Note: Descriptions are shown in the official language in which they were submitted.
CA 02240483 1998-06-12
,.
Proce~s of multisensor equalization allowing
multi-~ensor reception in the presence of interference
and m~ltiple propagation path~ and recei~er ~or the
implementation thereof
The invention relates to a process of
multlsensor equalization allowing the demodulation of a
digital message of serial digital modulation type in
the presence of multiple propagation paths and
interfering sources, also called jammers in respect of
modulations formed from frames comprising learning
sequences and information symbol sequences. It is based
on the techniques of antenna processing and therefore
requires the use of an array containing several
sensors.
For numerous applications in digital radio
communications, transmission between the transmitter
and the receiver occurs along several propagation
paths. Since the delay time between the various paths
may be greater than the symbol duration, equalization
becomes necessary in order to compensate for the inter-
symbol interference (ISI) thus generated.
This phenomenon occurs in particular in the HF
range, where the multiple propagation paths arising
from the reflections off the various ionospheric
layers, may be 5 ms apart, i.e. several times the
symbol duration (for modulations whose bandwidth is
typically of the order of 3 kHz). It also occurs in
other frequency ranges in respect of very high speed
communications, of the GSM type (270 kbits/s, i.e. a
symbol duration of 3.7 ,us), in an urban or mountainous
setting, where the various paths stemming from
reflections off various obstacles (buildings,
mountains, etc.) may be separated by 10 or even 20 ,us.
The invention may therefore be applied in
particular to the high-frequency (HF) range which is of
particular interest to radio communications since it
allows long-distance communications on account of the
phenomena of reflection off the various layers of the
- - c
CA 02240483 1998-06-12
- 2 -
ionosphere, or else in respect of GSM-type
applications. The invention may also lead to an
increase in the capacity of cellular radio
communication systems by allowing the implementation of
Space Division Multiple Access (SDMA) techniques which
consist in allowing several users who are sufficiently
far apart spatially to use the same frequency at the
same time.
In many systems currently in service,
adaptation to the conditions of propagation is made
possible by inserting learning sequences, which are
known to the receiver, into the waveform. Various
solutions are then possible for carrying out adaptive
equalization of the useful signal received, the two
most common being:
- equalization by a Viterbi algorithm,
requiring prior estimation of the propagation channel
using the learning sequence. This equalization has the
advantage of minimizing the probability of error with
regard to the complete sequence of information signals,
but it becomes very expensive when the duration of the
impulse response of the channel is much greater than
the symbol duration Ts. This is because the number of
states which the Viterbi algorithm must process is
equal to ML, where M is the size of the alphabet of the
modulation and L the length of the impulse response of
the channel in terms of number of symbol periods. This
solution is used for GSM-type applications where the
Viterbi algorithm typically contains 32 states (L=5 and
M=2)-
In the HF range, the number of states becomestoo large for the Viterbi algorithm to be usable
(typically, M is equal to 4 or 8, and L is equal to 12,
corresponding to an impulse response stretching over
- 35 5 ms) and the second solution using a DFE equalizer,
standing for "Decision Feedback Equalizer", is often
used.
This second solution consists in using the
learning sequences to optimize a MSE (Mean Square
. CA 02240483 1998-06-12
-- 3 --
Error) criterion. The equalizer attempts to provide the
decision facility, adapted to the modulation, with a
signal devoid of ISI, or in which the ISI has been
greatly reduced. For this purpose, the DFE equalizer
uses transverse filters and auto-adaptive recursive
filters, which are adapted by an algorithm of the
recursive least squares type (preferably to a gradient
algorithm for reasons of speed of convergence) or are
calculated directly from an estimate of the
transmission channel-see in this respect the article by
P.K. Shukla and L.F. Turner, "Channel-estimation-based
adaptive DFE for fading multipath radio channels",
Proc. of 1989 International Conference on
- Communications, ICC'89[1]. In the learning sequences,
the known symbols are used to adapt the various
coefficients. The tracking of the channel variations
outside of the known sequences is ensured by using the
symbols as and when decided as replica.
In the HF range, the various propagation paths
are usually affected by flat "fading". When this
"fading" is large, the performance of the DFE equalizer
is degraded.
On the other hand, when jamming is present,
these techniques rapidly become ineffective and special
anti-jamming techniques are necessary, such as error-
correcting coding, the removal of jamming by notch
filtering or the use of frequency-hopping links. These
techniques, used in numerous operational systems, are
nevertheless limited when the interference is strong
and occupies the whole of the useful signal band. Under
these conditions, higher-performance anti-jamming means
should be used, based on the use of antenna filtering
techniques.
Antenna filtering techniques, which appeared in
the early 1960s and are described in particular in an
article by P.W. Howells, "Explorations in fixed and
adaptative resolution at GE and SURC", IEEE Trans-Ant-
Prop, Vol. AP-24, No. 5, pp 575-584, Sept. 1976 [2], an
exhaustive overview of which is presented in a thesis
CA 02240483 1998-06-12
- 4
by P. Chevalier, "Antenne adaptative : d'une structure
linéaire à une structure non linéaire de Voltera
[Adaptative antenna : from a linear structure to a
nonlinear Voltera structure]", June 1991 [3], aim to
combine the signals received by the various component
sensors of the antenna, in such a way as to optimize
the response of the latter to the useful-signal and
jammers scenario.
The choice of sensors and of their arrangement
is an important parameter and has a major influence on
performance. Three types o~ possibilities may be
envisaged:
- the sensors are identical and arranged at
various points in space, discrimination between the
useful signal and the jammers being effected via the
direction of arrival,
- the sensors are arranged at one point in
space (co-localized antenna) and possess different
radiation patterns. Discrimination may then be effected
according to polarization and direction of arrival,
- the above two possibilities can be combined:
several co-localized antennas may be arranged at
various points in space.
However, since the propagation and jamming
conditions may alter over time, it is necessary to be
able to adapt the antenna in real time to these
variations through the use of a particular antenna
filtering technique: the adaptative antenna. An
adaptative antenna is an antenna which detects the
sources of interference automatically, while
constructing holes in its radiation pattern in their
direction, while simultaneously improving the reception
of the useful source, without a priori knowledge about
the interference and on the basis of minimum
- 35 information about the useful signal. Moreover, on
account of the tracking ability of the algorithms used,
an adaptative antenna is capable of responding
automatically to a changing environment.
CA 02240483 1998-06-12
-- 5
Adaptative antennas are characterized by the
way in which they discriminate between the useful
signal and the jammers, that is to say by the nature of
the information about the useful signal which they
exploit. This discrimination can be effected in five
different ways according to [3]:
- based on direction of arrival,
- based on modulation,
- based on time, for example, for frequency-
hopping links,
- based on power
- blindly (for example, the higher-order source
separation methods).
Until very recently, transmission systems were
still envisaged as operating independently of the
adaptative antenna and single-sensor adaptative
equalization techniques, this leading to sub-optimal
performance.
Thus, the Dobson system described in Patent No.
PCT/AU85/00157 by R. Dobson entitled "Adaptative
antenna array", Feb. 1986 [4], which uses time-based
discrimination, succeeds in effectively rejecting the
jammers but does not seek to optimize the useful
signal/background noise ratio. Moreover, it can only be
used when the waveform allows reception when no useful
signal is present.
Within a transmission context, and when
learning sequences are introduced into the waveform, it
is preferable to use antenna processing techniques with
modulation-based discrimination since these make it
possible to optimize the useful signal/noise ratio,
while avoiding the implementation of a direction-
finding step. However, those which are e~ployed
nowadays use complex weights in respect of each of the
sensors of the adaptative antenna which are adapted via
a criterion of minimization of an MSE between the
output signal of the antenna and a replica signal. Such
an antenna, known as an SAFR (Spatial Adapted Filter
adapted with the aid of a Replica), allows the
CA 02240483 1998-06-12
-
-- 6
rejection of jammers, but in the presence of multiple
propagation paths, it:
- "points" in the direction of one of the paths
(the one which is correlated with the replica), that is
to say puts the contributions from thls path back into
phase on the various sensors (for omnidirectional
sensors a gain is therefore obtained in the signal-to-
noise ratio of 10 log N, where N is the number of
sensors used),
- and attempts to reject the uncorrelated paths
thereof (thus losing the energy associated with these
paths), the latter being viewed by the antenna as
completely separate jammers. Such an antenna can
therefore be greatly impaired in the presence of
several useful propagation paths. This is because the
uncorrelated useful paths may be rejected to the
detriment of the rejection of the jammers, and the
performance of the multisensor receiver may even become
poorer than that of the single-sensor receiver when two
temporally uncorrelated propagation paths are highly
correlated spatially.
To improve the performance of this latter
antenna processing technique, the idea is to couple it
with a single-sensor equalization technique.
Multisensor equalizers are thus obtained which comprise
a spatial part, composed of various filters arranged on
each of the reception pathways, and a temporal part
arranged at the output of the spatial part.
Several multisensor equalizers of this type
have already been proposed and studied, essentially
within the field of mobile radio transmissions. See in
this regard the articles by K.E. Scott and
S.T. Nichols, "Antenna Diversity with Multichannel
Adaptative Equalization in Digital Radio" [5] and
P. Balaban and J. Salz, "Optimum Diversity Combining
and Equalization in Digital Data Transmission with
Applications to Cellular Mobile Radio - Part 1:
Theoretical Considerations", IEEE Trans. on Com.,
Vol. 40, No. 5, pp 885-894, May 1992 [6]. They have up
CA 02240483 1998-06-12
until now been envisaged for combating the selective
"fading" created by the multipaths, in an unjammed
environment. These equalizers consist of Finite Impulse
Response filters, one on each of the pathways, followed
by an adder, and then by a symbol-rate one-dimensional
equalizer. The criterion used to optimize these
multisensor equalizers is that of minimizing the MSE
between their output and a replica.
In the equalizer proposed by Scott et al. [5],
the adaptation of the coefficients is performed by a
least squares algorithm, and its use in respect of an
HF channel cannot be envisaged for the waveforms used,
since, if the temporal spreading of the multipaths is
taken into account, the number of coefficients to be
adapted is too large for the algorithm to be able to
converge on the learning sequence.
In the equalizer proposed by Balaban et al.
[6], the coefficients are calculated after estimating
the propagation channel. The article does not tackle
the problem of a jammed environment.
A multisensor equalizer which leads to an
improvement in the performance of existing multisensor
equalizers, in particular by allowing anti-jamming, has
formed the subject of a patent application filed in
France by the Applicant on 25 February 1994, entitled
"Procédé permettant une égalisation multivoies dans un
récepteur radioélectrique, en présence d'interférences
et de multitrajets de propagation [Process allowing
multichannel equalization in a radio receiver, in the
presence of interference and multiple propagation
paths]" [7], and published as No. 2 716 761. Spatial-
diversity equalizers based on an estimate of the
tr~nsmission channel and operating in an unjammed
environment can be made robust by this equalizer by
- 35 incorporating a jammer rejection function (performed by
preprocessing sensor signals) therein. This equalizer
is of special interest since it is optimal when the
noise is temporally white (temporally white jammer(s)
and background noise and jammer(s) possessing a single
CA 02240483 1998-06-12
-- 8 --
propagation path), irrespective of the number of paths
associated with the useful signal. On the other hand,
its implementation requires a computational power which
may become large when the length of the impulse
response of the useful propagation channel increases,
and this may become injurious for certain applicatlons.
The object of the invention is to alleviate
this drawback.
To this end, the subject of the invention is a
process of multisensor equalization in a radio
receiver, of the type comprising an array of sensors
and a spatial filtering part coupled to a temporal
filtering part each comprising a specified number of
coefficients, allowing the demodulation of a digital
message of serial digital modulation type received by
the receiver, in the presence of multiple propagation
paths and interfering sources, in respect of
modulations formed from frames comprising learning
sequences and information sequences, characterized in
that it comprises:
- a first step consisting in digitizing the
signal received by each sensor, in transforming the
digitized signal to baseband, and in filtering the
baseband signal by a low-pass filtering,
- a second step consisting in performing a
seizure of synchronization on the signals emanating
from the first step, in estimating the useful paths and
the frequency shift resulting from inaccuracies in the
transmission and reception frequencies and from
ionospherlc propagation,
- a third step consisting in compensating for
the shift in frequency of the signals delivered by each
sensor, on the basis of the estimation performed in the
second step,
- a fourth step consisting in calculating on
the one hand the coefficients of a spatial filter
applied to the signals emanating from the third step
and on the other hand the coefficients of a temporal
filter applied to the replica signal, made up either of
CA 02240483 1998-06-12
g
the known symbols for the learning sequences, or from
the demodulated symbols for the information sequences,
the coefficients of these two filters being calculated
so as to minimize, under a specified constraint, a
criterion of mean square error between the output
signal from the spatial filter and the output signal
from the temporal filter, and consisting in filtering
the signals emanating from the third step with the aid
of the thus calculated coefficients of the spatial
filter, thus optimizing the gain of the array of
sensors in the direction of the useful signal at the
output of the spatial filtering and ensuring rejection
of the interference, and
- a fifth step consisting in equalizing the
signal emanating from the fourth step by one-
dimensional equalization at a symbol rate deciding the
symbols transmitted;
- the coefficients of the spatial and
equalizing filters as well as the estimate of the
useful channel being updated according to a specified
sequencing of the frames.
The subject of the invention is also a
multiplier receiver for implementing the process
according to the invention.
The main advantage of the invention is that it
is implemented by a multisensor equalizer, which leads
to slightly poorer performance than the equalizer
according to [7], but is less complex numerically.
Although the process according to the invention
is implemented on the basis of a multisensor equalizer
possessing lower computational power than that of the
abovementioned equalizer, it nevertheless performs a
jammer rejection function. Furthermore, it improves the
performance of the SAFR: the spatial filtering of the
- 35 input signals is performed by a structure identical to
the SAFR, a narrow-band structure comprising one
complex coefficient per pathway, but the criterion of
optimized MSE is different. Unlike the SAFR, the
algorithm does not optimize the MSE between the output
~ CA 02240483 1998-06-12
-- 10 --
from the spatial part and a replica signal (correlated
with one of the paths associated with the useful
signal), but the MSE between the output from the
spatial part and the output from a temporal filter at
whose input the replica signal is present. The process
according to the invention allows the spatial part to
reject only the interference, and not the multipaths
associated with the useful signal which are
uncorrelated with the replica. It therefore leads to a
general improvement in the performance of the SAFR.
Other advantages and characteristics of the
present invention will emerge more clearly on reading
the description which follows and the appended figures
which represent:
- Figure 1, the main steps of the process
according to the invention,
- Figure 2, a functional diagram of a
multisensor receiver for implementing the process
according to the invention,
- Figure 3, a functional diagram of the spatial
filtering and channel estimation means according to the
invention, and
- Figures 4 and 5, the updating and chaining of
the processing operations of the receiver implementing
the process according to the invention.
The output from the spatial part is processed
by a symbol-rate one-dimensional equalizer which
decides the symbols transmitted. This equalizer may in
particular be based on a Viterbi algorithm, or be a DFE
equalizer.
The present invention therefore carries out the
following functions jointly:
- rejection of jammers,
- optimization of the gain in the direction of
- 35 the useful signal,
- reduction in the distortions created by the
multipaths associated with the useful signal.
CA 02240483 1998-06-12
.
The first two functions are performed by the
spatial part, and the third by the equalizer placed at
the output thereof.
An exemplary embodiment is given below within
the context of HF transmissions using QPSK ("Quadri-
Phase-Shift Keying") modulation:
- 1/2 Nyquist transmission filter whose 3 dB
band is 2400 Hz,
- bit rate equal to 2400 baud,
- symbols transmitted made up of frames of 256
symbols comprising an 80-symbol learning sequence
placed at the start of the frame (to perform
synchronization and to calculate the coe~ficients of
the equalizer), followed alternately by sequences of 32
information symbols and sequences of 16 known symbols
(to allow the equalizer to track the variations in the
channel).
The process according to the invention,
illustrated in Figure 1, comprises five main steps 1 to
5:
- a first step 1 for digitizing the signal on
each pathway, the baseband conversion thereof and
Nyquist filtering thereof,
- a second step 2 for synchronizing the signal
and estimating the frequency shift, resulting from the
inaccuracies in the transmission and reception
frequency synthesizers and ionospheric propagation,
- a third step 3 for compensating for the
frequency shift in the sensor signals,
- a fourth step 4 of spatial filtering of the
signals and for estimating the useful channel at the
output of the spatial filter, which carries out
interference rejection and optimizes the gain in the
direction of the useful signal, and
- a fifth step 5 of one-dimensional
equalization at a symbol rate, which decides the
symbols transmitted (decided symbols).
The coefficients of the spatial and equalizing
filters as well as the estimate of the useful channel
. CA 02240483 1998-06-12
- 12 -
are updated at the start of each of the information
sequences SI of the current frame.
In the exemplary embodiment which relates to
the HF range, equalization is performed by a DFE
equallzer, the coefficients of which can be calculated
either directly from the estimate of the useful channel
at the output of the spatial filter, or by an adaptive
algorithm operating independently of the spatial
~iltering.
The process according to the invention is
implemented by a multisensor receiver a functional
diagram of which is illustrated in Figure 2.
It comprises an array of sensors 1 to N,
coupled to the input of means 6 for digitization,
baseband band conversion and low-pass filtering of the
signals received by the array of sensors. They are
output-coupled to means 7 for compensating for the
frequency shift between the transmission and reception
frequencies, which means are themselves output-coupled
to means 8 of spatial filtering and channel estimation.
The output of the spatial filtering means 8 is coupled
to the input of an equalizer 9, for example a DFE,
Viterbi or other equalizer.
Synchronizing means 10 receive the signals
delivered by the digitization, baseband conversion and
low-pass filtering means 6 and inject their own
information into the frequency-shift compensation means
7 (information relating to the estimation of the
frequency shift) and into the spatial filtering and
channel estimation means 8 (information relating to the
detection of the useful paths: number, delays, powers).
A transmitted signal d(t) arrives at the array
of sensors 1 to N, also referred to as an antenna,
comprising N sensors, after it has passed through the
- 35 ionospheric channel. Each of the P propagation paths is
received by the antenna with a complex gain ai(t) and a
delay ~i with respect to the signal transmitted. Let x~t)
be the vector formed by the signals received by the N
component sensors of the antenna:
- CA 02240483 l998-06-l2
- 13 -
x(t) = ~ t) d(t - ~) 51 + ~(t) (1)
j 1
where:
- s; is the direction vector associated with
path i,
- b(t) is additive noise, which is independent
of the useful signal and takes into account the
contributions from background noise and jammers.
The non-stationarity of the channel impinges on
the amplitudes and phases of the various paths, and
hence on the time-dependence of the quantities ai(t).
On the other hand, the delays ~i are relatively steady
over durations of the order of a quarter of an hour and
can therefore be regarded as constant.
In the signal digitization and Nyquist
filtering step 1, the signals are digitized at a
frequency which is a multiple of the symbol frequency,
so as to obtain sufficient accuracy with regard to the
instant of synchronization. For the exemplary
embodiment described, the signals are digitized at
9600 Hz, this corresponding to an oversampling by a
factor of 4. The signals are next transposed to
baseband and then filtered by a low-pass filter, of the
Nyquist type for example.
The multisensor equalization implemented by the
invention is necessarily preceded by a synchronization
step 2. This step 2 implements a multisensor
synchronization process described in particular in a
patent filed by the Applicant on 21 January 1994,
entitled "Synchronisation en présence de brouilleurs et
de multitrajets [Synchronization in the presence of
jammers and multipaths]", published as No. 2 715 488
[8], or any other process allowing synchronization in
the presence of jammers and multipaths. It is used in
order to:
- perform the seizure of synchronization,
- CA 02240483 1998-06-12
- 14 -
- estimate the number of paths, as well as the
delay times relating to the various paths and their
relative powers,
- estimate the frequency shift between the
synthesizers at the transmitting and receiving ends.
This frequency shift ls compensated for before carrying
out the multisensor equalization.
Let Te denote the sampling period in respect of
synchronization and Ts the symbol-period of the
modulation transmitted (Te = 4 in the exemplary
embodiment described).
The estimated delay times can be expressed as a
function of Te, ~i = Pi Te, and the sampled signal
received by the antenna can then be written:
x(nTe) = ~ aj(nTe) d(nTe-pi Te) s; + ~(nTe) 2)
js1
The computation algorithm of the spatial part
works at the symbol rate, the input signal sampled at
the symbol rate being written:
x(n) = ~ ~j(n~ cl(nTs-pi Te) s; + b(n) (3)
~=1
Step 3 makes it possible to compensate for the
frequency shift (3) ~f estimated at the completion of
the synchronization step. This shift is compensated for
in the input signals by applying the following formula:
x'(n) = x(n) exp~ f F--) (4)
s
A structure of the spatial filtering and
channel estimation means 8 is illustrated by the
diagram of Figure 3.
- CA 02240483 1998-06-12
-
- 15 -
It comprises a spatial filtering part 11
delimited by a discontinuous closed line and a temporal
filtering part 12. The spatial filtering part 11
implements a filter 13i with a single complex
coefficient per pathway, which makes it possible to
weight the input signal by a first weighting vector w.
The signals arising from each complex coefficient are
summed by a summator 14. The temporal filtering part 12
implements a temporal filter comprising R+1
coefficients which makes it possible to weight the
replica signal by a second weighting vector h. The
vector h makes it possible to obtain an estimate of the
useful channel at the output of the spatial part 11
The output signal from the spatial part, denoted
y(t)=w x(t), is then supplied to the DFE equalizer 9
coupled to the output of the spatial part 11.
Letting d(n)=[d(nTs),d(n-l)Ts,...,d(n-R)Ts]T, be the
input vector of the temporal part 12, sampled at the
symbol rate, then the optimized criterion for
calculating h and w is an MSE criterion which is
expressed by the following formula:
MSE =E~¦¦e(t)¦¦2]=E~¦¦w+x(t)-h+~t)~
where ¦¦e(t) ¦¦ corresponds to the norm of e(t)
and E[¦¦w+x(t)-h+d(t)¦¦~to the mathematical expectation,
and writing:
Rxx = E[x(t)x(t) ],
RDX = E[d(t)x(t) ],
RDD = E[d(t)d(t)]-
The superscript + designating the conjugate
transpose operator.
The minimized criterion is expressed by the
following formula:
- CA 02240483 1998-06-i2
-
' - 16 -
MSE = = w+Rxxw--fi+ ~Xw - W ~X h--fi ~Dfi i6)
Since the minimization of this criterion leads
to the null solution, it is necessary to append a
constraint. Two types of constraints may be envisa~ed:
- a first constraint or h+h=l, that is to say a
norm constraint on the vector h, and
- a second constraint or h+f=l, where f is a
vector with (R+l) components containing R zeros and one
one corresponding to the path of index io of highest
power (which path is determined through the
synchronization 2): f = [0, ..., 0, 1, G, ~-, 0] T
where the superscript T denotes the transpose
operator. This constraint allows the spatial part 11 to
"point" in the direction of the principal path.
Advantageously, the synchronization 2 is
performed in such a way that the delay of the path of
index io is a multiple of the symbol period.
The calculation of the solution to the
optimization problem is described below for each of the
above constraints.
Taking the constraint h+f=l, and letting h ,
respectively d , denote the vector with R coefficients
which is formed from h, respectively d, by deleting
the component io, the minimized MSE can be written:
MSE=E~ t)¦¦] =E[¦¦W+X(t)-h+d'(t)- ~t-pjOTelD~ (7)
and the solution to the minimization problem is
given by Wiener's formula:
= ~ E ( ) (X(t)+ a~(t~+) ~ E (_ ) d(t - Pi~)Te) (8)
-h' d~(t) d~(t)
the superscript designating the conjugate
operator.
CA 02240483 1998-06-12
- 17 -
. Writing:
~'X =E[d(t)X~t)+],
R{,~ = E [~(t) ~(t)t}
rxd = E [~t) d( t - pjoTe) 1
rD-d=E[~(t)~t~PioTe) ]
We obtain the following two equations:
RXXW - ~ X h=rXd
RD'X W--F~D'D'h = rD'd
The vector h is therefore expressed as a
function of the vector w:
h~ D (RD XW rD~d)
and the vector w can be written:
W = A 1(rXd- ~'X RD~D~ rD'd ) ( ~ ~~
with:
A=RXX-RDX RD~D~ X (11)
To provide a better understanding of the
behaviour of the spatial part 11, the expression for
the filters w and h when the array receives two
useful paths s,~ds2, whose contributions are
uncorrelated, is given below:
x(t~=~1d(t)s1+ ~2 ~t-r)S2 +b(t)
- Under these conditions, the matrix RD'X may be
expressed, assuming also that the symbols transmitted
are mutually uncorrelated (RD'D = Id, where Id
CA 02240483 1998-06-12
-
- 18 -
corresponds to the Identity matrix and rDd=O), as
follows:
~'X = ~2 ~~~ 52+~~. ~~~ ~ where the vector ~ is
placed in the row corresponding to the delay 1.
We therefore obtain:
A=RXX -1~21 S252+. i.e., letting R denote the
correlation matrix for the background noise component +
jammers:
A=1all2s1s1 +1~2~2S252++ R - 1~212 S2 s2+ = ¦a1l2 s1 51~ + R.
The matrix A therefore corresponds to the
correLation matrix RXX which would be obtained in the
presence of the first path only. Moreover, the second
path does not come into the correlation vector rxd.
The weight vector defining the spatial part ll
is therefore the weight vector corresponding to the
SAFR adapted to path l, as if the second path were not
present. Thus, the antenna "points" its main lobe in
the direction of path l and places zeros in the
direction of the jammers. The gain in the direction of
path 2 is a priori arbitrary. At the output of the
spatial part ll; the second path is therefore not
eliminated and an equalization of the signal at the
output is necessary.
Considering the second constraint h+h=l,
minimization of the MSE is obtained, for a
vector w which zeros the gradient of the criterion
with respect to w through the following formula:
Vw MSE=RXXW - ~X h (12)
The vector w is expressed as a function of the
vector h by the following formula:
w =Rxx ~ X h (13)
CA 02240483 1998-06-12
~ .
- 19 -
Replacing w by its value as a function of h in
the expression for the minimized criterion, we obtain:
MSE =h (~ D ~ ~X RXX ~X ) fi (14)
The vector h which is the solution to this
problem is therefore the eigenvector associated with
the minimum eigenvalue of the matrix B, with:
~ = ~ D- ~X RXX ~X (15)
The vector w may be deduced from this using
the formula (13).
The equalization step 5 is implemented by an
equalizer 9 of the single-sensor DFE type. It consists
of a transverse filter, not represented, at the symbol
rate, and of a recursive filter. The input signal for
the transverse filter is the signal emanating from the
spatial filtering means 8: y(t) = w+x(t). The input
signal for the recursive filter is formed from the
known symbols of the learning sequences SA and from the
decided symbols. A decision facility, not represented
either, is placed at the output of the transverse and
recursive filters and allows access to be had to the
useful symbols transmitted.
The processing operations are performed
according to a timing diagram illustrated by Figures 4
and 5.
In a first step, the weighting vectors w and h
are updated at the start of each of the information
sequences SI (= end of the learning sequences SA), i.e.
four times per frame in the example considered. This
updating thus ensures correct tracking of the non-
stationarities of the useful propagation channel and
jammer(s).
In a second step, the data supplied to the DFF
equalizer 9 so that it can demodulate the next
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information sequence SI, are filtered with the aid of
the vector w. The vector h can be used to calculate
the coefficients of the DFE equalizer 9 directly.
In a third step, the DFE equalizer 9
demodulates the information sequence SI.
In a fourth step, the symbols o~ the
information sequence SI which are demodulated by the
equalizer 9 and the known symbols of the next learning
sequence SA are used as inputs to the algorithm for
~ 10 estimating w and h (tracking of the variations in the
propagation channel).
The calculation of the weighting vector w
allowing calculation of the output from the spatial
part 11 and calculation of the estimate of the useful
channel h at the output of the spatial filtering 8 is
performed jointly while optimizing the criterion
described above.
The calculation of the weightings can be
performed in two modes:
A first initialization mode is used to
calculate w and h over the first learning sequence SA
of the first frame received, or when there are
discontinuities in the processing (readjustment of
synchronization for example). The calculation is
performed over the L symbols of the learning sequence
with the aid of formulae (9) (10) (11) (constraint
h+f=1) or (13)(14) (constraint h+h=1), using the
conventional unbiased estimator for calculating various
correlations:
L Rk=R+1 (16)
where U(k) and V(k) can represent
d~(k)~x~(k)ord(t-pioTe) for the constraint h+f=l, and
d(k)orx(k) for the constraint h+h=1. For this latter
constraint, the calculation of h entails a
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eigenvalues, and eigenvectors which can be produced for
example by a Jacobi algorithm.
(The summation begins with k = R+1) so as to
take into account the fact that dO involves the
symbols d(k) to d(k-R). It is possible to begin the
summation for k=1 by regarding d(k) = 0 for k<0).
In the normal mode, the tracking of the
variations in the use~ul propagation channel and jammer
can be performed by several algorithms:
10- least squares algorithms with neglect factor:
w ~dh are calculated over the symbols of the
information sequence which has just been demodulated
and over the learning sequence which follows it with
the aid of formulae (9) (10) (11) (constraint h+f=l ) or
15(13) (14) (constraint h+h=1), using a neglect factor
~(0< ~ < 1) to calculate the various correlations at
each iteration n:
v(n)= ~ A n-k U(k) V(k)+ (17)
k=1
The calculation of w ~dh is then performed on
the basis of these correlations for each iteration n
corresponding to the start of an information sequence
SI.
25- gradient algorithm with adaptive step. See in
this regard an article by P. Bragard and G. Jourdain,
"A fast self optimized LMS algorithm for non-stationary
identification", IEEE proceedings ICASSP 1990, pp 1425-
1428[9] where w ~dh are calculated over the symbols of
the information sequence SI which has just been
demodulated and over the learning sequence which
follows it by a gradient algorithm, the adaptation step
of which is itself optimized in respect of the non-
stationary channels.
35It should be observed that the gradient
algorithm with adaptive step is also used over the
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first learning sequence SA of the first frame, after
the initialization of w and h described above has been
performed. The data of this first sequence are
therefore used twice, thus making it possible to obtain
good initialization of the gradient algorithm.
The DFE equalization 9 which follows the
spatial part 11 can be carried out by any existing type
of DFE equalizer.
In a first type of DFE equalizer 9, the
estimate c of the propagation channel at the output of
the spatial part 11 is calculated firstly from h,
through the following formulae:
- for the constraint h+f=l:
c = h ~~min f, where ~:min represents the m; n; mum MSE
of the criterion (5).
The components of h therefore give the
coefficients of the channel at the output of the
spatial part 11, except for the coefficient
corresponding to the constraint, for which ~min must be
taken away.
- for the constraint h+f=l:
c=(l~~min) h=(l-;~min) h,
where ~min represents the minimum eigenvalue of
the matrix B defined by formula (15).
The channel at the output of the spatial part
11 is proportional to h, the proportionality factor
being equal to l-~n.
The coefficients of the DFE equalizer 9 are
calculated secondly directly from the estimate c of the
propagation channel [1]. The updating of the DFE
equalizer 9 is therefore performed consecutively to
that of the filters w ~dh, at the start of each of the
irformation sequences SI.
If this possibility is used, only the samples
corresponding to the information sequences SI are
filtered by the spatial part.
In a second type of DFE equalizer 9, the
coefficients of the DFE equalizer 9 are calculated on
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the basis of an algorithm of the least squares type
(for example the so-called "spatial trellis" algorithm
detailed in the thesis by L. Fety, "Méthodes de
traitement d'antenne adaptées aux radiocommunications
[Antenna processlng methods adapted to radio-
communications]", ENST doctoral thesis, June 1988 [10])
independently of the channel estimation. In this case,
the known symbols are used as replica over the learning
sequences SA and the demodulated symbols are used as
replica over the information sequences SI.
Consequently, unlike the previous case, all the samples
have to be filtered by the spatial part (learning
sequences SA and information sequences SI).
In a third type of DFE equalizer 9, the
equalization can comprise, upstream, a filtering
adapted to the channel, the output from which is
sampled at the symbol rate and the input of which is
sampled at one or two times the symbol rate. In this
case, the output from the spatial part 11 is calculated
with a rate compatible with the channel-adapted input
of the filter. The channel estimation can be performed
either independently of the calculation of the spatial
part 11, or by taking the spatial part 11 into account
and in the latter case the filter h must be sampled
with a rate which is compatible with the sampling at
the input of the channel-adapted filter. The DFE
equalization 9 at the output of the adapted filter is
then performed as in the first or second type of DFE
equalizer.
The DFE equalizer 9 can be replaced, in
particular for applications of the GSM type where the
length of the channel impulse response expressed in
terms of number of symbols is smaller, with a decision
facility based on the Viterbi algorithm. The
- 35 observations made above in respect of the DFE equalizer
9 are still valid:
- the estimation of the useful channel at the
output of the spatial filtering 11 can be done either
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independently o~ the calculation of the spatial part,
or by using the vector h.
- if the vector h is used, it must be sampled
at a rate equal to that at the input of the channel-
adapted filtering.
