
RESEARCH ON
PREDICTION OF MOBILE RADIO CHANNELS,
PARAMETER TRACKING
AND ADAPTIVE FILTERING
Signals and Systems, Uppsala University
Researchers:
Mikael Sternad
,
Rikke Apelfröjd
and
Joachim Björsell
Previous PhD students:
Daniel Aronsson,
Torbjörn Ekman,
Lars Lindbom, and
Jonas Rutström.
Prediction of Mobile Radio Channels
(Research 1999present)

We study and develop highperformance algorithms
that predict the shortterm fading of mobile radio
channels.
We investigate both algorithm design and the
theoretic limits of performance.
Channel quality prediction
is of increasing
interest for a range of applications such as
adaptive coding and modulation as well as allocation of time, frequency
and spatial transmission resources.
Channel prediction is important for advanced multiantenna
transmit schemes such as zeroforcing beamforming.
Due to backhaul delays, it is crucial for
joint transmission coordinated multipoint schemes.
In general, prediction of the power of a Rayleigh fading parameter
is possible with useful accuracy around 0.20.3 wavelengths ahead
in space. The attainable accuracy depends on the signalto noise ratio,
the positioning and fraction of pilots (known transmitted
symbols that are used for channel estimation) as well as on
the fading statistics.
The best performance that can be attained by linear predictors
based on past data and channel statistics
is obtained by Kalman prediction schemes. Kalman theory
also provides analytical expressions for the obtainable
prediction accuracy, for a given fading statistics,
pilot pattern and SNR. We have studied and utilized
Kalmanbased adaptive predictors on real measured
channel data at WCDMA as well as 3GPP LTE bandwidths.
Our results show that channel predictions of sufficient
accuracy for link adaptation and scheduling
can be obtained
in downlinks and uplinks of OFDM systems like 3GPP LTE
working in the "digital dividend" band (700800 MHz).
This could enable increasing scheduling gains for wireless
broadband systems such as LTE.
Different frequency resource blocks can also be predicted
separately, in downlinks as well as multiuser uplinks,
in FDD as well as TDD systems.
In addition to Kalman predictors, we have also utilized
and investigated
FIR Wiener predictors and various nonlinear filtering structures.
A conclusion is that nonlinear prediction of complex channel gains
is nonrobust when applied to measured channel data.
More recently, we are investigating and developing the
"predictor antenna concept" for use in connected vehicles:
It is a simple way to improve the attainable
channel prediction horizon for vehicles by at least an order
of magnitude. This can be done by placing antennas on
the roof of a vehicle, and letting the first antenna,
in the direction of travel, perform channel prediction
for the rearward antennas. See the
original publication from 2012
and a more recent
proposal for using the concept in
5G massive MIMO TDD links.
Top of page
References on prediction of mobile radio channels:

PhD Thesis
by Rikke Apelfröjd, 2018.

Report
by Rikke Apelfröjd, 2014, revised 2018, on Kalman prediction of multipoint OFDM
channels.

Licentiate Thesis
by Rikke Apelfröjd, 2014.

PhD Thesis
by Daniel Aronsson, 2011.

Proceedings of the IEEE paper (2007, Invited Paper),
giving an overview of adaptive transmission in OFDMA systems,
also using channel prediction.

Licentiate Thesis by Daniel Aronsson, 2007.

IEEE PIMRC 2007 paper on
Kalman predictor design for frequencyadaptive scheduling
of FDD OFDMA uplinks.

EUSIPCO 2007 paper
on OFDMA uplink channel prediction.

IEEE ICASSP 2005 paper
on channel estimation and prediction for adaptive
OFDMA/TDMA uplinks based on overlapping pilots.

ISTSummit2005 paper
on adaptive TDMA/OFDMA for widearea coverage and
vehicular velocities.

VTC 2003paper on
Channel estimation and prediction for adaptive OFDM downlinks.
PhD Thesis
by Torbjörn Ekman, 2002.

VTC 2002Fall
Conference Paper on unbiased power prediction of
broadband radio channels.

VTC 2001Spring
Conference Paper on longterm prediction of
broadband radio channels.

Licenciate Thesis
by Torbjörn Ekman, summarizing our results up to november 2000.

VTC 1999Fall
Conference Paper on
linear and quadratic predictors.
Top of page
LowComplexity Tracking of Timevarying
Parameters of Linear Regression Models
(Research 19902005, together with
Lars Lindbom)
We often need to construct a linear dynamic model based on data,
by first selecting
a suitable model structure, and then adjusting
(estimating) its parameters.
In situations with timevarying parameters,
the parameter estimation problem
becomes a parameter following (or tracking) problem.
Standard Algorithms: LMS and Windowed RLS

Ad hoc tracking schemes can be obtained
by modifying algorithms
for the timeinvariant case, under the assumption of
slow parameter variations.
The modifications introduce moving
data windows and nonvanishing adaptation gains.
The choice of adaptation gain (or data window)
is a compromise between
noise sensitivity and tracking capability.
For example, the use of modified stochastic approximation
gives LMS while GaussNewton schemes
lead to e.g. windowed Recursive Least Squares.
These two algorithms are in frequent use.
They in general work well if the
regressors data provides sufficiently rich information, and if
the timevariations are slow.
"Slow" is here a relative concept. It depends on
the speed of
parameters drifts as compared to noise power, and on the number of
parameters to be estimated.
The example above illustrates the tracking performance of the
LMS algorithm (solid line).
The dashed line represents a timevarying scalar
"true" parameter.
A too low adaptation gain (left) will result in bad tracking,
while a high gain (right) increases the noise sensitivity of the
estimate.
For fast timevariations,
the performance of both LMS and RLS tracking
schemes can be poor;
We may find no reasonable adjustment of the data window,
since both types of algorithms will, in general,
have a suboptimal structure.
The most efficient way of improving
the tracking performance is to utilize any existing prior information
about the
nature of the time variations. For example, it may be known that the
parameters behave approximately
as sinusoids. Such information
about smooth variations can be included into
algorithms based on Kalman filters,
either in the form of stochastic models
or as functional series.
In the latter case, the parameters are modelled within
the data window e.g. as ramps, parabolas or
sinusoids with adjustable parameters.
Other types of schemes,
using fault detection or hidden Markov models, are
used when rare but abrupt
parameter changes can be expected.
Tracking Timevarying Mobile Radio Channels

This was, roughly, the state of the art for tracking problems
when we faced the challenging problem of
estimating models of timevarying radio channels
in digital cellular systems.
It may be of interest to briefly describe this problem.
A communication channel for baseband signals can be
represented by a FIRfilter with timevarying parameters (taps).
In present TDMA systems,
digital data are transmitted in bursts of fixed length.
Within each burst, a small
fraction of the transmitted data (the training sequence)
is known to the receiver.
The channel can be estimated by correllating the known
channel input with the received output signal.
A detector (equalizer) is then designed
by using the model, with the aim of retrieving
the remaining, unknown,
symbols. This procedure is repeated for each data burst.
The time dispersion of the channel is
caused by multipath propagation.
Due to reflections in the environment, the
receiver is reached by the superposition of
several delayed versions of the transmitted signal.
The time variability, fading,
is due to the mobile moving through standing wave patterns.
These wave patterns are also a result of the multipath propagation.
Among other factors, the properties of discretetime channels
depend on the sampling rate, which is related to the symbol
transmission rate.
For example, with the high symbol rate of the GSM system,
FIR channels of
length 35 are obtained, which are almost timeinvariant over the
duration of one burst. A channel model estimated
from the training sequence
will therefore be almost correct
within the whole data burst. One equalizer (or Viterbi detector)
with fixed parameters
can then be used within the whole burst, but it may be
of interest to
robustify
the design
with respect to somewhat timevarying channel dynamics.
In contrast, the low symbol rate utilized in the
North American DAMPS
standard causes the discretetime
FIR channel to be very short, having just one or two coefficients.
These coefficients will vary appreciably over timewindows of
10 samples, while a data burst consists of 168 symbols.
The timevariation is even more rapid
in systems with carrier frequencies around 1.8 GHz.
A model based on the training sequence can
therefore not be relied upon
over the whole duration of a burst. Adaptation of a timevarying
model is required.
A recursive algorithm
for simultaneous adaptation and detection is
illustrated above. It is
initialized with a model based on the
training sequence
{ t = 1 ... N_{tr} }.
"Decisiondirected" adaptive modelling
is then applied on the remaining
received data { y }, with detected
symbols used as substitutes for the
unknown channel input. The use of an adaptation algorithm
that attains small tracking errors is of crucial importance in this
type of receiver.
When we studied the IS136 scenario a few years ago,
existing methods for
analysis and design turned out to be unsuitable,
for the following reasons:
 The parameter variations of the FIRchannel can
not be regarded as ``slow".
 The performance of LMS and RLS algorithms
was unacceptable, so a scheme for using a priori
information about the nature of the timevariations had to be
developed.
Such information was available from physical considerations,
but
 the use of Kalmanbased algorithms was out of the question, due
to severe limitations on the allowable computational complexity.
A Method for Systematic Design of Adaptation Algorithms
with Fixed Gains

As a response to the problem formulated above, we
have developed a novel class of
algorithms
for tracking smooth but fast variations in the parameters of
linear regression models, in particular FIR models.
The novel design technique is the subject of a
PhD Thesis
by Lars Lindbom.
The performance of a resulting lowcomplexity algorithm,
the Simplified WienerLMS or SWLMS scheme, is illustrated below.
It is compared to a welltuned LMS algorithm
for a timevarying parameter typical of the IS136 environment.
The (patented) SWLMS algorithm works well in
IS136 equalizers
also in difficult situations
with flat fading, i.e. for singletap FIR channels.
While the novel technique for analysis and design
has been inspired by
mobile radio applications, the results have wider significance.
The key tool is a Wiener filtering approach
to the design of tracking algorithms.
From this viewpoint, the understanding of algorithms such as LMS,
momentum LMS
and signed regressor LMS can be improved
and a general class of algorithms with timeinvariant gains can be
proposed and optimized.
The new class of algorithms
combines low computational complexity
with the possibility for a significant performance increase
as compared to LMS/windowed RLS.
This is attained by
introducing stochastic "hypermodels"
which describe the second order properties of
the vector of timevarying parameters:
h(t+1) = F h(t) + C
e(t) , or
D h(t) = C
e(t) .
Here, h(t) is the parameter column vector, while
F, C and
D = qI
 F
are polynomial
matrices in the shift operator q and
e(t) is a white noise column vector.
The optimal structure of an adaptation algorithm
with constant adaptation gain will then be as follows:
h_{h}(t+kt) = F
h_{h}(t+k1t1) +
G fi(t) eps(t) , (a)
where
h_{h}( . ) 
is the parameter estimate (column vector) 
fi(t) 
is the transposed regressor matrix 
eps(t) 
is the prediction error, or output error 
F 
is obtained directly from the hypermodel, while 
G 
is in general a matrix of transfer functions. 
The LMS algorithm is obtained if
F = I and if
G
is a diagonal
matrix containing adaptation gains. This structure is optimal only
if the true parameter vector
h(t)
has random walk statistics
h(t+1) = h(t) + e(t).
The polynomial matrix
F will
be given directly by the
hypermodel. The adjustment of
G which
provides a minimal sum of
squared parameter errors can be obtained by solving a linear
(Wiener) design problem.
This problem is illustrated below, where
R is
the covariance matrix of the regressors and the
leftmost block represents the hypermodel.
The rational matrix
G in the adaptation law (a)
is uniquely determined by the resulting
optimal stable rational matrix
L_{k} below.
The Wiener problem can in general be solved via
a spectral factorization
and a bilateral Diophantine equation.
In simplified but powerful variants, the design
equations become trivial, and no equations
need to be solved.
The design can also be made
robust
against uncertainties in the hypermodels.
Adaptation laws for parameter prediction (k>0), filtering
(k=0) and fixed lag smoothing (k<0) can be derived.
The use of smoothing improves the attainable performance,
while multistep prediction of channel coefficients
is of interest e.g. in adaptive Viterbi receivers for TDMA
mobile radio systems, or in power control algorithms in CDMA.
In digital communications, the resulting tracking algorithms
can be applied to the multiinput multioutput FIR channels
appearing in
multiuser detection,
in CDMA systems as well as in OFDM systems.
In other applications,
the method can be applied to timevarying output error models
and various functional series models.
A restriction is that analysis and design has not yet been
developed for models with lagged output data as regressors,
such as ARMA models.
This work has also resulted in an analysis leading to
exact expressions for parameter error
covariances for fast timevariations, in situations
of relevance for mobile communications.
Top of page
References on Modelbased Design
and Analysis of Adaptation laws:

Paper 1 on
design of constantgain adaptation algorithms.
(Also IEEE ICASSP 2001)

Paper 2 on
analysis of stability and performance. (Also IEEE ICASSP 2001,2002)

Paper 3 on
the Wiener LMS adaptation algorithm, a special case.
(Also IEEE VTC 2000)

Paper 4 on
a case study on IS136 channels. (Also IEEE VTC 2000)

Conference paper in IEEE VTC 2003Fall
on ODFM channel adaptation with the
constantgain tracking algorithms.

Conference paper in IEEE VTC 2002Fall
on gain adaptation in WLMS tracking algorithms.

Conference paper
at the European Control Conference, 2001.

Robust design
of adaptation laws with constant gains, IFAC Como 2001.

Licentiate Thesis by Jonas Rutström, 2005.

PhD Thesis by Lars Lindbom 1995.

Licentiate Thesis by Lars Lindbom, 1992.

Conference paper on the simplest variant, SWLMS,
and a channel tracking example.

Master Thesis on the use of
a fixed grid of algorithms in IS136.

Conference paper in IEEE
ICASSP'93 on an early version of the method.

Deterministic modelling
of timevariations in digital mobile radio channels.

PhD Thesis by Kenth Öhrn,
May 1996, on robust filtering and Kalman tracking.
