Robust adaptive method for suppressing interference in the presence of a signal of interest

Abstract

A method for receiving a signal, includes a useful signal, interfering signals and noise, and for suppressing interfering signals in a multi-channel receiver, comprising steps of: (a) reception, frequency transposition and digital conversion of the received signal; (b) estimation of a correlation matrix of the received signals; (c) estimation of the variance of the noise; (d) initial estimation of the arrival directions of the useful and interfering signals; (e) initialization of the powers of the useful and interfering signals; (f) iterative computation: of the current directional vectors of the useful and interfering signal; of the powers of the useful and interfering signals; of the amplitude/phase errors of assumed directional vectors with respect to the current directional vectors; and of the arrival directions of the useful and interfering signals; (i) suppression of the interfering signals from the signal received in step (a).

Claims

1. A method for (i) receiving a signal, the signal comprising a signal of interest, interfering signals, and noise, and (ii) suppressing interfering signals in a multi-channel receiver, comprising steps of: (a) reception, frequency transposition, and digital conversion of the signal received over each of a plurality of channels of the multi-channel receiver, to obtain a digital multi-channel signal corresponding to a sum of the signal of interest, the interfering signals, and the noise, the receiver comprising an antenna array that comprises a plurality of radiating elements, each of which corresponds to one channel of the multi-channel receiver, and that is defined by a complex vector function a(, ) of two variables and defining a direction in space, comprising one component for each of the channels of the receiver and each component of which represents an amplitude and a phase response of the respective channel of the receiver in the direction in the space (, ), the signal of interest being defined by an unknown amplitude u[k] and by an unknown current arrival direction (.sub.u, .sub.u), the interfering signals being defined by an unknown amplitude s.sub.i[k] and by an unknown current arrival direction (.sub.i.sub.l, .sub.i.sub.l), l representing an l-th interfering signal, a current directional complex vector a(.sub.u, .sub.u) of the signal of interest comprising one component for each of the channels of the receiver, each component representing an amplitude and a phase response of the respective channel of the receiver in the current arrival direction (.sub.u, .sub.u) of the signal of interest, and, each of a plurality of current directional complex vectors a(.sub.i.sub.l, .sub.i.sub.l) of the interfering signals comprising one component for each of the channels of the receiver, each component representing an amplitude and a phase response of the respective channel of the receiver in the current arrival direction (.sub.i.sub.l, .sub.i.sub.l) of the interfering signals; (b) estimation, from the digital multi-channel signal, of a correlation matrix {circumflex over (R)}.sub.x of the signal received over the channels of the receiver; (c) estimation of a variance of the noise, from eigenvectors and eigenvalues of the correlation matrix {circumflex over (R)}.sub.x; (d) initial estimation of an arrival direction ({circumflex over ()}.sub.u, {circumflex over ()}.sub.u) of the signal of interest and of an arrival direction ({circumflex over ()}.sub.i.sub.l, {circumflex over ()}.sub.i.sub.l) of the interfering signals from computation of a multiple signal classification (MUSIC) spatial spectrum, then computation of assumed directional vectors ({circumflex over ()}.sub.u, {circumflex over ()}.sub.u) in a direction estimated for the signal of interest and of assumed direction vectors ({circumflex over ()}.sub.i.sub.l, {circumflex over ()}.sub.i.sub.l) in directions estimated for the interfering signals; (e) initialization of a: computation of a diagonal matrix elements of which are powers of the signal of interest and of the interfering signals computed from the directional vectors assumed in step (d) and from the correlation matrix {circumflex over (R)}.sub.x, and computation of an amplitude/phase error matrix elements of which represent disparity between the current directional complex vectors and the directional vectors assumed in step (d); (f) iterative computation: of a matrix of current estimated directional vectors elements of which are a product of the elements of the amplitude/phase error matrix and of the directional vectors assumed in step (d) in the estimated directions; of the powers of the signal of interest and the interfering signals, from the matrix of the current estimated directional vectors; of the amplitude/phase error matrix; and of the arrival direction ({circumflex over ()}.sub.u, {circumflex over ()}.sub.u) of the signal of interest and the arrival direction ({circumflex over ()}.sub.i.sub.l, {circumflex over ()}.sub.i.sub.l) of the interfering signals, the current directional complex vectors of the signal of interest and the interfering signals being computed, in a first iteration, with respect to the directional vectors assumed in step (d) and amplitude/phase errors of the amplitude/phase error matrix, then, for each of a plurality of following iterations, with respect to the directional vectors assumed in step (d) and to the amplitude/phase errors computed in the preceding iteration, a number of the iterations being predefined by a user; (g) reconstruction of a correlation matrix of the interfering signals and of the noise; (h) computation of a weighting matrix from the correlation matrix computed in step (g); and (i) suppression of the interfering signals from the signal received in step (a) and retrieval of the signal of interest.

2. The method for receiving the signal and for suppressing the interfering signals as claimed in claim 1, wherein the number of iterations is between 15 and 25.

3. The method for receiving the signal and for suppressing the interfering signals as claimed in claim 1, wherein said number of iterations is 20.

4. A multi-channel receiver configured to (i) receive a signal comprising a signal of interest and interfering signals over a plurality of channels and (ii) reject the interfering signals, comprising: an antenna comprising at least three radiating elements; at least three radio chains for receiving, transposing, and discretizing said signal received over each of the channels of the receiver, to obtain a discretized multi-channel signal, the at least three radio chains each comprising one of the at least three radiating elements of the antenna; and computing circuits, wherein the computing circuits are configured to suppress said interfering signals using the method of claim 1.

5. The multi-channel receiver as claimed in claim 4, wherein the computing circuits comprise at least one of a digital signal processor, a programmable integrated circuit, and an application-specific integrated circuit.

6. The multi-channel receiver as claimed in claim 5, wherein said multi-channel receiver belongs to a receiving portion of a payload of a satellite.

7. The multi-channel receiver as claimed in claim 4, wherein said multi-channel receiver belongs to a base station of a terrestrial mobile-radio system.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Other features, details and advantages of the invention will become apparent on reading the description given with reference to the appended figures, which are given by way of example and show, respectively:

(2) FIG. 1, an explanatory schematic of beamforming in reception;

(3) FIGS. 2a and 2b, an example of suppression of interference carried out with a prior-art method, the Capon method;

(4) FIG. 3, a chart illustrating the interference suppression method according to one embodiment of the invention;

(5) FIGS. 4a and 4b, an example of interference suppression carried out according to one embodiment of the invention; and

(6) FIG. 5, a multi-channel receiver according to one embodiment of the invention.

DETAILED DESCRIPTION

(7) Below, the following notations are used: {circumflex over ()} (hat) indicates an estimated quantity; {tilde over ()} (tilde) indicates a quantity the value of which is approximately known (assumed value) .sup.H is the transpose-conjugate operator; and .sup.T is the transpose operator.

(8) FIG. 3 shows a chart illustrating the interference suppression method according to one embodiment of the invention. The received signal comprises a useful signal, interfering signals and noise. To simplify the notations, a one-dimensional antenna is considered. In this case, the directional vectors a() depend solely on elevation angle . The method is generalizable without difficulty to the case of a two-dimensional antenna the directional vectors a(, ) of which depend on elevation and azimuth .

(9) The first step of the method, step (a), consists in reception, frequency transposition and digital conversion of a signal received by each of the channels of a multi-channel receiver so as to obtain a digital multi-channel signal. The multi-channel signal corresponds to the sum of the useful signal, of the interfering signals and of the noise. The response of the antenna in the direction .sub.u of the useful signal is described by the current directional vector a(.sub.u), which comprises one component for each channel of the multi-channel receiver. The response of the antenna in the direction .sub.i.sub.l of the l-th interfering signal is described by the current directional vector a(.sub.i.sub.l), which comprises one component for each channel of the multi-channel receiver.

(10) It is assumed that the digital multi-channel signal comprises a finite number K of sample vectors and the multi-channel receiver comprises N radiating elements, N being an integer higher than or equal to 3 and K being a positive integer. The following are also assumed to be known: the maximum angular error .sub.max in the position of the useful signal; the assumed angular position {tilde over ()}.sub.u of the useful signal; and for any direction , assumed directional vectors {tilde over (a)}(), these vectors being measured in the laboratory or computed using a model.

(11) It is also assumed that the directions of the interference signals are not located in the angular sector [{tilde over ()}.sub.u.sub.max; {tilde over ()}.sub.u+.sub.max], and that the amplitude/phase errors are independent of direction. This allows a complex yet diagonal matrix G to be obtained, G being the matrix of the amplitude/phase errors. Nevertheless, it is also possible to apply the method in the case of amplitude/phase errors that are dependent on direction.

(12) In the second step of the method, step (b), a correlation matrix, denoted {circumflex over (R)}.sub.x, is estimated from the K sample vectors x[k] of the received signal using the conventional sample estimator:

(13) $\begin{array}{cc}{\hat{R}}_x=\frac{1}{K}\underset{k=1}{\overset{K}{.Math.}}\underset{\_}{x}\left[k\right]{\underset{\_}{x}\left[k\right]}^H& \left(6\right)\end{array}$

(14) Step (c) of the method consists in estimating the power of the noise included in the received signal. To do this, the estimated correlation matrix {circumflex over (R)}.sub.r is decomposed into eigenvalues and eigenvectors. The matrix {circumflex over (R)}.sub.x may then be written:
{circumflex over (R)}.sub.x=UU.sup.H(7)
where U is a complex identity matrix of NN size containing the eigenvectors of {circumflex over (R)}.sub.x and A is a real diagonal matrix of NN size containing the eigenvalues of {circumflex over (R)}.sub.x. As {circumflex over (R)}.sub.x is Hermitian, i.e. {circumflex over (R)}.sub.x={circumflex over (R)}.sub.x.sup.H, and defined to be positive, its eigenvalues are real positive numbers.

(15) The number of interfering signals is denoted L, where L is an integer higher than or equal to 1. If this number L is not known, the total number M of signals (useful signal plus interfering signals) is estimated using the Akaike information criterion (H. L. Van Trees, Optimum Array Processing, Part IV of Detection, Estimation and Modulation Theory, Wiley Interscience, 2002), when the signal-to-noise ratio of the signals is sufficiently high, typically higher than 10 dB.

(16) According to the publication by Schmidt (R. O. Schmidt, Multiple Emitter Location and Signal Parameter Estimation, IEEE Transactions on Antennas and Propagation, 276-280, 1986) the matrix possesses (NM) identical eigenvalues, equal to the variance of the noise, which is denoted .sup.2. By reordering the eigenvalues (and conjointly the eigenvectors), the following is obtained:
=diag[.sub.1,.sub.2, . . . ,.sub.M,.sup.2, . . . ,.sup.2](8)
where .sub.1>.sub.2> . . . >.sub.M are the eigenvalues of {circumflex over (R)}.sub.x.

(17) The form of the matrix A allows the variance of the noise {circumflex over ()}.sup.2 to be directly estimated, this variance {circumflex over ()}.sup.2 being obtained by averaging the (NM) lowest diagonal elements of .

(18) In step (d), the arrival directions of the useful and interfering signals are estimated using the conventional MUSIC method. To do this, the matrices U and are decomposed into two portions, one for the noise and the other for the useful signal and the interfering signals. Equation (7) then becomes:
{circumflex over (R)}.sub.xU.sub.s.sub.sU.sub.s.sup.H+.sup.2U.sub.bU.sub.b.sup.H(9)
where .sub.s is the real diagonal matrix of the M eigenvalues .sub.1 to .sub.m>{circumflex over ()}.sup.2, U.sub.s is the matrix of the M associated eigenvectors and U.sub.b is the matrix of the (NM) eigenvectors associated with the (NM) eigenvalues approximately equal to {circumflex over ()}.sup.2. The matrix U.sub.s is a complex identity matrix of NM size and of rank M and that defines the signal subspace (useful signal and interfering signals). The matrix U.sub.b is a complex identity matrix of N(NM) size and of rank (NM) and that defines the noise subspace.

(19) The noise subspace and the signal subspace are orthogonal. The scalar product of any vector of the signal subspace and of any vector of the noise subspace is therefore zero. However, the current directional vector a(.sub.u) of the useful signal and the current directional vectors a(.sub.i.sub.l) of the interfering signals belong to the signal subspace, therefore:

(20) $\begin{array}{cc}{U}_b^H\underset{\_}{a}\left({}_u\right)=\underset{\_}{0}{U}_b^H\underset{\_}{a}\left({}_{i_1}\right)=\underset{\_}{0}\mathrm{.Math.}{U}_b^H\underset{\_}{a}\left({}_{i_L}\right)=\underset{\_}{0}& \left(10\right)\end{array}$

(21) The property of orthogonality is exploited to identify the arrival directions .sub.u, .sub.i.sub.1, . . . , .sub.i.sub.L of the useful and interfering signals. To do this, for each direction , the positive real quantity P() is computed, to construct the so-called MUSIC spatial spectrum or the MUSIC spectrum. This spectrum becomes infinite when is identical to one of the arrival directions of the signals and therefore allows these directions to be identified. It is expressed by the following equation:

(22) $\begin{array}{cc}P\left(\right)=\frac{1}{{\underset{\_}{a}\left(\right)}^H{U}_b{U}_b^H\underset{\_}{a}\left(\right)}& \left(11\right)\end{array}$
and has the property that

(23) $P\left(\right)\underset{={}_u}{.Math.}\mathrm{and}P\left(\right)\underset{={}_{i_l}}{.Math.}$
where l=1, 2, . . . , L.

(24) In practice, the current directional vectors a() are not known, only the assumed directional vectors {tilde over (a)}() being known. An estimate of the MUSIC spatial spectrum is thus calculated, this estimate taking the form:

(25) $\begin{array}{cc}\hat{P}\left(\right)=\frac{1}{{\underset{\_}{\tilde{a}}\left(\right)}^H{U}_b{U}_b^H\underset{\_}{\tilde{a}}\left(\right)}& \left(12\right)\end{array}$

(26) The M highest maxima, i.e. the M values of that maximise {circumflex over (P)}(), correspond to the arrival directions of the M signals (useful signal and interfering signals). Under the initial assumptions, the angle {circumflex over ()}.sub.u hypothetically located in the interval [{tilde over ()}.sub.u.sub.max; {tilde over ()}.sub.u+.sub.max] corresponds to an estimation of the angle of the useful signal, whereas the L=M1 other angles {circumflex over ()}.sub.i.sub.l, located outside of this interval, correspond to estimations of the angles of the L interfering signals. By virtue of these estimations, it is possible to obtain an initial estimation of the assumed directional vector {tilde over (a)}({circumflex over ()}.sub.u) of the useful signal and of the assumed directional vectors {tilde over (a)}({circumflex over ()}.sub.i.sub.l) of the interfering signals in the estimated directions. It is then possible to form the matrix {circumflex over ()}=[{tilde over (a)}({circumflex over ()}.sub.u), {tilde over (a)}({circumflex over ()}.sub.i.sub.1), . . . , {tilde over (a)}({circumflex over ()}.sub.i.sub.L)] of the assumed directional vectors in the estimated directions.

(27) Noting A=[a(.sub.u), a(.sub.i.sub.1), . . . , a(.sub.i.sub.L)] the NM matrix of the current directional vectors and P the real diagonal matrix of the powers of the M signals, the correlation matrix {circumflex over (R)}.sub.x may be written:
{circumflex over (R)}.sub.xAPA+{circumflex over ()}.sup.2I.sub.N(13)

(28) Using the eigen-decomposition of {circumflex over (R)}.sub.x, the above equation is equivalent to:
APAU.sub.s.sub.sU.sub.s.sup.H(14)
with .sub.s=.sub.s{circumflex over ()}.sup.2I.sub.m.

(29) Weiss and Friedlander (A. J. Weiss and B. Friedlander, Almost blind steering vector estimation using second-order moments, IEEE Transactions on Signal Processing, 56: 5719-5724, 2008) have shown that equation (14) is true if and only if there is a complex identity matrix Q (rotation matrix) such that
AP.sup.1/2U.sub.s.sub.s.sup.1/2Q(15)

(30) The computation of the matrix A may then be computed by minimizing the square of the Frobenius norm (sum of the moduli squared of the elements) of the difference of the two sides of the above equation, namely AP.sup.1/2U.sub.s.sub.s.sup.1/2Q.sub.F.sup.2. This minimization is carried out using the iterative algorithm of step (f), the principle of which is after Weiss and Friedlander.

(31) To do this, it is assumed that the matrix A of the current directional vectors may be written in the form:
A=G(16)
with G an NN diagonal complex matrix. The matrix G is the matrix of the amplitude/phase errors, which are independent of direction. The matrix G is unknown and must be estimated in step (f). The real diagonal matrix P of the powers of the signals is also unknown and will also be estimated in step (f). Below, the estimates of the matrices A, G and P are denoted , and {circumflex over (P)}, respectively. Therefore, it is assumed that:
={circumflex over ()}(17)

(32) Step (e) is a step of initialization of the iterative portion (f) of the method. The matrix is initialized to the identity matrix, this amounting to initializing the matrix to {circumflex over ()}.

(33) Using the Capon power estimator, the elements of the matrix {circumflex over (P)} are initialized to 1/[{tilde over (a)}().sup.H{circumflex over (R)}.sub.x.sup.1{tilde over (a)}()] where ={circumflex over ()}.sub.u, {circumflex over ()}.sub.i.sub.1, . . . , {circumflex over ()}.sub.i.sub.L.

(34) The following constant matrices are also computed:
.sub.s=.sub.s{circumflex over ()}.sup.2I.sub.M(18)
B=U.sub.s.sub.s.sup.1/2(19)

(35) The matrix .sub.s is a real diagonal square matrix of MM size, the matrix I.sub.m is an identity matrix of order M and the matrix B is a complex rectangular matrix of NM size.

(36) Step (f) then consists in computing, iteratively, the matrix so as to compute the current directional vectors from the assumed directional vectors in the estimated directions. The number of iterations is finite and set by the user. It is generally comprised between 15 and 25 and may for example be equal to 20 for an equispaced linear array of 10 radiating elements. In the first iteration, the matrix is calculated from the matrices and obtained in step (e). In the following iterations, the matrix is computed using equation (17), with the matrices and obtained in the preceding iteration.

(37) In each iteration, firstly the singular value decomposition (SVD) of the matrix B.sup.H{circumflex over (P)}.sup.1/2 is calculated so as to obtain:
B.sup.H{circumflex over (P)}.sup.1/2=UV.sup.H(20)
with U and V the matrices of the eigenvectors to the left and right of B.sup.H {circumflex over (P)}.sup.1/2 and the diagonal matrix of the singular values. The matrices U and V are complex identity matrices of MM size. It may then be shown that the rotation matrix Q is such that:
Q=UV.sup.H(21)

(38) Secondly, the elements {circumflex over (p)}.sub.m.sup.1/2 of the matrix {circumflex over (P)}.sup.1/2 are computed. To do this, the m-th column of the matrix is denoted u.sub.m and the m-th column of the matrix BQ is denoted v.sub.m. The complex vectors u.sub.m and v.sub.m are of N1 size. The real diagonal elements p.sub.m.sup.1/2 of {circumflex over (P)}.sup.1/2 may be written, form a natural integer comprised between 1 and M:

(39) 0$\begin{array}{cc}{\hat{p}}_m^{1/2}=\max \left\{0;\frac{\mathrm{.Math.}\left[{\underset{\_}{v}}_m^H{\underset{\_}{u}}_m\right]}{{.Math.{\underset{\_}{v}}_m.Math.}^2}\right\}& \left(22\right)\end{array}$

(40) Thirdly, the amplitude/phase errors, i.e. the matrix , are estimated. To do this, the column vector corresponding to the transposition of the n-th row of the matrix {circumflex over (P)}.sup.1/2 is denoted y.sub.n, and the column vector corresponding to the transposition of the n-th row of the matrix BQ is denoted z.sub.n. The vectors {right arrow over (y)}.sub.n and z.sub.n are M1 in size. The complex diagonal elements .sub.n of the matrix d are calculated using the following equation, where n is a natural integer comprised between 1 and N:

(41) $\begin{array}{cc}{\hat{g}}_n=\frac{{\underset{\_}{y}}_n^H{\underset{\_}{z}}_n}{{.Math.{\underset{\_}{y}}_n.Math.}^2}& \left(23\right)\end{array}$

(42) The .sub.n represent the estimation of the amplitude/phase errors, which are assumed to be independent of direction.

(43) By virtue of the new estimation of , it is possible to re-estimate more precisely the current directional vectors. Next, these new current directional vectors will be used to compute a new MUSIC spatial spectrum and to obtain a new estimation of the arrival directions. Afterwards, the following iteration is passed to and the matrices Q, {circumflex over (P)}.sup.1/2, , etc., are computed anew.

(44) Equations (21) to (23) are based on the algorithm of Weiss-Friedlander (A. J. Weiss and B. Friedlander, Almost Blind steering vector estimation using second-order moments, IEEE Transactions on Signal Processing, 44:1024-1027, 1996).

(45) At the end of these iterations, the following are obtained: an estimate of the arrival directions {circumflex over ()}.sub.u, {circumflex over ()}.sub.i.sub.1, . . . , {circumflex over ()}.sub.i.sub.L of the signals; an estimate of the complex diagonal matrix of the amplitude/phase errors; and an estimate of the real diagonal matrix {circumflex over (P)} of the powers of the signals.

(46) Using these results, it is possible to estimate the current directional vectors of the useful signal and of the interference signals using two different methods, called method 1 and method 2, which are described below.

(47) For method 1, the estimate of the current directional vector of the useful signal is denoted {circumflex over (a)}.sub.u.sup.(1) and the estimate of the current directional vector of the interference signal l is denoted {circumflex over (a)}.sub.i.sub.1.sup.(1).

(48) Likewise, for method 2, the estimate of the current directional vector of the useful signal is denoted {circumflex over (a)}.sub.u.sup.(2) and the estimate of the current directional vector of the interference signal l is denoted {circumflex over (a)}.sub.i.sub.l.sup.(1).

(49) For method 1, the following follow directly from (17):
{circumflex over (a)}.sub.u.sup.(1)={circumflex over (a)}({circumflex over ()}.sub.u)(24)
{circumflex over (a)}.sub.i.sub.l.sup.(1)={circumflex over (a)}({circumflex over ()}.sub.i.sub.l)(25)

(50) For method 2, equation (15) is used and it is deduced therefrom that:
U.sub.s.sub.s.sup.1/2Q{circumflex over (P)}.sup.1/2=BQ{circumflex over (P)}.sup.1/2(26)

(51) The directional vector {circumflex over (a)}.sub.u.sup.(2) is then the first column of the matrix BQ {circumflex over (P)}.sup.1/2 and the directional vector {circumflex over (a)}.sub.i.sub.l.sup.(2) is the l-th column thereof.

(52) The matrix of the estimated current directional vectors of the interfering signals for method j (j=1, 2) is denoted .sub.i.sup.(j)=[{circumflex over ({right arrow over (a)})}.sub.i.sub.1.sup.(j), . . . , {circumflex over (a)}.sub.i.sub.L.sup.(j)] and the diagonal matrix of the estimated powers {circumflex over (p)}.sub.i.sub.1, . . . , {circumflex over (p)}.sub.i.sub.L of the interfering signals is denoted {circumflex over (P)}.sub.i.

(53) In step (g), it is then possible to estimate (reconstruct) the correlation matrix {circumflex over (R)}.sub.ib of the interference and noise in the form (for j=1, 2):
{circumflex over (R)}i.sub.b.sup.(j)=.sub.i.sup.(j){circumflex over (P)}.sub.i.sup.(j).sub.i.sup.(j).sup.H+{circumflex over ()}.sup.2I.sub.N(27)

(54) The correlation matrix {circumflex over (R)}.sub.ib.sup.(j) of the interference and noise may then be used to apply the MVDR method, in order to calculate the beamforming weighting vector in the following form (H. L. Van Trees, Optimum Array Processing, Part IV of Detection, Estimation and Modulation Theory, Wiley Intersciences, 2002):

(55) $\begin{array}{cc}{\underset{\_}{w}}_{\mathrm{MVDR}}=\frac{R_{\mathrm{ib}}^{-1}{\underset{\_}{a}}_u}{{\underset{\_}{a}}_u^H{R}_{\mathrm{ib}}^{-1}{\underset{\_}{a}}_u}& \left(28\right)\end{array}$

(56) As the matrix R.sub.ib does not contain the useful signal, the MVDR method is robust.

(57) Neglecting the denominator, which is merely a proportionality factor that has no influence on the SINR, it is therefore possible to calculate a weighting vector for each method:
w.sup.(j)=[R.sub.ib.sup.(j)].sup.1{circumflex over (a)}.sub.u.sup.(j)(29)

(58) The weighting vectors obtained for j=1, 2 are then normalized so as to have w.sup.(1)=w.sup.(2)=1. The choice between the two weighting vectors is made by comparing the total output power and by choosing the weighting vector that delivers the lowest power, because it is this weighting vector that necessarily best rejects the interfering signals, provided of course that the useful signal has been preserved.

(59) The final weighting vector is then obtained:
w=w.sup.(1), if w.sup.(1)H{circumflex over (R)}.sub.xw.sup.(1)<w.sup.(2)H{circumflex over (R)}.sub.xw.sup.(2)
w=w.sup.(2), if not(30)

(60) In practice, in simulations it is observed that method 1 is chosen most often and that the performance of the two methods coincides when the number of samples K becomes high.

(61) This interference suppression method may be implemented in the computing circuits of a multi-channel receiver. The computing circuits may be a digital signal processor (DSP), a programmable integrated circuit (FPGA), or an application-specific integrated circuit (ASIC). FIGS. 4a and 4b show an example of suppression of interference signals according to one embodiment of the invention implemented with an ELA of 10 omnidirectional radiating elements. The figures show the pattern (the directivity) of a beam formed with the method according to the invention for this antenna array. Four interference signals are present in the received signal. In FIG. 4a, the signal-to-noise ratio (SNR) is 10 dB and in FIG. 4b, the SNR is 20 dB. It may be seen that in both cases the useful signal is preserved and that the interference is indeed suppressed.

(62) FIG. 5 shows a multi-channel receiver according to one embodiment of the invention. This receiver comprises N radio-frequency (RF) chains, with N an integer higher than or equal to 3. Only the first RF chain C1 and the N-th RF chain CN are shown in this figure. A signal S comprising a useful signal, interfering signals and noise is received by the N RF chains by virtue of their radiating element 501. The signal thus received by each of the N RF chains is frequency transposed 502 then converted to digital by an analogue-digital converter 503. The computing circuits 500 of the multi-channel receiver thus receive a sample vector x[k], such that x[k]=[x.sub.1[k], . . . , x.sub.N[k]].sup.T is the signal received, frequency transposed and converted to digital by the n-th RF chain, n being an integer comprised between 1 and N. The computing circuits 500 apply the method for suppressing interfering signals according to the invention in order to deliver as output the useful signal S.sub.u[k].