodiment, a processor determines the
scatterer parameters for the reception channel based on the
received signal samples. The present invention may, for example,
use the teachings of the Ser. No. 12/478473 application and/or the
teachings of U.S. application Ser. No. 12/478520 to determine
and/or track the scatterer parameters for a reception channel
associated with a reception time and a reception frequency. The
scatterer parameters comprise a plurality of scattering
coefficients and associated Doppler frequencies for each of a
plurality of path delays. The set of scattering coefficients and
associated Doppler frequencies corresponding to a given path delay
characterize the different scattering objects in the reception
channel associated with that path delay. The determined scatterer
parameters collectively correspond to the reception time and
frequency.
[0030] FIG. 4 shows one exemplary Continuous Transform method 60
for calculating the extrapolated scattering coefficients for the
transmission channel associated with a transmission time and
transmission frequency. To that end, the processor determines a
frequency difference between the reception and transmission
frequencies (block 62), and determines rotated scattering
coefficients by rotating a phase of the reception channel
scattering coefficients based on the frequency difference (block
64). The processor also determines a time difference between
reception and transmission times (block 66), and calculates the
extrapolated scattering coefficients by rotating a phase of the
rotated scattering coefficients based on the time difference (block
68). While not shown in FIG. 4, the processor may also calculate
extrapolated Doppler frequencies by determining the ratio between
the transmission channel frequency and the reception channel
frequency, and using the scaling factor to scale the reception
channel Doppler frequencies. The processor uses the resulting
scatterer parameters to characterize the transmission channel,
e.g., to determine channel estimates for the transmission
channel.
[0031] In another exemplary embodiment, referred to herein as the
Kalman embodiment, the processor determines the scatterer
parameters for the reception channel based on the received signal
samples. The present invention may, e.g., use the teachings of the
Ser. No. 12/478473 application and/or the Ser. No. 12/478520
application to determine and/or track the scatterer parameters for
a reception channel associated with a reception time and a
reception frequency. The scatterer parameters comprise a plurality
of scattering coefficients and associated rate of change of delay
for each of a plurality of path delays. For this embodiment, the
scattering coefficients comprise reflection coefficients, which are
independent of time and frequency, rotated by the time and
frequency of the corresponding channel, where each reflection
coefficient corresponds to a different scattering object, and where
each reflection coefficient has an associated rate of change of
delay. The determined scatterer parameters collectively correspond
to the reception time and frequency.
[0032] FIG. 5 shows one exemplary Kalman method 70 for calculating
the extrapolated scattering coefficients for the transmission
channel associated with a transmission time and transmission
frequency using a Kalman filter process. To that end, the processor
calculates extrapolated path delays for the transmission channel
based on the reception channel path delays and the corresponding
rates of change of delay (block 72). The processor then calculates
the extrapolated scattering coefficients based on the extrapolated
path delays and the transmission frequency by rotating a phase of
the reception channel reflection coefficients based on the
extrapolated path delays and the transmission channel frequency
(block 74).
[0033] Before describing the details of the extrapolation process
of the present invention, the following provides the details
associated with the Ser. Nos. 12/478473 and 12/478520 applications.
Broadly, the Ser. No. 12/478473 invention determines the actual
path delay and Doppler parameter information for a plurality of
scattering objects in a wireless channel. Based on the path delay
and Doppler frequency information, the receiver determines channel
estimates useful for higher order modulation processing, channel
prediction, etc. More particularly, the receiver 14 applies a
frequency-to-time transform to a plurality of OFDM subcarrier
signal samples received over a plurality of OFDM symbol periods to
determine a set of non-equally spaced path delays and a set of
associated complex delay coefficients. Further, the receiver 14
applies a time-to-frequency transform to the complex delay
coefficients determined for individual path delays over multiple
OFDM symbol periods to determine a set of Doppler parameters
comprising a plurality of non-equally spaced Doppler frequencies
and their corresponding scattering coefficients for individual path
delays.
[0034] Because the transform operations of the Ser. No. 12/478473
invention are not constrained to determining output values at
equally spaced time or frequency intervals, the non-equally spaced
path delays, the associated complex delay coefficients, and the
associated Doppler parameter sets have fewer errors than those
produced by conventional techniques. The transform operations
described therein therefore fully characterize the scattering
objects 10 while avoiding the accuracy problems of the prior art.
The increased accuracy of the resulting scattering object
characterizations enable the receiver 14 to better track the
channel estimates.
[0035] To facilitate the following detailed explanations, FIGS. 6
and 7 first show simplified internal details of an exemplary OFDM
transmitter 12 and OFDM receiver 14, respectively. Transmitter 12
comprises an antenna 13, Inverse Fourier transform unit 20,
parallel-to-serial converter 22, modulator 24, and power amplifier
26. Generally, the transmitter uses an Inverse Discrete Fourier
Transform (IDFT) to encode symbols, and the receiver uses a
Discrete Fourier Transform (DFT) to decode signals. However, the
IDFT and DFT may be interchanged, and are so similar that they are
simply referred to herein as Fourier Transform units 20. Signal
values to be transmitted (S1 . . . Sn) are input to the Fourier
transform unit 20 which may be a specialized, hardwired FFT (or
IFFT) circuit or a DSP implementation. Fourier transform unit 20
transforms the n input values to at least n output values. It is
advantageous to use more than n output values, termed
"over-sampling". For example, n=700 input values could be
transformed to m=1024 output values, using a 1024-point FFT. The
524 unused inputs would be set to zero, representing 262 empty
spectral bins on either side of the 700 spectral bins used for the
700 input values. Oversampling simplifies subsequent anti-aliasing
filtering needed to limit out-of-band spectral energy.
[0036] Parallel-to-serial unit 22 converts the output values of the
Fourier transform unit 20 to serial form by selecting them
successively in a fixed order. Each value is complex, so the serial
stream comprises a stream of real parts and a stream of imaginary
parts, i.e., a stream of (I, Q) values. The stream of I-values and
the stream of Q-values are converted to continuous-time I and Q
signals by digital-to-analog conversion and filtering within
modulator 24. The filter frequency response is required to pass
frequencies corresponding to the used spectral bins, e.g., the 700
bins exemplified above, while attenuating frequencies beyond the
exemplary 1024 bins. Thus, oversampling leaves a margin between the
required passband and the required stop band so that the filter is
not required to have an impossibly steep rate of cut-off. The
modulator 24 further uses the continuous-time I and Q signals to
modulate cosine and sine wave carrier frequency signals,
respectively, to generate an OFDM modulated radio frequency signal,
which is amplified to a transmit power level in amplifier 26 and
transmitted via antenna 13.
[0037] FIG. 7 shows a receiver 14 according to one exemplary
embodiment of the present invention. Receiver 14 comprises an
antenna 15, front-end receiver elements (e.g., amplifier 30, down
converter 32, serial-to-parallel converter 34, and Fourier
transform unit 36), channel processor 38, and signal processor 40.
The front-end receiver elements generate a plurality of signal
samples corresponding to a plurality of frequencies from a signal
received via antenna 15. More particularly, amplifier 30 amplifies
an OFDM symbol received via antenna 15, and down converter 32 down
converts the amplified OFDM symbol to the complex digital baseband.
The down converter 32 may comprise any known down converter that
has means to select an operating frequency, means to filter the
received signal to select the signal bandwidth centered on the
selected operating frequency, and means to sample and
analog-to-digital convert the filtered signal to generate the
complex digital I, Q signals. For example, down converter 32 may
comprise a zero-IF or homodyne down converter, a low-IF down
converter, or a conventional superheterodyne down converter in
which the final IF signal is demodulated by mixing with cosine and
sine reference signal waveforms in a quadrature mixer arrangement.
Exemplary down converters include those described by U.S. Pat. No.
5,048,059 (reissued as U.S. Pat. No. RE37,138), U.S. Pat. Nos.
5,084,669, and 5,070,303.
[0038] As in the case of the transmitter 12, it is useful to
oversample the filtered signal in order to permit a relaxed
specification, for the signal selection filters. The digital I, Q
samples from the I, Q downconverter are then assembled into a block
by serial-to-parallel converter 34, which can for example comprise
a DSP memory. The block is then Fourier Transformed by Fourier
transform unit 36 which is the reverse or conjugate process to the
transmit Fourier transform unit 20. The output of Fourier transform
unit 36 comprises the same number of samples as in the input block,
which, with oversampling, is greater than n. Only n samples are
used however, and the rest, which correspond to out-of-band
spectral components not completely suppressed by the signal
selection filters, are discarded. The output samples {tilde over
(S)}1 to {tilde over (S)}n correspond to the samples input to the
transmitter 12, with the addition of transmission noise and any
distortion effects caused by the propagation channel. Channel
processor 38 processes samples {tilde over (S)}1 to {tilde over
(S)}n to determine the channel estimates. Signal processor 40 uses
the channel estimates to process (e.g., decode) samples {tilde over
(S)}1 to {tilde over (S)}n to recover the transmitted data symbols
S1 to Sn.
[0039] More particularly, channel processor 38 applies a
frequency-to-time transform to the pilot samples within samples
{tilde over (S)}1 to {tilde over (S)}n to determine a set of
non-equally spaced path delays and the corresponding complex delay
coefficients. It will be appreciated that the frequency-to-time
transform may be jointly applied to a matrix of pilot symbols
obtained from multiple OFDM symbol periods to determine a matrix of
complex delay coefficients, where a given row of the delay
coefficient matrix corresponds to a given OFDM symbol period, and
where a given column of the delay coefficient matrix corresponds to
a given path delay within the set of non-equally spaced path
delays. It will further be appreciated that the joint operation may
alternately be replaced with an individual operation, where the
frequency-to-time transform is individually applied to individual
sets of pilot samples from individual OFDM symbol periods. In this
case, different rows of the delay coefficient matrix are produced
by individual frequency-to-time transform operations applied to
signal samples from individual OFDM symbols, where different rows
of the matrix correspond to different OFDM symbol periods. The
complex delay coefficients in each column of the resulting matrix
generally correspond to a common path delay, plus or minus a small
path delay differential. It will be appreciated that while the
operation of jointly determining a common set of non-equally spaced
delays that apply over multiple different OFDM symbol periods
represents a preferred implementation, other implementations of the
invention may determine the delay values independently for each
OFDM symbol period.
[0040] Subsequently, channel processor 38 applies a
time-to-frequency transform to individual columns of the delay
coefficient matrix to determine a Doppler spectrum for each path
delay. The determination of a Doppler Spectrum from a column of
delay coefficients for a given path delay presumes that the path
delay is common to all the OFDM symbol periods of the column, and
thus is optimum when the receiver determines the path delays
jointly over multiple different OFDM symbol periods. However,
individual determination of the path delays could be used for each
OFDM symbol period, providing the delay coefficients in individual
columns of the resulting matrix are conformed to the same path
delay prior to Doppler analysis of the column of complex delay
coefficients. This conforming operation may be achieved by rotating
each delay coefficient in phase angle by W.sub.odT, where W.sub.o
represents the center frequency of the signal, and dT represents
the amount of delay change needed to conform the path delay for a
complex delay coefficient in a particular column to a common delay
for that column.
[0041] In any event, each Doppler spectrum comprises a set of
determined Doppler parameters, which each comprise a plurality of
non-equally spaced Doppler frequencies and their corresponding
complex scattering coefficients. Unlike the joint determination of
the path delays over different OFDM symbol periods, determining the
Doppler spectra is not a joint operation over different path
delays. Instead, the channel processor 38 determines the Doppler
spectrum individually for a given path delay, e.g., delay column.
Collecting different sets of Doppler parameters determined for
different ones of the non-equally spaced path delays into a matrix
produces a Doppler parameter matrix, where a given column of the
Doppler parameter matrix provides a set of Doppler parameters for a
given path delay from the set of non-equally spaced path delays,
and where each entry in the Doppler parameter matrix comprises at
least a Doppler frequency and an associated complex coefficient for
a particular path delay. Channel processor 38 uses the non-equally
spaced path delays and corresponding Doppler parameters to
characterize the channel, e.g., to determine the channel estimates
as described herein or according to any known means. Because the
path delays and Doppler parameters have significantly more accuracy
than those obtained from conventional approaches, the resulting
channel estimates are also significantly more accurate, as
discussed above.
[0042] The simplified receiver 14 of FIG. 7 was deliberately
illustrated in the same form as the simplified transmitter 12 of
FIG. 6 to explain how the transmitter 12 and receiver 14 processes
are essentially inverses of each other, with the result that n
complex samples (S1,S2, . . . ,Sn) input to the transmitter 12
appear at the receiver output, effectively establishing n parallel
channels of communication. These are normally employed to send
digital information, using a suitable modulation constellation to
map bit patterns to points in the complex I, Q plane. A practical
OFDM communication system comprises many more details than shown in
FIGS. 6 and 6, such as pulse shaping, cyclic prefixes, equalizers
and such, which, although not essential to an understanding of the
current invention, may be found in the following disclosures to the
current applicant filed in the United States: "Method and Apparatus
for Communicating with Root-Nyquist, Self-Transform Pulse Shapes"
(U.S. Patent Provisional Application Ser. No. 60/924673 filed 25
May 2007, and subsequent PCT Application Serial No. PCT/US08/64743
filed 23 May 2008), "Use of Pilot Code in OFDM and Other Non-CDMA
Systems" (U.S. patent application Ser. No. 12/255343 filed 21 Oct.
2008), and "Compensation of Diagonal ISI in OFDM Signals" (U.S.
patent application Ser. No. 12/045157 filed 10 Mar. 2008), all of
which are hereby incorporated by reference herein.
[0043] A detailed description of the improved method will be made
using an exemplary OFDM transmission scheme. In the following
description, reference will be made to different time periods and
intervals. A clarification of the different time periods involved
will therefore be given first, followed by the details associated
with the inventive transforms described herein.
[0044] A wideband signal is produced by modulating a carrier
frequency with a time-waveform that changes rapidly, in a short
period that may be termed a modulation interval, a chip period, or
the like. This is the shortest time period involved. An OFDM symbol
comprises a large number of such modulation intervals--at least as
many as there are subcarrier frequencies in the OFDM symbol. The
set of modulation samples, spaced in time by the modulation
interval, is computed by Inverse Fourier Transforming a set of
phases and amplitudes, one per subcarrier frequency. Data symbols
are encoded into the choice of each phase and amplitude by some
chosen modulation scheme, such as 256 QAM, so that every subcarrier
frequency carries a data symbol.
[0045] The total duration of the time-waveform output by the IFT is
equal to the reciprocal of the subcarrier frequency spacing, and is
called the OFDM symbol period. This may be extended by appending a
so-called cyclic prefix, but some OFDM systems, known as
Pulse-Shaped OFDM, do not need to extend the duration of the OFDM
symbol to accommodate a cyclic prefix. In effect, the cyclic
repeats of the OFDM symbol in pulse shaped OFDM symbols are
permitted to overlap adjacent symbols, and therefore do not add a
time-overhead. Therefore the potential use of a cyclic prefix is
ignored for the rest of the discussion. A number of OFDM symbols
may be collected together over a total analysis time interval, the
total analysis time interval therefore being an integral number of
OFDM symbol periods.
[0046] Reference will be made to various time domains and frequency
domains which are also clarified herein. The frequency domain of
the signal comprises the frequency span from the first to the last
OFDM subcarrier frequency used. The OFDM signal also exists as a
time waveform in the signal time domain, which is related to the
signal frequency domain by the Fourier Transform.
[0047] A second frequency domain arises when looking at variations
in signals arriving via scattered rays that are received from
different objects with different Doppler shifts, due to having
different relative velocities to the communicating station. If data
symbol modulation is removed, the signal on any subcarrier
frequency would still therefore be perceived to vary with time, and
therefore possess a spectrum of finite width. This Doppler spectrum
exists in the frequency domain also, but is very narrow even
compared to a single OFDM subcarrier frequency spacing. For
example, a typical subcarrier frequency spacing is 15 kHz, while a
typical Doppler spectrum is only 100-200 Hz wide. The signal time
variation that gives rise to the Doppler spectrum is from one OFDM
symbol period to the next, and a total analysis interval of many
OFDM symbol periods is required to resolve the Doppler
spectrum.
[0048] The value of the amplitude and phase of a given sub-carrier
frequency in a given OFDM symbol, ignoring data symbol modulation,
is the result of the sum of many scattered waves of different phase
and amplitude, and these may add constructively or destructively in
each sub-carrier frequency bin. If the resultant phase and
amplitude is plotted versus sub-carrier frequency, it will exhibit
a frequency variation which is the channel frequency response. If
the channel frequency response is inverse frequency transformed,
the channel impulse response will be obtained. The impulse response
indicates very approximately that the composite signal comprises
the sum of a number of relatively delayed rays, and is a plot of
phase and amplitude versus delay. This is therefore referred to as
the Delay Domain.
[0049] Orthogonal Frequency Division Multiplexing (OFDM) is one
method of reducing the complexity of equalizing methods needed to
communicate high data rates in a multi-path channel. Using the
transmitter 12 and receiver 14 described above, signals received
from an OFDM transmitter 12 are applied to the Fourier transform
unit 36 to produce a complex numerical value in each of the
plurality of subcarrier frequency bins for each OFDM block period.
For example, the receiver 14 may process data comprising a 1296
sub-carrier OFDM system having 15 kHz subcarrier frequency spacing,
each OFDM symbol period thus being approximately 66.7 .mu.s in
duration (the reciprocal of 15 kHz). The total occupied bandwidth
of such a signal is a little over 1296.times.15 kHz or 19.44 MHz,
and therefore, the symbol period is 1/19.44 MHz, or 51.44 ns. For
generating and analyzing such a signal, a 2048-point Fourier
transform unit 36 may be used, leaving a margin for filtering as
described above. In the above test system, every fourth subcarrier
frequency contained a known pilot symbol, meaning that the phase of
the pilot sub-carrier frequencies were set to values that were
pre-agreed between receiver 14 and transmitter 12. Thus, 324 pilot
symbols are transmitted per OFDM symbol interval of 66.7 .mu.s. The
pilot symbols are used to estimate the phase in adjacent channels
by interpolation in both the frequency and time domain. To collect
data from the test system, the complex value received for each
pilot subcarrier frequency was averaged over 8 successive OFDM
symbol periods to give one value per 8.times.66.7=533 .mu.s. This
is adequate sampling density for modest relative velocities between
the transmitter 12 and receiver 14. Thus, as a first step in
smoothing channel estimates, an average along the time domain of
samples corresponding to the same frequency in the frequency domain
was employed. This is typical of conventional channel estimation
methods, but not the preferred implementation according to this
invention.
[0050] If the 324 pilot symbols are extracted from the output of
the receiver Fourier transform unit 36 and the known phase
rotations of the pre-agreed pilot symbol pattern are removed, the
result is an estimate of the transmission channel phase and
attenuation at equally spaced points spaced 60 kHz apart along the
frequency domain. These may be inverse frequency transformed to
produce complex delay coefficients. In some CDMA and TDMA systems,
these complex delay coefficients may represent a first estimate of
the channel impulse response of the channel.
[0051] In some systems, the pilot symbols are equi-spaced in both a
first half of the subcarriers and in a second half of the
subcarriers, but the spacing between the first half and the second
half is non-commensurate. This can be handled by treating the first
half and second half symbols as two separate symbols with frequency
displacement between the pilots of one half and the pilots of the
other half. The method described herein can handle an arbitrary
frequency displacement between the pilots of one symbol, or part
symbol, and the pilots of another symbol, or part symbol, and still
process them jointly to uncover a common set of scatterer delays.
Moreover, when symbols that have already been decoded are included
in the calculation, it is possible that all of the OFDM subcarrier
frequencies can be used, and not just those bearing known pilot
symbols.
[0052] FIG. 8 shows typical values of the impulse response
magnitudes computed from field test data recorded while driving
through Stockholm, Sweden. Only the magnitudes of the value for
each delay bin are shown in FIG. 8, although the values are
actually complex. Once the channel impulse response is known, it
can be used to compute channel phases and amplitudes for the other
subcarrier frequencies lying in between the pilot channels. These
values are then used as channel phase references for the decoding
of data symbols carried in the data-modulated subcarrier
frequencies. As discussed above, noise or other impairments in
these phase references may hinder the use of higher order
modulations such as 256 QAM and/or the prediction of channel
estimates for future time intervals.
[0053] Complex delay coefficients from successive time intervals
may be stored to form a two dimensional array. Applying an
individual time-to-frequency transform to the set of delay
coefficients associated with individual delays results in a Doppler
spectrum for each delay. The different Doppler spectrums for
different delays may be collected into a new 2-D array called the
Doppler parameter matrix. Because signal components are now
separated by both delay and their relative velocities of the
receiver 14 (or transmitter 12) with respect to their scattering
objects 10, which is related to the bearing between the receiver 14
and the scattering object 10, the scattering objects 10 are now
separated in two spatial dimensions (distance and angle) with the
expectation that individual scattering objects 10 will now become
resolvable. This indeed appears to be so, as shown in the plot of
FIG. 9, which plots intensity of signal rays in the Doppler
parameter matrix from a short segment of field test data comprising
40, 324 subcarrier frequencies, 8-symbol, partially pre-smoothed
channel estimates collected over a period of 21.32 ms.
[0054] However, there exist a number of problems in using prior art
frequency-to-time or time-to-frequency domain transforms to carry
out the above. One problem is that conventional transform
operations rely on the assumption that path delays will fall into
equally-spaced time-bins, and likewise that Doppler frequencies
will fall into equally-spaced frequency bins. For example, a
fundamental assumption in Fourier analysis is that the entire
function being transformed is the sum of harmonics of a common
fundamental frequency, which means that the function is assumed to
be repetitive with a repetition period that is the reciprocal of
that common fundamental frequency. Consequently, attempts to use
Fourier analysis of a function over samples 1 to N, which includes
sample k, to predict the function for future sample N+k will merely
return the same value as sample k, which is practically
useless.
[0055] The algorithm known as Prony's algorithm implements a
time-to-frequency transform that may be used to generate the
Doppler parameter matrix without the assumption of equally spaced
path delays or Doppler frequencies. Prony's algorithm has been
traditionally applied to diverse fields such as Linear Predictive
Speech Coding, direction finding using antenna arrays, and spectral
analysis in Nuclear Magnetic Resonance Spectroscopy. A version in
finite field arithmetic, known as the Massey-Berlekamp algorithm,
is used for decoding Reed-Solomon error-correcting codes. The Prony
algorithm is basically a method of spectral analysis that does not
assume the spectrum falls into integrally-related frequency
bins.
[0056] Unlike other transforms, the Prony algorithm is specifically
formulated to spectrally analyze finite time segments of a signal,
and therefore, gives precise results. The Prony algorithm
decomposes the signal segment into a sum of exponentially decaying,
exponentially growing, or static sinusoids which are all described
by the expression:
Ce.sup.(.alpha.+j.omega.) (1)
where C is a complex coefficient indicative of phase and amplitude,
.alpha. is the exponential growth(+) or decay(-) rate factor, and
.omega. is the angular frequency. Prony expresses a signal S(t)
according to:
S ( t ) = k = 1 M C k ( a k + j.omega. k ) t . ( 2 )
##EQU00001##
When the signal waveform is recorded at equally spaced intervals of
time idt, Equation (2) becomes:
S i = k = 1 M C k ( a k + j.omega. k ) t . ( 3 ) ##EQU00002##
Letting Z.sub.k=e.sup.(.alpha..sup.k.sup.+j.omega..sup.k.sup.)dt,
Equation (3) becomes:
S i = k = 1 M C k Z k i . ( 4 ) ##EQU00003##
Many variations or improvements to Prony's algorithm have been
reported, and a good compendium of these techniques may be found in
Debasis Kundu's book "Computational Aspects in Statistical Signal
Processing", Chapter 14. A modification of Prony's algorithm by
Kundu and Mitra adapted to detect undamped sinusoids is reported in
the above reference.
[0057] The Ser. No. 12/478473 invention provides an inverse
modified Prony algorithm for one exemplary frequency-to-time
transform, where the inverse modified Prony algorithm is adapted to
accept an input comprising channel values taken at equally spaced
sample frequencies along the frequency domain, as in the OFDM test
system described above, and to produce an output of delay domain
parameters, comprising non-equally spaced delays and their
associated complex delay coefficients (phase and amplitude of a
delayed signal). The resulting non-equally spaced path delays are
not restricted to multiples of any particular time interval, e.g.,
a 51.44 ns signal sampling period.
[0058] The inverse modified Prony algorithm described herein is
different than that normally expressed by Equation (2) above.
Normally, if one had obtained frequencies Z.sub.k and their
associated amplitude/phase coefficients C.sub.k using Prony's
analysis method, then the inverse, namely determining the signal at
desired times t (other than the given times idt) would involve
substituting the determined frequencies and coefficients into
Equation (2). Equation (2) therefore represents the conventional
inverse of the Prony frequency analysis procedure.
[0059] Equation (2) may also be written in term of Z.sub.k as:
S ( t ) = k = 1 M C k Z k t . ( 5 ) ##EQU00004##
By contrast, the frequency-to-time transform described herein,
referred to herein as an inverse modified Prony Algorithm,
comprises an algorithm for determining the delays T.sub.i and their
associated complex delay coefficients S.sub.i,q in the
equation:
C q ( W ) = i - 1 M S i , q - j.omega. T i . ( 6 ) ##EQU00005##
Given the channel frequency response C.sub.k,q at instant q at N
equally spaced sample frequencies
.omega..sub.k=.omega..sub.o+(k-1).DELTA..omega., k=1, . . . , N,
Equation (6) becomes:
C k , q = i = 1 M S i , q - j ( .omega. o + ( k - 1 )
.DELTA..omega. ) T i , k = 1 , , N . ( 7 ) ##EQU00006##
Defining A.sub.i=S.sub.ie.sup.-j.omega..sup.o.sup.T.sup.i and
Z.sub.i=e.sup.-j.DELTA..omega.T.sup.i, Equation (7) becomes:
C k = i = 1 M A i Z i k - 1 , k = 1 , , N . ( 8 ) ##EQU00007##
Equation (8) does not yet represent the inverse modified Prony
Algorithm described herein, but it does represent the inverse of
the inverse modified Prony Algorithm. The inverse modified Prony
Algorithm is a method of solving (e.g., inverting) Equation (8) for
Z.sub.i and A.sub.i,q given C.sub.k,q, and using Equation (9) to
determine the path delays T.sub.i once Z.sub.i has been
determined.
T i = jlog ( Z i ) .DELTA..omega. ( 9 ) ##EQU00008##
Equation (9) provides purely real values for T.sub.i as long as
Z.sub.i is constrained to be purely imaginary. This means Z.sub.i
should lie on the unit circle (i.e., magnitude=1) so that its
logarithm will have a zero real part.
[0060] The above represents the time-frequency inverse of
constraining Prony's algorithm to find only undamped sinusoids
(e.g., all .alpha..sub.k=0 in Equation (2)). First, try adapting
Prony's method to solve Equation (8). This proceeds by letting
T.sub.i be the roots of a polynomial P(T) for i=1,. . . , M. The
coefficients of this polynomial (p.sub.0,p.sub.1,p.sub.2, . . . ,
p.sub.M) may be found by multiplying all factors
(T-T.sub.1)(T-T.sub.2) . . . (T-T.sub.M), given the T.sub.1.
Conversely, given the coefficients (p.sub.0,p.sub.1,p.sub.2, . . .
,p.sub.M), T.sub.i can be found by root-finding programs, which are
well developed, reliable, and fast.
[0061] Forming
p 0 C 1 q + p 1 C 2 q + p 2 C 3 q + p M C M + 1 q = k = 0 M p k C k
+ 1 q , ( 10 ) ##EQU00009##
and substituting C.sub.k,q from Equation (8) obtains:
k = 0 M p k i = 1 M A i q Z i k . ( 11 ) ##EQU00010##
By interchanging the order of summation, Equation (11) becomes:
i = 1 M A i q k = 0 M p k Z i k = i = 1 M A i q P ( z i ) . ( 12 )
##EQU00011##
However, by definition z.sub.i are the roots of P(z), and
therefore, all P(z.sub.i) equal zero. Thus,
p.sub.0C.sub.1,q+p.sub.1C.sub.2,q+p.sub.2C.sub.3,q . . .
+p.sub.MC.sub.M+1,q=0 represents one equation for the coefficients
of P. Since this is true for any M+1 successive values of
C.sub.k,q, other equations may be obtained to solve for the
coefficients, leading to:
[ C 1 C 2 C 3 C M + 1 C 2 C 3 C 4 C M + 2 C 3 C 4 C 5 C M + 3 C N -
M C N - M + 1 C N - M + 2 C N ] ( p 0 p 1 p 2 p M ) = 0. ( 13 )
##EQU00012##
For simplicity, the index q has been dropped from the C-values in
the matrix of Equation (13). It shall be understood, however, that
all of the C-values in the matrix belong to the same (q.sup.th)
symbol period. Because the polynomial gives the same roots if
scaled by an arbitrary factor, Prony proceeded to just let
p.sub.0=1 in Equation (13), moving it to the right hand side of the
equation, and then solving for the remaining p values.
[0062] In "Mathematical Notes, Note 59," titled "An Improved Prony
Algorithm for Exponential Analysis," Harold J. Price contends that
the above-described solution according to Prony is non-optimum. Due
to noise on the received signal, which corrupts the observed
C-values, Equation (13) will not be satisfied exactly but should
read:
[ C 1 C 2 C 3 C M + 1 C 2 C 3 C 4 C M + 2 C 3 C 4 C 5 C M + 3 C N -
M C N - M + 1 C N - M + 2 C N ] ( p 0 p 1 p 2 p M ) = . ( 14 )
##EQU00013##
Then the desired solution should minimize the length of the error
vector .epsilon.. Because it is the direction of the p vector, and
not the length, that determines the roots of the polynomial, the
search for the best p using Equation (14) should search only
direction space while keeping the length of p unchanged, e.g.,
setting |p|=1.
[0063] The error vector length squared is given by .epsilon.#
.epsilon.=p#[C]#[C]p. If p is normalized to unit length by dividing
by its own length {square root over (p# p)}, then
# = p # [ C ] # [ C ] p p # p . ( 15 ) ##EQU00014##
Differentiating the above with respect to p (e.g., calculating the
gradient with respect to p) and setting the gradient to zero
provides an equation that is satisfied at the maxima and minima of
the expression (p#p)2[C]#[C]p-(p#[C]#[C]p)2p=0, leading to:
[ C ] # [ C ] p = ( p # [ C ] # [ C ] p ) p # p p = .lamda. p ,
where .lamda. = ( p # [ C ] # [ C ] p ) p # p is a real scalar ( 16
) ##EQU00015##
Equation (16) represents the definition of an eigenvector of a
matrix, namely that the product of the matrix with a vector yields
that same vector with just a length scaling by .lamda.. Thus, the
maxima and minima of .epsilon.#.epsilon. occur when p is an
eigenvector of [C]#[C], and the associated eigenvalue is the value
of .epsilon.#.epsilon. at that point. The absolute minimum is thus
obtained by choosing p to be the eigenvector associated with the
smallest eigenvalue of [C]#[C].
[0064] Equations (13) and (14) can first be simplified by requiring
that all roots of P(z) have unit magnitude. This is physically
justified because the effect of a delayed ray adding to an
undelayed ray is to create a sinusoidal variation of the channel
frequency response along the frequency domain, and this sinusoidal
curve is of constant amplitude, i.e., undamped. In the
above-referenced book to Debasis Kundu, the polynomial P(z) is
shown to be a conjugate palindrome in the case where all roots
correspond to undamped sinusoids and lie on the unit circle. That
is, the polynomial has the form p.sub.M-i=p*.sub.i. To show this,
consider that a single factor can be written in the form
z-e.sup.-j.phi., or equivalently as
e.sup.j.phi./2z-e.sup.-j.phi./2=bz-b*=(b,b*). A single factor,
therefore, is evidently a conjugate palindrome. By the method of
induction, if a conjugate palindromic polynomial of order N is
still palindromic when extended to order N+1 through multiplication
by one extra factor, such as (b,b*), then the product of any number
of such factors yields a conjugate palindrome.
[0065] Exploiting the conjugate palindromic property of P(z) is
best achieved by writing out Equation (14) in terms of its real and
imaginary parts, respectively indicated by R and I, as:
[ [ CR 1 CR M / 2 - CI 1 - CI M / 2 CR N - M CR N - M / 2 + 1 - CI
N - M - CI N - M / 2 + 1 CI 1 CI M / 2 CR 1 CR M / 2 CI N - M CI N
- M / 2 + 1 CR N - M CR N - M / 2 + 1 ] + [ CR M + 1 CR M / 2 + 1
CI M + 1 CI M / 2 + 1 CR N CR N - M / 2 + 2 CI N CI N - M / 2 + 2
CI M + 1 CI M / 2 + 1 - CR M + 1 - CR M / 2 + 1 CI N CI N - M / 2 +
2 - CR N - CR N - M / 2 + 2 ] ] ( PR 0 PR M / 2 PI 0 PI M / 2 ) = .
( 17 ) ##EQU00016##
Equation (17) has the above form if M is even. When M is odd, there
is a slight modification due to the center coefficient of the
conjugate palindromic polynomial being real. Equation (17) has
twice as many equations in the same number of variables, as before,
but all quantities are real. Calling the matrix in Equation (17) Q,
and denoting by q the vector of p-values arranged as in Equation
(17), the error .epsilon. is now minimized when q is the
eigenvector of Q#Q associated with the smallest eigenvalue. Thus,
the inverse modified Prony Algorithm described herein reduces to
finding the eigenvectors of a real matrix, which, because of its
block skew-symmetry and the fact that the blocks have the Hankel
structure, may admit a more efficient solution than in the case of
a matrix with no structure. If desired, Equation (17) may be
rewritten by reverse-ordering PR.sub.0 . . . PR.sub.M/2 and
PI.sub.0 . . . PI.sub.M/2, which makes the four partitions of each
matrix Toeplitz instead of Hankel.
[0066] Once the eigenvector q is found, the conjugate palindromic
polynomial P(Z) can be constructed and its roots Z.sub.i found.
Then the delays T.sub.i are found using Equation (9). The
amplitude/phase coefficients A.sub.i in Equation (8) then have to
be found. Equation (8) can be written:
( C 1 C 2 C 3 C N ) = [ 1 1 1 1 Z 1 Z 2 Z 3 Z M Z 1 2 Z 2 2 Z 3 2 Z
M 2 Z 1 N - 1 Z 2 N - 1 Z 3 N - 1 Z M N - 1 ] ( A 1 A 2 A 3 A M ) ,
( 18 ) ##EQU00017##
which represents the equation for best-fitting a polynomial with M
coefficients A to a set of N+1 data points C. Denoting the matrix
in Equation (18) by Z ,the solution is given by:
A=[Z#Z].sup.-1 Z#C. (19)
Equation (19) is solved for each OFDM symbol period (or every few
symbol periods if the values C.sub.k were the average over a number
of successive symbol periods) to give the amplitude/phase
coefficients of signals with the determined delays for each symbol
period.
[0067] Because it is desired to further analyze the phase and
amplitude values for each path delay along successive time periods,
e.g., along successive OFDM symbol periods, we impose the
additional constraint that the inverse modified Prony Algorithm
shall produce the same path delay estimates for each time period,
at least for a total evaluation period over which the delays can be
assumed to change by negligible amounts. For example, a change in
delay of 5 ns may occur due to a movement of 5 feet by the
transmitter 12 or receiver 14, which movement would occur over the
relatively long time interval of 56.8 ms at 60 mph. Despite the
requirement that the determined path delays shall be the same over
the evaluation period, the inverse modified Prony algorithm still
allows the amplitudes and phases of the signal for each delay value
to be determined independently for each successive time interval
within the evaluation period. Therefore, we want to find P(z)
according to Equations (13), (14), and (17) by including all of the
pilot symbol amplitude/phase values C.sub.k for all OFDM symbols in
the evaluation period, the resulting path delays being those path
delays that best explain the signal in all of the OFDM symbols.
This is done by adding blocks vertically to the matrices of
Equations (13), (14), and (17) for each symbol period. Denoting the
matrix in Equation (17) by Q1 for symbol period 1, Q2 for symbol
period 2, etc., the solution q that we seek is the eigenvector
associated with the smallest eigenvalue of:
[ Q 1 Q 2 Q 3 QL ] # [ Q 1 Q 2 Q 3 QL ] = [ Q 1 # Q 2 # Q 3 # QL #
] [ Q 1 Q 2 Q 3 QL ] = [ Q 1 # Q 1 Q 2 # Q 2 Q 3 # Q 3 QL # QL ] ,
( 20 ) ##EQU00018##
which will then yield the delay values which best fit all L
successive symbol periods. Equation (19) may then be used with the
common Z-roots but with their individual C-values to determine the
amplitude/phase coefficients A separately for each symbol
period.
[0068] After determining delays T.sub.i for L successive OFDM
symbols, and their associated amplitude/phase coefficients
A.sub.i,q the values of the original amplitude/phase values
S.sub.i,q may be computed according to:
S.sub.i,q=A.sub.i,qe.sup.jW.sup.o.sup.T.sup.i (21)
for each OFDM symbol period q=1, . . . , L, obtaining the
two-dimensional delay/time array S.sub.i,q. By performing an
analysis of each delay along the time dimension q=1, . . . , L, the
Doppler parameters may be obtained. This is what is shown in FIG.
9. It is undesirable to constrain the Doppler frequencies to
discrete bins. Thus, an application of Prony's frequency analysis
procedure provides a preferred method of Doppler analysis. Further
modifications to both the inverse modified Prony Algorithm for
estimating the delay profile and the Prony Algorithm for estimating
the Doppler spectrum are possible. For example, the paper "Exact
Maximum Likelihood Parameters Estimation of Superimposed
Exponential Signals in Noise" (Bresler and Macovksi, IEEE
transactions on Acoustics and Signal Processing (1986), vol. 34, p
1081-1089, develops an algorithm called Iterative Quadratic Maximum
Likelihood Estimation (IQML). This is derived from the Prony
algorithm by noting that the determination of the polynomial P(z)
first by solving Equation (14) for the least square error
.epsilon.#.epsilon., followed by the determination of the optimum
coefficients A using Equation (19), does not guarantee that a
different choice of polynomial coefficients could not have produced
a lower residual least square error when using the solution of
Equation (19) in Equation (18). To rectify this, following Bresler
and Macovski, if the solution A from Equation (19) is used in
Equation (8), the least square error obtained is given by
C#[I-Z(Z#Z).sup.-1 Z#]C. Now, defining a band matrix G having size
N.times.(N-M) as:
G = [ p 0 0 0 0 0 p 1 p 0 0 0 0 p 2 p 1 p 0 0 0 p 3 p 2 p 1 p 0 0 p
3 p 2 p 1 p 0 P M p 3 p 2 p 1 0 P M p 3 p 2 0 P M p 3 P M 0 0 0 0 P
M ] ( 22 ) ##EQU00019##
it can be shown that [I-Z(Z#Z).sup.-1 Z#]=G(G#G).sup.-1 G#.
Furthermore, C#G may be replaced by g#[C]#, where [C] comprises an
(N-M).times.(M+1) matrix given by:
[ C ] = [ C 1 C 2 C 3 C M + 1 C 2 C 3 C 4 C M + 2 C 3 C 4 C 5 C M +
3 C N - M C N ] , ( 23 ) ##EQU00020##
which is the same matrix as in Equation (13), and where
g#=(p.sub.0,p.sub.1,p.sub.2, . . . ,p.sub.M). As a result,
C#[I-Z(Z#Z).sup.-1 Z#]C=g#[C]#(G#G).sup.-1[C]g. Minimizing this
expression means that g should be chosen to be the eigenvector
associated with the smallest eigenvalue of [C]#(G#G).sup.-1[C], as
opposed to [C]#[C] in the above-mentioned improvement to Prony's
algorithm proposed in the Howard J. Price reference.
[0069] Because G depends on g, the procedure is to find an initial
approximation for g using, for example, Prony's method or Price's
method, which is the equivalent to initializing G#G to I, and then
using that value of g to calculate G, followed by iteration. It is
also desirable to restrict P, and therefore, g, to being conjugate
palindromes, e.g.,
g=(p.sub.0,p.sub.1,p.sub.2, . . . p.sub.M/2,p*.sub.M/2, . . .
,p*.sub.2, p*.sub.1,p.sub.0), (24)
if M is even and
g=(p.sub.0,p.sub.1,p.sub.2, . . .
p.sub.(M-1)/2,p.sub.M/2p*.sub.(M-1)/2, . . .
,p*.sub.2,p*.sub.1,p*.sub.0), (25)
if M is odd, where the center coefficient p.sub.M/2 is real. Thus,
when M is odd, Equation (17) will have one more value of PR to find
than values of PI.
[0070] Once the matrix [C]#(G#G).sup.-1[C] is found, it is
partitioned as was the matrix [C] in Equation (17) in order to
solve for the real and imaginary parts of the palindromic
polynomial coefficients, and then iterated. Furthermore, it is
desired that the same delay profile should hold for an evaluation
period of L successive OFDM symbol periods, similar to Equation
(20). Namely, letting QL equal the matrix [C] obtained from symbol
period L, then the expression from Equation (20) should be used to
obtain the starting value of g as the eigenvector associated with
its smallest eigenvalue. Then g should be successively refined to
be the eigenvector associated with the smallest eigenvalue of:
q = 1 L Q q # ( G # G ) - 1 Q q . ( 26 ) ##EQU00021##
[0071] At each iteration, the above matrix should be partitioned as
was the matrix [C] in Equation (17) in order to solve for the real
and imaginary parts of the conjugate palindrome eigenvector g. Then
G is recalculated for the next iteration. This constitutes the
preferred version of the inverse modified Prony algorithm of the
Ser. No. 12/478473 invention, which is used to determine a delay
profile of non-equally spaced path delays consistent across an
evaluation period of L OFDM symbol periods.
[0072] FIG. 10 provides a process 100 for determining path delays
and Doppler parameters according to one exemplary embodiment of the
Ser. No. 12/478473 invention. Broadly, process 100 includes
applying a frequency-to-time transform to a plurality of received
signal samples corresponding to a plurality of frequencies (e.g.,
OFDM signal samples in an OFDM symbol) to determine a set of
non-equally spaced path delays and a set of associated complex
delay coefficients (block 110). Each of the non-equally spaced path
delays and its associated complex delay coefficient correspond to
one or more scattering objects of the wireless communication
channel. The complex delay coefficients and path delays are
determined for multiple OFDM symbols in an evaluation period to
provide a matrix of complex delay coefficients. The complex delay
coefficients in a given column of the matrix correspond to a given
path delay in the set of non-equally spaced path delays, and the
complex delay coefficients in a given row correspond to a given
OFDM symbol in the evaluation period.
[0073] Subsequently, process 100 applies a time-to-frequency
transform to the complex delay coefficients in a column of the
delay coefficient matrix to determine a set of Doppler parameters
for that path delay (block 150). The Doppler parameters comprise a
plurality of non-equally spaced Doppler frequencies and their
corresponding complex scattering coefficients, where each Doppler
frequency/complex scattering coefficient pair corresponds to a
scattering object. The sets of Doppler parameters are collected
into a matrix of Doppler parameters, where a given column of the
Doppler parameter matrix corresponds to a given path delay in the
set of non-equally spaced path delays.
[0074] FIGS. 11A and 11B show details for implementing the
frequency-to-time transform (block 110) and the time-to-frequency
transform (block 150), respectively, according to one exemplary
embodiment. In the embodiment of FIG. 11A, the frequency-to-time
transform comprises the inverse modified Prony algorithm discussed
above. In the embodiment of FIG. 11B, the time-to-frequency
transform comprises the Prony algorithm discussed above. It will be
appreciated, however, that the present invention is not limited to
the Prony algorithms discussed herein. Instead, any transforms that
determine the actual time and frequency data without restricting
the time and frequency data to equally spaced and predefined bins
may be used.
[0075] FIG. 11A shows the inverse modified Prony process 110 of the
Ser. No. 12/478473 invention. Before the process begins, the
channel processor 38 initializes a counter (block 112) to track the
OFDM symbols of the evaluation period. The channel processor 38
then increments the counter (block 114), receives OFDM symbol q
(block 116), and processes the OFDM symbol using Fourier analysis
to determine complex amplitude and phase coefficients C.sub.k,q for
the k=1, . . , N pilot symbols in the symbol period (block 118).
Channel processor 38 arranges the N C-values for symbol period q as
per the matrix of Equation (14) to obtain the matrix Q.sub.q (block
120). The channel processor then repeats the process of blocks
114-120 until q=L (block 122).
[0076] After Q.sub.q has been formed for the L OFDM symbols of the
evaluation period, the channel processor 38 forms the matrix
sum
q = 1 L Q q # Q q , ##EQU00022##
and partitions the result as in Equation (17) into the sum of
Toeplitz+Hankel matrices (block 124). Subsequently, the channel
processor 38 finds the initial values of the conjugate palindromic
polynomial coefficients g as the eigenvector of the Toeplitz+Hankel
matrix partitioning associated with the smallest eigenvalue (block
126), uses g to form the matrix G, and computes (G#G).sup.-1 (block
128). Channel processor 38 then forms the matrix sum
q = 1 L Q q # ( G # G ) - 1 Q q , ##EQU00023##
which represents cumulative noise whitened channel frequency
responses, and partitions the result as in Equation (17) (block
130). After finding improved values of the conjugate palindromic
polynomial coefficients g as the eigenvector of the partitioned
matrix formed for block 130 associated with the smallest eigenvalue
(block 132), the channel processor 38 repeats blocks 126-132 until
a converged value of g is obtained (block 134).
[0077] The iterative procedure described by blocks 126-134 has a
new, unique, and desirable property. Namely, this iterative
procedure determines a set of path delays, common to the L OFDM
symbol periods, that explain the L observed frequency responses
with minimum total least square error, given that the
amplitude/phase coefficients for each delay will be determined
separately for each OFDM symbol period. This is due to the fact
that g#Q.sub.1#(G#G).sup.-1 Q.sub.1g is the square error for OFDM
period q=1 when the path delays implied by g are used, after
choosing the optimum amplitude/phase coefficients for period q=1.
Likewise, g#Q.sub.2#(G#G).sup.-1 Q.sub.2g is the square error for
OFDM period q=2 when the path delays implied by g are used, after
choosing the optimum amplitude/phase coefficients for period q=2,
and so forth. Thus,
q = 1 L g # Q q # ( G # G ) - 1 Q q g ##EQU00024##
is the square error summed over all L symbol periods when the path
delays implied by g are used, given that the amplitude/phase
coefficients associated with each delay have been optimized
separately for each symbol period. Taking out g as a common factor
gives
g # [ q = 1 L Q q # ( G # G ) - 1 Q q ] g . ##EQU00025##
Hence finding g to be the eigenvector associated with the smallest
eigenvalue of the cumulative noise whitened channel frequency
responses, as described by blocks 130-134 gives the solution with
the desirable properties.
[0078] Returning back to the inverse modified Prony process 110,
the channel processor 38 finds the roots z.sub.k of the conjugate
palindromic polynomial P(z) whose coefficients are given by the
converged value of g from block 134 (block 136). The channel
processor 38 arranges the powers of the roots z.sub.k to form the
matrix [Z] of Equation (18), and hence computes [Y]=[Z#Z].sup.-1 Z
(block 138). Channel processor 38 uses the matrix [Y] computed for
block 138 to find N coefficients A.sub.i,q for symbol period q from
the corresponding coefficients C.sub.k,q obtained for block 118 for
symbol period q, using Equation (1 9) (block 140). Namely,
A.sub.i,q=[Y]C.sub.i,q, where ";" corresponds to the MATLAB
notation and indicates arranging C.sub.k,q values for all k=1, . .
. , N to form a vector of size N.times.1. Lastly, the channel
processor 38 converts the coefficient vector values A.sub.i,q into
corresponding complex delay coefficient values S.sub.i,q by using
Equation (21) (block 142). Note: if the pilot symbols are not in
the same sub-carrier frequency slots in each OFDM symbol period,
but are displaced in a way that can be accounted for by using a
different base frequency .omega..sub.o for each OFDM symbol, then
the different .omega..sub.o values for each of the q symbol periods
should be used for Equation (21) in this step.
[0079] Blocks 112-142 of FIG. 11A detail the inverse modified Prony
algorithm, which provides an improved method of finding path delays
and the associated complex delay coefficients that explain the
observed channel frequency responses for one or more OFDM symbol
periods. Further improvements are possible by performing a Doppler
frequency analysis of the complex delay coefficients for each path
delay over many symbol periods, using a second transform, namely a
time-to-frequency transform such as provided by Prony's
algorithm.
[0080] FIG. 11B proves details for the exemplary Prony process 150.
Broadly, the channel processor 38 applies the Prony algorithm to
the L complex delay coefficients S.sub.i,q corresponding to one
path delay. More particularly, channel processor 38 arranges the L,
S-values for path delay i into a matrix (block 152), as shown by
Equation (27).
[ S ] = [ S i 1 S i 2 S i m + 1 S i 2 S i 3 S i m + 2 S i L - m S i
L ] ( 27 ) ##EQU00026##
The channel processor 38 then finds the eigenvector h associated
with the smallest eigenvalue of [S]#[S] (block 154), constructs an
L.times.L matrix [H] by using h in place of g in Equation (22)
(block 156), and finds an improved version of h as the eigenvector
associated with the smallest eigenvalue of [S]#[H#H].sup.-1[S]
(block 158). The channel processor 38 repeats blocks 156-158 until
h converges (block 160). Subsequently, the channel processor 38
finds the roots w.sub.k for k=1, . . . , m of the polynomial with
coefficients of the converged h (block 162), and forms the
L.times.m matrix [W] by using the roots w.sub.k in place of z.sub.k
in Equation (18), and hence computes [X]=[W#W].sup.-1 W (block
164). Lastly, the channel processor 38 finds the m Doppler
coefficients D.sub.i=(d1,d2,d3, . . . ,dm)# for path delay i from
D.sub.i=[X]S.sub.i,;, where ";" means the values for the q=1, . . .
,L symbol periods are stacked vertically to form a 1.times.L vector
(block 166).
[0081] There are many mathematical devices available to reduce the
computational effort needed for performing the transforms of FIGS.
11A and 11B. For example, in block 158 the matrix [H#H] is
Hermitian-symmetric Toeplitz, having only 2(L-m)-1 distinct element
values, which represent the autocorrelation function of h* with h.
The autocorrelation may be rapidly calculated by padding out h with
zeros and using an FFT, according to known theory. Also, the
inversion of the Hermitian-symmetric Toeplitz matrix [H#H] can be
carried out in O(N.sup.2) operations using Trench's algorithm.
Furthermore, its inverse has to multiply another Toeplitz/Hankel
matrix S, whose rows are shifts of each other. This multiplication
may also be performed using fewer operations with the help of an
FFT, as is well known, and by using the Gohberg-Semencul form of
the inverse. The Fourier Transform of the Toeplitz generating
sequence for S may be saved and used again when the result is
pre-multiplied by S#.
[0082] At the conclusion of block 166, we have m Doppler parameters
for each of M path delays, forming a two-dimensional m.times.M
array, which is the Doppler-delay diagram of FIG. 9. Doppler-delay
diagrams have been obtained from cellular telephone signals before,
as reported in "Estimation of scatterer locations from urban array
channel measurements at 1800 MHz", Henrik Asplundh and Jan-Erik
Berg, conference proceedings of Radio Vetenskap och Kommunikation,
(RVK99), pp. 136-140, Karlskrona, Sweden June 1999. These diagrams
were obtained using more conventional transform operations. The
Delay-Doppler analysis using Prony frequency analysis and the
inverse modified Prony Algorithm described herein to compute a
delay profile common to several successive OFDM symbols, is
expected to yield superior results to those previously obtained.
Because of the increased accuracy, the path delays and Doppler
parameters obtained by the Ser. No. 12/478473 invention may be used
to determine channel estimates having the requisite accuracy to
process higher order modulation (e.g., 256 QAM) signals and/or to
accurately predict future channel estimates.
[0083] An objective of determining more accurate delay-Doppler
analysis is to enable more precise channel estimation for decoding
data. Having obtained the more accurate delay-Doppler profile, it
is now filtered by one or other methods to reduce or eliminate
noise. For example, elements corresponding to impossibly high
Doppler values can be set to zero. Likewise, impossible delays,
such as negative delays, may be eliminated, as may delays of
unlikely high values. Also, some number of spectral coefficients
may be selected based on predetermined criteria. For example, the N
largest spectral coefficients may be selected, or a threshold may
be used to select the spectral coefficients.
[0084] In still another embodiment, a Minimum Mean Square Error
(MMSE) procedure may be applied to the Doppler parameter matrix. A
simplified explanation of MMSE is as follows. A noise level in the
Delay-Doppler diagram can be estimated either by reprocessing
recently decoded data to determine the noise level on data symbols,
or by looking at the values eliminated on the grounds of impossible
or unlikely Doppler and delay. In the remaining values, it is not
known whether a value of the same order as the RMS value of the
estimated noise is a true scatterer or noise. Suppose the value is
d. Then using a value ad in place of d when using the delay-Doppler
profile to predict a received symbol value will create an expected
signal estimation error squared of (1-.alpha.).sup.2|d|.sup.2 times
the signal power S, while the noise power contribution will be
reduced to .alpha..sup.2 times the noise power N. The total error
is thus (1-.alpha.).sup.2|d|.sup.2 S.sup.2+.alpha..sup.2N.
Differentiating with respect to .alpha. and equating to zero yields
the value of .alpha. giving the least square error as:
.alpha. = d 2 d 2 + N / S , ( 28 ) ##EQU00027##
where N/S may be identified as the reciprocal of the
signal-to-noise ratio that would be present on a Doppler-delay
value of magnitude |d|=1. Thus, it may be concluded that the
Doppler delay values should be scaled down in dependence on their
signal to noise ratios and their amplitudes, such that smaller
values are reduced much more than larger values. This is a "softer"
method than just clipping out values below a threshold. Other
variations of the MMSE method may be used taking account of the
correlation matrices between error sources. When the delay-Doppler
coefficients scaled by MMSE are employed to re-compute the channel
estimate for any OFDM symbol period and subcarrier frequency,
substantial reduction of noise on the channel estimate will be
evident.
[0085] Having selected or weighted the Doppler-delay coefficients
as above, the value of a Delay coefficient at some desired time
instant (e.g., past, present or future) is computed by summing
terms comprising the Doppler-Delay coefficient rotated in phase by
the time difference between the reference time and the desired time
instant multiplied by the Doppler frequency. Then to find the
channel estimate for any OFDM subcarrier frequency, the sum is
computed of terms, each of which is the just-found Delay
coefficient for the desired time instant rotated in phase by the
product of the subcarrier frequency multiplied by the associated
path delay. When the desired time instant is a future instant, as
was mentioned before, the use of conventional transforms, i.e.,
Fourier Transforms, for prediction of a function returns the same
value as a past value of the function. This deficiency of the prior
art was due to the use of equally-spaced bins for either delays,
Doppler frequencies, or both. By using non-equally spaced bins,
functions are not assumed to be repetitive, and thus a future
prediction does not merely return a past value.
[0086] One application of the Ser. No. 12/478473 invention is thus
the reduction of noise on channel estimates to facilitate the use
of higher order modulations for increasing data rate. The invention
may also be used for other purposes, for example, to predict the
frequency response of the channel for some future symbol, or to
determine the location of a mobile transmitter by performing the
inventive analysis of the signal received from the mobile
transmitter at a network station to identify a pattern of
scattering objects 10, the pattern then being compared with a
previously stored data base of scattering object patterns using a
pattern recognition algorithm.
[0087] When considering the operation of algorithms such as the
above over an extended time period, various modes of operation may
be employed. For example, the above methods could be used on a
block-by-block basis, e.g., by processing a block of previous OFDM
symbol waveform samples jointly with the signal samples for the
current OFDM symbol to determine a set of scattering objects 10
pertinent to that block. However, if it is not desired to increase
latency in processing the current symbol, then each OFDM symbol
would need to be processed along with previous symbols, resulting
in previous symbol data being reprocessed multiple times. There is
at least one advantage of such a method, namely that older symbols
reprocessed with the current symbol waveform samples may now have
been error-correction decoded and thus data as well as pilot
symbols can be used to estimate the older symbols' frequency
responses. Including already-decoded data will also be considered
with the continuous tracking algorithms described below.
[0088] Improvements to processing efficiency are now sought for the
continuous case. Yet another variation of the above Prony
algorithms may be called "The Continuous Sequential Inverse Prony
Algorithm" (CSIPA). The characteristic of CSIPA is that it operates
for each OFDM symbol period without waiting for the collection of a
data block. It is analogous to the sequential least squares
solution first invented by Gauss, and to the continuous least
squares process known as a Kalman filter. The use of a Kalman
filter to continuously track scatterer parameters will be shown
later.
[0089] At least two versions of CSIPA can be envisaged: Moving
Window, and Exponential Forgetting. To obtain the CSIP algorithm
with exponential forgetting, rewrite Equation (26) to be an
infinite sum with exponential de-weighting of older values, as
shown in Equation (29).
.LAMBDA. L = q = - .infin. .infin. .lamda. ( L - q ) Q q # ( G # G
) - 1 Q q ( 29 ) ##EQU00028##
In the above, .lamda. is a factor less than unity which de-weights
older errors by a factor that reduces by .lamda. for each
successive symbol period further into the past. The current symbol
period (L) is not de-weighted, as the power of .lamda. is zero for
q=L.
[0090] The matrix G can also be assumed to change only marginally
from one symbol period to the next. This is justified because, in
the block formulation, G was assumed constant over the block, and
delays were assumed not to drift over the block. Which assumption
is more accurately representative of reality is therefore moot.
Moreover, traditional Prony analysis succeeds even with
(G#G).sup.-1 omitted. Thus, using for each symbol period the value
of G indexed with the index q is thus an improvement over the
traditional Prony method and close to optimum. We thus obtain:
.LAMBDA. L = q = - .infin. L .lamda. ( L - q ) Q q # ( G # G ) - 1
Q q , ( 30 ) ##EQU00029##
which immediately leads to:
.LAMBDA..sub.L=.lamda..LAMBDA..sub.L-1+Q#.sub.L(G#.sub.LG.sub.L).sup.-1
Q.sub.L. (31)
The CSIP algorithm over a moving window can be obtained similarly
by adding the contribution at one end of the block while
subtracting the oldest contribution from the other end,
obtaining:
.LAMBDA..sub.L=.LAMBDA..sub.L-1+Q#.sub.L(G#.sub.LG.sub.L).sup.-1
Q.sub.L-Q#.sub.L-m(G#.sub.L-mG.sub.L-m).sup.-1 Q.sub.L-m (32)
[0091] Now since we do not yet have g for period L, we do not have
G.sub.L. This can either be solved by commencing with the use of
G.sub.L-1 to obtain a first value of g.sub.L and then forming
G.sub.L therefrom and iterating, or else a better approximation to
an initial G.sub.L can be obtained in the following manner.
Assuming that each delay value comprises only one dominant
scatterer and therefore only one Doppler shift, note that the delay
of that scatterer for period L will be its delay determined for
period L-1 minus the distance moved in its direction during one
symbol period, divided by the speed of light. The distance moved in
units of wavelengths is simply the Doppler frequency times the
elapsed time, e.g.,
T i ( L ) = T i ( L - 1 ) - .DELTA..omega. i T .omega. o , ( 33 )
##EQU00030##
where T.sub.i(L) represents the delay of the i.sup.th scatterer for
OFDM symbol period L, T.sub.i(L-1) represents the delay of the
i.sup.th scatterer for OFDM symbol period L-1, T represents the
ODFM symbol period, .DELTA..omega..sub.i represents the Doppler
shift of the i.sup.th scatterer, and .omega..sub.o represents the
transmission frequency. Thus using the Doppler frequency determined
for a scatterer, its delay can be accurately updated for one period
ahead. Using the updated delays, the polynomial g.sub.L can then be
formed by multiplying first order factors corresponding to the
updated delays. This value of g.sub.L is used to,form G.sub.L to an
accuracy sufficient for Equation (31) to yield its smallest
eigenvalue/vector g.sub.L, which may be further iterated if
considered or determined to be beneficial.
[0092] If each delay value comprises for example two scattering
objects 10 of different Doppler shifts .DELTA..omega..sub.q1,
.DELTA..omega..sub.q2, each contributing a complex portion
D.sub.1,q1 and D.sub.1,q2 to the total delay coefficient
S.sub.i,L-1 for time period L-1, then their contributions for time
period L may be updated to
D.sub.1,q1e.sup.j.omega..sup.i,q1.sup..DELTA.T and
D.sub.1,q2e.sup.j.omega..sup.i,q2.sup..DELTA.T for period L,
.DELTA.T later. FIG. 12 shows how the resultant vector changes by
an amount .theta., which is computable by vector arithmetic, and
that angular change is then attributed to a change .DELTA.T.sub.i
of the time delay T.sub.i, where .DELTA.T.sub.i=.theta./.omega.,
.omega. being the center frequency.
[0093] Effectively, when a delayed ray is due to the combination of
several different scattering objects 10 of different Doppler, the
above method gives a method of defining the mean delay change, at
least so long as the delays of the scattering objects 10 do not
diverge so far as to become considered different delays. The latter
may be detected by maintaining the updated delays of individual
scattering objects 10 by means of Equation (33) and determining
whether the updated delay of any scatterer of one group has become
closer to the delays of scattering objects 10 in a second group, at
which point its contribution may be removed from the first group
and added to the second group using similar vector combination
procedures.
[0094] Note that past history has been taken into account twice in
the above procedure. Firstly, the previously determined delays were
updated using their associated Doppler shifts. Then corrected
values for the delays were obtained via determining g.sub.L by a
procedure in which exponentially de-weighted past history was taken
into account again. One or other means of using historical values
seems to be redundant in the above procedure. From a numerical
perspective, it is of greater interest to eliminate the more
complex matrix procedure of computing Equation (31), than to
eliminate the trivial procedure of updating previous delays using
the Doppler shift, which is also likely to be more accurate, since
it is wavelength related.
[0095] An alternative procedure is therefore to regard the modified
inverse Prony process as merely providing a long term correction or
"nudge" of the delays towards their correct positions, while the
short term corrections to the delays are provided by integrating
their Doppler shifts. This is analogous to a navigation system in
which short term position changes are calculated by dead-reckoning
using velocity times time, while eliminating drift error from that
open-loop process by means of an occasional absolute position fix.
Thus in principle, a per-symbol-period modified inverse Prony
algorithm may be used to estimate delays (or g-coefficients), and
g-coefficients estimated using previous values updated by Doppler
are then moved towards the Prony values.
[0096] A limitation of per-symbol period inverse modified Prony is
that the number of estimated path delays cannot exceed half the
number of subcarriers in the OFDM symbol (e.g., about 160 for the
324-subcarrier test system). Thus, a hybrid method of using past
history may be to perform CSIPA over a moving rectangular window,
using the results as a means of drift-correcting values obtained
just before the window that have been updated using integrated
Doppler. If delays are updated using integrated Doppler, this takes
the place of updating Doppler based on the symbol-to-symbol
variation of phase, and an additional means of estimating Doppler
from symbol-period to symbol period would then be required. This is
best described in the context of using an integrated Doppler
approach in the form of a Kalman process to track delays and their
derivatives, which may be formally equated with Doppler shifts.
[0097] A Kalman tracking process may be constructed by assuming
that the channel at frequency .omega. is explained by a sum of
scattered waves from individual scattering objects 10 of strength
S.sub.i,q at time qT. Each scattered wave is delayed in phase by
propagating through a delay T.sub.i which is assumed to change
linearly with time due to the mobile station's resolved velocity in
its direction, leading to the formula for delay at time qT as:
T.sub.i,q=T.sub.i,q-1+T.sub.i,q.DELTA.T, (34)
where .DELTA.T is the (OFDM) symbol period. Thus,
C q ( .omega. ) = i S i , q - j.omega. ( T i o + qT i ' .DELTA. T )
, ( 35 ) ##EQU00031##
where the index "i" ranges over all scattering objects 10. Since
phase is now explained by delay, and Doppler, which is rate of
change of phase, is explained by rate of change of delay, there
seems no longer any need for the scatterer parameters S.sub.i,q to
be complex, and it would seem to be reducible to a real signal
strength factor. A reason for retaining complex scatter parameter
values however is that the mobile station antenna pattern can be
quite distorted, and have a varying phase dependent on the
direction of the sightline to the scatterer. Ascribing that phase
to slightly different scatterer positions, on the order of
millimeters different, is a small inaccuracy, but is avoided by
retaining complex scatterer parameters.
[0098] A Kalman tracking filter seeks to successively refine
estimates of the scatterer parameters based on a channel frequency
response vector C(.omega.) of channel frequency response
observations at different frequencies at the current time q. An
exemplary integrated Doppler process 200 corresponding to the
operations of a Kalman tracking filter is shown in FIG. 13. The
channel processor 38 predicts the scatterer parameters and
corresponding channel frequency responses for the new symbol period
associated with time q (block 210). For example, the channel
processor 38 predicts the scatterer parameters by predicting the
values of S.sub.i,q and T*.sub.i,q, which can collectively be
denoted by a vector U, from the values of U at time q-1. This may
be done simply by assuming S.sub.i,q=S.sub.i,q-1,
T*.sub.i,q=T*.sub.i,q-1, and
T.sub.i,q=T.sub.i,q-1+T*.sub.i,q-1.DELTA.T. It is usually possible
to choose a scaling convention for T*.sub.i,q such that the factor
.DELTA.T is included, obviating the need for a multiply.
Subsequently, the channel processor 38 predicts the next channel
frequency response vector C(.omega.) for time q using the
predictions for S.sub.i,q and T.sub.i,q. Channel processor 38 then
calculates an observed channel frequency response vector C(.omega.)
based on the OFDM symbol received at time q (block 220), and
computes an error vector .epsilon. between the predicted C(.omega.)
and the observed C(.omega.) (block 230). The channel processor 38
subsequently corrects the scatterer parameter prediction (block
240) in such a way as to reduce the error vector .epsilon..
[0099] The scatterer parameter prediction of block 210 may be
written in matrix form as:
( S 1 q T 1 q T 1 q ' S 2 q T 2 q T 2 q ' S m q T m q T m q ' ) = [
1 0 0 0 0 0 0 0 0 0 1 .DELTA. T 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 1 .DELTA. T 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 1 .DELTA. T 0 0 0 0 0 0 0 0 1 ] ( S 1 q - 1 T 1
q - 1 T 1 q - 1 ' S 2 q - 1 T 2 q - 1 T 2 q - 1 ' S m q - 1 T m q -
1 T m q - 1 ' ) . ( 36 ) ##EQU00032##
The matrix in Equation (36) is often denoted by .PHI.. In block
240, correction of the predictions made in block 210 comprises the
use of the inverse of the covariance matrix, commonly denoted by P.
Since P is also initially unknown, it is also predicted and
corrected based on receipt of new observations.
[0100] Different means may be used to predict P. For example, P may
be predicted using:
P.sub.q=.PHI.P.sub.q-1.PHI.#+Q, (37)
which is appropriate where the parameters S, T, and T* may be
subject to random wandering and Q describes their propensity to do
so. Alternatively, P may be predicted using:
P.sub.q=.lamda..sup.-1.PHI.P.sub.q-1.PHI.#, (38)
which is appropriate for exponential de-weighting of past history,
where .lamda.<1 represents an exponential forgetting factor. In
still another example, P may be predicted using:
P.sub.q=.PHI.P.sub.q-1.PHI.#, (39)
which is appropriate in the case of "least squares forever," where
all past history is used and no de-weighting is desired.
[0101] The correction implemented in block 240 uses derivatives
(e.g., the GRADient) of the observation channel frequency response
vector with respect to the vector of parameters S and T, which is
obtained from Equation (35) and using
T.sub.i,q=T.sub.i,o+q.DELTA.T*.sub.i as:
C ( .omega. ) S i q = - j.omega. T i q and C ( .omega. ) T i q = -
j.omega. S i q - j.omega. T i q , ( 40 ) ##EQU00033##
and the derivative with respect to T* is zero. Hence,
GRAD ( C ( .omega. ) ) = ( - j.omega. T 1 q - j.omega. S 1 q -
j.omega. T 1 q 0 - j.omega. T 2 q - j.omega. S 2 q - j.omega. T 2 q
0 - j.omega. T m q - j.omega. S m q - j.omega. T m q 0 ) . ( 41 )
##EQU00034##
When the GRADient vectors for each .omega. for which C(.omega.)
will be observed are stacked side by side, the result is a 3
m.times.N matrix where N represents the number of scattering
objects 10 and m represents the number of frequencies at which C is
observed. When, as above, the GRADient is not constant but is a
function of the parameters (S and T), the process is known as a
"linearized" or "extended" Kalman filter process.
[0102] The correction implemented in block 240 comprises updating
the vector of parameters denoted by U using:
U.ltoreq.U-PGRAD[R+GRAD#PGRAD].sup.-1 .epsilon., and (42)
P.ltoreq.P-PGRAD[R+GRAD#PGRAD].sup.-1 GRAD#P. (43)
In the above update step, it is usually possible to choose the
scaling of the Q-matrix, which represents the tendency of the
tracked parameters to exhibit a random walk, such that the matrix
R, which represents covariance of noise on the observation vector,
is the unit vector I.
[0103] Another variation of the extended Kalman filter may be
derived by defining the error between predicted and observed
C(.omega.) vectors to be the scalar .epsilon.#.epsilon.. The new
gradient vector would then be 2.epsilon.#GRAD(C(.omega.)). The
benefit of this formulation is that the matrix inverse
[R+GRAD#PGRAD].sup.-1 is avoided, being replaced by division by a
scalar 1+.epsilon.GRAD#PGRAD.epsilon..
[0104] The above extended Kalman filter can be used to track the
scatterer parameters, e.g., delay, Doppler (rate of change of
delay), and signal strength of already identified scattering
objects 10, and functions even when the updated delays of different
scattering objects 10 move through one another in value.
Eventually, a tracked scatterer may become distant and weak, while
a previously untracked scatterer gets nearer and stronger. Thus, a
procedure intended to operate for long periods of time, e.g., for
minutes or hours, should include ways to discard scattering objects
10 that have become insignificant and to detect the appearance of
and then track new scattering objects 10.
[0105] In one exemplary embodiment, the channel estimator 38 may
track known scattering objects 10 using the extended Kalman filter
described above, subtract out their contributions to the received
signal to leave a residual which would be expected to comprise
noise and untracked scattering objects 10, and process the residual
using the Prony-based algorithms of FIGS. 11A and 11B to identify
new scattering objects 10. Periodically, any scattering objects 10
identified by the Prony algorithm would be compared in strength to
those being tracked by the Kalman algorithm. The channel estimator
38 replaces a weak, Kalman-tracked scatterer with a Prony-detected
scatterer in the event of the latter becoming stronger.
[0106] The addition or deletion of a tracked scatterer from the
Kalman algorithm occurs through deletion or addition of appropriate
rows and columns of the P, Q, and .PHI. matrices. For example, if
128 scattering objects 10 are being tracked, and it is desired to
discard scattering object number 79, then rows and columns numbered
3.times.78+1, 3.times.78+2, and 3.times.78+3 are deleted from the
P, Q, and .PHI. matrices. Conversely, if 127 scattering objects 10
are being tracked and it is desired to add a 128.sup.th, then rows
and columns 1, 2, and 3 of the Q and .PHI. matrices are copied to
rows and columns 3.times.128+1, 3.times.128+2 and 3.times.128+3,
extending the dimensions by 3. The P-matrix is also extended by
three rows and columns from 3.times.127 to 3.times.128 square. The
additional rows and columns are initialized to zero everywhere
except on the main diagonal. The main diagonal is initialized to
values inversely indicative of the confidence in the initial values
of the parameters S, T, and T* of the 128.sup.th scattering object
10. If the values are obtained from Prony analysis of the residual
signal mentioned above, and are considered reasonably accurate, the
three new diagonal P-elements may be initialized to zero, or to the
mean of corresponding P-matrix elements for scattering objects
1-127. It may be appropriate to use the block formulation of the
Prony procedures, such that the above-defined signal residuals are
collected over a number of OFDM symbol periods and processed en
block to detect the appearance of new scattering objects 10. The
time over which new scattering objects 10 are expected to appear or
disappear is of the order of the time required for the mobile
station to move a few meters, which, at 70 mph, would be on the
order of 100 ms. Furthermore, in that period of time, older OFDM
symbols may have been error-correction decoded, making observations
of C(.omega.) available not only at the subcarrier frequencies of
pilot symbols, but also at the data symbol frequencies. It may in
fact be intelligent to deliberately collect signal residuals over a
block period that is aligned with one or more error-correction code
blocks, such as a turbo-code block, such that the block Prony
procedure is performed using observations of the channel at both
pilot and data subcarrier frequencies. Any new scattering objects
10 thereby identified are compared with scattering objects 10 being
tracked by the extended Kalman filter, and transferred from the
Prony results to the Kalman tracking procedure by addition of new
scatterer parameters, with or without deletion of scatterer
parameters corresponding to scattering objects 10 that have become
weak.
[0107] The following shows a procedure for processing a signal
received continuously based on a collection of the algorithms
disclosed above. [0108] a) A power-up synchronization phase occurs,
in which the receiving station would receive signals from the
transmitting station and determine symbol and block boundaries with
the aid of pilot symbols and other pre-agreed clues that may be
inserted into the transmitted stream. [0109] (b) An initial channel
identification phase occurs, in which channel frequency responses
(e.g., complex values C(.omega.) at one or more sets of equally
spaced frequencies .omega.=.omega..sub.o+k.DELTA..omega.) are be
determined with the aid of pilot symbols. [0110] (c) Individual
scattering objects 10 are resolved using specially adapted versions
of the Prony method for both delay and Doppler resolution, as
described herein and claimed in the Ser. No. 12/478473 application.
[0111] (d) Scatterer parameters are extracted from the Prony
algorithms of step (c) for tracking by an extended Kalman filter
adapted to track delay, rate of change of delay and scatterer
signal amplitude, which may be real or complex. [0112] (e) Using
the tracked scatterer parameters, improved estimates of the channel
complex frequency response are provided for the purposes of
demodulating data symbols. [0113] (f) Data symbols are collected
over error-correction code blocks and error-correction decoding is
performed. [0114] (g) Using correctly decoded data symbols and
known pilot symbols in combination with said estimates of the
channel complex frequency response, the likely received signal is
reconstructed and subtracted from the actual received signal to
obtain a residual signal. [0115] (h) The residual signal is
collected over one or more error-correction coding block periods
and reprocessed using same Prony procedure as in step (c) to
identify scattering objects 10 other than those being tracked in
step (d). [0116] (i) The strengths of the scattering objects 10
identified in step (h) are compared with the strengths of the
scattering objects being tracked in step (d). The channel processor
40 transfers the parameters of any scattering objects 10 identified
in step (h) that are stronger than the weakest scattering objects
10 being tracked in step (d) to the Kalman tracking procedure. To
maintain the same number of scatterer parameters, scatterer
parameters due to the weakest scattering objects 10 may be deleted.
Note that the procedure of steps (a)-(i) be preformed using signals
other than OFDM signals if they are suitably constructed. For
example, a CDMA signal using superimposed pilot codes to permit
channel estimation may be processed in the above manner. In the
above description, a number of algorithms have been disclosed which
may be used in various combinations together with other algorithms
previously disclosed or already known in the art, in order better
to decode data transmitted between a mobile station and a network
station. The direction of data transmission is immaterial, the
method being suitable for improved decoding of signals transmitted
by a mobile station and received by a fixed network station, or
vice versa.
[0117] In the above, improved methods have been described for
resolving a multi-path signal received at a receiver into a sum of
scattered waves of different relative delays and strengths. Doppler
shift of each scattered wave caused by motion of either the
transmitter of the receiver relative to the scattering objects 10
was furthermore determined either as a frequency shift, or more
precisely, as a rate-of-change of delay. Expressing Doppler shift
as a rate-of-change of delay is sometimes preferable, as it is a
description that is independent of the actual frequency, whereas a
Doppler frequency shift caused by a given relative motion is
proportional to the frequency on which it is measured. When the
frequency response of a channel is measured and then resolved into
delays as described above, each delay is in fact a measure of the
rate of change of a phase shift of a scattered signal across the
frequency band, that is:
delay = .PHI. .omega. . ( 44 ) ##EQU00035##
[0118] FIG. 14 illustrates a number of phase slopes as determined
across a first frequency band and extrapolated to a second
frequency band. The upper line corresponds to a path when an excess
delay over line-of-sight equal to 3 .mu.s (an excess path length of
900 m), which causes an additional phase shift of
3.times.2000.times.2 .pi. at a frequency of 2000 MHz (the lower
edge of the first frequency band) increasing to
3.times.2010.times.2 .pi. at 2010 MHz (the upper edge of the first
frequency band). By receiving a signal having frequency components
more or less evenly spread over the 10 MHz bandwidth of the first
frequency band, resolving the signal into a sum of scattered waves
according to the teachings of the Ser. Nos. 12/478473 and 12/478520
applications repeated herein above, and determining the phase shift
at multiple frequencies across the band of the scatterer
responsible for the upper line, the line can be determined by
best-fitting a straight line to the determined phase shifts, which
are marked as x.
[0119] The lower line corresponds to an excess path delay of 0.15
.mu.s (an excess path length of 45 m), or 0.15.times.2000.times.2
.pi. in excess phase shift at 2000 MHz. Using the same procedure, a
best-fit straight line to the phase shift versus frequency
determined for that scattered wave is obtained. Both the upper and
lower lines are then extrapolated to the second frequency band,
which may for example be 2100 MHz to 2110 MHz. Due to the 10:1
extension of the line, any error in matching the phase/frequency
points within the 10 MHz first frequency band will be multiplied by
10 upon reaching the second frequency band. Thus, if an accuracy of
say .+-.10.degree. is required at the second frequency band, an
accuracy of .+-.1.degree. must be achieved in the first frequency
band. This can also be expressed as a slope error of 0.1.degree.
per MHz, which translates to a delay error of 0.28 ns. Given that
the accuracy of the best-fit straight line is presumably accurate
enough for channel estimation over the first frequency band, the
accuracy requirement for extrapolating to the second frequency can
also be expressed as needing an order of magnitude improvement.
[0120] Hitherto, the achievement of such accuracy was considered
beyond the capability of the art. However, the Ser. Nos. 12/478473
and 12/478520 applications provide several improvements to the art
which each allow significant advance in delay determination.
Firstly, the disclosure of a modified Inverse Prony Algorithm in
the Ser. No. 12/478473 application, estimates the best set of
delays that explain a frequency response given at equally spaced
frequencies across the first frequency band, and the use of a Joint
Inverse Prony Algorithm determines the best set of delays that
jointly explain a plurality of frequency responses measured for the
first frequency band at successive instants at which the delays are
expected to be constant. Further, the use of an extended Kalman
algorithm to track delays and their time derivatives over a series
of successive instants over which the delays are expected to be
constant apart from a systematic Doppler drift due to motion of the
transmitter or receiver, is described in the Ser. No. 12/478520
application. Together, these improvements are expected to achieve
the desired order of magnitude improvement in scattered wave
parameter estimation over the first frequency band to allow
extrapolation to the second frequency band.
[0121] If a single transmitter having a single antenna is able to
predict the propagation channel frequency response to a receiver
before transmitting, it may be able to optimize its transmission to
provide improved communications. In general, the receiver would
need to know what it did in order to take advantage of the
improvement, but it is possible that such information could be
included in the transmission as an overhead or deduced by the
receiver, for example by attempting decoding in a plurality of ways
corresponding to the different ways the transmitter may have
adapted to its foreknowledge of the frequency response. For
example, one simple adaptation would be for the transmitter to
choose a higher order modulation constellation for OFDM sub-carrier
frequencies located on transmission peaks and a lower order
modulation constellation, or else placing no data, on sub-carrier
frequencies corresponding to troughs in the frequency response.
Such adaptation in its optimum form is sometimes known as
"Waterfilling". Since the receiver can determine the actual
downlink channel upon receipt of the signal, it can surmise
therefrom what the transmitter may likely have done and decode
accordingly. In borderline cases, there may be some uncertainty for
some sub-carrier frequencies requiring the receiver to attempt
decoding in a plurality of ways. The number of different decodings
may be limited by reducing the number of combinations that the
transmitter can select. For example, in the limit, the transmitter
can be restricted to selecting either high order modulation or low
order modulation for all sub-carrier frequencies, but less
restrictive choices can also be devised, with the aim of reducing
the number of decodings the receiver shall attempt.
[0122] If multiple, independent transmitters can each determine the
frequency response of the channel to a receiver before
transmitting, there are ways to optimize their joint transmission
of information to one or more receivers without needing to
communicate to the receivers what they did. Such systems are
described in the above incorporated U.S. Pat. No. 6,996,380.
[0123] If also, at one transmitter site, multiple antennas are
available in the form of a closely spaced array or widely spaced
array or a hybrid of close and wide spacing, other advantageous
possibilities arise. In particular, the scattering parameter
estimation is now extended to encompass multi-antenna scatterer
estimation, which adds a third dimension to the Doppler and delay
dimensions. A first case of multi-antenna scattering parameter
estimation arises with close element spacing such that the array
does not generate significant grating lobes. In that case, the
different path delays to different antenna elements may be treated
as identical path delays but with a different per-element phase
shift, without ambiguity. Joint estimation over antennas is done in
the same way as joint estimation over multiple OFDM symbol periods,
namely, by summing matrices related to each and finding the
smallest eigenvalue/vector of the sum. In this way a joint
estimation of delays may be done over all antenna elements and over
multiple symbol periods. Having obtained scatterer delays by joint
estimation as above, the associated complex coefficients are
determined for each symbol period and antenna element. The Doppler
spectrum for each path delay is then determined by joint estimation
over the antenna elements, which are assumed to be of identical
directivity. Antennas of identical directivity should be receiving
each scattering object wave at equal strength and thus the
expectation is that the Doppler spectrum will be the same for
each.
[0124] When the Doppler spectrum is obtained for each path delay,
the set of complex coefficients for different antenna elements but
the same Doppler/delay combination is submitted to another
Prony-type analysis to partition scattered waves by
direction-of-arrival (d.o.a). Only two possible d.o.a.'s are
anticipated for each Doppler/delay combination, therefore the
polynomials found by Prony analysis will simply be quadratics.
After the just-described 3-dimensional Prony analysis in the
dimensions of path delay, Doppler, and d.o.a., a three-dimensional
array of complex values is obtained. Negligible or unlikely values
in the three-dimensional array can then be eliminated and the
values down-selected to those values corresponding to physically
likely scattering objects. After translating the retained values
from the reception to the transmission frequency, the values can be
used by the transmitter to optimize its transmission to the same
station from which it just received.
[0125] FIG. 15 shows one exemplary procedure 250 for translating
the retained values from the reception frequency to the
transmission frequency for a multiple antenna element device. The
transmitter rotates the phase of each value though an angle equal
to its associated delay (the phase/frequency slope) times the
frequency difference between the reception and transmission
frequencies (block 252). The transmitter further rotates the phase
of each value though an additional angle equal to the associated
Doppler frequency times the time difference between the reception
time and the future transmission time, times the ratio of the
transmission frequency to the reception frequency (block 254). The
transmitter then calculates the phase progression required across
the antenna elements to obtain the same transmission direction as
the reception direction for each scattering object 10, based on the
transmission and reception frequencies (block 256).
[0126] As an alternative to the procedure 250 of FIG. 15, the
following procedure 260, shown in FIG. 16 can be used. The
transmitter interprets Doppler as rate-of-change of delay, then the
delay for each scattering object 10 is updated for the new time
period by adding or subtracting an amount proportional to the
Doppler, thus obtaining a new phase slope (block 262). The
transmitter uses the updated phase slopes from block 262 to
extrapolate the phase from the reception frequencies to the
transmission frequencies by adding to the reception phase shifts
the product of the updated phase slope and frequency difference
(block 264). The transmitter then calculates the phase progression
required across the antenna elements to obtain the same
transmission direction as the reception direction for each
scattering object 10, based on the transmission and reception
frequencies (block 266).
[0127] In block 262, altering the phase slope implies pivoting a
straight line of phase vs. frequency about some point. This point
should be the same for all scattering objects 10, and is logically
the zero phase, zero frequency point. It is therefore desired to
shift all phase/frequency lines so that they pass through the
origin. This is accomplished by projecting the phase/frequency line
to zero frequency to obtain the intercept, which should not be
reduced modulo 2.pi., and then subtracting that intercept phase
from the equation of the line. The resulting modified
phase/frequency line then represents absolute phase vs. frequency.
Because the modified phase/frequency line now passes through the
origin, it has the form .phi.(.omega.)=.omega.T(i), where T(i)
represents the delay of the i.sup.th scattering object 10 and
.omega. represents the frequency. The phase of the scattering
coefficient A(i) is then altered by the amount of the intercept,
reduced modulo 2.pi., to compensate.
[0128] The delay T(i) may now be updated to T(i)+dT(i) for the new
period, where dT(i) is determined from velocity multiplied by time
divided by the speed of light, and where the velocity is given by
the Doppler shift for the i.sup.th scattering object 10. Using the
Doppler-updated delay and the transmission frequency for .omega.
yields the expected phase for that scattered wave at any given
transmission frequency, and the phase factor e.sup.j.phi. is then
combined with the scattering coefficient A(i) to give the scattered
wave complex amplitude expected at any transmission frequency
.omega..
[0129] When prediction of the transmission channel is made
available to the transmitter by the above methods before
transmission, and most particularly for multiple transmit antennas,
the transmitter may perform more advantageous coding or weighting
of the signals transmitted by each antenna in order to optimize
reception at the receiver, including steps which result in
cancellation of interference at unintended receivers, MISO and MIMO
systems or beamforming.
[0130] The present invention may, of course, be carried out in
other ways than those specifically set forth herein without
departing from essential characteristics of the invention. The
present embodiments are to be considered in all respects as
illustrative and not restrictive, and all changes coming within the
meaning and equivalency range of the appended claims are intended
to be embraced therein.
* * * * *