Method for locating transmitting sources by the use of the mutual
coupling of a small-base antenna array and slow-switching singlechannel
receiving system using the method
s The present invention relates to the field of radiogoniometry and more
precisely that of the location of sources by determination of the direction of
arrival of the signal transmitted by these sources.
The invention relates to a method and a system of single-channel
location, that is to say for which the receiver that is used has only one
io receiving channel associated with a small-base or small-diameter antenna
array. The invention is particularly adapted to a switching of the receiving
channel between the various elements of the antenna array, a switching that
is slow compared with the duration of a symbol of the source signal.
In the rest of the description, the expression "source location" is aimed
is notably at the determination of the number of sources transmitting a given
signal in a given radioelectric environment and the determination of the
directions of arrival of the signals transmitted by these sources. A sourcelocation
method comprises, in the broad sense, any method of
radiogoniometry, of separation of sources, of identification of spatial
20 signatures or of identification of source-directing vectors.
The objective of the invention is to propose a method and a system of
locating sources based on the signals transmitted by these sources and
received by a single-channel receiver associated with a small-base antenna
25 array.
The system produced must have a limited manufacturing cost and
space requirement, notably for the purpose of incorporating it into a portable
item of equipment fitted with a small-base antenna array. It must also make it
possible to relax the constraints on the calibration of the said array.
30 The method according to the invention makes it possible notably to
carry out an analysis of the received signal in a continuous or a quasi2
continuous manner and thereby is applied to a large number of different
signals transmitted in continuous or discontinuous waveforms, for example
waveforms associated with protocols of the TDMA type or linked to
frequency-evasion mechanisms, with broad or narrow-band frequency, and in
s any type of stationary or non-stationary, even complex, radioelectric
environment in the presence of interference or of scrambling.
The field of radiogoniometry has been the subject of many works.
However, the performance of the systems that are low cost and/or have a
io reduced number of receiving channels has limitations with respect to the
performance that they can achieve.
In particular, certain systems use sectorized or directive antennas
which provide a reduced interception capability and which are limited in low
frequency by the insufficient size of the antennas. In order to increase the
15 interception capability, scans that are costly in time or in mechanical
components are required for those solutions.
Other solutions are based on Doppler methods which require a largebase
antenna array and are not adapted to the small-base antenna arrays for
portable systems.
20 The known single-channel systems also have a limitation with respect
to the discontinuity of the observations made. Specifically, when the
radiogoniometry system has only one receiving channel, the latter switches,
by means of a switch, to the various antenna elements of the array. A
discontinuity associated with the switching time therefore appears over the
25 overall observation made by the antenna array. This problem has an impact
because it requires a consequent increase in the switching speed and the
sampling frequency and requires reducing the integration periods. Moreover,
a discontinuous observation causes degraded performance for signals to be
located that are transmitted in a waveform that is in bursts. This type of signal
30 is characterized by rapid non-stationarities of the waveform in contrast to a
continuous waveform. The discontinuity of the observations is also
3
problematical when it involves discriminating between several sources
transmitting simultaneously.
Furthermore, the solutions of the prior art are not adapted to smallbase
or small-diameter antenna arrays. Specifically, this type of array
5 induces not inconsiderable contributions of the couplings between antenna
elements of which it is difficult to take account reliably in the calibration
processes.
Also known are solutions based on the use of antennas with parasitic
1o elements, for example that described in the publication entitled "High-
Resolution Direction Finding using a switched parasitic antenna", Thomas
Svantesson et al, 11th IEEE-Signal processing workshop, Singapore 2001,
p. 508-511.
The principle of these solutions is based on a rapid switching of the
15 antenna diagram, in times much shorter than the symbol duration. The
antenna array consists of several antenna elements of which the majority are
in open circuit and are used as concentrators. At a given instant, the voltage
at the terminals of a single element is measured. A control circuit, based on
diodes, is used to independently activate each antenna element in order to
20 form the desired antenna diagram and thus achieve a rapid switching.
In addition to the need to switch rapidly, these solutions have the
drawback that their performance is closely linked to the constricted
geometries of the antennas and to the calibration tables of the various
diagrams formed by the various configurations of the parasitic elements,
25 tables that have to be very precisely determined.
Moreover, if the switching is not rapid enough, the interception
capability is reduced because the generated antenna diagram is directional,
the "parasitic" antenna elements being used mainly as reflectors in order to
increase the antenna gain in the main direction of the diagram.
4
Finally, these solutions also suffer from problems of discontinuity and
of transitory regime of the observations made during the switchings, even
when they are rapid.
5 The object of the invention is to remedy the aforementioned limitations
of the prior art by proposing a single-channel radiogoniometry solution
adapted to a slow switching of the receiving channel on the various antenna
elements of the antenna array.
The invention makes it possible to reconstitute a quasi-continuous
io observation of the input signal by using couplings and the mutual influence
between antenna elements. The invention therefore makes it possible to
produce statistical estimators of the observed signal over long periods of
integration in order to significantly improve the performance of the processes
of source separation or of determination of the direction of arrival of a signal.
1 5
Accordingly, the subject of the invention is a method for locating
sources each transmitting a signal S, characterized in that it comprises at
least the following steps executed by a single-channel receiving system:
® Receiving the signal or signals at the input of an antenna array
20 comprising a plurality N of radiating elements by successively
switching the receiving channel to the N radiating elements with a
predetermined switching period At,
® Sampling, after each successive switching, at the output of each
radiating element, a sample of the received signal in order to
25 construct a vector X of the spatial signal received by the antenna
array,
® Computing at least one first statistical estimator M(^';, of order Q
greater than or equal to 1 of the spatial signal X at the output of
the antenna array,
5
® Estimating the values of at least one statistical estimator of order Q
M(; S of the function of modulation of the said transmitted signal S,
® Determining at least one second statistical estimator M^;l of the
same order Q, for the spatial signal X at the input of the antenna
5 array by resolving the systems of equations M. =M^s.C(Q).MQ°t
where C(o) is a self tensor product of order Q of the coupling matrix
C of the antenna array , the components of the said coupling matrix
C being equal to the mutual coupling coefficients between each
pair of radiating elements of the said antenna array, the said
10 coupling matrix C being previously determined and stored in a
database contained in the said system,
® Applying a source-location method, such as a method of
radiogoniometry, of separation of sources, of identification of
spatial signature or of identification of source-directing vectors, to
15 the said second statistical estimator QY
According to a particular aspect of the invention , the statistical estimators
M(Q) ,,, Mac's , MW^', are estimators of the moments or of the cumulants of order
Q.
According to a particular aspect of the invention , the statistical estimators
20 M^;'l,, M(Q) , M^;'; are estimators of the crossed products , of the variance, of
the covariance or of the quadricovariance.
In a variant embodiment of the invention , the statistical estimator of order
Q M(Q) of the function of modulation of the transmitted signal S is estimated
on sets of multiple temporal values of the switching period At based on the a
25 priori knowledge of the modulation of the said signal S.
In a variant embodiment of the invention, the statistical estimator of order
Q MQC's of the function of modulation of the transmitted signal S is estimated
6
on a sequence of reference symbols that are known a priori and contained in
the said signal S.
In a variant embodiment of the invention, the successive sampling at the
output of each radiating element is carried out according to a circular
5 switching.
According to a particular aspect of the invention , in order to generate the
coupling matrix C, each mutual coupling coefficient between a first and a
second radiating element is determined by imposing a voltage and/or by
injecting a current at the terminals of the first radiating element and by
io measuring the voltage and/or the current at the terminals of the second
radiating element.
According to a particular aspect of the invention, the location of a source
consists in determining the direction of arrival of the wave transmitted by this
source.
is According to a particular aspect of the invention, the source - location
method is chosen from the following methods: a correlative interferometry
method , a vector correlation method , an adaptive channel formation method,
a second-order or fourth-order subspace method , or a JADE method.
A further subject of the invention is a receiving system for the location of
20 sources each transmitting a signal S comprising an antenna array consisting
of a plurality of radiating elements , of a switch in order to successively
sample the output signal of each radiating element, of a receiving channel
comprising an analogue-digital converter and of means of analysis and of
computation comprising a computing unit and a database, containing the
25 predetermined values of the coupling matrix C of the antenna array,
characterized in that the means of analysis and of computation are adapted
to apply the source-location method according to the invention.
7
Other features and advantages of the invention will become evident from
the following description made with respect to appended drawings which
represent:
5 - Figure 1, a block diagram of a receiving system adapted to use the
method according to the invention,
- Figure 2, a diagram showing the switching and sampling of the
received signal,
- Figure 3, a diagram illustrating the construction of the vector of the
10 signals at the input of the computing unit of a receiving system
according to the invention,
- Figures 4a and 4b, two diagrams illustrating the principle of
measurements of the coupling coefficients between elements of an
antenna array,
15 - Figure 5, an example of the autocorrelation function of a known
signal modulated by a BPSK modulation.
Figure 1 represents, in a block diagram, a receiving system 100
adapted to use a method of radiogoniometry or of source separation
20 according to the invention.
The system 100 comprises at least one antenna array 101 with a
small base or small diameter comprising a plurality of radiating elements
111,112,113.... 11 n, that are capable of receiving a signal X transmitted by a
source to be located in a predetermined frequency band, for example the HF
25 (High Frequency) or VHF (Very High Frequency) band. The system 100 also
comprises a switch 102 capable of successively switching on the output of
one of the radiating elements of the array 101 in order to transmit the output
signal X' of this element to a receiving channel 103. An important parameter
of the switch 102 is its switching speed, or its period At for switching between
30 two radiating elements. The invention makes it possible to carry out a quasi8
continuous observation of the signal even for a switching speed that is slow
relative to the speed of modulation of the received signal.
The receiving channel 103 comprises at least one amplification and/or
filtering system 131 and an analogue/digital converter 132 capable of
5 digitizing the received signal at a given sampling frequency Fe.
The system 100 also comprises means 104 for analyzing and
processing the digitized signal, which means comprise a computing unit, a
database and optionally an operating interface. The computing unit is
adapted to use a method of processing the received signals in order to
to characterize them. The database contains certain items of predetermined
information concerning the antenna array and, where necessary, concerning
the nature of the received signal, notably its modulation.
The method according to the invention can be applied irrespective of
15 the switching speed of the switch 102 and in particular when the latter is slow
relative to the symbol frequency of the received signal to be located. In this
case, the duration of a spatial sampling of the received signal on all of the
elements of the antenna array may be greater than the duration of a symbol
of the received signal.
20 In this manner, the switch 102 carries out a complete run-through of
the antenna array on more than one symbol of the observed signal.
Figure 2 illustrates, in a diagram, the principle of a slow switching
relative to the symbol time of the received signal.
Figure 2 represents several successive symbols indexed by K, K+1
25 and K+2, of the received signal S. Each symbol has a duration TS defined by
its modulation rhythm. Figure 2 also represents the samplings x'l...x'N made
by the switch 102 on each output of a radiating element of the antenna array
101 at the instants t, t+At,... t+ (N-1)At, where At is the switching period. A
complete run-through of the antenna array 101 is carried out by the switch
30 102 at the end of a duration NAt greater than the duration TS of a symbol.
9
The signal sampled by the switch 102 is then digitized at a given
sampling frequency Fe. In the non-limiting example of Figure 2, the sampling
rhythm Te is equal to a quarter of the switching period At and the spatial
switching period At is equal to 3Ts/(2N).
5 All of the samplings x'1.... x'N made during the duration N.At form a
vector X of the output signal of the antenna array 101. The samples x'1.... x'N
of this signal X are taken in several successive symbols K of the received
signal because of the slow switching of the switch 102.
The construction of the vector X is illustrated in Figure 3. Each
io component of the vector X is equal to the sample taken at an instant t+k;'At
of the output signal of a radiating element of the antenna array . The switching
period At also corresponds to the spatial sampling period of the received
signal . Specifically, the same signal is received by the various elements of
the antenna array and the use of the spatial diversity in receive mode makes
is it possible to better characterize the signal for the purpose of identifying its
direction of arrival.
In a variant embodiment of the invention, the run-through of the
elements of the antenna array at the instants t+k ;At, where i is the index of an
20 element, i varying from 1 to N, is not necessarily circular. Specifically, the
series kl, ... kN is not necessarily increasing or strictly periodic. In the case of
a circular switching as described in the examples of Figures 2 and 3, k;+1=k; +
1, but the run -through of the antenna array may also be carried out according
to a pseudo-random series . In this case , Ak is the maximum value (k; - kjj of
25 the difference between two temporal indices k; and kj after switching on all
the elements of the array. Ak.At is the temporal medium of the digital
samplings making it possible to constitute the vector X from the instant t.
The method and the system according to the invention
3o advantageously apply for small-base or small-diameter antenna arrays. For
such arrays, the radiating elements are close to one another and the mutual
10
radioelectric influence of one element on the others is not inconsiderable.
Making use of the mutual influence between elements of the array makes it
possible to ensure a quasi -continuous observation of the received signal.
The electromagnetic field received by the antenna array induces a
s voltage signal at the terminals of the matching circuit of each antenna
element.
This voltage signal consists of the total of one direct signal and several
indirect signals.
The direct signal is the voltage signal induced at the terminals of the
io matching circuit of a radiating element by the electromagnetic field in the
immediate vicinity of this element.
The indirect signals are the voltage signals induced at the terminals of
the matching circuit of a radiating element by the electromagnetic fields in the
immediate vicinities of the other antenna elements of the array.
1s When the distance between the antenna elements is small, the
indirect signals are not negligible.
The signal x'no(t) sampled at the output of an element of index no of
the antenna array therefore results both in the received signal xno(t) at the
input of this element and also in the received signals xn (t) at the input of the
20 other elements of the array.
The input signal xn (t + n.At) corresponding to a transmitting source,
sampled on the antenna element n on the nth switching of duration At, may
therefore be modelled with the aid of the following general relation:
x,, (t + n.AT) = p,,.e'l°.S(t + n.AT - z) + b„ (t + n.AT)
25 S being the signal transmitted by the source, pn, (pn and tin being the phase
attenuation and delay induced by the propagation, bn being the received
noise.
The output signal x ' no(t + no.At) sampled on the antenna element no on
the nth switching of duration At can therefore be modelled with the aid of the
30 following general relation:
11
N N
x',,o (t+n0AT) jC,.,,x,,(t+noAT-z0 ,) jC0 ,.x.(t+nozT) (1)
n=1 n=1
where
z is the propagation time of the signal between the antenna elements of
index no and n. This time is considered to be negligible for a
5 narrowband signal Bw for the antenna array, that is to say which verifies
the relation D.Bw/c << 1 where Bw is the band of the signal, D is the
diameter of the antenna array, and c=3.108 m/s is the speed of light in a
vacuum, which is systematically the case for all the signals of
communications and all the small-base antenna arrays considered in
10 the invention.
c, ,, is the coefficient of coupling between the antenna elements of index no
and n, which reflects the influence of each element on its neighbours.
The signal vector at the output of the antenna array X'(t), constructed on the
is basis of signal samples at the output of each antenna element, is given by
the following relation (2):
F X', (t + At) r CI1 ... CIN Xi(t +At)1
X'(0 = = C.X(t) (2)
[x', (t + Not) [CNI •.. CNN _I [xN,(t+NAt)
where
20 x(t) is the signal vector at the input of the antenna array , that is to say of
which the components are the received signals , at the successive instants
t+At, t+2At, ..., t+N\t, on the surface of each element of the array, and
emanating from the transmitting sources,
c is the coupling matrix of the antenna elements of the array . The coefficient
25 of the line i and of the column j of this matrix is equal to the coefficient of
coupling between the antenna element of index i and the antenna element of
index j. The matrix c has dimensions N by N.
12
The expression of the signal X'(t) at the output of the antenna array given by
the relation (2) therefore makes it possible to render the observation of the
continuous signal, irrespective of the antenna element connected to the
receiving channel by the switch, because of the contribution induced by
5 coupling by each of the other elements of the antenna array.
This expression should be differentiated from those used by the methods of
the prior art which do not use mutual coupling between elements of the array.
The coupling matrix of the antenna array may be obtained by
to measuring the voltage at the terminals of the matching circuit of each
antenna element with the aid, for example, of a network analyzer, or by any
other equivalent method. In order to determine each mutual coupling
coefficient between two antenna elements, a voltage is imposed or a current
is injected at the terminals of the circuit of the first antenna element while
15 measuring the voltage or the current at the terminals of the circuit of the
second antenna element. This operation is reiterated for each pair of
radiating elements taken two-by-two amongst the N elements of the antenna
array.
The coupling matrix C is previously determined and stored in the
20 database of the system according to the invention 100.
Figure 4a schematizes the principle of characterization of a fourterminal
element Q.
The coupling coefficient C11 by reflection at the input of the fourterminal
element Q is determined by the ratio between the signal b, reflected
25 at the port 1 of the four-terminal element and the signal a, that is incident at
the port 1, it being assumed that no signal is injected at the port 2 (i.e. a2=0).
The coupling coefficient C22 by reflection at the output of the fourterminal
element Q is determined by the ratio between the signal b2 reflected
at the port 2 of the four-terminal element and the signal a2 that is incident at
30 the port 2, it being assumed that no signal is injected at the port 1 (i.e. al=0).
13
The coupling coefficient C21 by transmission at the input of the fourterminal
element Q is determined by the ratio between the signal b2
transmitted at the port 2 of the four-terminal element and the signal a1 that is
incident at the port 1, it being assumed that no signal is injected at the port 2
5 (i.e. a2=0).
The coupling coefficient C12 by transmission at the output of the fourterminal
element Q is determined by the ratio between the signal b1
transmitted at the port 1 of the four -terminal element and the signal a2 that is
incident at the port 2, it being assumed that no signal is injected at the port I
10 (i.e. a1=0).
Based on these principles, it is possible to determine the mutual
coupling coefficients between the antenna elements of an array.
Figure 4b illustrates an example of using the computation of the
15 coupling matrix of an antenna array 403 comprising five individual antennas.
A vector network analyzer 400 is used to measure the coupling
coefficients between each pair of elements (n,,n2) of the array 403.
The analyzer 400 comprises two ports 401,402. The first port 401 is
connected to the terminals of the first antenna element n1. The second port
20 402 is connected to the terminals of the second antenna element n2. To
measure the mutual coupling coefficient C12 between the first and the second
antenna element, a reference signal ant is injected from the port 401 to the
first antenna element n1. In response to this signal , a first signal bn1 is
reflected to the port 401 and a second signal bn2 is transmitted to the port
25 402 . The mutual coupling coefficient C21 is measured like the ratio between
the signal bn2 transmitted to the port 402 and the injected reference signal an1
from the port 401 , it being assumed that no signal is injected at the port 402
(i.e. ant=0). The coupling coefficient C11 of the first antenna element n1 alone
is measured like the ratio between the signal bn1 reflected to the port 401 and
30 the injected signal an1 and the first signal , it still being assumed that no signal
is injected at the port 402 (i.e. ant=0).
14
Similarly, in order to measure the reciprocal mutual coupling
coefficients C12 and C22 between the two antenna elements n1, n2, a
reference signal ant is injected from the second port 402 to the terminals of
the second antenna element n2, it being assumed that no signal is injected at
5 the port 401 (i.e. ant=0).
This operation is reiterated for each pair (n1, n2) nWn2 of antenna
elements in order to compute all of the coupling coefficients that form the
coupling matrix C.
In order to improve the process, the measurements made by the
io network analyzer 400 can be first preceded by a calibration of the said
network analyzer in order to compensate for the influence of the errors that
may be associated with the source generating the reference signal, with the
frequency response of the analyzer or else with the residual coupling
between the two ports 401, 402. It is likewise possible to use the redundancy
15 of the coupling measurements or to reiterate these operations several times
in order to improve the statistical convergence of the coupling
measurements. It is also possible to particularize these measurements to
specific frequency bands or to specific ranges of temperature and humidity.
20
Based on the relation (2) that links the input and output signals of the
antenna array, it is possible to reconstitute the statistical estimators that are
used as a medium for the application of a method of source separation, of
radiogoniometry or more generally of determination of the direction of arrival
25 of the received signal.
The method according to the invention makes it possible to restore the
statistical estimators of the input signal X of the antenna array that are then
used to apply a method of goniometry or of source separation.
30
15
Several examples of statistical estimators that can be applied to the
input received signal X of the antenna array will now be described. One of
the objectives of the invention is to determine at least one statistical estimator
of the signal X based on the same statistical estimator computed for the
s signal X' sampled at the output of the antenna array and the coupling matrix
C. Without departing from the context of the invention, the latter is applied in
an equivalent manner to any other estimator of a spatially sampled signal
used by any method of source separation or of radiogoniometry,
10 Considering the complex signal vector X(t) at the input or output of an
[Xi(t)1
antenna array, x(t) _ , sampled at the sampling period Te and thereby
1XN (t)j
defining the temporal sequence
x, (k7)
X(kT) _ ... ; k = -oo,+co
xN(ke)
, the statistics of the signal that are mainly
used in the known methods of source separation and of goniometry are as
is follows.
The 1St order moment or probabilistic mean E[X(to)] of the signal X. It
is estimated by a temporal mean of the samples of the signal X, taken on a
temporal horizon of K samples from the sample of index ko corresponding to
20 the instant t=koTe according to the following formulation:
K
MI,[X(k )l = K ^ X((ko +k)T J
The first and second 2nd order moments of the signal X, defined by the
expressions E[X(to).XH(tJ)] and E[X(to).XT(ti)], where E[X] is the expectation
25 of the signal X, XT is the transpose vector of X and X" is the conjugate
transpose vector of X. In all generality , these are 2nd order symmetrical
16
tensors estimated by temporal means on the samples of X, taken on
temporal horizons of K samples based on samples of indices ko and k1
corresponding to the instants to=koTe and ti=kiTe according to the following
formulations:
5
K
M2')[X(k ); X(kI)] _ -L X((ko + k)Te) • [X ((k, + k)2 )]'
° K k=1
and
M22)[X(kJ;x(k1)] = 1LX((ko + k)T ) . [X ((k, + k)T )1"
K k=,
The covariances of the signal X defined by the expressions E[(X(to)-
1o E[X(to)]).(X(t1)-E[X(t1)]H)] and E[(X(to)-E[X(to)]).(X(t1)-E[X (t1)]T)]. These are
also 21,d order symmetrical tensors , estimated by temporal means on the
samples of the signal X , taken on temporal horizons of K samples based on
the samples ko and k1 corresponding to the instants to=koTe and t1=k1Te
according to the following formulations:
15
X((ko+ k)T) -MI [X(1°)]I•( [X((k,+k)7A -MI[x(k")]
and
R[X2 k°);X(kI)] =
I K
KI
k=l
X ((ko + k)7:) -MI L (^^ ))]] . X((k, + h^Te)] - MI [x(k, )] j
H
T
More generally , it is possible to define the statistical tensors , moments
20 and cumulants with any order Q in the following manner.
For the random variables defined by the complex signal received on
the various antennas x;, x;Q; ii.... iQ E {1,...,N} taken at the instants koTe,
kiTei k2Te, ..., kQ_iTe ko,...,kQ_l c {c- o, ..., co}, and for the indices of
conjugation *o, *1, *2, ..., *Q-i, the delayed products of order Q and of indices
25 of conjugation *o, *1, *2, ..., *Q-i are written with these conventions:
Xi (*°)(ko.Te). x, (*I)(k,.TJ ...
Xi,
(*e 4)(kQ-1 .Te)
17
5
The following writing conventions are chosen for the conjugation
indices: if *q = , ' xq() = xq; *q Xq(*q) = Xq*).
The mean of this product constitutes the scalar moment of order Q of
the variables x;o ... x;Q-1 defined by the indices *o , * 1, *2, ..., *Q-1.
Mp#,J.',^ (koT) (k,T,);...; xiQ(kQ.,T,.)] = E[xi^(*°)(ko.Te) Xi (*')(1C,.Te) ...xI ,(*Q-I) (kQ_I.TJj
Considering the input signal vectors, the delayed products of order Q
and of conjugation *o, *1, *2, ..., *Q-1 define a "tensor of the delayed products
of order Q" which is formally expressed as a function of the delayed signal
to vectors in the following form:
(,. ^. >Q-,) (*, )^ (*Q')(
[X OXO...O X] [ ) ^V
i e ) ...
= Xio kO.Te X (*,)(ICI.T Xi Q 1CQ_1.Te N
kQ.t7 __N
When there are no delays ( ko = k1 _ ... = kQ-1), this tensor defines a
tensor Q-power of the signal vector X.
is The mean of this product tensor constitutes the tensor of the delayed
moments of order Q of size N defined by the conjugations *o, *1, *2, ..., Q-1,
which is formally expressed with the aid of the following relation:
MQ*Mke);X(k,);...;X(kQ-,)] - E
,2..Q
[XOXO...OX]
ho . . .. j)
(k,,.T, k,.T ,..,kQ.,.T )
=
[Ellr1(
*o)(k0.Te) xi'(*,)(kl.TJ ... XP(*Q')(riQ_1.Te^lf.°=h...
if,-,=1,...,N
20 When there is no delay (ko = k, _ ... = kQ-1), the following simplified
notation will be used:
A"t 1
Q,[X(ko);X(ke );...;X(ko)I MQ*,^X^ko)) *o,)
By combining the various delayed products and scalar moments of
25 order q<_Q, the scalar cumulants of the signal are defined by the conjugation
18
indices *o, *1, *2, ...,*Q-i and by the following Leonov and Shiryayev
formulations that are well known to those skilled in the art.
The scalar cumulants of order Q are expressed as a function of the
5 scalar moments of lower order with the aid of the following relation:
C102 ** tz ..., 1)(q_1)
*92)
4
X k T 7^ X k TV X Q^^Ip (ko7^l ; iii lklT )^.. ;^ip^2 x)1 9 k T
(
*¢^} 1
-I
^^(** ^}( 9r e^^ fj ( 92
^^... iqq
r n71tS
Us'=(" ..N)
Tr
The scalar moments of order Q are expressed as a function of the
scalar cumulants of lower order with the aid of the following relation:
MQ1x (kOT,);X. (kIT,);...; x;p(k2T,)1
10
( q
11 2,•••,carsl(S -)-I
q-pm'trtrons \ q'=1 S, .....Sq de {1,...N}
US,.={1,...,N}
L 111" a
I cm•d(S^^),^xiq" / 1kq" eJ 9"eSy. ]
This formulation defines, as above, a tensor of the cumulants of order
Q, of size N, which is formally expressed with the aid of the following relation:
021111{***2,...,vo {* ,*_,}
•*^,* ..
Q,IX(ko(ki);...;X(k^ ^^ Cwi1
P,
`
^x^o(kzo, T);g x;,(kiT);...;sj {kC-iT'}]
When there is no delay (ko=k1= ,., = kQ-1), the following simplified
Is notation will be used
011131(*0•**2,...,* -i} = 021711{*o,*,*
z,...,*Q_,}
Q,(X
j
(
,
ko^;X(ko^;...;X(ko)] Q^(X(ko)]
All the tensors described have properties of real and/or Hermitian
symmetry and can be represented in practice:
20 - with the even orders by an appropriately ordered and symmetrical
matrix of dimensions NQ/2 x NQ/2
- with any order by an appropriately ordered column vector of
dimension No x 1,
,, gq'9
/
q.
\ 7J" "'S
4
19
The moments and cumulants thus defined are advantageously used
with the order 1, 2 or 4 for the applications that are the object of the present
invention,
At the 1st order, the moment and the cumulant are equal to the mean
5 of the signal represented in scalar writing by the expression:
Vn =1,...,N; " Li =Cum; [col =E[x(')]
and in vector writing by a 1 st order tensor:
M^(,[Y1 = E[X(*)]
At the 2nd order, the moments correspond respectively to the crossed
to products of the signal and the cumulants correspond respectively to the
variances and covariances of the signal.
The 2nd order moments are represented in scalar writing by the
expressions:
tno,n1 =1....;N; ^lI{1 ^x^ x M ^^ 0:X,]=E [s„ot„ *}: .1h')X^ x=1tI2
nx., ]=E [Y"ox^i
is and in matrix writing by a 2nd order tensor:
=lllE [^iYHj: 11I^`X^ =11I^'L^=E LXT1
The 2nd order cumulants are represented in scalar writing by the
expressions:
Cum
"^` ^u I C11117 z'^^po X^i l E [(x,, - E[,-.. Ix., - E[x., D*.1;
C11111 1= C1u11 1 = E [(x., -
E[x,, J x, _ E[x,
20 and in matrix writing by a 2nd order tensor:
LL U^
Cut) i = C1111 *^^=E (X-E[XDH];Cun4Xi =Cunzz)L)=E (X-E[XD(X-E[XDT]
Similarly , the expressions of the 4t" order moments and cumulants are
given.
25 The 4th order moments are represented in scalar writing by the
expression:
Vno,n„n2;n3 = 1,...,N; M4
, x00;xn,)Xnz;x-3 1 = ELXno')Xni 2 >X113
20
and in tensor writing by the expression:
11^q*^^'*v*a)
= E^^r(*u
5
X(*3)]= E ((*a) (x(*,
)H X(*2)
O
(X(*3))
)
The 4th order cumulants are represented in scalar writing by the
expression:
Cun{,`f^n„^^^02;^ ] '')14X('2)X(3)_Y(^))(*)WX(^)X(^)^_^(^)X(t3)^YhJX('^)1
-X(*)XJK('2)Y(,)j_^X(*)Y(
,I, 'I, n3 2 112
X('olHX(*JX(*2)X(5)]_ ]Xh)] X(*,)X(*2)X('2)]_ X(*2)]4X(*I)X(*^)Xh2)]_EiX(*3)] X(*JX(*2)X(')]
n, n2 n2
r
n, nZ rn, n2 III n„ nj n3 r "1 n2
'+ '24X(*n)X(*.)] `(*2)]/^l(*3)]+.24X(*)x(*2)]j^,r(*^)]]^`r(*J)]^'2 X(*n)`(•J)] `.(*2)] ,(*1)] n, 4 n2 ^+L n u2 ^` n1 'y
1,
n2 n2 +_-
(((
` n'
+2 ` X(*i)x(*2)]4X(*n)]E'X(*")]+. 24X(*i)X(*a)] X(*n)] X(*z)]+'2 X(*z)X(*2)]4Y(*o)^p^, ('^)]
n' n2 n.n3 n, n3 n,i n2 n2 n2 nn f'l^ III
-6.4X
n„
)]4X(* )]4X2)]4X
ni
-
n2
n'
n2
and when the signals are centred , the expression is simplified as:
I *2,*J) _ j^ K) (*1) (*2) .'))]_ (*U) (*^)'J^ (*2) .(*J )]_ (*0) (*2)] ` (*1) (*2)]_
AIX.,
CUTT' (*))]].^ (*') (*2)]
:-n,: ` n' ;-n31
X N X i X 2 `^ no „1
III III Xno Xnz
X„1 Xn2 Xno X12 Xn1 Xn2
In tensor writing , the expression of the 4th order cumulant is:
*„ ,>ja4 =^^® ^^+2 *,>> o *=^l^l •=)jo *)^+ *,) o * )hod _)^©4 )^
+2 ',) ©x^ 2) o >) © *^) + ,) ©x(**) © 4**) ®• •2) + > *) © •*) ® )•^) ©, *,)
10
and when the signals are centred:
The quadricovariance is the 4th order tensor most widely used in the
1s methods of source separation and of goniometries at the orders higher than
2. It corresponds to the 4th order cumulant defined by the conjugation indices
1 and 3.
For a centred complex scalar signal X with zero delays , it corresponds
to the product of the flattening (or Kurtosis ) coefficient by the variance, and
20 equals Quadx = E[Ix14] - 21E [ Ix12]12 - IE[x2]12. For a real scalar signal X that is
centred and with zero delays , it equals Quadx = E[x4] - 3 ( E[x2])2.
For a complex signal vector X that is centred and has zero delays, it is
written in the tensor form Quadx =Cum4,x(
E[XOX*OXOX*]-2, E[XOX*]O(E[XOX*])-E[XOX]O(E[X*OX*])
21
For a real signal vector X that is centred and with zero delays, it is
written in the tensor form Quadx=Cum4,x(,*,*)=E[XOXOXOX]
- 3E[XOX]O(E[XOX]).
If X is a Gaussian signal, then Quadx =0.
5
In practice, on signals that are appropriately sampled at a sampling
frequency Fe = 1/Te complying with the Shannon condition , these tensors are
estimated by temporal means of the products of order q <_ Q of the signal
vector.
10 At the 1 st order, in order to construct the mean of the signal vector, the
probabilistic means of each component of the signal is estimated by a time
integration
no
[Xn o
(k°T
K
.1 x„ ((k° + k)T )
_1
Since communication signals are usually centred , the mean is a priori
15 zero.
At the order 2, in order to construct moments and covariances, the 2nd
order products of each component of the signal vector are estimated with and
without conjugation by a time integration:
no, n, =1,...,N; E[x;° (k°T) x*' (k,T,)] zt^ Kl x*° ((ka + k)T ). xn' ((k1 +k)T0 )
20 At the order 3, the same process is carried out with the 3rd order
products , with and without conjugation , then time integration.
Since communication signals are considered to be centred and
balanced , the 3rd order moments and cumulants are usually zero.
At the order 4, in order to construct moments and quadricovariances,
25 the means, 2nd order products and 4th order products of each component of
the signal vector are estimated with and without conjugation by a time
integration:
22
n0,n1 ,n n3=1,...; E[x'- 1100(k0Te)x (k1TQ)xn, (k,T,) x,3 (k3Te)]
x,,0((1,P +k)Tc) .x;`((k1+k)T,).xn ((J +k)Te ((r^3+1,:) ,)
K k_, n 11 1 ).x*u_
An equivalent process is carried out in order to construct any moment
or cumulant of an order higher than 4.
5 The relations between a statistical estimator of the signal X at the
output of the antenna array and its equivalent for the signal X at the input of
the antenna array will now be described. These relations involve the coupling
coefficients between elements of the array.
10 The relations (1) and (2) correspond to a linear transformation of the
signal at the input of the antenna array X into an output signal of the antenna
array which is written in the condensed form X'=CX, the vectors X and X
implicitly taking account of the samples delayed because of the switchings.
The products, moments and cumulants of the signal X then sustain the
is following multilinear transformations.
20
The products of order Q of the received signals X with or without conjugation
(marked (*) by convention) are linked to the products of order Q of the signals
X by the relation:
x'(*°) (t + n0At).x'(;' (t + n1At) ...x'(*Q-Q (t + nQ_lAt)
u
_
(C(*°) .C(*,) ...C(*P-') ).(x(*°)(t +m ^t)x')(t +na Ot).. x(*Q'^(t +m 0t)) nom. n,m, nP-,mQ_, m^ 0 mi t m,_, Q-1
mp=1
ny =1
MQ_,=1
Similarly, the moments of order Q of the signal X are written:
.,, (t+n„4t);x', (t+n,At);...;x'„Q_1(t+nQ_,A0,
mo=,
m,=1
(C(*.)) ^
C(*') C(*QI) " n.m npn, 11Q_,mQ-h Q,^xm (t+mOAt);x I (t+m,dt );...;x.,O I (t+mQ-,4t))
mQ_,=1
23
and the cumulants of order Q:
Cum(*' '*''*2,...,*Q_1)
°'Ix (t+n04t);x'01((+n1At);...;x'^Q , (t+nQ_1At)l
N
N (C(*^') .C(*1) ... C(*Q-1)
0 01110 111.71 11 Q -11 1 Q -1
rn^=1
nq=1
mp_1=1
Q,^x-0 (t+m114t);x n1 (t+,n At);...;xmQ I (t+m0_,4t)]
5 All the above formulations are written in condensed tensor forms in which the
linear operator of the transformation by coupling of the input signal X of
antenna array into an output signal X (transformation x' = c.x , operator c) is
considered to be a 2nd order tensor. At the statistical order Q, the tensor
autoproducts of order Q of this 2nd order tensor c, formally marked c(Q)
io define tensors of order 2Q (which may be seen as matrices of dimensions
(No x No) appropriately ordered). These tensor autoproducts of order Q
operate on tensors of order Q (which can be seen as vectors of size No x I
appropriately ordered).
1s These tensor operations are written according to the following formal
relations in which the delays due to the switchings are implicitly taken into
account:
- the tensor Q-power of X as a function of that of X
(•o 'I.•2,..."0-1) ('0. '1.•2... .•Q_1) ('0,•1.•z, ....'Q-1) 20 [x'®x'®...®x'} - QC®C ®... ®C1 [x®x ®... ®x]
- expression of the moments of order Q of X, as a function of those of X
M(*u, *1, *z,...,*Q_I ) = RC®C®...®CE(o.9.z.....'Q)
/LI(*u
* 1. *z,.... *Q_i)
Q x
- expression of the cumulants of order Q of X as a function of those of X
Cu,1J 0 , ,. z,..., Q z...., Q - QC 0 C 0 ... 0 C^ . 011111b, X
24
In general, the equation linking a statistical estimator of order Q of the
output signal X', marked MQ,x', with the statistical estimator of order Q
corresponding to the input signal X, marked MQ,x, is:
5 Mo,, =QCOC0...OCJJ .M0,,=C .Mo, (3)
where the delays due to the switchings are implicitly taken into account in X
and in X' and where C(Q) is the formal notation of the tensor autoproduct of
order Q of the coupling matrix C of the antenna array, Q being the order of
the moment or cumulant that the statistical estimators noted MQ,x and MQ,x.
io represent.
For example, the covariance of the output signal X', which is a 2nd
order moment, is linked to the covariance of the input signal X by the
following relation:
15 R(*) _ C C (*) r((n2 m )At)R(*^ [x',0 (t+no.4t); x'ot (t+nt.4t) ]
nom . ntmi S I - 0 [xmp (t+mo.At); xmi (t+mtdt)]
mo=1
ntt =1
which is written in the condensed form (4) below:
R,t, =C®C(*).R.v (4)
where C®C(*) is the tensor product of the coupling matrix by its conjugate
represented by a matrix of dimension N2 by N2.
20 where R,L,, R_ are defined as being 2t,d order tensors represented by vectors
of dimension N2 or by matrices of dimension N by N.
The method according to the invention will now be described for the
particular example of determining the covariance of the signal to be located.
25 The method is applied in a similar manner for the other statistical estimators
described below in the description or their equivalents.
25
By virtue of the taking account of the coupling coefficients between
antenna elements, each sampling of signal x'n by the switch contains the
contribution of the input signal on the antenna element of weighted index by
the impedance specific to this element, and the contribution of the other
5 antenna elements, at the same instant, weighted by the associated coupling
coefficient. The observation of the signal is thus made continuous to the
extent that the antenna elements to which the switch is not connected
contribute indirectly to the received signal via the antenna coupling, and this
is so at all the instants of switching.
10 The statistical estimators of the signal X', for example its covariance,
appear as linear combinations of the statistical estimators of the signal X,
considered at all the instants that are delayed because of the switching (i.e.
not only at the instants of taking of reception by the switch).
is Since the switching speed is assumed to be slow compared with the
duration of a symbol of the received signal, the influence of the
autocorrelation function rs('L) of the signal S must be taken into account
because it is not negligible for the significant delays compared with the
symbol duration (delays linked to the switching and close in practice to
20 multiple integers of the period At).
The term rs(,r) intervenes as a corrective term in the relation (4) which
makes it possible to link the covariances of the signals X and X. Starting with
the general expression (1), the relation (4) is modified to arrive at the
25 following relation:
RM [s'„ n (t+n^.Ot); x'„, (t+n,.4t)j
C,,,n, .Cn m
M . N, ((nr 1 - mO )At)R(
*)[ (t); X., (t)] (5)
;0=1
m,=1
which is expressed in the condensed form (6).
R. =C©C(*).[rs &R,]
(6)
26
The & operator indicates the term-to-term product of the 2nd order tensors rs
and k ,
R,,, in this instance corresponds to the covariance of the signal X that is not
delayed at the input.
5
The component of index ( i-1)N+j of the tensor is is equal to the
autocorrelation function rs((j-i).At) of the transmitted signal S (t) delayed by the
delay (j-i).At.
The components of the tensor is can be precomputed for all the delays 0,
l0 At,... N.At, when the information on the modulation of the transmitted signal
S(t) is available . The period of spatial sampling At may be chosen such that
the value of rs(At) is sufficiently high, preferably higher than 0.1. In practice,
an appropriate choice consists in taking At to be substantially equal to 3TS/2.
Figure 5 illustrates , in a diagram, the allure of the autocorrelation function
is rs('C ) of a signal modulated by a BPSK modulation and filtered by a root-
Nyquist filter and with a roll-off coefficient of 0.5. The choice of At=3TS/2
corresponds to the 1st secondary lobe of the function of which the level is
substantially equal to 0.14.
Such signals with non-zero secondary loads are very frequently
20 encountered in practice and their characteristics can be known a priori or
predetermined by analysis. For many filtered modulations , the choice of
At=3TS/2 ensures a secondary lobe level higher than 0.1, which makes it
possible to use the method according to the invention for levels of payload
signals that are sufficiently strong , that is to say for signal-to-noise ratios of
25 more than 20 dB.
In a variant embodiment of the invention for which the received signals
are not independent and identically distributed, the precomputation of the
autocorrelation function rs(u) must be carried out on a sequence of reference
symbols contained in the received signal. Many signals comprise this type of
27
sequence; this is the case notably for the frequency -synchronization tones in
the signalling and in the multi-carrier modulations but also for the unbalanced
repetitive signals contained in the complex modulations such as for example
the pilot signals for the COMA modulations . In general , any sequence of
5 reference symbols contained in the received signal and known a priori can be
used to estimate the autocorrelation function rs (t) and give rise to an
application of the method to the corresponding signal portion.
If a 41h order estimator is used, for example the quadricovariance or a
l0 4th order cumulant , the relation (3) becomes:
Quad,,, = [C & C(*) © C © C (*)1 • [[&Quad ,11
with
& designating the term -to-term product of the 4th order tensors Quad,, and
qs quadricovariance tensor of the non-delayed input signal X
15 qs the delayed quadricovariance function of the source signal S, of which the
modulation is assumed to be known , represented by the expression:
gs(til,ti2,ti3)= E[s(t) S(t+rl)*S(t+r2 ) S(t+r3)*J- E[s(t) S(t+ T1 ) *JE[S(t+T2)S(t+r3) *J - E[s(t)
S(t+T2)JE [S(t+T1) S(t+T3 ) J - E[S(t) S(t+T3 ) JE[S(t+rl)S(t+r2)FJ)
20 The quadricovariance function qs can be predetermined in the same
way as the autocorrelation function r, for all the sets of delays T1, i2, i3
amongst the values {At ,..., NOt} when the information on the modulation of the
signal S is available or determined in advance by analysis.
In general, the relation (3) is written for a statistical estimator
25 representing a moment or a cumulant of order Q : M , = M(s .C(O).MQ
where
28
M^,^';, is the statistical estimator of order Q corresponding to the output signal
affected by the delays associated with the switchings
, is the statistical estimator of order Q corresponding to the undelayed
input signal
5 MLJ is the statistical estimator of order Q corresponding to the modulation
function of the signal S(t).
The method according to the invention therefore consists in carrying
out the following steps.
10 The signal X' vector is sampled by the switch 102 at the output of the
antenna array 101 with a sufficiently rapid switching speed compared with
the speed of modulation of the received signal.
The signal X' vector is digitized at a given sampling frequency Fe and
then integrated over a predetermined period of observation.
is The covariance Rx of the signal X' is computed, then the covariance
R, of the undelayed signal X at the input of the antenna array is determined
by resolving the system of equations (6) based on the coupling matrix C of
the antenna array that has been previously determined and stored and based
on the predetermined values of the autocorrelation function of the modulation
20 of the received signal S.
A method of radiogoniometry or a method of source separation is
applied to the matrix of covariance Rx in order to determine the number of
sources and/or their direction of arrival. In advance or alternatively, a method
of source separation or of identification of source-directing vectors may also
25 be applied.
In order to improve the performance of the method, a sampling, by the
switch, of the signal samples in the middle of the switching intervals, as
29
illustrated in Figure 2, is preferred so as to prevent a sampling during the
transitory regime of the control circuits of the switch.
The possible uses of the abovementioned statistics in signal
5 processing and antenna processing will now be described.
All the information on the signal is contained in the series of its
moments which appear as the coefficients of the development in series of the
first characteristic function of probability distribution of the random signal
vector X (at the instant t omitted for the purposes of simplification in the
to following formulae)
(xI) (it,)
x = ;U= E CN; i,,'(U)E C
(1^,,. (U) = E[exp(/Re{U" .X})I =1+2 j i
00
(D,, (U) =1 + l I Re
Q=I combinationS
Rej
Z
E[x(
Ill i, *(l)x('1) ...x('YIll .1) j u(i^ll 0)u i,
(.J... u^"41)
ombinolhm
U
All the information on the signal is also contained in the series of its
cumulants which appear as the coefficients of the development in series of
15 the second characteristic function of probability distribution of the signal X
random variable
UEC`;'Y,.(U)EC
'Y,.(U)= Log(E[exp(j Re{U".X})D=1+Z j
a
q=1 i,,....1,
`1'x(U) =1 +I
Q=1 combinations
Re
combbmiims
u.tl,...iy.l
Q
. Re ^(Cllnv[ U
I!i2!..aN!
i. !i, !...i,r i
20
30
Therefore, knowing the series of the moments or the series of the cumulants
of the signal at the input of an antenna array makes it possible to completely
characterize the "input signal X vector" statistical process.
When the input signal vector is real , the first characteristic function is
5 determined at the order Q by a single tensor of the moments, of order Q; the
second characteristic function is determined at the order Q by a single tensor
of the cumulants , of order Q.
When the input signal vector is complex, the first characteristic function is
determined at the order Q by ^Q=1+LQ/2i tensors of moments of order Q
io where LQ/2J is the entire portion of Q/2 (^1=1, ^2=^3=2, i;4=3), the other
moments being deduced by conjugation ; the second characteristic function is
determined at the order Q by 4Q tensors of cumulants of order Q, the other
cumulants being deduced by conjugation.
is Often, the study of the statistics of the 1st orders 1 and 2 provides the main
information on the process X. For example, the principal component analysis
that is well known to those skilled in the art consists in breaking down the
matrices of covariances into specific elements and directions, which makes it
possible to determine and classify in order of importance the principle
20 relations of statistical dependencies between coordinates of the vector X. In
antenna processing, these methods lead to the subspace methods such as
MUSIC2 ("Multiple Signal Classification 2"). When X additionally has strongly
non-Gaussian characteristics, which is frequently the case with transmission
signals, the statistics of orders higher than 2 provide additions of
25 discrimination. In antenna processing, these methods lead to the methods
known as "with higher orders" such as MUSIC4 which works on the 4t" order
cumulants, or the JADE method which uses 2nd and 4th order cumulants
jointly.
31
The possible uses of the abovementioned statistics will now be
described for applying a known method of source separation or of
radiogoniometry.
5 With respect to communication transmitters , most of the methods of
source separation , of identification of directing vectors and of conventional
parallel goniometry at super and high resolution that are known to those
skilled in the art use the 2nd order and 4th order moments or cumulants of the
input signal vector.
10
It is possible to cite for example:
- The correlative interferometry that consists in considering the N phases of
one of the column vectors of the covariance matrix of the input signal, and in
searching in a precomputed calibration table the phase N - uplet closest to the
is direction of a distance criterion (for example a criterion of least squares), the
direction associated with this N -uplet then providing the estimate of the
direction of arrival of the signal.
- The vector correlation which consists in considering the N phases and the N
amplitudes of one of the column vectors of the covariance matrix of the input
20 signal , and in searching in a precomputed calibration table for the 2N-uplet of
phases and amplitudes that is closest to the direction of a distance criterion
(for example a criterion of least squares ), the direction associated with this
2N-uplet then providing the estimate of the direction of arrival of the signal.
- The formation of adaptive channel which consists in using the estimate of
25 the covariance matrix of the signal to form the spatial filter in each direction
defined by a directing vector as by the relation
ru, (as )= [R[J as
then in applying this filter to the input signal X vector in order to construct the
criterion
32
C,.4S(aS)=XH
the maximization of which gives an estimate of the directing vector or vectors
as corresponding to the sources received at the input; the corresponding
directions of arrival are then produced by searching in a calibration table
5 previously produced by computation and/or measurement.
- The subspace methods of the MUSIC type which consist in breaking down
the covariance tensors (for a 2nd order MUSIC method) and quadricovariance
tensors (for a 4th order MUSIC method) in order to search for the specific
subspaces thereof, constructing orthogonal projectors, then producing
to estimates of the directing vectors as of the estimated input sources which
produce a criterion of minimization of the said projections; the corresponding
directions of arrival are then produced by searching in a calibration table
previously produced by computation and/or measurement.
is The reference works entitled "Advances in DOA estimation, chap 8, S.
Chandran" and "J.L. Lacoume, P.O. Amblard, P. Comon, "Statistiques
d'Ordre Superieur pour le traitement de signal" ["Higher order statistics for
signal processing"] Editions Masson, 1997" describe the aforementioned
MUSIC2, MUSIC4 and JADE methods and other methods of radiogoniometry
20 and of source separation that use the statistical estimators of a signal X with
spatial diversity and which are compatible with the use of the method
according to the invention.
The invention advantageously applies when the transmitting sources
25 to be located are homogeneous, that is to say that they all transmit a signal
generated according to the same waveform.
The invention may be used in a radiogoniometry system, a
radioelectric sensor, a land, maritime or aeronautical radio system.
It can be used to produce a control function of the spectrum or a
30 sensing function in a cognitive radio for the purpose of optimizing the access
33
of the radio to the array by the detection, the estimation of spatial signatures
and the determination of angle of arrival of the adjacent interfering sources.
The invention uses the couplings between antenna elements of a
5 small-base array and has the advantage of enhancing the performance of the
methods known to those skilled in the art by making the observation of the
received signal virtually continuous despite the switching of a single receiving
channel on several antenna elements. The invention therefore makes it
possible to detect any type of signal whether they are generated with a
io continuous or discontinuous waveform, to process complex environments
(propagation multipath interference) and non-stationary environments.
Finally, the use of the coupling matrix of the antenna array has the
advantage of preventing a too precise and awkward antenna calibration.
34
CLAIMS
1. Method for locating sources each transmitting a signal S, characterized in
5 that it comprises at least the following steps executed by a single-channel
receiving system:
® Receiving the signal or signals at the input of an antenna array
(101) comprising a plurality N of radiating elements (111, 112,11 n)
by successively switching the receiving channel to the N radiating
to elements with a predetermined switching period At,
® Sampling , after each successive switching, at the output of each
radiating element ( 1111, 112,11 n), a sample of the received signal in
order to construct a vector X' of the spatial signal received by the
antenna array (101),
15 ® Computing at least one first statistical estimator MQ^';, of order Q
greater than or equal to 1 of the spatial signal X' at the output of
the antenna array (101),
® Estimating the values of at least one statistical estimator of order Q
M(Q) of the function of modulation of the said transmitted signal S,
20 ® Determining at least one second statistical estimator MQQ; of the
same order Q, for the spatial signal X at the input of the antenna
array (101) by resolving the systems of equations
MQQ,, =MQS.C(Q).^i^QQ, where C(Q) is a self tensor product of order Q
of the coupling matrix C of the antenna array ( 101), the
25 components of the said coupling matrix C being equal to the
mutual coupling coefficients between each pair of radiating
elements of the said antenna array ( 101), the said coupling matrix
C being previously determined and stored in a database contained
in the said system,
35
® Applying a source-location method, such as a method of
radiogoniometry, of separation of sources, of identification of
spatial signature or of identification of source-directing vectors, to
the said second statistical estimator M^Qt
5
2. Source-location method according to Claim 1, characterized in that the
said statistical estimators M(Q) ,,, MQS , M^Q; are estimators of the
moments or of the cumulants of order Q.
io 3. Source-location method according to Claim 2, characterized in that the
said statistical estimators MQQ,,, ML; S , M(^'), are estimators of the crossed
products, of the variance , of the covariance or of the quadricovariance.
4. Source-location method according to one of the preceding claims,
is characterized in that the statistical estimator of order Q MQQS of the
function of modulation of the transmitted signal S is estimated on sets of
multiple temporal values of the switching period At based on the a priori
knowledge of the modulation of the said signal S.
20 5. Source-location method according to one of Claims I to 3, characterized
in that the statistical estimator of order Q M(Qs of the function of
modulation of the transmitted signal S is estimated on a sequence of
reference symbols that are known a priori and contained in the said signal
S.
25
6. Source-location method according to one of the preceding claims,
characterized in that the successive sampling at the output of each
radiating element is carried out according to a circular switching.
30 7. Source-location method according to one of the preceding claims,
characterized in that, in order to generate the coupling matrix C, each
36
mutual coupling coefficient between a first and a second radiating
element is determined by imposing a voltage and /or by injecting a current
at the terminals of the first radiating element and by measuring the
voltage and/or the current at the terminals of the second radiating
5 element.
8. Source-location method according to one of the preceding claims,
characterized in that the location of a source consists in determining the
direction of arrival of the wave transmitted by this source.
10
9. Source-location method according to one of the preceding claims,
characterized in that the source-location method is chosen from the
following methods: a correlative interferometry method , a vector
correlation method , an adaptive channel formation method, a secondis
order or fourth-order subspace method, or a JADE method.
10. Receiving system for the location of sources each transmitting a signal S
comprising an antenna array ( 101) consisting of a plurality of radiating
elements ( 111,112,113,11n), of a switch ( 102) in order to successively
20 sample the output signal of each radiating element, of a receiving channel
(103) comprising an analogue -digital converter (132) and of means (104)
of analysis and of computation comprising a computing unit and a
database, containing the predetermined values of the coupling matrix C of
the antenna array (101), characterized in that the means (104) of analysis
25 and of computation are adapted to apply the source - location method
according to one of Claims 1 to 9.