Note: Descriptions are shown in the official language in which they were submitted.
2 1 9432~
PROCESS FOR MULTI-SENSOR EQUI~I ISATION IN A
RADIO RECEIVER IN THE PRESENCE OF
INTERFERENCE AND MULTIPLE PROPAGATION PATHS
s Background of the invention.
This invention cGnc~r,~s a process for multisensor equalization
in a radioelectric receiver co,)sisl;ng of de",o~ ing a digital mess~ge in the
presence of multi-propag~iG" paths and inte,rering sources, reducing the
number of factors to be adapted necessary for the multisensor equalizer
calculation, for modulations formed of frames comprising learning sequences
and inror"~alion symbol sequences. The invention also concerns a
radioelectric receiver embodying such a process. The invention is based on
anter",a processing techniques, and thererore requires the use of a network
co",p,ising several sensors.
S There are many fields of application of this invention, all
conceming communications that need an equalizer to perform the single
sensor demodulation, such as for example:
- high throughput modulation (2400 biVs, etc.) in the high frequency (HF)
range,
- modulations of systems in the V/UHF range such as GSM, DECT, etc.
For many applications in digital radio communication, transmission
between the transmitter and the receiver takes place along several
propagation paths:
- in the HF range, multi-propagation paths output from reflections
on the various ionospheric layers may be sp~ced by 5 ms, or several times
the symbol duration in thé case of modulations with a typical band width of 3
kHz.
- in the VIUHF range, for very high GSM type throughputs (270
kbiVs, giving a symbol duration of 3.7 ,us) in urban or mountainous
environ",ents, the various paths originating from reflections on various
obstacles (buildings, mountains, etc.) may be separated by 10 or even 20 ,us.
Since the delay time for these various applications may exceed the
symbol duration, equalization becomes necessary to compensate for the
inter-symbol interference (IIS) thus generated. In many systems currently in
21 q4326
service adaptation to these prop~g~tion conditions is made possible by
insertion of the known receiver learning sequence in the wave shape.
Dirrerenl solutions are then possible for adaptive equalization of the received
useful signal.
The first two solutions described below concern single sensor
equalization. Antenna filtering techniques described below use multisensors.
A first solution consists in using a Viterbi algorithm which requires a
prior estimation of the prop~a~tion channel using the learning sequence. This
equalisation method has the advantage of minimising the probability of error
o across the whole sequence of info""alion symbols but becomes very costlywhen the duration of the pulse response of the channel is much greater than
the symbol duration. In fact the number of states that the Viterbi algorithm
must process is equal to ML where M is the size of the modulation alphabet
and L is the length of the pulse response of the channel expressed as a
number of symbol periods. This solution is used for GSM type applications
where the Viterbi algo.ill"n typically consists of 32 states (L = 5 and M = 2).
In the HF band the particular field of application of the invention the
number of states becomes too great for the Viterbi algorithm to be practically
realisable (typically M is 4 or 8 while L is equal to 12 which corresponds to
a pulse response spread over 5 ms) and a second solution using a DFE
equaliser is often used.
This second solution consists in using learning sequences as the
response of an adaptive algorill"" used to minimise a MQE (Mean Quadratic
Error) criterion. This solution uses a Decision Feedback Equaliser (DFE).
Such an equaliser is intended to supply to a decision module adapted
to the modulation in question a signal in which ISI has been eliminated or at
least reduced to a great extent. To this end the DFE equaliser uses
transverse and recursive self-adapting filters which are adapted by a least
squares type algorill"" prerer~ed to a gradient algorithm for reasons of speed
of convergence. The known symbols in the learning sequences are used for
the adaptation of the different coefficients. The tracking of channel variationsbeyond the known sequences is effected using symbols which are selected
(detemined) as responses as necess~ry during the execution of the process.
- - 21 q4326
The single-sensor DFE equaliser can compensate for ISI caused by
multiple propagation paths, but is not capable of phase realigning these
dirrerent paths. Thus, in the pres~,)ce of two stationary paths of the same
amplitude, the DFE equaliser produces losses of approximately 3 d~ with
s respect to a white Gaussi-n noise channel: it endeavours to retain the
co.lt,ibution of one of the paths and to eliminate the second using the
recursive part.
Moreover, in the HF band the dirrerent prop~g~tion paths are very
often affected by flat fading. Fading is a phenomenon linked to the variation
l0 of the multiple paths which in turn produees a variation of the received power,
or even in extreme cases fading or dying out of the signal paths. When fading
is strong, a DFE equaliser's performance is seriously reduced.
In addition, these techniques rapidly become inefficient in the
presence of jamming, which means that it is necess~ry to use known specific
15 antijamming techniques such as error correction encoding, elimination of
jalr,l"ing by notched filtering, use of frequency evasion links, etc.. These
techniques are used in many operational systems, but are nonelheless of
limited effect when interference is strong and occupies the whole of the useful
signal band. In such conditions, it is necessary to use more effective
20 antijamming means based on the use of antenna filtering techniques.
Antenna filtering techniques appeared in the early 1960's. One in
particular is described in an article of P.W. HOWELLS "Explorations in fixed
and adaptive resolution at GE and SURC", IEEE Trans-Ant-Prop, vol. AP-24,
no. 5, pp 575-584, Sept. 1976, while an exhaustive synthesis is presented in
25 a doctorate thesis presented by P. CHEVALIER at the University of Paris sud
in June 1991 entitled "Antenne adaptalive: d'une structure linéaire à une
structure non lineaire de Volterra" ('~he adaptive antenna: from a linear
structure to a non-linear Volterra structure"). These techniques are designed
to combine the signals received by the various sensors making up the
30 antenna so as to optimise its response to the useful signal and jamming
sce"a~ io in question.
The selection of sensors and their disposition is an important
parameter which has a central influence on the performance of the system.
Three basic configurations are possible:
4 21 94326
- the sensors are identical and disposed at dirrere"t points in space,
discrimination between the useful signal and inte, rerence being effected
according to the direction of arrival;
- the sensors are all disposed at the same point in space (colocalised
antenna) and have dirrerent radiation diagrams. This means that
discrimination can be carried out on the basis of polarisation and direction of
arrival;
- the two configurations desuibed above can be combined: several
colcc~lised anlennas can be disposed at difrer~nt points in space.
o In addition, since propagation and jamming conditions can change
over time, it is essential that the system be capable of adapting the antenna
to these variations in real time through the use of a particular antenna filtering
technique: the adaptive antenna. An adaptive antenna is one which detects
and reacts to sources of interference automatically by constructing holes in
its radiating diagram in their direction, while at the same time improving
reception of the useful source, without any prior knowledge of the
interference and on the basis of a minimal amount of infor",ation on the
useful signal. Moreover, the tracking capabilities of the algorithms used make
an adaptive antenna able to respond automatically to a changing
environment.
Adaptive antennas are characterised by the way in which they
discriminate between the useful signal and interference, i.e. by the nature of
the infor",ation relating to the useful signal which they use. This
discrimination process can be carried out in one of five different ways:
- according to direction of arrival,
- accorcling to modulation,
- according to time, for example, with frequency evasion links,
- according to power,
- blindly (for example, higher order source separation methods).
Up until very recently, transmission systems have always been based
upon the independent operation of single-sensor adaptive equalisation and
adaptive antenna techniques, which results in less than optimised
performance.
'_ 21 94326
Thus, the system described in an article by R. Dobson entitled
"Adaptive antenna array", patent no. PCT/AU85/00157 of February 1986l
which uses disc,i",ination according to time, is efficient in terms of
Inte,rerence rejection, but makes no ~tlempt to improve the useful signal to
5 noise ratio.
In a transmission context, and when learning sequences are
introduced into the wave forml it is preferable to use antenna processing
techniques based on discrimination accor~Ji. I9 to modulationl as these
techniques enable optimisation of the useful signal to noise ratio. Most
lO techniques used nowadays attribute complex weightings to each of the
s~nso,s of the adaptive antenna. Such an antenna is capable of rejecting
interference, but in the presence of multiple propagation paths:
- it llalignsll on the direction of one of the pathsl i.e. it phase realigns
the contributions of this path on the various sensors (for omnidirectional
15 sensors, a signal to noise ratio gain of 10 log N is obtained, where N is the number of sensors used),
- it also alle,npts to eliminate non-correlated paths from the signal
thus losing the energy associated with these paths.
In order to improve the perfol"~ance of this type of antenna processing
20 in the presence of multiple propaga~ion pathsl it is possible to combine it with
a single-sensor equalisation technique to obtain a multi-sensor equaliser
consisting of a spatial partl composed of different filters disposed on each of
the reception channelsl and a temporal part located at the output of the
spatial part. All the filters making up the spatial part and the temporal part are
25 jointly adapted to the same error signal.
Several multi-sensor equ~lisers have already been proposed and
studiedl principally in the field of mobile radio transmissions, and these are
particularly described in an article by K.E. Scott and S.T. Nichols entitled:
IlAntenna diversity with Multichannel Adaptive Equalization in Digital Radio'l
30 and in an article by P. Balaban and J. Salz entitled IlOptimum Diversity
Combining and Equalisation in Digital Data Transmission with Applications to
Cellular Mobile Radio - Part 1: Theoretical Considerationsll, IEEE Trans. on
Com., vol. 40, no. 5, pp 885-894, May 1992.
6 21 94326
Up to now, such eq~ isers have been intended to combat the
selective fading enge,)de~d by multiple paths in a nonjammed environment.
They consist of Finite Pulse Response filters, one on each channel, followed
by an adder then a monodimensional eg~ ~liser equ~lising at the symbol rate.
s The criterion used for the optimisation of these multi-sensor equalisers is the
minimisation of MQE between their output and a response determined by the
leaming sequences.
In the equ~liser proposed by Scott et al, coefficient adaptation is
carried out by a least squares algorili~,n, and its use for a HF channel cannot
be envisaged given the wave forms used. Taking into account the temporal
spread of the multiple paths, the number of coefficients to be adapte-J is too
great for the algo, il~"n to be able to converge with the learning sequence.
Summary of the invention.
The aim of the invention is to resolve these problems.
S To this end, the invention relates to a process for multi-sensor
equalisation in a radio receiver consisting of a spatial part connected to a
te""~ordl part composed respectively of a determined number of filters and
receiving a radio signal consisting of at least a learning sequence made up of
symbols known to the receiver and an information sequence made up of
useful symbols, and consisting in a first stage for the preliminary processing
of the signal received by the receiver, of the transformation of the signal
received by at least two sensors into an equivalent baseband signal, of the
sampling of the b~seb~nd signal at a rate which is a multiple of the symbo
rate and of the filtering of the sampled signal using a low-pass filtering
process, wherein, in the presence of inte,ference and multiple propagation
paths, it consists, in order to reduce the number of filter coefficients to be
adapted, in a second stage, of a synchrol,isation measurement process, of
the estimation of the number of paths in the signal, the delay times
~ssociated with the various paths and their relative powers, and the
frequency offset between the emission and reception of the signal in order to
compensate for it, and wherein, in a third stage of multi-sensor equalisation, it
consists in selecting a determined number of paths according to a determined
criterion from the number of paths estimated in the synchronisation stage, in
filtering via a spatial processing procedure the signal received by the receiver
21 94326
using the filters of the spatial part, in filtering via a temporal processing
proce-lure the signal output by the spatial part using the filters of the temporal
part, the respective coefficients of the filters of the spatial part and the
tei"poral part being jointly and periodically recalcul~ted at each iteration by
an adaptive algorithm working at the symbol rate in order to minimise the
esli",dlion error produc~d between the receiver output signal and the
response signal.
The invention also relates to a radio receiver featuring at least one
multi-sensor spatial diversity equaliser consisting of a spatial part connected
to a te,nporal part and receiving a digital radio signal composed of at least a
leaming sequence made up of symbols known to the receiver and an
inro""a~ion sequence made up of useful symbols, featuring, in order to
reduce the number of filter coeffficients to be adapted in the spatial and
temporal part in the presence of interference and multiple propagation paths:
-at least two sensors connected to a unit carrying out the preliminary
processing and syl,chronisation of the receiver input signal, the outputs of
this unit being connected respectively to a first series of inputs and a second
series of inputs of the spatial part of the equaliser, the first series of inputs
corresponding respectively to the inputs of the spatial filters relating to eachof the paths selected from a determined number of paths detected, and the
second series of inputs corresponding respectively to the inputs of a unit for
the calculation of the input signals of the transverse part of the temporal partof the equaliser, and wherein the transverse part of the temporal part features
a transverse filter of determined coefficients, the temporal part also featuringa recursive part consisting of a decision module whose output is connected to
the input of a recursive filter of determined coefficients, the recursive filterbeing located in a loop and receiving on its input the sum of the output
signals of the spatial part and of the transverse part, from which is subtractedthe signal output by the recursive part.
The process according to the invention on the one hand enables an
improvement upon the performance of the various single-sensor equalisers
currently in existence: in the case of a stationary environment, the process
according to the invention enables an improvement of 10 log N in antenna
gain, where N is the number of sensors, where the sensors are identical, with
21 94326
a gain of 3 dB on the phase realignment of the paths in the case of two
stationary paths of the same power.
Moreover, the multi-sensor equalisation process according to the
invention improves to an even greater extent the performance of
5 sins'~ scnsor equalisation in the presence of flat fading on the various
prop~g~tion paths.
The structure of a receiver accordi,lg to the invention using a
single-sensor equaliser also greatly re~luces the number of coefficients to be
adapted in co,nparison with the structure proposed by Scott et al, and can
o ll ,ererore be implemented on a HF or GSM channel.
Brief clesc, i~tion of the drawings
Other characteristics and advantages of the invention will be made
clear in the following desc,ip~ion, acco,llpanied by the appended figures
which represent, respectively:
- figure 1, the main stages of the process according to the invention;
- figure 2, the main stages of the preliminary processing stage;
- figure 3, the main stages of the synchronisation stage of the process
according to the invention;
-figure 4, the main stages of the multi-sensor adaptive equalisation
20 stage of the process according to the invention;
- figure 5, an example structure of a radio receiver according to the
invention;
-figure 6, an algorithm of the spatial matrix used by the process
according to the invention;
- figure 7, an array of antennas used by the receiver according to the
invention;
-figure 8, a graphic representation demonstrating the importance of
the spatial part in the structure of the equaliser of the receiver according to
the invention.
30 Description of the invention.
Stage 1 of the process according to the invention represented in figure
1 consists of the preliminary processing of a digital signal received by at least
two sensors Cn, where n = 1 to N, of a radio receiver.
-
21 94326
Stage 2 of the process according to the invention consists in
sy"chronising the pre-processed received signal with an emitted signal
consisting of synchronisation sequences known to the receiver in the
pr~sence of inte,rerence and multiple paths.
Syn~llronisation stage 2 necess~rily precedes multi-sensor
equalisation stage 3, which consists of spatial processing of the signal
followed by te",pGral processing, both processing procedures being jointly
adapted.
Preliminary processing stage 1 is subdivided into three main stages 4,
lO 5 and 6 as illustrated in figure 2:
- stage 4 consists of the transformation of the radio signal output by sensors
Cn into a baseband signal;
- stage S consists in sampling the transformed b~seband signal at a rate Te,
Te being a multiple of the symbol rate Ts, and
- stage 6 consists in filtering the sampled signal using a low-pass filtering
procedure.
The pre-processed and sy"chronous signal derived from stages 1 and
2 is suhseq~ently referred to as " the signal output by the reception
channels ".
Multi-sensor synchronisation stage 2 is subdivided into three main
stages 7, 8 and 9 as illustrated in figure 3:
- stage 7 consists in measuring the synchronisation of the signal received by
the sensors against learning sequences made up of symbols known to the
recelver;
25 - stage 8 consists in estimating of the number of paths followed by the useful
signal as well as the delay times associated with these paths and their
relative powers, and
- stage 9 consists in estimating the frequency offset between emission and
reception. This frequency offset is co,npensated for before the multi-sensor
30 equalisation stage is carried out.
Multi-sensor adaptive equalisation stage 3 is subdivided into five main
stages 10 to 12 as illustrated in figure 4.
~~ 21 94326
In stage 10 the process accordi"g to the invention chooses to adapt to
K paths selected from the P paths identified at the end of synchronisation
stage 2. This selection can be based on a number of different criteria:
- limit the number of coefficients of the spatial processing cor"po"ent of the
s equalisation for reasons of c.~cul~tion power or optimisation of the
conver~e"ce speed, by imposing, for example, K < 2;
- select all paths of which the relative power with respect to the main power issufficiently great for phase realignment to be beneficial, for example a relative
power of -5 dB;
- use the two criteria described above simultaneously and concurrently.
Spatial processing stage 11 consists in filtering the input signal using
filters disposed on each of the sensors making up the array, and phase
realigns the contributions of all the paths selected, provided that these are
sufficiently spaced in spatial terms, which implies a coefficient of spatial
correlation between the different direc~ing vectors which is u su~ficiently~ less
than 1, as well as the positioning of the gain of the antenna in the direction of
the useful signal.
Spatial processing stage 11 also rejects interference.
Temporal processing stage 12 consists in filtering the signal output by
spatial processing stage 11 with a filter consisting of a transverse part and a
recursive part, and combats any ISI remaining after the spatial processing of
stage 11 due either to paths not selected in the algorithm or to paths which
are spatially too close to one another for the spatial processing of stage 11 tobe capable of separating them.
The coefficients of the filters used for the spatial and temporal
processing ~ssoci~ted respectively with stages 11 and 12 are jointly adapted
to the symbol rate Ts by the adaptation algorithm so as to minimise MQE
between a response signal and the result of equalisation stage 3. The
response signal consists either of known symbols belonging to a leaming
sequence or of u determined n symbols where the symbol in question belongs
to an info, mation sequence.
A radio receiver according to the invention receiving a digital signal
including learning sequences and information sequences is schematically
illustrated in figure 5.
- 21 94326
This receiver imple"~enls the process according to the invention and
the desuiption which follows is intended to aid understanding of its operation.
An emitted signal d(t) arrives at a reception array of a receiver
according to the invention featuring a determined number of sensors Cn,
s where n = 1 to N, after its journey through the ionospheric channel. Each of
the P propagation paths followed by the signal is received by the antenna
with a complex gain aj(t) and undergoes a delay tj with respect to the emitted
signal. The vector X(t) forrned by the signals received by the sensors is
determined by the following formula:
X(t) = ~aj(t)d(t- ~j)Sj +B(t) (1)
i=1
where: Sj represents the direction vector associated with path i,
and B(t) is added noise independent of the useful signal which takes
into account the contributions of background noise and interference.
The non-stationary nature of the channel affects the amplitudes and
phases of the various paths, hence the dependence in time of the quantities
aj(t). On the other hand, the delays tj are relatively stable over periods of the
order of a quarter of an hour and can therefor~ be considered constant.
Sensors Cn are respectively connected to the input of a preliminary
processing and synchronisation unit 13 featuring conventional means, which
are not represented, for the transr~"nalion of the signal received by sensors
Cn into a baseband signal, its sampling at the rate Te, its transformation into
a b~-seb~nd signal and its low-pass filtering, as well as conventional means
for sy"cllronisation in the presence of jamming. Each output of unit 13
corresponds to the reception channel associated with one of sensors Cn, and
each supports a part of the complex baseband signal sampled at rate Te.
The estirnated delay times can be expressed as a function of Te:
= pj Te, and the sampled signal X(nTe) received by the antenna can thus
be written as follows:
X(nTe) = ~ajd(nTe-pjTe)Sj +B(nTe) (2).
i=1 '
The structure of the multi-sensor equaliser connected at its output to
unit 13 consists of a first part termed the u spatial part" and a second part
21 94326
termed the L temporal part". The dimensions S of the spatial part, which
defines the number of coerricients required for its calculation, are determined
by the product of the number K of paths selected at the end of stage 6 and
the number N of sensors C1 to CN. The spatial part rejects any inte,rere"ce
5 and positions the gain of the antenna equivalent to the array of sensors Cn inthe direction of the useful signal, and if possible realigns the phase of the
multiple paths A~soci-ted with the useful signal.
In a conventional multi-sensor e~u~liser such as that proposed by
Scott et al, the spatial part consists of a Finite Pulse Response filter, or FPR,
10 disposed on each reception channel. Each filter consists of a determined
number of coefficients so as to cover the whole of the transmission channel.
Each of these coefficients is represented in figure 5 by a broken line box. To
cover a channel whose length in the HF band can be typically 5 ms, and with
sampling at 3 kHz, the number of coefficients required on each channel is
15 3x5=15.
In the spatial part of the receiver accordi,)g to the invention, the
number of coefficients to be adapted is greatly reduced. Only K coefficients
per channel, typically one, two or even three in the HF band, need to be
G~'cl~l~ted. Each coefficient selected is represented in figure 5 by a solid line
20 box (K = 2 in figure ~). These K coefficients per channel enable the definition
of K vectors, each of these vectors respectively forming a vertical spatial filter
Wk, where k = 1 to K, represented by a solid line. Each of these filters Wk
weights a signal vector Xk(n).
Xk(n) is defined as the vector which enables the symbol d(n) on path k
25 to be taken into account by the equaliser at moment n.
This structure therefore reduces the number of coefficients of the
spatial part. The outputs of filters Wk are summed by a first summing circuit
14 whose output, which delivers the signal Zs(n), is connected to a first
positive operand input of a first comparator 15, which also corresponds to a
30 first input of the t~,nporal part.
It should be noted that synchronisation step 2 has been carried out by
oversampling the input signal d(t) with respect to the symbol rate, which
enables the delays of the various paths to be estil"ated with greater precision
at the synchronisation stage, and therefore means that the maximum possible
21 94326
amount of energy is recovered on each of the paths selected subsequently at
multi-sensor equalisation stage 3.
The precision of the esti",d~ion of the delays is therefore particularly
i,."~o,lant in op~l,nising the pe,rormance of the multi-sensor equaliser of the
5 receiver accord:ng to the invention. In ~dc~ition the structure is not fixed and
sy"chronisation step 2 means that the spatial part of the structure can be
IlloniloreJ and updated when one of the paths disappears (fading hole) or
appears or when the delay times are modified for example in the case of
clock drift between emission and reception.
The spatial part also features a unit 16 for the calculation of the input
signals of a first part of the te""~oral part termed the utransverse part~.
Calculation unit 16 receives the signals output respectively by the preliminary
processing and synchronisation unit 13 on a first series of inputs and
receives signal vectors Xk(n) output respectively by filters Wk on a second
series of inputs.
The operation of unit 16 is described in detail below.
The transverse part is designed to compensate for inter-symbol
inte, rerence (ISI) remaining in the signal at the output of the spatial part.
The transverse part receives the signals delivered by calculation unit
16 and features a transverse filter with T coefficients hereafter termed UHr.
The outputs of filter HT are summed by a second summing circuit 17 whose
output which delivers the signal ZT(n) is connected to a first positive
operand input of comparator 15.
The output of comparator 15 is connected to a first input of a second
part of the temporal part ter"1ed the ~recursive partn. The recursive part
consists of a decision module 18 situated in a main circuit and a recursive
filter hereafter termed HR~ with R coefficients situated in a loop. This filter
HR receives the signal delivered by the decision module on its input and its
output signal is delivered to a third negative operand input of co,nparator 15.
The output of co",parator 15 is on the one hand returned to the input
of decision module 18 and on the other hand delivered to a first positive
operand input of a second comparator 20 which receives on a second
negative operand input the response signal also termed response d(n). The
_ 21 94326
output of second co")parator 20 delivers a minimised error estimation signal
e(n).
The output of the temporal part delivers the u determined n symbols.
The spatial and temporal parts are jointly adapted to the symbol rate
s Ts represented by a switch located between summing circuit 14 of the spatial
part and the temporal part in such a way as to minimise a MQE criterion
between the response signal also termed response d(t) and the multi-sensor
equaliser output signal z(t).
Ideally, the optimised criterion for the calculation of the various filters
o Wk, HT and HR making up the structure is a criterion of MQE between output
signal z(t) and response d(t). It is determined by the following formula:
~, = E[lZ(t) - d(t)l ] (3).
Given that the statistics relating to the signals are not precisely known,
the r~lu~ tjon of different filters Wk, HT and HR is carried out using an
15 adaptive algorithm operating at symbol rate Ts and optimising for each
iteration, i.e. for each sample n, a MQE criterion estimated using the followingformula:
~(n) =--~¦z(i) - d(i)¦2 (4).
The adaptive algorithm is here defined for a stationary channel, and
20 converges on the solution which obtains the minimum MQE between d(t) and
z(t). In a non-stationary environment, the algorithm minimises MQE over a
short period related to the degree to which the channel is non-stationary. This
is achieved by weighting the MQE samples with a window which is generally
exponential. The criterion to be minimised for each sample is determined by
25 the following formula:
~, (n) ~n-i¦z(i)-d(i)¦2 = ~,(n-1)+¦z(n)-d(n)¦ (5),
i=1
where ~ is the omission factor of the algorithm (0 < ~ < 1). The stationary
environment corresponds to an omission factor equal to 1. In order to follow
channel variations as efficiently as possible, the algorithm must minimise
30 ~,(n) for each sample n of signal d(t), which means that it is necess~ry to
'5 21 943~6
know the response d(n) to each sample. The response is by definition only
known on learning sequences. On info""alion symbol sequences, it is
possible to continue the algorill "n's adaptation by using the principle
implemented in the DFE eq!J~liser, which first calculates the output z(n)
5 obtained using the filters optimised at moment n-1 and then determines the
symbol d(n). The symbol d(n) thus eslimated is used as a response,
d(n)=d(n), to carry out a new iteration of the algorithm.
For each sample n the signal z(n), on which decision module 18 works,
is divided into three quantities derived respectively from the spatial part, thel0 recursive part and the transverse part. Signal z(n) is therefore defined by the
following formula:
z(n) = Zs(n)-zR(n)+zT(n) (6).
At the input of the spatial part, the following signal vectors, each one
associated with one of sensors Cn, where n = 1 to N, are used by the
15 adaptive algorilh", and have the following form:
Xk(n)=X(nTs+pkTe) fork=1,..., K (7)
i.e. Xk(n) = akd(nTs)Sk + ~ a jd[nTs - (Pi ~ pk)Te]Sj + B(nTs + pkTe) (8),
i~k
where k corresponds to a determined path selected at synchronisation stage
20 1.
Thus, each one of these vectors Xk(n) contains a part correlated with
the response d(n), the term akd(nTs) Sk and an ISI part which must be
compensated for by the spatial part and/or the temporal part. The adaptive
algorithm will seek to realign the phase of the different conl~ibutions of
25 vectors Xk(n) correlated with response d(n).
The advantage of the proposed structure is therefore clearly evident
upon analysis of formula (8):
to phase realign the K paths arriving at the antenna, i.e. to Ltake
advantage of" the energy of the K paths in the equaliser, it is not necess~ry to30 place a FPR filter on each sensor as in the multi-sensor equaliser proposed
by Scott et al. The dimensions of the FPR filter must be linked to the size of
the channel and therefore contain a large number K' of coefficients. All that isrequired is to insert one filter containing K coefficients, which is equivalent to
16
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selecting K coefficients from the K' coefficients making up the FPR filter of the
multi-sensor equaliser proposed by Scott et al. The number of coefficients is
ther~fore greatly reduced, which means that the adaptive algorithm can
converge towards the optimum solution more quickly. Given that the algorithm
s adapts to the leaming sequences, i.e. to a given number of iterations, the
proposed structure thererore produces improved pe,ror"~ance in comparison
with the multi-sensor equaliser proposed by Scott et al. In addition, in order to
guarantee good results in non-stationary enviror""enls, the number of
coerriciants to be adapted should be reduced as far as possible.
The output of the spatial part is expressed by the following formula, the
weight vector weighting signal Xk(n) being represented by Wk:
zs(n) = y(n) = ~ Wk+Xk(n) (9).
k=1
where + in superscript represents the transposition-conjugation operation.
By using the notation Xs(n)=[X1T(n)...XKT(n)]T, where T in superscript
15 represents the transposition operation in a vectorial space, to represent theinput signal vector of the spatial part and Ws=[W1T... WKT] T to represent the
wei~l,(ing vector of the spatial part, the output signal of the spatial part is
expressed by the following formula:
ZS(n) = y(n)= Ws+xs(n) (10).
The output of the recursive part is written as a function of HR, the filter
weighting the recursive part, and of symbols n-1 to n-R, and is expressed by
the following formula:
zR(n) = ~HRjd(n-i) (11),
i=1
where d(n) = d(n) on the information sequences,
and where ~ in superscript represents the conjugation operation on complex
numbers.
Symbols n-1 to n-R are either the known symbols in the learning
sequences or the symbols, d(n) = d(n), determined during the previous
iterations on the information sequences.
17 2 1 9 4 326
The input samples of the transverse part are calc~ ted by calculation
unit 16 on the basis of the signals output by unit 13 and from filters Wk at
insta,)ts n+1 to n+T and are therefore dependent upon the weighting system
of the spatial part. Two methods can be used in the algo,ill"n for the
5 ~nlc~ll tion of these samples:
- a first method consists in updating all the samples of the transverse
part with the vector Ws(n-1) calcul~ted at the previous iteration using the
following formula:
y(n+k/n-1)=Ws(n-1)+Xs(n+k) k=1 ... T (12)
A second method can be used which enables the optimisation of the
calculation power:
- under this second method the transverse part consists of a delay line.
For the symbol n the algorithm therefore calculates only the sample y(n+T/n-
1) on the basis of the weighting vector Ws(n-1) the other samples having
15 been î~lc~ ted during the previous iterations. y(n+T-1 /n-1 ) is therefore
~!cul~ted on the basis of weighting vector Ws(n-2) y(n-T-2/n-1) on the
basis of Ws(n-3) and so on.
On the basis of samples y(n+k/n-1) ~AIcul~ted using one of the above
methods the output of the transverse part is expressed by the following
20 formula:
zT(n) = ~HTj y(n + i / n -1) (13)
where HT is the filter of the transverse part.
At each iteration of the algorill "" for the update of the system of filters
(W HR HT) making up the system the samples of the transverse period
25 y(n+k/n-1 ) for k = 1 ... T must be calculated first. The samples thus
calcul~te~l become the input of the adaptation algorithm in the same way as
the vector X(n) and the symbols corresponding to the previous iterations
d(n-1) to d(n-R). The adaptation algorili"" then seeks the system (W(n)
HR(n) HT(n)) which minimises the criterion ~ (n).
Different algorithms can be used to calculate the filter system (W HR
HT) giving the minimum value of estimated MQE ~ (n) for each iteration. The
algo,ill"" selected is a least squares algorill"n which is chosen in preference
18
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to a gradient algorithm for reasons of speed of convergence. Of the least
squares algorill"l~s available, the spatial matrix algorill"" illuslraled in figure
6 is used to provide joint adaptation of the spatial and temporal part. Any
other least squares algo,iti,m would produce the same basic results.
The spatial matrix algoril~"~ does not eslimale the filter system (W,
HR, HT) directly. At each iter~lion the samples corresponding to the spatial,
recursive and transverse parts are fed into the matrix structure and the
coefficients of the matrix C(i, j), which are also termed adaptive multipliers,
are calculated so as to minimise the power of the estimation error
l0 e(n) = z(n)~(n). The spatial matrix algorithm exists in two versions: the a
priori version and the a posteriori version. The a priori version is
expressed by the following series of instructions, based on the one hand on
the known sequence symbols;
the order of the matrix is noted: order = R+T+S+1.
15 - in an initialisation phase:
i=1->R E(i)=d(n-i) initialisation of the recursive part
i=1->T E(R+i)=y(n+i/n-1 ) initialisation of the transverse part
i=1->S E(R+T+i)=x(i) initialisation of the spatial part, where x(i)
is the ith component of vector X(n)
20 i = Order E(Order)=d(n) initialisation of the response signal
- then from p = 1->Order:
a(p) = ~a(p) + y(p ~ ¦E(P)¦¦2
y(p) = y(p-1)-~(p-1) ¦¦E(P)¦¦ 'a(p)
i=p+1 ->Order:
E(i)=E(i)-C(i,P)*E(P)
C(i,p)=C(i,p)+y(p-1)E(p)E(i) */a(p)
and on the other hand on the information symbol sequences:
the initialisation phase is identical to the preceding initialisation phase,
apart from the fact that E(Order) is not initialised as the response is not
30 known. The response must therefore be estimated. To do this, the adaptation
algorithm first updates the various quantities involved in the spatial matrix
algorill ,m which have no effect upon E(Order), i.e.:
- from p=1-> Order-1:
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a(p) = ~a(p) + y(P~ E(P)¦¦
Y(P) = Y(P -1) + Y(P 1) ¦¦E(P)¦¦ , a(p
then from i=p+1 Order-1:
E(i)=E(i)-C(i.P)~E(P)
s C(i,p)=C(i,p)+y(p-1)E(p)E(i) */a(p)
The output of the multi-sensor equaliser is then calc~ ted using the dirrerent
error signals and is ex~ressed by the following formula:
z(n)- ~ C(Order,i)~E(i) (14).
i -
Decision module 18 then determines signal d(n) on the basis of z(n)
10 and updates the final part of the matrix structure:
- in an initialisation phase:
E(Order)=d(n)
then from p=1 Order-1:
E(Order) = E(Order)-C(Order,p)~E(p)
C(Order, p) = C(Order, P) +y(p-1)E(p)E(Order)~/a(p)
For the calculation of the transverse part at each iteration, the samples
of the transverse part, i.e. the samples obtained at the output of the spatial
part for X(n+1), ..., X(n+T), must be calculated first.
The output of the spatial part corresponds to the contribution of the
20 spatial part to the signal subtracted from the response. The signal subtracted
from the response is expressed on the basis of the .lirrerent error signals
E(1 )->E(Order-1 ) by the following formula:
z = ~ C(Order,i)~ E(i) (15).
,=.
In order to c~lcul~te the output of the spatial part corresponding to
25 X(n+k) where k=1->T, it is therefore necess~ry to simply calculate the
contribution of the spatial part to the dirrerent error signals. In order to reduce
the calculation power, the samples cor,esponding to the spatial part are
placed on the right of the matrix, and it is therefore only necess~ry to
calculate the contribution of the spatial part to error signals (E(R+T+1) to
30 E(R+T+S): this means that only that part of the matrix marked by the solid
line in figure 6 is involved in the calculation.
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Let us suppose that ~s(i) is the conl, ibution of the spatial part to error
signal E(i). Es(i) is thus ~Ic~ ted using the following series of instructions:
- in an initialisation phase:
Es(i+R+T)=x(i) for i + 1->S, where x(i) is the ith
COlllpGI ,ent of vector X(n+k).
- then for 1 = R+T+1-~R+T+S, update of error signals Esa) for j = i+1->R+T+S
on the basis of error signal Es(i):
i = R+T+1->R+T+S
j = i+1 ->R+T+S Esa)=Esa)-Ca,i)~Es(i).
The output of the spatial part is thus expressed as a function of error
signals Es(i) calculated above by the following formula:
y= ~ C(Order,i)~E(i) (Order-1=R+T+S) (16).
PR+T+1
The following example demonstrates the relative usefulness of the
spatial and temporal parts of the multi-sensor equaliser.
A useful signal arrives at the antenna along two prop~g~tion paths.
The signal vector received by the antenna is expressed by the following
formula:
X(t) = a1d(t)S1 + a2d(t - ~)S2 + B(t) (17).
According to formula (7), the spatial part of the structure is composed
20 of the vectors X(t) and X(~+t). The output of the spatial part y(t) is therefore
expressed as follows:
y(t) = W1 X(t)+W2X(t+~) (18)
That is:
y(t) = d(t)[a1 W1 S1 + a2 W2 2]
d(t-l)[a2 W1+S2]+d(t+~)[a1W2 S1] (19)
W1+B(t)+W2+B(t+~)
The output of the spatial part therefore consists of three components:
one component corresponding to the useful signal d(t), one component
corresponding to the ISI generated by d(t-~) and d(t+~), and one component
corresponding to the noise (background noise ~ interference).
- - 21 94326
Let us now suppose that the temporal part of the structure is absent:
T=R=0. The algo, ill ,m adapting the structure minimises the MQE between y(t)
and d(t), and therefore seeks to cancel the two terms containing ISI, since
these are non-correlated with respect to response d(t). ISI is processed by
5 the anlen,)a in the same way as any possible inte, rerence.
The following simulation is designed to analyse the behaviour of such
a structure without a te"~pordl part. An example antenna used for the
simulation featuring five monidirectiol~al sensors C1 to Cs disposed on the
sides of an equilateral triangle is illustrated in figure 7. The angle between
o any two sides of the triangle is 60~.
The antenna receives two non-correlated paths of identical bearing of
0~ and of power "s = 10 dB. The elevation of the first path is 40~ and that of
the second path is varied. The background noise has a power of ~ = 0 dB.
The output powers of the useful signal, the ISI and the background noise are
15 expressed respectively by the formulas given below:
S = ¦a1 W1+ S1 + a2 W2+ S2~ 5[W1 S1 + W2 S2 ] (20)
IIS = 7~s 1W1+ S21 +1W2+ S112 (21)
B = W1+RbbW1 + W2+RbbW2 = ~2[W1 W1 + W2 W2] (22)
In figure 8, the curves S/(ISI+B), S/B, ISI/B are traced on a Cartesian
20 co-ordinate graph, on which the y-axis represents the amplitude in dB and thex-axis represents the elevation angle in degrees. The antenna processes ISI
in the same way as interference, and therefore optimises the ratio S/(ISI+B).
When the coefficient of spatial correlation between the two paths is
low, the ratio S/(ISI+B) at the output of the antenna is close to 20 dB. The
25 determination of the symbols emitted is carried out on signal y(t), which
means that the same performance as on a stationary channel featuring one
path of power 20 dB is obtained. In co,nparison, the single-sensor DFE
equaliser produces performances similar to those of a stationary channel
featuring one path of power 10dB. The processing carried out therefore
30 enables a gain of 10 dB, a gain which is made up as follows:
22 21 ~4326
''_
. 7 dB = 10 logN due to the gain in S/B of the antenna aligned in the
direction of each of the two paths.
- 3 dB due to the phase realignment gain of the two paths.
In such a configuration, the spatial part eliminates ISI, directs one lobe
s in the direction of each of the two paths and phase realigns the two paths.
The temporal part no longer makes any useful co"l, ibution.
When the two paths are close in spatial terms, it becomes more and
more difficult for the antenna to eliminate ISI while at the same time
maintaining a S/B gain which is sufficient for the two paths.
o Thus, for elevations < 36~ or ~ 44~, the antenna is always able to reject
ISI below the level of the background noise, but this is achieved at the cost ofa deterioration of the S/(ISI+B) ratio with respect to the previous case (at 36~,
12 dB are lost). The pe,ro",lance of the decision module is therefore lower
than in the previous case.
For elevations between approximately 36~ and 44~ the two paths are
too close in spatial terms, and the antenna is no longer capable of eliminating
ISI. The ratio S/(ISI+B) tends towards 3 dB. It should be noted that this resultis obtained whatever the value of the common power of the two paths. A
decision module placed at the output of the spatial part would therefore give
less satisfactory results than the single-sensor DFE equaliser, which is
evidently unacceptable.
The disadvantage of such a structure without a temporal part is
therefore clear from the analysis of this example: ISI is processed by the
antenna in the same way as intelrere"ce, and the antenna therefore uses
varying degrees of liberty to eliminate it.
The addition of a temporal part to the structure and the adaptation of
the temporal and spatial parts to the same error signal results in the overall
behaviour described below.
For paths which are "sufficiently" non-correlated in spatial terms, the
spatial part enables the system in all cases to direct the main lobe of the
antenna in the direction of each of the two paths and to realign their phase,
while at the same time elil"inaling ISI. The work of the temporal part is
thererore reduced. The overall gain with respect to the single-sensor DFE
equaliser is 10 log N+3 dB.
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For spatially correlated paths the temporal part handles the elimination
of ISI which means that the spatial part will no longer seek to optimise the
antenna gain in the direction of each of the two paths. The overall gain with
respect to the single-sensor DFE equaliser is 10 log N.
A gain with respect to a single-sensor DFE equaliser of between 10 log
N and 10 log N+3dB for two paths of the same power in a stationary
enviror""ent can thererore be re~lised in all cases.
Moreover in the presence of jamming of a useful signal the spatial
part will reject inte, rerence.
