U.S. patent application number 13/558906 was filed with the patent office on 2012-11-29 for adaptive channel prediction system and method.
This patent application is currently assigned to UNIVERSITY OF WATERLOO. Invention is credited to Abdorreza HEIDARI, Amir K. KHANDANI, Derek MCAVOY.
Application Number | 20120300659 13/558906 |
Document ID | / |
Family ID | 39537601 |
Filed Date | 2012-11-29 |
United States Patent
Application |
20120300659 |
Kind Code |
A1 |
HEIDARI; Abdorreza ; et
al. |
November 29, 2012 |
ADAPTIVE CHANNEL PREDICTION SYSTEM AND METHOD
Abstract
A method and system for predicting channel fading, particularly
in a mobile wireless environment, that is accurate for long-range
predictions. The method comprises estimating a model parameters
based on a current channel estimate, and recursively adapting the
model parameters to predict future channel fading coefficients
until a predetermined re-acquisition condition is satisfied. Once
the re-acquisition condition has been satisfied, the model
parameters are again estimated based on a current channel estimate.
The acquired model parameters are adaptively updated and used in a
Kalman filter.
Inventors: |
HEIDARI; Abdorreza;
(Kitchener, CA) ; KHANDANI; Amir K.; (Kitchener,
CA) ; MCAVOY; Derek; (Toronto, CA) |
Assignee: |
UNIVERSITY OF WATERLOO
Waterloo
CA
BCE INC.
Montreal
CA
|
Family ID: |
39537601 |
Appl. No.: |
13/558906 |
Filed: |
July 26, 2012 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
11694474 |
Mar 30, 2007 |
8233570 |
|
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13558906 |
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Current U.S.
Class: |
370/252 |
Current CPC
Class: |
H04B 17/3911 20150115;
H04L 25/0222 20130101; H04L 25/025 20130101 |
Class at
Publication: |
370/252 |
International
Class: |
H04W 24/00 20090101
H04W024/00 |
Foreign Application Data
Date |
Code |
Application Number |
Dec 18, 2006 |
CA |
2571385 |
Claims
1. A method of predicting channel fading in a wireless network,
comprising: estimating channel model parameters, including
estimating a frequency shift of each component of a current sampled
signal; adapting the channel model parameters to predict channel
variables, by: monitoring the frequency shifts; estimating a vector
of future channel variables based on the tracked frequency shifts
and the channel estimate; and determining the future channel
variables based on the state vector, until a predetermined
re-acquisition condition is satisfied.
2. The method of claim 1, wherein estimating the channel model
parameters comprises applying a sum-sinusoidal model.
3. The method of claim 1, wherein estimating the channel model
parameters comprises applying a fast Fourier transform to estimate
a Doppler frequency shift of each signal component.
4. The method of claim 1, wherein the re-acquisition condition is
satisfied when an error trend in the predicted channel variables
exceeds a predetermined threshold.
5. The method of claim 1, wherein the re-acquisition condition is
satisfied when a predetermined time has elapsed.
6. A channel fading predictor for use in a wireless receiver, the
channel fading predictor comprising: a tangible processor-readable
medium storing instructions, which, when executed by a processor,
cause the processor to provide: a model acquisition unit to
estimate Doppler frequency shifts for each component of a channel
estimate; a predictor to determine the future channel fading
coefficient based on the state vector; and a re-acquisition
detector which, when a predetermined re-acquisition condition has
been satisfied, controls the model acquisition unit to re-estimate
the Doppler frequency shifts based on a current channel estimate,
and to provide the re-estimated Doppler frequency shifts to the
adaptive filter.
7. The channel fading predictor of claim 6, further comprising a
selector to selectively provide Doppler frequency shifts, from the
model acquisition unit or from an output of the adaptive filter, to
an input of the adaptive filter.
8. The channel fading predictor of claim 6, wherein the model
acquisition unit applies a sum-sinusoidal model.
9. The channel fading predictor of claim 6, wherein the model
acquisition unit applies a fast Fourier transform to estimate the
Doppler frequency shift of each signal component.
10. The channel fading predictor of claim 6, wherein the
re-acquisition detector determines that the re-acquisition
condition has been satisfied when an error trend in the predicted
channel fading coefficients exceeds a predetermined threshold.
11. The channel fading predictor of claim 6, wherein the
re-acquisition detector determines that the re-acquisition
condition has been satisfied when a predetermined time has
elapsed.
12. A wireless mobile communication device comprising: a receiver
having a channel fading predictor to predict channel fading
coefficients, the channel fading predictor comprising: a tangible
processor-readable medium storing instructions, which, when
executed by a processor, cause the processor to provide: a model
acquisition unit to estimate Doppler frequency shifts for each
component of a channel estimate; an adaptive filter to recursively
track the Doppler frequency shifts; a Kalman filter to estimate a
state vector of future channel fading coefficients based on the
tracked Doppler frequency shifts and the channel estimate.
13. The wireless mobile communication device of claim 12, further
comprising a selector to selectively provide Doppler frequency
shifts, from the model acquisition unit or from an output of the
adaptive filter, to an input of the adaptive-filter.
14. The wireless mobile communication device of claim 12, wherein
the model acquisition unit applies a sum-sinusoidal model.
15. The wireless mobile communication device of claim 12, wherein
the model acquisition unit applies a fast Fourier transform to
estimate the Doppler frequency shift of each signal component.
16. The wireless mobile communication device of claim 12, wherein
the re-acquisition detector determines that the re-acquisition
condition has been satisfied when an error trend in the predicted
channel fading coefficients exceeds a predetermined threshold.
17. The wireless mobile communication device of claim 12, wherein
the re-acquisition detector determines that the re-acquisition
condition has been satisfied when a predetermined time has
elapsed.
18. The wireless mobile communication device of claim 12, wherein
the adaptive filter applies a gradient-based adaptive approach to
track the Doppler frequency shifts.
19. The wireless mobile communication device of claim 18, wherein
the gradient-based adaptive approach comprises a least mean squares
algorithm.
20. The wireless mobile communication device of claim 12, wherein
the Kalman filter sets a measurement matrix M.sub.n=[1, 1, . . . ,
1], and determines a state transition matrix
A.sub.n=diag[e.sup.j.omega.(1)Ts, e.sup.j.omega.(2)Ts, . . . ,
e.sup.j.omega.(N)Ts], where .omega.(n) is the Doppler frequency
shift of each component, and Ts is the sampling period.
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] This application is a Continuation of U.S. patent
application Ser. No. 11/694,474, filed on Mar. 30, 2007, which
claims the benefit of priority from Canadian Patent Application No.
2,571,385, filed on filed on Dec. 18, 2006.
FIELD OF THE INVENTION
[0002] The present invention relates generally to channel
estimation in wireless communications systems. More particularly,
the present invention relates to adaptive channel prediction in
wireless networks subject to fading.
BACKGROUND OF THE INVENTION
[0003] In wireless communication systems, a received signal
experiences significant power fluctuations due to fading. Signal
fading is caused by multipath propagation and Doppler frequency
shift. Multiple scatterers cause interference between reflected
transmitter signal components. As a mobile receiver moves through
the interference pattern set up by the multiple scatterers, it
experiences a specific fading pattern, which is unique to the
mobile path and the scattering environment, and is usually
time-varying. The superposition of scattered component waves can
lead to constructive and destructive interference, which create
fading peaks and deep fades, respectively.
[0004] Channel fading prediction can be used to improve the
performance of communication systems. Having estimates of future
channel characteristics can facilitate and enhance the performance
of many tasks of the receiver and the transmitter, such as channel
equalization, data symbol decoding, antenna beamforming, and
adaptive modulation.
[0005] To predict a process, a time evolution model of the process
is required. Channel fading can be modeled using linear models,
such as auto-regressive moving-average (ARMA) models. Such linear
models are easy to use, and have low complexity. However, the
fading process is highly nonlinear, and can not be exactly modeled
with a reasonable linear filter. Therefore, for short-range
applications, an approximate low-order auto-regressive (AR) model
has been used to capture most of the fading dynamics. However,
linear models do not perform well for long-range predictions, and
exhibit poor performance for high mobility channels, as they are
solely dependent on the correlation parameters of the fading
process.
[0006] The use of deterministic sum-sinusoidal models to estimate
channel fading has also been proposed. These models rely on complex
estimations of amplitude, phase and Doppler shift frequencies.
Thus, the shorter the estimation window, the higher the complexity,
and the longer the estimation window, the higher the prediction
errors. As a result, such models tend to be highly complex, or
inaccurate.
[0007] It is, therefore, desirable to provide a low-complexity
channel prediction system and method effective for long-range
predictions.
SUMMARY OF THE INVENTION
[0008] In a first aspect, the present invention provides a method
of predicting channel fading in a wireless network. The method
comprises estimating channel model parameters from a channel
estimate; recursively adapting the channel model parameters to
predict channel fading coefficients, until a predetermined
re-acquisition condition is satisfied; and then repeating the first
two steps.
[0009] In a further aspect, the present invention provides a
processor-readable medium containing statements and instructions,
which, when executed, cause a processor to perform steps of
estimating channel model parameters from a channel estimate;
recursively adapting the channel model parameters to predict
channel fading coefficients, until a predetermined re-acquisition
condition is satisfied; and then repeating the first two steps.
[0010] Estimating the channel model parameters comprises estimating
a Doppler frequency shift of each component of a current sampled
signal, such as by applying a sum-sinusoidal model to the channel
estimate and applying a fast Fourier transform to estimate the
Doppler frequency shift of each signal component. The
re-acquisition condition can, for example, be satisfied when an
error trend in the predicted channel fading coefficients exceeds a
predetermined threshold or when a predetermined time has elapsed.
Recursively adapting the channel model parameters comprises
estimating a state vector of the sum-sinusoidal model and applying
a gradient-based adaptive approach, such as a least mean squares
algorithm, to track the Doppler frequency shifts. Estimating the
state vector comprises applying a Kalman filter, which can have a
measurement matrix M.sub.n=[1, 1, . . . , 1], and a state
transition matrix A.sub.n=diag[e.sup.j.omega.(1)Ts,
e.sup.j.omega.(2)Ts, . . . , e.sup.j.omega.(N)Ts], where .omega.(n)
is the Doppler frequency shift of each component, and Ts is the
sampling period. The channel fading coefficients can be predicted
as a function of the state vector.
[0011] In further aspects, the present invention provides a channel
fading predictor for use in a wireless receiver and a wireless
mobile communication device incorporating such a channel fading
predictor. The channel fading predictor comprises a model
acquisition unit to estimate Doppler frequency shifts for each
component of a channel estimate; an adaptive filter to recursively
track the Doppler frequency shifts; a Kalman filter to estimate a
state vector of future channel fading coefficients based on the
tracked Doppler frequency shifts and the channel estimate; a
predictor to determine the future channel fading coefficient based
on the state vector; and a re-acquisition detector which, when a
predetermined re-acquisition condition has been satisfied, controls
the model acquisition unit to re-estimate the Doppler frequency
shifts based on a current channel estimate, and to provide the
re-estimated Doppler frequency shifts to the adaptive filter. The
channel fading predictor can further comprise a selector to
selectively provide Doppler frequency shifts, from the model
acquisition unit or from an output of the adaptive filter, to an
input of the adaptive filter.
[0012] According to various embodiments, the model acquisition unit
can apply a sum-sinusoidal model to estimate the Doppler frequency
shift of each signal component. The re-acquisition detector can
determine that the re-acquisition condition has been satisfied when
an error trend in the predicted channel fading coefficients exceeds
a predetermined threshold or when a predetermined time has elapsed.
The adaptive filter can apply a gradient-based adaptive approach,
such as a least mean squares algorithm, to track the Doppler
frequency shifts. The Kalman filter can set a measurement matrix
M.sub.n=[1, 1, . . . , 1], and determine a state transition matrix
A.sub.n=diag[e.sup.j.omega.(1)Ts, e.sup.j.omega.(2)Ts, . . . ,
e.sup.j.omega.(N)Ts], where .omega.(n) is the Doppler frequency
shift of each component, and Ts is the sampling period.
[0013] Other aspects and features of the present invention will
become apparent to those ordinarily skilled in the art upon review
of the following description of specific embodiments of the
invention in conjunction with the accompanying figures.
BRIEF DESCRIPTION OF THE DRAWINGS
[0014] Embodiments of the present invention will now be described,
by way of example only, with reference to the attached Figures,
wherein:
[0015] FIG. 1 is a block diagram of a receiver according to an
embodiment;
[0016] FIG. 2 is a block diagram of a channel fading predictor
according to an embodiment;
[0017] FIG. 3 is a flowchart of a method of channel fading
prediction according to an embodiment; and
[0018] FIG. 4 is a comparison of simulation results for a channel
fading predictor, according to an embodiment, and a linear
predictor, in a Jakes' fading environment; and
[0019] FIG. 5 is a comparison of simulation results for a channel
fading predictor, according to an embodiment, and a linear
predictor, in a non-stationary environment.
DETAILED DESCRIPTION
[0020] The present invention provides a method and system for
predicting channel fading, particularly in a mobile wireless
environment. The method comprises estimating channel model
parameters based on a channel estimate of a current sampled signal;
and recursively adapting the model parameters to predict channel
fading coefficients until a predetermined re-acquisition condition
is satisfied. Once the re-acquisition condition has been satisfied,
the model parameters are again estimated based on a current sampled
signal. The model parameters are adaptively updated and used in a
Kalman filter to provide a powerful fading prediction algorithm.
The method has been found to be effective in performing long-range
predictions and is of relatively low complexity.
[0021] Referring to FIG. 1, a receiver 10 according to an
embodiment of the present invention is shown. The receiver 10 can
be an element of a transceiver in a mobile communication device,
such as a cellular telephone, personal digital assistant, or
wireless-enabled laptop computer. The mobile communication device
can be operating under commonly used protocols, such as those
specified in IEEE 802.11, 802.15, 802.16, 802.20 and their
variants, and according to any standard, including CDMA2000 1xRTT,
W-CDMA (Wideband-CDMA), EDGE, CDMA EVDO, or GSM. A single path flat
fading channel from a transmit antenna to a receive antenna is
assumed. Under conditions where the path delay variations are not
negligible in comparison to the symbol period, the same analysis
can apply to each resolvable multipath component.
[0022] Only those elements of the receiver 10 that are necessary to
the present invention are depicted. A channel estimator 12
estimates a channel estimate h.sub.n using a sampled signal
(observation sample), such as the available pilot signals, a
training sequence, or other accepted channel estimation techniques.
Channel estimation is well known in the art, and any suitable
channel estimation technique can be used.
[0023] The channel estimate h.sub.n provided to a channel fading
predictor 14 to predict a future channel fading coefficient
h.sub.n+D|n, at a prediction depth, or time increment, D. The
future channel fading coefficient h.sub.n+D|n can then be used by
the receiver 10, or provided to the transmitter (not shown), to
improve performance of the system, as is well known in the art. The
channel fading coefficient h.sub.n is zero mean, and has a variance
of .sigma..sub.h.sup.2=1. The channel fading coefficient estimated
by the channel fading predictor 14 can be shown as
h.sub.n=h.sub.n+.nu..sub.n, where h.sub.n is the estimate of the
channel fading, and .nu..sub.n is the estimation error modeled as a
zero mean Gaussian noise with variance .sigma..sub..nu..sup.2. As
an indicator of the estimation quality, the observation
signal-to-noise ratio (SNR) is defined as
SNR.sub.z=.sigma..sub.h.sup.2/.sigma..sub..nu..sup.2=1/.sigma..sub..nu..s-
up.2.
[0024] Referring to FIGS. 2 and 3, the channel fading predictor 14
and its operation are shown in greater detail. In an embodiment,
the channel fading predictor 14 comprises a model acquisition unit
20, a selector 25, an adaptive filter 22, a Kalman filter 24, a
predictor 26, and a re-acquisition detector 28. A re-acquisition
indication signal, provided by a re-acquisition detector 28,
controls the model acquisition unit 20, selector 25 and adaptive
filter 22.
[0025] In an initialization mode or a re-acquisition mode, the
re-acquisition indication signal is set to an "acquire" value that
activates the model acquisition unit 20 and holds the adaptive 22
filter in an inactive state (i.e. its input .omega..sub.k(n) equals
its output .omega..sub.k(n+1)). The channel estimate h.sub.n is
provided to the model acquisition unit 20, which determines the
Doppler frequency shift .omega..sub.k of each scattered component
of the estimated channel at time n (step 40). The selector 25 is
activated to accept the Doppler frequency shifts .omega..sub.k from
the model acquisition unit 22, as indicated by the path A, and to
feed them to the adaptive filter 22. The adaptive filter is in its
inactive state, and outputs .omega..sub.k(n+1)=.omega..sub.k. The
Kalman filter 24 then determines a state vector x.sub.n (step 42),
based on the outputs .omega..sub.k(n+1) of the adaptive filter 22
and the channel estimate h.sub.n. The Kalman filter 24 can also
determine information concerning the amplitude .alpha..sub.k of the
scattered components. As used herein, the Doppler frequency shifts
.omega..sub.k, the amplitudes .alpha..sub.k, and the state vector
x.sub.n are parameters of the model, and referred to, collectively
or interchangeably, as model parameters.
[0026] When the channel fading predictor 14 is in its standard
operational tracking mode, the re-acquisition indication signal is
set to a "track" value that deactivates the model acquistion unit
20, activates the adaptive filter 22, and causes the selector 25 to
set up a feedback loop between the input and output of the adaptive
filter 22, as indicated by the return path T. The adaptive filter
22 estimates a future Doppler frequency shift .omega..sub.k(n+1)
for each scattered component, by applying an adaptive tracking
algorithm based on a previous Doppler frequency shift .omega..sub.k
and a current state vector x.sub.n. The previous Doppler frequency
shift .omega..sub.k is input to the adaptive filter 22 by the
feedback loop from the output of the adaptive filter 22. The state
vector x.sub.n is determined by the Kalman filter 24 (step 42),
which, as described above, can also determine information
concerning the amplitude .alpha..sub.k of the scattered
components.
[0027] In initialization, re-acquisition or tracking modes, the
current state vector x.sub.n is provided to a predictor 26, which
outputs the predicted future channel fading coefficient h.sub.n+D|n
(step 44). The predicted future channel fading coefficient
h.sub.n+D|n and the current observation sample h.sub.n, can then be
processed by the re-acquisition detector 28 to determine a model
re-acquisition condition (step 46), and to determine if the
re-acquisition condition meets or exceeds a predetermined threshold
(step 48). The re-acquisition condition can be, for example, a
calculated error trend E.sub.n+D or an elapsed time since a
previous acquisition. If the re-acquisition condition is not
satisfied, the re-acquisition indication signal is set or held to
the track value, and the selector 25 provides the previously
estimated Doppler frequency shifts to the input of the adaptive
filter 22. If re-acquisition is indicated, the re-acquisition
indication signal is set to the acquire value, and the model
acquisition unit 20 is activated to reacquire the channel fading
model to provide a new estimate of the Doppler frequency shifts
.omega..sub.k.
[0028] Until such time as the maximum permissible error trend or
other re-acquisition condition has been met, the adaptive filter 22
and Kalman filter 24 operate in the tracking mode as a recursive
loop to continue estimating the future fading coefficients.
Re-acquisition of the channel model parameters can be done
frequently to keep the frequency Doppler estimates updated.
However, to decrease the required computational overhead and
complexity, consecutive acquisitions are preferably spaced as far
as possible. This also permits other elements of the system to have
sufficient time to catch up with the re-acquired frequency
estimates. The operation of each element of the channel predictor
14 will now be described in greater detail.
[0029] The model acquisition unit 20 uses a sum-sinusoidal model to
determine the Doppler frequency shift .omega..sub.k of each
scattered component. Flat fading, i.e., one resolved multipath
component, is assumed for the channel. But the same analysis can
apply equally to each resolved multipath component where the delays
are not negligible in comparison to the symbol period. When all
delayed, or faded, components arrive at the receiver within a small
fraction of the symbol duration, the fading channel is considered
frequency-nonselective, or flat. Such flat fading commonly occurs
in narrowband signaling. Jakes' model, also known as Clarke's
model, is a special case of the sum-sinusoidal model described
below, and is mathematically valid for a rich-scattering
environment where the number of the scatterers is significant.
[0030] Jakes' fading model has been used for some time to simulate
mobile channels. In an environment with no dominant line-of-sight
between the transmitter and the receiver, it is well known that the
envelope of a transmitted carrier at the receiver has a Rayleigh
distribution, and a uniform phase. Assuming a two-dimensional
isotropic scattering and an omni-directional receiving antenna, it
is known that power spectral density (PSD) of the fading process is
given by:
S h ( f ) = { 1 .pi. f d 1 1 - ( f f d ) 2 f < f d 0 , otherwise
, ( 1.1 ) ##EQU00001##
where f.sub.d is the maximum Doppler frequency. The Doppler PSD of
a fading channel describes how much spectral broadening it causes.
This shows how a pure frequency, such as a pure sinusoid, which is
an impulse in the frequency domain, is spread out across frequency
when it passes through the channel. It is the Fourier transform of
the autocorrelation function R.sub.h(.tau.), which can be shown
as:
R h ( t , t - .tau. ) = E [ h ( t ) h * ( t - .tau. ) ] .sigma. h 2
= J 0 ( 2 .pi. f d .tau. ) ( 1.2 ) ##EQU00002##
where J.sub.0() is a zeroth order Bessel function of the first kind
and .tau. is the time difference.
[0031] Jakes' fading results from a statistical modeling of fading.
However, fading can be observed as a deterministic signal. Jakes'
model for Rayleigh fading is based on summing sinusoids. When the
receiver, the transmitter, and/or the scatterers are moving, each
scattered component undergoes a Doppler frequency shift given
approximately by:
f.sub.k=f.sub.d cos(.theta..sub.k) (1.3)
where .theta..sub.k is the incident radiowave angle of the k'th
component with respect to the motion of the mobile and f.sub.d is
the maximum Doppler frequency defined as:
f d = .upsilon. c f c ( 1.4 ) ##EQU00003##
where f.sub.c is the carrier frequency, .nu. is the mobile speed
and c is the speed of light. Assuming N.sub.sc scatterers, the
complex envelope of the flat fading signal at the receiver is:
h ( t ) = k = 1 N sc a k j ( .omega. k t + .phi. k ) ( 1.5 )
##EQU00004##
where for the n'th scatterer, .alpha..sub.k is the (real)
amplitude, .phi..sub.k is the initial phase, and
.omega..sub.k=2.pi.f.sub.k where f.sub.k is defined in (1.3). In
real mobile environments, there are generally a few main scatterers
that construct the fading signal.
[0032] Assuming N.sub.sc scatterers, there are 2N.sub.sc unknown
parameters to be determined for the model. Using 2N.sub.sc fading
samples, an equation set can be solved to find .omega..sub.k and
.alpha..sub.k, k=1, . . . , N.sub.sc, as detailed in A. Heidari, A.
K. Khandani, and D. McAvoy, "Channel Prediction for 3G
Communication Systems," tech. rep., Bell Mobility, August 2004, but
it is evident that using noisy measurements can result in poor
estimations.
Looking at the problem in the frequency domain, a Fourier transform
of the fading signal shown in (1.5) results in:
H ( .omega. ) = k = 1 N sc .alpha. k .delta. ( .omega. - .omega. k
) ( 1.6 ) ##EQU00005##
[0033] Thus, the components are decoupled in the frequency domain
and it is appropriate to find the parameters using a Fourier-based
transform method, such as a Fast Fourier Transform (FFT) over an
observation window (as described, for example in H. Hallen, S. Hu,
A. Duel-Hallen, "Physical Models for Understanding and Testing Long
Range Prediction of Multipath Fading in Wireless Communications,"
submitted to IEEE Transactions on Vehicular Technology),
Root-MUSIC, ESPIRIT, or other suitable spectral estimation method.
A FFT gives a good estimation of .omega..sub.k if the Doppler
frequencies do not change drastically over the window, such as when
a mobile device undergoes an abrupt path change.
[0034] In an embodiment, a Fourier transform, as described above,
is used to estimate the .omega.(k), k=1, . . . , N.sub.sc by
performing FFT over an observation window of N.sub.win recent
samples, H=FFT[h]. An FFT length of N.sub.FFT=2N.sub.win can be
used to increase the frequency resolution. Each sinusoid can be
projected on up to 3 samples in H. Therefore, first the peak of H
is found, and then the .omega.(1) is calculated by averaging over
the amplitudes of the three adjacent frequency samples. At
initialization, or re-acquisition, an initial estimate of
.alpha.(1) is also achieved in this way. Other .omega.(k) and
.alpha.(k) are found by continuing this procedure.
[0035] As can be seen in (1.6), the amplitude .alpha..sub.k can
also be estimated from the Fourier analysis. However, .alpha..sub.k
usually changes more quickly than .omega..sub.k as the mobile moves
and the scattering environment changes. Therefore, knowing
.omega..sub.k, the Kalman filter 24 can be used instead to
efficiently track .alpha..sub.k.
[0036] The Kalman filter 24 is a recursive estimator. This means
that only the estimated state from the previous time step and the
current measurement are needed to compute the estimate for the
current state. In contrast to batch estimation techniques, no
history of observations and/or estimates is required.
[0037] An evolution model can be shown as a state-space model, as
follows:
{ x n = A n x n - 1 + q n z n = M n x n + .upsilon. n ( 2.1 )
##EQU00006##
where x.sub.n is a N.times.1 state vector at time n, A.sub.n is a
N.times.N matrix which controls the transition of the state vector
in time, and q.sub.n is a (usually Gaussian) noise vector, with a
covariance of Q=E[q.sub.nq.sub.n.sup.H], which represents the model
error. M.sub.n is known as the measurement matrix, and .nu..sub.n
is the observation noise with the variance .sigma..sub..nu..sup.2.
In effect, z.sub.n is the system output which is the available
(noisy) measurement of the state. In practice, A.sub.n, Q and
M.sub.n are generally constant or very slow time varying.
[0038] Assuming a state-space model, the Kalman filter 24
efficiently estimates the state vector x.sub.n, which is used to
track the Doppler frequencies and to predict the future samples of
the fading signal. In an embodiment, applicable to the general
fading model described above, the Kalman filter 24 can use the
following state-space model:
A.sub.n=diag[e.sup.j.omega.(1)Ts, e.sup.j.omega.(2)Ts, . . . ,
e.sup.j.omega.(N)Ts] (2.2)
and
M.sub.n=[1, 1, . . . , 1] (2.3)
where z.sub.n=h.sub.n is the available channel estimate, and the
state vector is:
x.sub.n[.alpha.(1)e.sup.jn.omega.(1)Ts,
.alpha.(2)e.sup.jn.omega.(2)Ts, . . . ,
.alpha.(N)e.sup.jn.omega.(N)Ts].sup.T (2.4)
[0039] The state of the filter is represented by two variables:
x.sub.n, the estimate of the state at time n; and the error
covariance matrix P.sub.n, which is a measure of the estimated
accuracy of the state estimate. The Kalman filter 24 has two
distinct phases: predict and update. The predict phase uses the
estimate from the previous time step to produce an estimate of the
current state. In the update phase, measurement information from
the current time step is used to refine this prediction to arrive
at a new estimate.
[0040] In the predict phase:
x.sub.n.sup.-=Ax.sub.n-1.sup.+ (2.5)
P.sub.n.sup.-=AP.sub.n-1.sup.+A.sup.T+Q (2.6)
[0041] While, in the update phase:
x.sub.n.sup.+=x.sub.n.sup.-+K.sub.n(z.sub.n-M.sub.nx.sub.n.sup.-)
(2.7)
P.sub.n.sup.+=(I-K.sub.nM.sub.n)P.sub.n.sup.- (2.8)
where
K.sub.n=P.sub.n.sup.-M.sub.n.sup.H(M.sub.nP.sub.n.sup.-M.sub.n.sup.H+.si-
gma..sub..nu..sup.2).sup.-1 (2.9)
where Q is the covariance matrix of the model noise; z.sub.n is the
observation sample; x.sub.n.sup.- is the a priori estimate of the
state x.sub.n (also shown as x.sub.n|n-1); x.sub.n.sup.+ is the a
posteriori estimate of the state x.sub.n, (i.e., having the
observation z.sub.n; also shown as x.sub.n|n); P.sub.n.sup.- is the
covariance matrix of the a priori error; and P.sub.n.sup.+ is the
covariance matrix of the a posteriori error.
[0042] Since .omega..sub.k generally changes slowly over time, the
adaptive filter 22 can be used to track the Doppler frequencies. An
adaptive algorithm is used to track the fine changes of the Doppler
frequencies. Suitable tracking algorithms include Least Mean
Squares (LMS) and Recursive Least Mean Squares (RLS) algorithms. In
an embodiment, using a gradient-based approach, the following LMS
algorithm can be applied:
.omega..sub.n+1(k)=.omega..sub.n(k)+.mu.Im[X.sub.n.sup.+(k).sup.HM.sub.n-
(k).sup.He.sup.n] (3.1)
where
e.sub.n=z.sub.n-h.sub.n (3.2)
and where
h.sub.n=M.sub.nX.sub.n.sup.+ (3.3)
[0043] Given the current state x.sub.n, which carries all the
information about the past, The predictor 26 can predict the future
channel state. According to an embodiment, a Minimum Mean Squares
Estimate (MMSE) of the D-step prediction can be given as:
{circumflex over (x)}.sub.n+D=A.sup.Dx.sub.n (3.4)
Hence, the predicted future channel fading coefficient is
h.sub.n+D=M{circumflex over (x)}.sub.n+D.
[0044] The error trend E can be calculated by any suitable error
smoothing method, such as exponential windowing and moving average
methods. For example, given the predicted future channel
coefficient h.sub.n+D, the re-acquisition detector 28 can use an
exponential window for calculation of the error trend from known
sample errors e.sub.n, as follows:
E.sub.n+1=.lamda..sub.EE.sub.n+(1-.lamda..sub.E)|e.sub.n|.sup.2
(4.1)
where .lamda..sub.E is a forgetting factor chosen such that
0<<.lamda..sub.E<1.
[0045] FIGS. 4 and 5 compare simulation results for channel fading
prediction using the channel fading predictor (KF) of the present
invention and a prior art linear predictor (LP). In practice,
channel coefficients are estimated, using the conventional pilot
signals or other means, which usually introduces some error in the
available channel coefficients. The channel estimation error can be
modeled as an Additive White Gaussian Noise (AWGN), and observation
SNR, SNR.sub.z, which is defined as the ratio of the channel power
to the noise power. The MSE of the linear prediction versus mobile
speed for different linear orders at different SNR.sub.z can be
different. It is observed that at each SNR.sub.z and each mobile
speed, there is an optimum order p, which could be different in
other situations. This variable order makes the implementation of
the prediction algorithm difficult. Therefore, for the SNR.sub.z
corresponding to a specific application, an overall good order
should be chosen. For example, consider SNR.sub.z=40 dB. For low to
moderate mobile speeds, p=2 is optimum, while at high mobile speed,
p=3 or 4 appears better.
[0046] For the simulations: carrier frequency f.sub.c=2.15 GHz;
sampling frequency f.sub.s=1500 Hz; and SNR.sub.z=10 dB. The two
prediction algorithms are compared with respect to the average mean
square error (MSE) versus the prediction depth D. The results are
reported for various linear orders N.sub.AR, and various scattering
orders N.sub.ray, respectively (N.sub.ray is an estimate of
N.sub.sc in (1.5)). FIG. 4 shows the results for Jakes' fading for
the mobile speeds of V=25 kmph and V=100 kmph. It is observed that
the present channel fading predictor significantly outperforms the
linear predictor if N.sub.ray is large enough (here, for
N.sub.ray.gtoreq.8), while the linear predictor fails at high
prediction depths, regardless of the linear order.
[0047] Jakes' fading is a valid model for a rich scattering area.
However, because Jakes' fading is stationary, it cannot accurately
model the changes in the scattering environment. To test the
present channel fading predictor vs. the linear predictor with a
more realistic fading signal, a ray-tracing simulation environment,
as described in A. Heidari, A. K. Khandani, and D. McAvoy, "Channel
Prediction for 3G Communication Systems," tech. rep., Bell
Mobility, August 2004, was used. The mobile device is assumed to be
randomly moving vertically and horizontally in the scattering area
and experiences different combinations of signal rays. At each
point in the mobile path, it undergoes a different Doppler
frequency shift and a different signal power for each ray.
Therefore, the generated fading can closely resemble the fading in
a real mobile environment.
[0048] FIG. 5 shows the results for ray-tracing fading for V=25
kmph and V=100 kmph. It is observed that the present channel fading
predictor always outperforms the linear predictor. As ray-tracing
fading does not represent a very rich scattering environment, it is
observed that increasing N.sub.ray does not necessarily improve the
performance. Note that the linear predictor is sensitive to the
linear order at high mobile speeds. In fact, it is observed in the
simulations that a linear model is not dependable for higher mobile
speeds because the pattern of the performance fluctuation follows
the correlation properties of the fading, i.e., a lower correlation
results in a higher MSE. In conclusion, the simulations show that
the present channel fading predictor performs very well in real
mobile environments, and is significantly more efficient than the
linear predictor.
[0049] In the preceding description, for purposes of explanation,
numerous details are set forth in order to provide a thorough
understanding of the embodiments of the invention. However, it will
be apparent to one skilled in the art that these specific details
are not required in order to practice the invention. In other
instances, well-known electrical structures and circuits are shown
in block diagram form in order not to obscure the invention. For
example, specific details are not provided as to whether the
embodiments of the invention described herein are implemented as a
software routine, hardware circuit, firmware, or a combination
thereof.
[0050] Embodiments of the invention can be represented as a
software product stored in a machine-readable medium (also referred
to as a computer-readable medium, a processor-readable medium, or a
computer usable medium having a computer-readable program code
embodied therein). The machine-readable medium can be any suitable
tangible medium, including magnetic, optical, or electrical storage
medium including a diskette, compact disk read only memory
(CD-ROM), memory device (volatile or non-volatile), or similar
storage mechanism. The machine-readable medium can contain various
sets of instructions, code sequences, configuration information, or
other data, which, when executed, cause a processor to perform
steps in a method according to an embodiment of the invention.
Those of ordinary skill in the art will appreciate that other
instructions and operations necessary to implement the described
invention can also be stored on the machine-readable medium.
Software running from the machine-readable medium can interface
with circuitry to perform the described tasks.
[0051] The above-described embodiments of the invention are
intended to be examples only. Alterations, modifications and
variations can be effected to the particular embodiments by those
of skill in the art without departing from the scope of the
invention, which is defined solely by the claims appended
hereto.
* * * * *