METHOD FOR REMOVING SPATIAL AND TEMPORAL MULTI-PATH INTERFERENCE FOR A RECEIVER OF FREQUENCY-MODULATED RADIO SIGNALS

Abstract

A method for decreasing multi-path interference, for a vehicle radio receiver including at least two radio reception antennas that each receive a plurality of radio signals composed of time-shifted radio signals resulting from a multi-path effect. The plurality of radio signals combined to deliver a combined radio signal y.sub.s to be played, with: y.sub.n=W.sub.n.sup.T[G.sub.1,n.sup.S, X.sub.1,n+G.sub.2,n.sup.S, X.sub.2,n ] at time n, where x.sub.1 and x.sub.2 are vectors the components of which correspond to the plurality of signals received by the first antenna and by the second antenna, respectively, G.sub.1,n.sup.S and G.sub.2,n.sup.S are scalars the components of which are the complex weights of a spatial filter and w.sub.n.sup.T is the transpose matrix of a vector the components of which are the complex weights of a temporal filter. The method includes implementation of an iterative adaptation algorithm to determine the complex weights of the spatial filter and the complex weights of the temporal filter.

Claims

1. A method for decreasing multi-path interference, for implementation thereof in a vehicle radio receiver, said radio receiver being intended to receive an emitted radio signal and comprising at least two radio reception antennas that each receive a plurality of radio signals corresponding to said emitted radio signal, each of said plurality of signals received by each of said antennas being composed of time-shifted radio signals resulting from a multi-path effect, said plurality of radio signals being combined to deliver a combined radio signal y.sub.n to be played, with y.sub.n=W.sub.n.sup.T[G.sub.1,n.sup.S, X.sub.1,n+G.sub.2,n.sup.S, X.sub.2,n] at the time n, where X.sub.1 is a vector the components of which correspond to a plurality of signals received by a first antenna, expressed in complex baseband, X.sub.2 is a vector the components of which correspond to the plurality of signals received by a second antenna, expressed in complex baseband, G.sub.1,n.sup.S and G.sub.2,n.sup.S are scalars the components of which are the complex weights of a spatial filter and W.sub.n.sup.T is the transpose matrix of a vector the components of which are the complex weights of a temporal filter, said method comprising: the implementation of an iterative adaption algorithm to determine said complex weights of the spatial filter and said complex weights of the temporal filter, wherein the respective variations in the components of the matrix the components of which form the complex weights of the temporal filter and in the components of the scalars the components of which form the complex weights of a spatial filter are written: $\begin{matrix} W_{n + 1}^{t} = W_{n}^{t} -_{W} .Math. .Math. \frac{.Math. y_{n} .Math. - R}{.Math. y_{n} .Math.} .Math. \overline{y_{n}} (\overline{G_{1, n}^{s}} .Math. X_{1, n} + \overline{G_{2, n}^{s}} .Math. X_{2, n}) \\ G_{1, n + 1}^{s} = G_{1, n}^{s} -_{G .Math. .Math. 1} .Math. .Math. \frac{.Math. y_{n} .Math. - R}{.Math. y_{n} .Math.} .Math. {\overline{y_{n}} (\overline{W_{n}^{t}})}^{T} .Math. X_{1, n} \\ G_{2, n + 1}^{s} = G_{2, n}^{s} -_{G .Math. .Math. 2} .Math. .Math. \frac{.Math. y_{n} .Math. - R}{.Math. y_{n} .Math.} .Math. {\overline{y_{n}} (\overline{W_{n}^{t}})}^{T} .Math. X_{2, n} \end{matrix}$ where .sub.W, .sub.G1 and .sub.G2 are iterative steps chosen for the update of the gains and phases of each of the complex weights.

2. The method as claimed in claim 1, wherein the iterative adaptation algorithm is configured to minimize a cost function J such that
J=E{|y.sub.n|R).sup.2} where R is a constant to be determined, corresponding to the constant modulus of the combined signal y.sub.n.

3. The method as claimed in claim 2, wherein said iterative adaptation algorithm is a constant modulus adaptation algorithm configured to minimize the cost function.

4. The method as claimed in claim 1, further comprising introducing a correlation between said complex weights of the temporal filter and said complex weights of the spatial filter, said correlation being dependent on the time shift between said plurality of radio signals received by said at least two antennas, by the expression of said complex weights in polar coordinates, so that the instantaneous gradient of the cost function is written: $J = 2 .Math. \frac{.Math. y_{n} .Math. - R}{.Math. y_{n} .Math.} [\begin{matrix} R .Math. e [\overline{y_{n}} .Math. .Math. e^{j .Math. .Math._{n}^{t}} (\overline{G_{1, n}^{s}} .Math. X_{1, n} + \overline{G_{2, n}^{s}} .Math. X_{2, n})] \\ - Im [\overline{y_{n}} .Math. .Math. A_{n}^{t} .Math. .Math. e^{j .Math. .Math._{n}^{t}} (\overline{G_{1, n}^{s}} .Math. X_{1, n} + \overline{G_{2, n}^{s}} .Math. X_{2, n})] \\ R .Math. e [\overline{y_{n}} .Math. .Math. {e^{j .Math. .Math._{1, n}} (\overline{W_{n}^{t}})}^{T} .Math. X_{1, n}] \\ - Im [\overline{y_{n}} .Math. .Math. b_{1, n} .Math. .Math. {e^{j .Math. .Math._{1, n}} (\overline{W_{n}^{t}})}^{T} .Math. X_{1, n}] \\ R .Math. e [\overline{y_{n}} .Math. .Math. {e^{j .Math. .Math._{2, n}} (\overline{W_{n}^{t}})}^{T} .Math. X_{2, n}] \\ - Im [\overline{y_{n}} .Math. .Math. b_{2, n} .Math. .Math. {e^{j .Math. .Math._{2, n}} (\overline{W_{n}^{t}})}^{T} .Math. X_{2, n}] \end{matrix}]$ $with .Math. :$ $W_{n}^{t} = A_{n}^{t} .Math. .Math. e^{- j .Math. .Math._{n}^{t}}, .Math. with .Math. :$ $A_{n}^{t} = {[a_{0, n} .Math. .Math. a_{1, n} .Math. .Math. a_{2, n} .Math. . . . .Math. a_{K - 1, n}]}^{T}$ $_{n}^{t} = {[e^{- j .Math. .Math._{0, n}} .Math. .Math. e^{- j .Math. .Math._{1, n}} .Math. .Math. e^{- j .Math. .Math._{2, n}} .Math. . . . .Math. e^{- j .Math. .Math._{K - 1, n}}]}^{T}, .Math. and .Math. :$ $G_{1, n}^{s} = b_{1, n} .Math. e^{- j .Math. .Math._{1, n}}$ $G_{2, n}^{s} = b_{2, n} .Math. e^{- j .Math. .Math._{2, n}}$ so as to incorporate an interdependence between the real and imaginary parts of said complex weights.

5. The method as claimed in claim 4, wherein the respective variations in the components of the matrix the components of which form the complex weights of the temporal filter and in the components of the scalars the components of which form the complex weights of a spatial filter are written: $A_{n + 1}^{t} = A_{n}^{t} -_{A} .Math. \frac{.Math. y_{n} .Math. - R}{.Math. y_{n} .Math.} .Math. Re [\overline{y_{n}} .Math. .Math. e^{j .Math. .Math._{n}^{t}} (\overline{G_{1, n}^{s}} .Math. X_{1, n} + \overline{G_{2, n}^{s}} .Math. X_{2, n})]$ $_{n + 1}^{t} =_{n}^{t} +_{} .Math. \frac{.Math. y_{n} .Math. - R}{.Math. y_{n} .Math.} .Math. Im [\overline{y_{n}} .Math. .Math. A_{n}^{t} .Math. .Math. e^{j .Math. .Math._{n}^{t}} (\overline{G_{1, n}^{s}} .Math. X_{1, n} + \overline{G_{2, n}^{s}} .Math. X_{2, n})]$ $b_{1, n + 1} = b_{1, n} -_{b .Math. .Math. 1} .Math. .Math. \frac{.Math. y_{n} .Math. - R}{.Math. y_{n} .Math.} .Math. .Math. Re [\overline{y_{n}} .Math. .Math. {e^{j .Math. .Math._{1, n}} (\overline{W_{n}^{t}})}^{T} .Math. X_{1, n}]$ $_{1, n + 1} =_{1, n} +_{1} .Math. \frac{.Math. y_{n} .Math. - R}{.Math. y_{n} .Math.} .Math. .Math. Im [\overline{y_{n}} .Math. .Math. b_{1, n} .Math. .Math. {e^{j .Math. .Math._{1, n}} (\overline{W_{n}^{t}})}^{T} .Math. X_{1, n}]$ $b_{2, n + 1} = b_{2, n} -_{2, n} .Math. \frac{.Math. y_{n} .Math. - R}{.Math. y_{n} .Math.} .Math. .Math. Re [\overline{y_{n}} .Math. .Math. {e^{j .Math. .Math._{2, n}} (\overline{W_{n}^{t}})}^{T} .Math. X_{2, n}]$ $_{2, n + 1} =_{2, n} +_{2} .Math. \frac{.Math. y_{n} .Math. - R}{.Math. y_{n} .Math.} .Math. .Math. Im [\overline{y_{n}} .Math. .Math. b_{2, n} .Math. .Math. {e^{j .Math. .Math._{2, n}} (\overline{W_{n}^{t}})}^{T} .Math. X_{2, n}]$ where .sub.A, A.sub., .sub.b1, .sub.b2, .sub.1, .sub.2 are iterative steps chosen for the update of the gains and phases of each of the complex weights, and the operator .sup.a is defined as carrying out the multiplication of two vectors, component by component, the resultant being a vector.

6. The method as claimed in claim 1, wherein the temporal filter is an impulse response filter.

7. A radio receiver comprising a microcontroller configured to implement the method as claimed in claim 1.

8. A motor vehicle comprising a radio receiver as claimed in claim 7.

9. The method as claimed in claim 2, further comprising introducing a correlation between said complex weights of the temporal filter and said complex weights of the spatial filter, said correlation being dependent on the time shift between said plurality of radio signals received by said at least two antennas, by the expression of said complex weights in polar coordinates, so that the instantaneous gradient of the cost function is written: $J = 2 .Math. \frac{.Math. y_{n} .Math. - R}{.Math. y_{n} .Math.} [\begin{matrix} R .Math. e [\overline{y_{n}} .Math. .Math. e^{j .Math. .Math._{n}^{t}} (\overline{G_{1, n}^{s}} .Math. X_{1, n} + \overline{G_{2, n}^{s}} .Math. X_{2, n})] \\ - Im [\overline{y_{n}} .Math. .Math. A_{n}^{t} .Math. .Math. e^{j .Math. .Math._{n}^{t}} (\overline{G_{1, n}^{s}} .Math. X_{1, n} + \overline{G_{2, n}^{s}} .Math. X_{2, n})] \\ R .Math. e [\overline{y_{n}} .Math. .Math. {e^{j .Math. .Math._{1, n}} (\overline{W_{n}^{t}})}^{T} .Math. X_{1, n}] \\ - Im [\overline{y_{n}} .Math. .Math. b_{1, n} .Math. .Math. {e^{j .Math. .Math._{1, n}} (\overline{W_{n}^{t}})}^{T} .Math. X_{1, n}] \\ R .Math. e [\overline{y_{n}} .Math. .Math. {e^{j .Math. .Math._{2, n}} (\overline{W_{n}^{t}})}^{T} .Math. X_{2, n}] \\ - Im [\overline{y_{n}} .Math. .Math. b_{2, n} .Math. .Math. {e^{j .Math. .Math._{2, n}} (\overline{W_{n}^{t}})}^{T} .Math. X_{2, n}] \end{matrix}]$ $with .Math. :$ $W_{n}^{t} = A_{n}^{t} .Math. .Math. e^{- j .Math. .Math._{n}^{t}}, .Math. with .Math. :$ $A_{n}^{t} = {[a_{0, n} .Math. .Math. a_{1, n} .Math. .Math. a_{2, n} .Math. . . . .Math. a_{K - 1, n}]}^{T}$ $_{n}^{t} = {[e^{- j .Math. .Math._{0, n}} .Math. .Math. e^{- j .Math. .Math._{1, n}} .Math. .Math. e^{- j .Math. .Math._{2, n}} .Math. . . . .Math. e^{- j .Math. .Math._{K - 1, n}}]}^{T}, .Math. and .Math. :$ $G_{1, n}^{s} = b_{1, n} .Math. e^{- j .Math. .Math._{1, n}}$ $G_{2, n}^{s} = b_{2, n} .Math. e^{- j .Math. .Math._{2, n}}$ so as to incorporate an interdependence between the real and imaginary parts of said complex weights.

10. The method as claimed in claim 3, further comprising introducing a correlation between said complex weights of the temporal filter and said complex weights of the spatial filter, said correlation being dependent on the time shift between said plurality of radio signals received by said at least two antennas, by the expression of said complex weights in polar coordinates, so that the instantaneous gradient of the cost function is written: $J_{} = 2 .Math. \frac{.Math. y_{n} .Math. - R}{.Math. y_{n} .Math.} [\begin{matrix} R .Math. e [\overline{y_{n}} .Math. .Math. e^{j .Math. .Math._{n}^{t}} (\overline{G_{1, n}^{s}} .Math. X_{1, n} + \overline{G_{2, n}^{s}} .Math. X_{2, n})] \\ - Im [\overline{y_{n}} .Math. .Math. A_{n}^{t} .Math. .Math. e^{j .Math. .Math._{n}^{t}} (\overline{G_{1, n}^{s}} .Math. X_{1, n} + \overline{G_{2, n}^{s}} .Math. X_{2, n})] \\ R .Math. e [\overline{y_{n}} .Math. .Math. {e^{j .Math. .Math._{1, n}} (\overline{W_{n}^{t}})}^{T} .Math. X_{1, n}] \\ - Im [\overline{y_{n}} .Math. .Math. b_{1, n} .Math. .Math. {e^{j .Math. .Math._{1, n}} (\overline{W_{n}^{t}})}^{T} .Math. X_{1, n}] \\ R .Math. e [\overline{y_{n}} .Math. .Math. {e^{j .Math. .Math._{2, n}} (\overline{W_{n}^{t}})}^{T} .Math. X_{2, n}] \\ - Im [\overline{y_{n}} .Math. .Math. b_{2, n} .Math. .Math. {e^{j .Math. .Math._{2, n}} (\overline{W_{n}^{t}})}^{T} .Math. X_{2, n}] \end{matrix}]$ $with .Math. :$ $W_{n}^{t} = A_{n}^{t} .Math. .Math. e^{- j .Math. .Math._{n}^{t}}, .Math. with .Math. :$ $A_{n}^{t} = {[a_{0, n} .Math. .Math. a_{1, n} .Math. .Math. a_{2, n} .Math. . . . .Math. a_{K - 1, n}]}^{T}$ $_{n}^{t} = {[e^{- j .Math. .Math._{0, n}} .Math. .Math. e^{- j .Math. .Math._{1, n}} .Math. .Math. e^{- j .Math. .Math._{2, n}} .Math. . . . .Math. e^{- j .Math. .Math._{K - 1, n}}]}^{T}, .Math. and .Math. :$ $G_{1, n}^{s} = b_{1, n} .Math. e^{- j .Math. .Math._{1, n}}$ $G_{2, n}^{s} = b_{2, n} .Math. e^{- j .Math. .Math._{2, n}}$ so as to incorporate an interdependence between the real and imaginary parts of said complex weights.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0043] An aspect of the invention will be better understood on reading the following description, which is given solely by way of example, with reference to the appended drawing, in which:

[0044] FIG. 1 shows the conceptual diagram of a method for cancelling out multi-path radio signals, according to the prior art;

[0045] FIG. 2 shows the conceptual diagram of a method for cancelling out multi-path radio signals, according to an aspect of the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0046] The method for adapting an FM radio signal according to an aspect of the invention is presented with a view to an implementation, principally, in a radio receiver of a multimedia system on board a motor vehicle. However, an aspect of the present invention may also be implemented in any other technical field, and in particular in any type of FM radio receiver.

[0047] An aspect of the present invention proposes to introduce an adaptive spatial and temporal model, in order to take into account both the spatial correlation and the temporal correlation that exists, from the physical point of view, between the multi-path FM radio signals received by a plurality of antennas of the radio receiver in question.

[0048] It is known, in another technical field relative to radars, to use an adaptive temporal model to combine the signals received by a radar antenna. The techniques implemented in the field of radars is however not transposable as such to the field of FM radio reception.

[0049] The adaptive temporal model implemented in the world of radars is based on the implementation of an impulse response filter able to apply, to the vector of received complex signals, a complex weight vector that is written:

[00004] $Wn = [\begin{matrix} \exp (j .Math. .Math. 2 .Math. .Math. .Math. F_{d} .Math. 0 .Math. T) \\ \exp (j .Math. .Math. 2 .Math. .Math. .Math. F_{d} .Math. 1 .Math. T) \\ .Math. \\ \exp (j .Math. .Math. 2 .Math. .Math. .Math. F_{d} (K - 1) .Math. T) \end{matrix}]$

[0050] This model does not allow multi-path signals to be removed in the field of FM radio reception because each path followed by each of the time-shifted, received multi-path signals has, in the case of an FM radio signal, a specific gain that is dependent on the distance travelled by the radio wave, said distance not being a linear frequency-dependent function, contrary to the case of radar reception.

[0051] In addition, this model does not allow the spatial correlation that exists between signals received by an antenna array of a receiver to be taken into account.

[0052] With reference to FIG. 2, an aspect of the present invention proposes to simultaneously process the spatial filtering and the temporal filtering of the plurality of radio signals received by an antenna array comprising at least two antennas A1, A2. The antennas A1, A2 respectively receive a plurality of signals X1, X2 corresponding to one emitted FM radio signal. After acquisition via the input stages FE1, FE2, the received signals are filtered from the spatial and temporal standpoint by way of a dedicated stage H, the output of which is a recombined signal Y.sub.n that is intended to be played.

[0053] Thus, the filtered and recomposed signal after implementation of an iterative adaptation algorithm, in particular a CMA algorithm, is written:

[00005] $y_{n} = {(\overline{H})}^{T} .Math. X = [\begin{matrix} {\overline{H}}_{1}^{T} \\ {\overline{H}}_{2}^{T} \end{matrix}] [X_{1} .Math. .Math. X_{2}]$

[0054] where X.sub.1=[x.sub.1,n-K+1 . . . x.sub.1,n] and X.sub.2=[x.sub.2,n-K+1 . . . x.sub.2,n] represent the last K signals received by the antennas A1, A2; H.sub.1 and H.sub.2 are matrices the complex components of which represent weights to be applied to said received signals in order to ensure the solution of the spatial and temporal diversity system.

[0055] To eliminate redundant parameters, the above equation may be rewritten so as to separate linear combinations from the spatial point of view and from the temporal point of view. Thus, by choosing to carry out the spatial filtering first, the following is obtained:

y.sub.n=G.sub.1,n.sup.s[(W.sub.n.sup.t).sup.TX.sub.1,n]+G.sub.2,n.sup.s[(W.sub.n.sup.t).sup.TX.sub.2,n.sup.t]

[0056] In other words, it will be clear from FIG. 2, given that the matrices H.sub.1 and H.sub.2 are made up of a spatial component and of a temporal component, that the recombined signal is written:

y.sub.n=(W.sub.n.sup.t).sup.T[G.sub.1,n.sup.sX.sub.1,n+G.sub.2,n.sup.sX.sub.2,n]

[0057] where W.sub.n.sup.t is the matrix which components have complex weights corresponding to the components of an impulse response filter to be implemented for the temporal filtering; G.sub.1,n.sup.s and G.sub.2,n.sup.s are the scalars the components of which are complex weights corresponding to the components of a filter to be implemented for the spatial filtering; X.sub.1,n and X.sub.2,n are complex vectors corresponding to the signals received by two antennas A1, A2; and .sup.T is the notation for the transpose of the matrix.

[0058] For a K-coefficient impulse response filter, at the time n, the complex matrix W.sub.n.sup.t is written:

W.sub.n.sup.t=[w.sub.0,nw.sub.1,nw.sub.2,n . . . w.sub.K-1,n].sup.T

[0059] with, in cartesian coordinates: w.sub.k,n=w.sub.k,n.sup.T+j w.sub.k,n.sup.i

[0060] The complex scalars to be implemented for the spatial filtering are for their part written:

G.sub.1,n.sup.s=g.sub.1,n.sup.r+j g.sub.1,n.sup.i, G.sub.2,n.sup.s=g.sub.2,n.sup.r+j g.sub.2,n.sup.i

[0061] In the same way, the complex vectors corresponding to the signals received by the two antennas A1, A2 are respectively written:

[00006] $X_{1, n} = [\begin{matrix} x_{1, n} \\ x_{1, n - 1} \\ x_{1, n - 2} \\ .Math. \\ x_{1, n - K + 1} \end{matrix}], X_{2, n} = [\begin{matrix} x_{2, n} \\ x_{2, n - 1} \\ x_{2, n - 2} \\ .Math. \\ x_{2, n - K + 1} \end{matrix}]$

[0062] The following expression for the recombined signal is obtained there from:

[00007] $y_{n} = {.Math.}_{k = 0}^{K - 1} .Math. \overline{w_{k, n}^{r} + {Jw}_{k, n}^{i}} .Math. (\overline{g_{1, n}^{r} + {jg}_{1, n}^{i}} .Math. x_{1, n - k} + \overline{g_{2, n}^{r} + {jg}_{2, n}^{i}} .Math. x_{2, n - k})$

[0063] An iterative adaptive algorithm, in particular a CMA algorithm, is then implemented to determine the complex components of W.sub.n.sup.t, G.sub.1,n.sup.s, G.sub.2,n.sup.s allowing the following cost function to be minimized:

J.sub.CMA=E{(|y.sub.n|R).sup.2}

[0064] It will be noted that, in the present description, only a CMA algorithm of (2, 1) type is envisioned, but any other type of adaptive algorithm, in particular any other type of CMA algorithm, could equally well be implemented.

[0065] The aforementioned cost function is minimized by means of the instantaneous gradient technique:

[00008] $\begin{matrix} J_{CMA} = .Math. 2 .Math. (.Math. y_{n} .Math. - R) .Math. .Math. y_{n} .Math. \\ = .Math. 2 .Math. (.Math. y_{n} .Math. - R) .Math. {(y_{n} .Math. {\overline{y}}_{n})}^{1 / 2} \\ = .Math. (.Math. y_{n} .Math. - R) .Math. \frac{1}{.Math. y_{n} .Math.} .Math. (y_{n} .Math. .Math. {\overline{y}}_{n} + {\overline{y}}_{n} .Math. y_{n}) \end{matrix}$

[0066] namely:

[00009] $y_{n} = [\begin{matrix} \frac{y_{n}}{W_{n}^{t}} \\ \frac{y_{n}}{G_{1, n}^{s}} \\ \frac{y_{n}}{G_{2, n}^{s}} \end{matrix}] = [\begin{matrix} {\begin{matrix} \frac{y_{n}}{w_{0, n}} \\ .Math. \\ \frac{y_{n}}{w_{k, n}} \\ .Math. \\ \frac{y_{n}}{w_{K - 1, n}} \end{matrix} \\ {\begin{matrix} \frac{y_{n}}{g_{1, n}^{r}} \\ \frac{y_{n}}{g_{1, n}^{i}} \end{matrix} \\ {\begin{matrix} \frac{y_{n}}{g_{2, n}^{r}} \\ \frac{y_{n}}{g_{2, n}^{i}} \end{matrix} \end{matrix}] = [\begin{matrix} {\begin{matrix} .Math. \\ \overline{G_{1, n}^{s}} .Math. x_{1, n - k} + \overline{G_{2, n}^{s}} .Math. x_{2, n - k} \\ - j (\overline{G_{1, n}^{s}} .Math. x_{1, n - k} + \overline{G_{2, n}^{s}} .Math. x_{2, n - k}) \\ .Math. \end{matrix} \\ {\begin{matrix} {(\overline{W_{n}^{t}})}^{T} .Math. X_{1, n} \\ - {j (\overline{W_{n}^{t}})}^{T} .Math. X_{1, n} \end{matrix} \\ {\begin{matrix} {(\overline{W_{n}^{t}})}^{T} .Math. X_{2, n} \\ - {j (\overline{W_{n}^{t}})}^{T} .Math. X_{2, n} \end{matrix} \end{matrix}] = .Math. .Math. .Math. and .Math. .Math. \overline{y_{n}} = \overline{_{y_{n}}}$

[0067] The cost function is then written:

[00010] $J_{CMA} = 2 .Math. .Math. \frac{.Math. y_{n} .Math. - R}{.Math. y_{n} .Math.} .Math. \overline{y_{n}} [\begin{matrix} \overline{G_{1, n}^{s}} .Math. X_{1, n} + \overline{G_{2, n}^{s}} .Math. X_{2, n} \\ {(\overline{W_{n}^{t}})}^{T} .Math. X_{1, n} \\ {(\overline{W_{n}^{t}})}^{T} .Math. X_{2, n} \end{matrix}]$

[0068] and the complex components for the spatial and temporal filtering of received signals are updated using the following equations:

[00011] ${\begin{matrix} W_{n + 1}^{t} = W_{n}^{t} -_{W} .Math. \frac{.Math. y_{n} .Math. - R}{.Math. y_{n} .Math.} .Math. \overline{y_{n}} (\overline{G_{1, n}^{s}} .Math. X_{1, n} + \overline{G_{2, n}^{s}} .Math. X_{2, n}) \\ G_{1, n + 1}^{s} = G_{1, n}^{s} -_{G .Math. .Math. 1} .Math. \frac{.Math. y_{n} .Math. - R}{.Math. y_{n} .Math.} .Math. {\overline{y_{n}} (\overline{W_{n}^{t}})}^{T} .Math. X_{1, n} \\ G_{2, n + 1}^{s} = G_{2, n}^{s} -_{G .Math. .Math. 2} .Math. \frac{.Math. y_{n} .Math. - R}{.Math. y_{n} .Math.} .Math. {\overline{y_{n}} (\overline{W_{n}^{t}})}^{T} .Math. X_{2, n} \end{matrix}$

[0069] Thus, there is a correlation between the coefficients of the spatial filtering and those of the temporal filtering. Specifically, the update of the components of G.sub.1,n.sup.s, G.sub.2,n.sup.s depend on W.sub.n.sup.t, and vice versa.

[0070] Thus, the implemented iterative adaptation algorithm, in particular the CMA algorithm, converges more rapidly and above all on more stable solutions.

[0071] According to one preferred embodiment, an even stronger correlation between the components of the scalars used for the spatial filtering and the components of the impulse response filter implemented for the temporal filtering may be introduced.

[0072] Starting with the equation issued from FIG. 2, according to which, it will be recalled:

y.sub.n=(W.sub.n.sup.t).sup.T[G.sub.1,n.sup.sX.sub.1,n+G.sub.2,n.sup.sX.sub.2,n]

[0073] where w.sub.n.sup.t is the matrix which components have complex weights corresponding to the components of an impulse response filter to be implemented for the temporal filtering; G.sub.1,n.sup.s and G.sub.2,n.sup.s are the scalars the components of which are complex weights corresponding to the components of a filter to be implemented for the spatial filtering; X.sub.1,n and X.sub.2,n are complex vectors corresponding to the signals received by two antennas A1, A2; and .sup.T is the notation for the transpose of the matrix.

[0074] As already indicated, for a K-coefficient impulse response filter, at the time n, the complex matrix W.sub.n.sup.t is written:

W.sub.n.sup.t=[w.sub.0,nw.sub.1,nw.sub.2,n . . . w.sub.K-1,n].sup.T.

[0075] In polar coordinates, w.sub.k,n=a.sub.k,ne.sup.j.sup.k,n.

[0076] Thus, W.sub.n.sup.t=A.sub.n.sup.te.sup.j.sub.n.sup.t, with:

A.sub.n.sup.t=[a.sub.o,na.sub.1,na.sub.2,n . . . a.sub.K-1,n].sup.T

.sub.n.sup.t=[e.sup.j.sup.0,ne.sup.j.sup.1,ne.sup.j.sup.2,n. . . e.sup.j.sup.K-1,n].sup.T

[0077] In the same way, the scalars Gf.sub.x and for their part also being complex, are able to be expressed in polar coordinates. Thus:

G.sub.1,n.sup.s=b.sub.1,ne.sup.j.sup.1,n and G.sub.2,n.sup.s=b.sub.2,ne.sup.j.sup.2,n

[0078] It will be recalled that the complex vectors corresponding to the signals received by the two antennas A1, A2 are respectively written:

[00012] $X_{1, n} = [\begin{matrix} x_{1, n} \\ x_{1, n - 1} \\ x_{1, n - 2} \\ .Math. \\ x_{1, n - K + 1} \end{matrix}] .Math. .Math. and .Math. .Math. X_{2, n} = [\begin{matrix} x_{2, n} \\ x_{2, n - 1} \\ x_{2, n - 2} \\ .Math. \\ x_{2, n - K + 1} \end{matrix}] .Math.$

[0079] The following expression for the recombined signal is obtained there from:

[00013] $y_{n} = {.Math.}_{k = 0}^{K - 1} .Math. a_{k, n} .Math. .Math. e^{j .Math. .Math._{k, n}} (b_{1, n} .Math. .Math. e^{j .Math. .Math._{1, n}} .Math. .Math. x_{1, n - k} + b_{2, n} .Math. .Math. e^{j .Math. .Math._{2, n}} .Math. .Math. x_{2, n - k})$

[0080] Thus, as in the preceding embodiment, an iterative adaptive algorithm, such as a CMA algorithm, is implemented to determine the complex components of W.sub.n.sup.t, G.sub.1,n.sup.s, G.sub.2,n.sup.s allowing the following cost function to be minimized:

J.sub.CMA=E{(y.sub.n|R).sup.2}

[0081] It will again be noted that, in the present description, only a CMA algorithm of (2, 1) type is envisioned, but any other type of adaptive algorithm, in particular any other type of CMA algorithm, could equally well be implemented.

[0082] The aforementioned cost function is minimized by means of the instantaneous gradient technique:

[00014] $\begin{matrix} J_{CMA} = .Math. 2 .Math. (.Math. y_{n} .Math. - R) .Math. .Math. y_{n} .Math. \\ = .Math. 2 .Math. (.Math. y_{n} .Math. - R) .Math. {(y_{n} .Math. {\overline{y}}_{n})}^{1 / 2} \\ = .Math. (.Math. y_{n} .Math. - R) .Math. \frac{1}{.Math. y_{n} .Math.} .Math. (y_{n} .Math. .Math. {\overline{y}}_{n} + {\overline{y}}_{n} .Math. y_{n}) \end{matrix}$

[0083] Namely, this time round:

[00015] $y_{n} = [\begin{matrix} \frac{y_{n}}{W_{n}^{t}} \\ \frac{y_{n}}{G_{1, n}^{s}} \\ \frac{y_{n}}{G_{2, n}^{s}} \end{matrix}] = [\begin{matrix} \frac{y_{n}}{A_{n}^{t}} \\ \frac{y_{n}}{_{n}^{t}} \\ \frac{y_{n}}{b_{1, n}} \\ \frac{y_{n}}{_{1, n}} \\ \frac{y_{n}}{b_{2, n}} \\ \frac{y_{n}}{_{2, n}} \end{matrix}] = [\begin{matrix} \begin{matrix} .Math. \\ e^{j .Math. .Math._{k, n}} (\overline{G_{1, n}^{s}} .Math. x_{1, n - k} + \overline{G_{1, n}^{s}} .Math. x_{2, n - k}) \\ .Math. \\ j .Math. .Math. a_{k, n} .Math. .Math. e^{j .Math. .Math._{k, n}} (\overline{G_{1, n}^{s}} .Math. x_{1, n - k} + \overline{G_{1, n}^{s}} .Math. x_{2, n - k}) \end{matrix} \\ .Math. \\ e^{j .Math. .Math._{1, n}} .Math. .Math. {(\overline{W_{n}^{t}})}^{T} .Math. X_{1, n} \\ j .Math. .Math. b_{1, n} .Math. .Math. e^{j .Math. .Math._{1, n}} .Math. .Math. {(\overline{W_{n}^{t}})}^{T} .Math. X_{1, n} \\ e^{j .Math. .Math._{2, n}} .Math. .Math. {(\overline{W_{n}^{t}})}^{T} .Math. X_{2, n} \\ j .Math. .Math. b_{2, n} .Math. .Math. e^{j .Math. .Math._{2, n}} .Math. .Math. {(\overline{W_{n}^{t}})}^{T} .Math. X_{2, n} \end{matrix}] = .Math. .Math. .Math. and .Math. .Math. \overline{y_{n}} = \overline{_{y_{n}}}$

[0084] Substitution of these terms in the cost function expressed above gives:

[00016] $J_{CMA} = 2 .Math. .Math. \frac{.Math. y_{n} .Math. - R}{.Math. y_{n} .Math.} [\begin{matrix} R .Math. e [\overline{y_{n}} .Math. .Math. e^{j .Math. .Math._{n}^{t}} (\overline{G_{1, n}^{s}} .Math. X_{1, n} + \overline{G_{2, n}^{s}} .Math. X_{2, n})] \\ - Im [\overline{y_{n}} .Math. .Math. A_{n}^{t} .Math. .Math. e^{j .Math. .Math._{n}^{t}} (\overline{G_{1, n}^{s}} .Math. X_{1, n} + \overline{G_{2, n}^{s}} .Math. X_{2, n})] \\ R .Math. e [\overline{y_{n}} .Math. .Math. {e^{j .Math. .Math._{1, n}} (\overline{W_{n}^{t}})}^{T} .Math. X_{1, n}] \\ - Im [\overline{y_{n}} .Math. .Math. b_{1, n} .Math. .Math. {e^{j .Math. .Math._{1, n}} (\overline{W_{n}^{t}})}^{T} .Math. X_{1, n}] \\ R .Math. e [\overline{y_{n}} .Math. .Math. {e^{j .Math. .Math._{2, n}} (\overline{W_{n}^{t}})}^{T} .Math. X_{2, n}] \\ - Im [\overline{y_{n}} .Math. .Math. b_{2, n} .Math. .Math. {e^{j .Math. .Math._{2, n}} (\overline{W_{n}^{t}})}^{T} .Math. X_{2, n}] \end{matrix}]$

[0085] and the complex components for the spatial and temporal filtering of received signals are updated using the following equations:

[00017] ${\begin{matrix} A_{n + 1}^{t} = A_{n}^{t} -_{A} .Math. .Math. \frac{.Math. y_{n} .Math. - R}{.Math. y_{n} .Math.} .Math. .Math. Re [\overline{y_{n}} .Math. .Math. e^{j .Math. .Math._{n}^{t}} (\overline{G_{1, n}^{s}} .Math. X_{1, n} + \overline{G_{2, n}^{s}} .Math. X_{2, n})] \\ _{n + 1}^{t} =_{n}^{t} +_{} .Math. .Math. \frac{.Math. y_{n} .Math. - R}{.Math. y_{n} .Math.} .Math. .Math. Im [\overline{y_{n}} .Math. .Math. A_{n}^{t} .Math. e^{j .Math. .Math._{n}^{t}} (\overline{G_{1, n}^{s}} .Math. X_{1, n} + \overline{G_{2, n}^{s}} .Math. X_{2, n})] \\ b_{1, n + 1} = b_{1, n} -_{b .Math. .Math. 1} .Math. .Math. \frac{.Math. y_{n} .Math. - R}{.Math. y_{n} .Math.} .Math. .Math. Re [\overline{y_{n}} .Math. .Math. {e^{j .Math. .Math._{1, n}} (\overline{W_{n}^{t}})}^{T} .Math. X_{1, n}] \\ _{1, n + 1} =_{1, n} +_{.Math. .Math. 1} .Math. .Math. \frac{.Math. y_{n} .Math. - R}{.Math. y_{n} .Math.} .Math. .Math. Im [\overline{y_{n}} .Math. .Math. b_{1, n} .Math. .Math. {e^{j .Math. .Math._{1, n}} (\overline{W_{n}^{t}})}^{T} .Math. X_{1, n}] \\ b_{2, n + 1} = b_{2, n} -_{b .Math. .Math. 2} .Math. .Math. \frac{.Math. y_{n} .Math. - R}{.Math. y_{n} .Math.} .Math. .Math. Re [\overline{y_{n}} .Math. .Math. {e^{j .Math. .Math._{2, n}} (\overline{W_{n}^{t}})}^{T} .Math. X_{2, n}] \end{matrix} .Math. .Math._{2, n + 1} =_{2, n} +_{2} .Math. .Math. \frac{.Math. y_{n} .Math. - R}{.Math. y_{n} .Math.} .Math. .Math. Im [\overline{y_{n}} .Math. .Math. b_{2, n} .Math. .Math. {e^{j .Math. .Math._{2, n}} (\overline{W_{n}^{t}})}^{T} .Math. X_{2, n}]$

[0086] The strong interdependency between the real and imaginary parts of the complex weights to be determined will be evident from these formulae.

[0087] The implementation of iterative adaptation algorithms on these formulae, in particular CMA algorithms, with the constraint of minimizing the cost function described above, thus converges more efficiently than in the prior art. Specifically, the spatial and temporal correlations introduced above induce an interdependency in the update of the coefficients, decreasing the number of degrees of freedom, unlike CMA algorithms such as implemented in the prior art, with which the coefficients of the complex weights are independent linear cartesians.

[0088] By virtue of an aspect of the invention, the CMA algorithms converge to a smaller subset of solutions, said subset being included in the set of possible solutions of the CMA algorithms such as implemented in the prior art.

[0089] The implementation of the method according to an aspect of the invention therefore allows secondary signals produced by the multi-path effect to be removed with a better stability than in the prior art.

[0090] It will furthermore be noted that an aspect of the present invention is not limited to the embodiment described above, making recourse to CMA algorithms, and has variants that will appear obvious to those skilled in the art; in particular, other types of iterative algorithms may be implemented.

METHOD FOR REMOVING SPATIAL AND TEMPORAL MULTI-PATH INTERFERENCE FOR A RECEIVER OF FREQUENCY-MODULATED RADIO SIGNALS

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H04B1/082

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H04B7/0848

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H04B7/0842

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H04B1/1081

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H04L25/0307

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H04L25/03057

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H04L2025/0363

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H04B7/0404

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H04B7/0845

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H04B1/10

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H04B1/08

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H04B7/0404

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H04B7/08

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H04L25/03

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Abstract

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