Specification
Method for locating transmitting sources by the use of the mutual
coupling of a small -base antenna array and fast -switching singlechannel
receiving system using the method
5 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 switching of the receiving channel between the various elements
of the antenna array must be fast enough 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 associated with
frequency-evasion mechanisms , with broad or narrow-band frequency, and in
5 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
to 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
is 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
to 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 switching of the antenna
is diagram. 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 form the desired antenna diagram and thus
20 achieve a rapid switching.
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, tables that have to be very precisely determined.
25 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.
Finally, these solutions also suffer from problems of discontinuity and
30 of transitory regime of the observations made during the switchings, even
when they are rapid.
4
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 fast switching of the receiving channel on the various antenna
5 elements of the antenna array.
The invention makes it possible to reconstitute a quasi-continuous
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
io 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.
Accordingly, the subject of the invention is a method for locating
sources each transmitting a signal S , characterized in that it comprises at
15 least the following steps executed by a single-channel receiving system:
® Receiving the signal or signals at the input of an antenna array
comprising a plurality N of radiating elements by successively
switching the receiving channel to the N radiating elements, the
switching period At being configured to be strictly less than the
20 ratio between the half-duration TS/2 of a symbol of the said signal S
and the number N of radiating elements,
® Sampling, after each successive switching , at the output of each
radiating element , a sample of the received signal in order to
construct a vector X' of the spatial signal received by the antenna
25 array,
® Computing at least one first statistical estimator MQQ;,, of order Q
greater than or equal to 1 of the spatial signal X ' at the output of
the antenna array,
® Determining at least one second statistical estimator MQ of the
30 same order Q, for the spatial signal X at the input of the antenna
5
array by resolving the systems of equations MM.o = C«I.MQ X
where C(Q) 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
5 pair of radiating elements of the said antenna array , the said
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
to spatial signature or of identification of source-directing vectors, to
the said second statistical estimatorMQ'X .
According to a particular aspect of the invention, the said statistical
estimators are estimators of the moments or of the cumulants of order Q or
more precisely estimatiors of the crossed products, of the variance or of the
15 covariance.
In a variant embodiment , the method according to the invention also
comprises a step of compensating for the components of the second
statistical estimator of the spatial signal X with the values of the
autocorrelation function rs ( r) of the modulation of the said transmitted signal
20 S, the said values being delayed by a multiple delay of the switching period
AT.
According to a particular aspect of the invention , the said statistical
estimators are estimators of the quadricovariance.
In a variant embodiment , the method according to the invention also
25 comprises a step of compensating for the components of the second
statistical estimator of the spatial signal X with the values of the
quadricovariance function gs ('ci, T2, i3) of the modulation of the said signal S,
the said values being delayed by multiple delays cl, T2, i3 of the switching
period AT.
6
In a variant embodiment of the invention, the successive sampling at the
output of each radiating element is carried out according to a circular
switching.
According to a particular aspect of the invention, in order to generate the
s coupling matrix C, each mutual coupling coefficient between a first and a
second radiating element is predetermined 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 element.
to The location of a source may consist in determining the direction of arrival
of the wave transmitted by this source.
The source-location method may be 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,
is or a JADE method.
In a variant embodiment of the invention, the signal S is sought in an
instantaneous frequency band of minimum value F1 and of maximum value
F2, the said switch also being configured so that its switching period AT is
strictly less than the quantity 1/(2.N.F2).
20 A further subject of the invention is a receiving system for the location of
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
25 computation comprising a computing unit and a database, characterized in
that the said switch is configured so that its switching period AT is strictly less
than the ratio between the half-duration Ts/2 of a symbol of the said signal S
and the number N of radiating elements, the database contains tho
predetermined values of the coupling matrix C of the antenna array, and the
30 means of analysis and of computation are adapted to apply the sourcelocation
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:
- Figure 1, a block diagram of a receiving system adapted to use the
5 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
signals at the input of the computing unit of a receiving system
10 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 1 represents, in a block diagram, a receiving system 100
adapted to use a method of radiogoniometry or of source separation
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
20 111,112,113.... 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
(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
25 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
two radiating elements. A short switching period or a fast switching speed
has the advantage of limiting the discontinuities in the acquisition of the
signal that are associated with the time necessary to switch from one
3o antenna element to another.
8
The receiving channel 103 comprises at least one amplification and/or
filtering system 131 and an analogue/digital converter 132 capable of
digitizing the received signal at a given sampling frequency Fe.
The system 100 also comprises means 104 for analyzing and
5 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
characterize them. The database contains certain items of predetermined
information concerning the antenna array and, where necessary, concerning
to the nature of the received signal, notably its modulation.
The method according to the invention can be applied in the situation
in which the switch 102 is configured so that its switching speed is fast
relative to the symbol frequency of the received signal to be located. In this
is way, the duration of a spatial sampling of the received signal on all of the
elements of the antenna array remains much less than half the duration of a
symbol of the received signal.
More precisely, an essential feature of the invention is that the
switching period At is strictly less than the ratio between the half-duration Ts
20 of a symbol of the observed signal and the number N of elements of the
antenna array 101. In this manner, the switch 102 carries out, on each
symbol at least, a complete run-through of the antenna array before the end
of a symbol of the observed signal.
Figure 2 illustrates, in a diagram, the principle of a fast switching
25 relative to the symbol time of the received signal.
Figure 2 represents a symbol indexed by K of the received signal S of
duration Ts defined by its modulation rhythm and 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
30 period. A complete run-through of the antenna array 101 is carried out by the
switch 102 before the end of the symbol K. Specifically, in the example of
9
Figure 2, a complete run-through is carried out before the end of half of the
symbol K.
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
5 rhythm Te is equal to a quarter of the switching period At.
All of the samplings x'l,...x'N made during the duration N.At form a
vector X' of the output signal of the antenna array 101. The samples x'j ,...x'N
of this signal X' can be taken in the same symbol K of the received signal
because of the fast switching of the switch 102 in less than a half-duration of
to a symbol.
The construction of the vector X' is illustrated in Figure 3. Each
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
is 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
it possible to better characterize the signal for the purpose of identifying its
direction of arrival.
20 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
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; +
25 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 Ik; - kjI of
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. It is
30 this value Ak.At that must be strictly less than the half -duration TS/2 of a
symbol . In the case of a circular switching, Ak = N.
10
The method and the system according to the invention
advantageously apply for small -base or small-diameter antenna arrays. For
such arrays, the radiating elements are close to one another and the mutual
5 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
voltage signal at the terminals of the matching circuit of each antenna
to 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
matching circuit of a radiating element by the electromagnetic field in the
15 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.
When the distance between the antenna elements is small, the
20 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
other elements of the array.
25 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''°' .S(t + n.AT - z) + b„ (t + n.AT)
S being the signal transmitted by the source , pn, cpn and in being the phase
3o attenuation and delay induced by the propagation, bn being the received
noise.
11
The output signal x'„ o(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
following general relation:
N N
x'nn (t +n 0AT) _ XCn,,n.Xn(t +n0AT-Znpn ) XCnon.Xn(t+n0AT) (1)
n=1 ,1=1
5
Vn0,n =1...N; x',, ,, (t t
o N.4T«Ts/2 ; X' - O ;
x n(t+n0AT) N.AT<>]ode ,]+ ,,© ,^]®4 °'}®1E ]+24 ^® 1®4 ° 1® ^1
and when the signals are centred:
20
1
The quadricovariance is the 4th order tensor most widely used in the
methods of source separation and of goniometries at the orders higher than
21
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
5 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*])
to 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.
15 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.
At the 1St order, in order to construct the mean of the signal vector, the
20 probabilistic means of each component of the signal is estimated by a time
integration
K
no =1,...,N; E[x,,,, (koTe )] .1 x,,0 ((ko + k)Te )
K »_,
Since communication signals are usually centred, the mean is a priori
zero.
25 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:
K
110 , n,=1,...,N; E[x*°(koT)xn'(k,T)] 1 1x*°((ko +k)T ).x;' ((k,+k)Te)
~ Kk=1
22
At the order 3, the same process is carried out with the 31d 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.
5 At the order 4, in order to construct moments and quadricovariances,
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:
0 11 12
Y1. ,711117"173 =1, ...,^; E[xno (k 0I )x i (k1T )X (k,T') Xn3 (k37 )]
1
I
13
x1° (( 0 - f k)T,,).xni((/q +k) ).x ((/i,+ ^i)T,,).xn,A11^;+k)Te) K k_1
10
An equivalent process is carried out in order to construct any moment
or cumulant of an order higher than 4.
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
1s the antenna array will now be described. These relations involve the coupling
coefficients between elements of the array.
The relations (1 bis) and (2) correspond to a linear transformation of
the signal at the input of the antenna array X into an output signal of the
20 antenna array X'=CX.
The products, moments and cumulants of the signal X then sustain the
following multilinear transformations.
The products of order Q of the received signals X with or without conjugation
25 (marked (*) by convention) are linked to the products of order Q of the signals
X by the relation:
,(*,,) •(*J...x1(*Q) X no ) .C(*') ...C(*p') (*").x(*')...x(*Q-') ) .x ni nQ, npmp nom np. mQ. / Xmo m, mQ-I
m^=1
m^=1
m^-,=1
23
Similarly, the moments of order Q of the signal X' are written:
(C(*I,) C(*1) ...C(*Q-1) '. -'o. - lmi nQ_lrQ_I
1110=1
1111=1
711Q_I=1
and the cumulants of order Q:
k I , I, z,..., (J_Il II.,.11,..;.,,,Q_I
C2[YI?*
(C(*")
n m 'Cnm Cn m _ )•
Q^,A'^I
..;X ,,
11i 1
U V 1 1 Q-I Q I
Cun?
Q,IX,, ,Xm1 ;...;X Q_I
l111 =1
111 p_1=1
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
to 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«''
define tensors of order 2Q (which may be seen as matrices of dimensions
(N° x N°) appropriately ordered); these tensor autoproducts of order Q
operate on tensors of order Q (which can be seen as vectors of size N° x 1
15 appropriately ordered).
These tensor operations are written according to the following formal
relations:
20 - the tensor Q-power of X' as a function of that of X
]
fC ®C®...®C (^^^^: •Q^)
Y ®X®...®Xh^^^^
QI)
- expression of the moments of order Q of X', as a function of those of X
*o, *I,*v...,*Q-I) Q, Y' = QC ®C ®... ®C]I
K.h'z...,•Q-I) * * * +g-I)
- expression of the cumulants of order Q of X' as a function of those of X
24
Cu,n 0 = QC®C®...®CB Clin i
In general , the equation linking a statistical estimator of order Q of the
output signal X', marked MM i, , with the statistical estimator of order Q
5 corresponding to the input signal X, marked MM' is:
to> (^?) coy co) Mex. =QCOCO...OC^ M^„=C .M x (3)
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 MME and MMit represent.
1 0
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 relation
(4):
R,,.=C C(*).Rx (4)
is where C®C(*) is the tensor product of the coupling matrix by its conjugate
represented by a matrix of dimension N2 by N2.
where R.i., Ri are defined as being 2nd order tensors represented by vectors
of dimension N2 or by matrices of dimension N by N.
20 The method according to the invention will now be described for the
particular example of determining the covariance of the signal to be located.
The method is applied in a similar manner for the other statistical estimators
described 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
25
the impedance specific to this element, and the contribution of the other
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
5 contribute indirectly to the received signal via the antenna coupling.
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 not only at the instants of taking of reception by
the switch.
10
The method according to the invention therefore consists in carrying
out the following steps.
The signal vector X is sampled by the switch 102 at the output of the
antenna array 101 with a sufficiently rapid switching speed compared with
is the speed of modulation of the received signal.
The signal vector X is digitized at a given sampling frequency Fe and
then integrated over a predetermined period of observation.
The covariance Rx. of the signal X' is computed , then the covariance
Rx of the signal X at the input of the antenna array is determined by resolving
20 the system of equations (4) based on the coupling matrix C of the antenna
array that has been previously determined and stored.
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
25 of source separation or of identification of source -directing vectors may also
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
3 0 illustrated in Figure 2, is preferred so as to prevent a sampling during the
transitory regime of the control circuits of the switch.
26
In a variant embodiment of the invention , the performance of the
method can be improved by assuming that the modulation of the received
signal S is known and more precisely the autocorrelation function rs ('C) of the
modulation of the signal S.
5 The term rs(,r) intervenes as a corrective term in the relation (4) which
makes it possible to connect the covariances of the signals X and X. Starting
from the general expression ( 1), the relation (4) is modified to arrive at the
relation (6).
10 R,. = c ©c(*).[,s & n, I
_ (6)
The & operator indicates the term-to-term product of the 2nd order
tensors rs and Rx. More precisely , the component of index (i-1)N + j of the
tensor ^•,. is equal to the autocorrelation function rs((j-i).At) of the transmitted
signal S(t) delayed by the delay (j-i).At.
15 The components of the tensor , can be precalculated for all the
delays 0, At... N. At, when the information on the modulation of the
transmitted signal S(t) is available,
In this variant of the invention, the method therefore comprises an
additional step which consists , after having computed the covariance Rx of
20 the signal X with the aid of the relation (4), in compensating for each of its
components by dividing it by the delayed values of the autocorrelation
function rs of the transmitted modulated signal S(t).
This additional step makes it possible to improve the performance but
is not essential to the application of the method because the samples of the
25 signal vector X' belong to one and the same symbol of the received signal.
This requirement is fulfilled if the switching time At is less than the ratio
between the half-duration of a symbol Ts/2 of the appropriately filtered source
signal and the number of antenna elements N.
The modulation of the signal S can be estimated by means external to
27
the invention intervening as a preamble or may be known when the very
nature of the signal of which the direction of arrival is desired to be estimated
is known.
5 If a 4th order estimator is used , for example the quadricovariance or a
4th order cumulant , the relation (6) becomes:
Quads = [C® Ct*1 ® C ®C(*)]. [[9s & Quadx ]]
where qs is the delayed quadricovariance function of the source signal S, of
which the modulation is assumed to be known, represented by the
io expression:
r gs(t1,ti2,^3)= E[s(t) S(t+tl)*S(t+t2) S(t+t3)*]- E[s(t) S(t+tl)*7]7 E[s(t+t2)S(t+t3)*1 - E[s(t)
S(t+t2)]E[s(t+tl)*S(t+t3)
*J 1
- E[s(t) S(t+t3)*]E[s(t+tl)S(t+t2)*])
The quadricovariance function qs can be predetermined in the same manner
as the autocorrelation function rs for all the sets of delays 0, At.... NAt when
is the information on the modulation of the signal S is available or previously
determined by analysis.
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.
20
The possible uses of the abovementioned statistics in signal
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
25 first characteristic function of probability distribution of the random signal
vector X (at the instant t omitted for the purposes of simplification in the
following formulae)
28
(I/I )
X =
) I1fNJ
E CN; (DN(U)E C
x m q
[ 02 x(U)= E exp(iRe {UH .X})] =1+>
(I)x(U)=1+y Re
Q=1 combinntlons
*0, * *
Q-1
i,Ii,!..J.
Re
1,+i2 +..,+1,=q
M(*1„*r,*Z,..., *Q_r )
^),[x]
(*o) x,(*r) ...x [*yt] 1u (*o) u (*r) .., u1[o*vr]
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
5 the second characteristic function of probability distribution of the signal X
random variable
UEC';`u (U)EC
r
`I'r(u)= Log(E[exp(jRe{U' .X}b = 1+^ J
I' I I
`1',(U)=1+Z I J Re
Q=I conrhinalons IIl12l..'N!
o' Q-1
10
Re^ Cum^x;`°)xhr
mrAlnntiars
021731 (*°'*r'*z,...,*Q r)
U
x(*vr)}u(*J (*r).. U!*,,)
ly_, 1^ li 1q_1
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
1s 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/2] tensors of moments of order Q
20 where LQ/2J is the entire portion of Q/2 (E1=1, E2=43=2, ,4=3), the other
moments being deduced by conjugation; the second characteristic function is
.Q
29
determined at the order Q by ^Q tensors of cumulants of order Q , the other
cumulants being deduced by conjugation.
Often, the study of the statistics of the 1St orders I and 2 provides the main
s 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
relations of statistical dependencies between coordinates of the vector X. In
to 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
discrimination . In antenna processing , these methods lead to the methods
15 known as "with higher orders" such as MUSIC4 which works on the 4th order
cumulants , or the JADE method which uses 2nd and 4th order cumulants
jointly.
The possible uses of the abovementioned statistics will now be
20 described for applying a known method of source separation or of
radiogoniometry.
With respect to communication transmitters, most of the methods of
source separation, of identification of directing vectors and of conventional
25 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.
It is possible to cite for example:
30 - 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
30
searching in a precomputed calibration table the phase N-uplet closest to the
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.
5 - 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
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
io 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
the covariance matrix of the signal to form the spatial filter in each direction
defined by a directing vector as by the relation
1UrAS( s ) - [R[NJI '.as
is then in applying this filter to the input signal X vector in order to construct the
criterion
CFAS (as) =XH RX
the maximization of which gives an estimate of the directing vector or vectors
as corresponding to the sources received at the input; the corresponding
20 directions of arrival are then produced by searching in a calibration table
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
25 subspaces thereof, constructing orthogonal projectors, then producing
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.
31
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
5 signal processing"] Editions Masson, 1997" describe the aforementioned
MUSIC2, MUSIC4 and JADE methods and other methods of radiogoniometry
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.
10
The invention advantageously applies when the transmitting sources
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
15 radioelectric sensor, a land, maritime or aeronautical radio system.
It can be used to produce a control function of the spectrum or a
sensing function in a cognitive radio for the purpose of optimizing the access
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.
20 The method according to the invention can advantageously be applied
to all of the signals acquired in an instantaneous frequency band delimited by
two frequencies F1 and F2 where F2 > Fl. In this case, the constraint of fast
switching is reflected by the fact that the switching period AT between two
samplings must be configured to remain compatible with a signal of which the
25 symbol frequency is as high as possible in the band in question, namely
equal to F2. This condition is obtained when the switching period AT is strictly
less than the quantity 1/(2.N.F2).
The invention uses the couplings between antenna elements of a
30 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
32
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
continuous or discontinuous waveform , to process complex environments
5 (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.
33
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 (111,112,11n)
by successively switching the receiving channel to the N radiating
10 elements, the switching period At being configured to be strictly
less than the ratio between the half-duration TS/2 of a symbol of the
said signal S and the number N of radiating elements,
® Sampling, after each successive switching, at the output of each
radiating element ( 111,112,11n), a sample of the received signal in
is order to construct a vector X of the spatial signal received by the
antenna array (101),
® Computing at least one first statistical estimator M(Q(Q'X) , of order Q
greater than or equal to 1 of the spatial signal X' at the output of
the antenna array (101),
20 Determining at least one second statistical estimator MQ ) of the
same order Q, for the spatial signal X at the input of the antenna
array ( 101) by resolving the systems of equations
MQ(°i, = O`'i.lYtQ where C(Q) is a self tensor product of order Q of
the coupling matrix C of the antenna array ( 101), the components
25 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,
® Applying a source- location method, such as a method of
30 radiogoniometry , of separation of sources, of identification of
34
spatial signature or of identification of source-directing vectors, to
the said second statistical estimator MQ;
2. Source-location method according to Claim 1, characterized in that the
5 said first and second statistical estimators A'IQI,,MQI are estimators of
the moments or of the cumulants of order Q.
3. Source-location method according to Claim 2, characterized in that the
said first and second statistical estimators MQ , , MQ Y are estimators of
fo the crossed products, of the variance, or of the covariance.
4. Source-location method according to Claim 3, characterized in that it also
comprises a step of compensating for the components of the second
statistical estimator of the spatial signal X with the values of the
15 autocorrelation function rs(ti) of the modulation of the said transmitted
signal S, the said values being delayed by a multiple delay ti of the
switching period AT.
5. Source-location method according to Claim 2, characterized in that the
20 said statistical estimators are estimators of the quadricovariance.
6. Source-location method according to claim 5, characterized in that it also
comprises a step of compensating for the components of the second
statistical estimator of the spatial signal X with the values of the
25 quadricovariance function gs('r1, i2, T3) of the modulation of the said signal
S, the said values, being delayed by multiple delays rl, T2, i3 of the
switching period AT.
7. Source-location method according to one of the preceding claims,
30 characterized in that the successive sampling at the output of each
radiating element is carried out according to a circular switching.
35
8. Source-location method according to one of the preceding claims,
characterized in that, in order to generate the coupling matrix C, each
mutual coupling coefficient between a first and a second radiating
5 element is predetermined 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
element.
to 9. 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. Source-location method according to one of the preceding claims,
is 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 secondorder
or fourth-order subspace method, or a JADE method.
20 11. Source-location method according to one of the preceding claims,
characterized in that the said signal S is sought in an instantaneous
frequency band with a minimum value F1 and a maximum value F2, the
said switch (102) also being configured so that its switching period AT is
strictly less than the quantity 1/(2.N.F2).
25
12. 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
sample the output signal of each radiating element, of a receiving channel
30 (103) comprising an analogue-digital converter (132) and of means (104)
of analysis and of computation comprising a computing unit and a
database, characterized in that the said switch (102) is configured so that
36
its switching period AT is strictly less than the ratio between the halfduration
Ts/2 of a symbol of the said signal S and the number N of
radiating elements , the database contains the predetermined values of
the coupling matrix C of the antenna array, ( 101), and the means (104) of
5 analysis and of computation are adapted to apply the source - location
method according to one of Claims 1 to 11.
13. Receiving system according to Claim 12, characterized in that the said
signal S is sought in an instantaneous frequency band with a minimum
to value F1 and a maximum value F2, the said switch (102) also being
configured so that its switching period AT is strictly less than the quantity
1/(2. N. F2).