Method for cancelling multi-path signals for frequency-modulated radio signal receiver

Abstract

A method for decreasing multi-path interference, for the implementation thereof in a vehicle radio receiver including a radio reception antenna that receives a plurality of radio signals corresponding to an emitted radio signal, the plurality of signals received by the antenna being composed of time-shifted radio signals, the plurality of signals being intended to be combined in order to deliver a combined radio signal z.sub.n to be played, with z.sub.n=W.sub.n.sup.TY.sub.n, the method aiming to determine the complex components of the vector of complex weights and including: introducing a temporal correlation, between the real and imaginary parts of the complex weights, that is dependent on the time shift between said received signals, by the expression of the complex weights in polar coordinates, implementing an iterative adaptation algorithm in order to determine the gains and delays of said complex weights able to keep constant over time the modulus of z.sub.n.

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 a radio reception antenna that receives a plurality of radio signals corresponding to said emitted radio signal, said plurality of signals received by said antenna being composed of time-shifted radio signals resulting from a multi-path effect, said plurality of radio signals being intended to be combined in order to deliver a combined radio signal z.sub.n to be played, with z.sub.n=W.sub.n.sup.TY.sub.n at the time n, where Y.sub.n is a vector the components of which correspond to the plurality of received signals, expressed in complex baseband, and W.sub.n is a vector the components of which correspond to complex weights intended to be attributed to each of the radio signals of said plurality of received radio signals, respectively, in order to form the combined radio signal z.sub.n in which a set of secondary radio signals resulting from the multi-path effect are canceled out, said method aiming to determine said complex components of said vector of complex weights and comprising: Introducing a temporal correlation between the real and imaginary parts of said complex weights, said correlation being dependent on the time shift between said signals of said plurality of received radio signals, by means of the expression of said complex weights in polar coordinates, so that $Wn=\left[\begin{array}{c}{g}_o\exp \left(j{}_o\right)\\ g_1\exp \left(j{}_1\right)\\ \mathrm{.Math.}\\ \mathrm{.Math.}\\ g_{K-1}\exp \left(j{}_{K-1}\right)\end{array}\right],$ so as to incorporate an interdependence between the real and imaginary parts of said complex weights, and Implementing an iterative adaptation algorithm in order to determine the g.sub.0, g.sub.1, . . . , g.sub.k-1 and .sub.0, .sub.1, . . . , .sub.k-1 able to keep constant over time the modulus of z.sub.n.

2. The method as claimed in claim 1, wherein said iterative adaptation algorithm is a constant-modulus adaptation algorithm.

3. The method as claimed in claim 2, comprising determining a constant R corresponding to the modulus of the envelope of the frequency-modulated radio signal emitted, the implementation of the iterative adaptation algorithm consisting in determining G.sub.n, .sub.n able to minimize over time the cost function characterized by the following instantaneous gradient: $J_{CMA}=2\left({.Math.z_n.Math.}^2-R^2\right)\left[\begin{array}{c}2\mathrm{Re}\left[z_n\exp \left(j{}_n\right)\stackrel{\_}{Y_n}\right]\\ -2\mathrm{Im}\left[z_n{G}_n\exp \left(j{}_n\right)\stackrel{\_}{Y_n}\right]\end{array}\right]$ where G.sub.n is a vector composed of the complex gains of each of the complex weights of the vector of complex weights at the time n, .sub.n is the vector composed of the complex delays of each of the complex weights of the vector of complex weights of the time n and the operator is defined as performing the multiplication of two vectors, component by component, the resultant being a vector.

4. The method as claimed in claim 1, comprising determining a constant R corresponding to the modulus of the envelope of the frequency-modulated radio signal emitted, the implementation of the iterative adaptation algorithm consisting in determining G.sub.n, .sub.n able to minimize over time the cost function characterized by the following instantaneous gradient: $J_{CMA}=2\left({.Math.z_n.Math.}^2-R^2\right)\left[\begin{array}{c}2\mathrm{Re}\left[z_n\exp \left(j{}_n\right)\stackrel{\_}{Y_n}\right]\\ -2\mathrm{Im}\left[z_n{G}_n\exp \left(j{}_n\right)\stackrel{\_}{Y_n}\right]\end{array}\right]$ where G.sub.n is a vector composed of the complex gains of each of the complex weights of the vector of complex weights at the time n, .sub.n is the vector composed of the complex delays of each of the complex weights of the vector of complex weights of the time n and the operator is defined as performing the multiplication of two vectors, component by component, the resultant being a vector.

5. The method as claimed in claim 4, wherein the respective variations in G.sub.n and .sub.n over time are computed by means of the following formulae: $G_{n+1}=G_n-{}_g\left({.Math.z_n.Math.}^2-R^2\right)\mathrm{Re}\left[z_n\exp \left(j{}_n\right)\stackrel{\_}{Y_n}\right]$ ${}_{n+1}={}_n+{}_{}\left({.Math.z_n.Math.}^2-R^2\right)\mathrm{Im}\left[z_n{G}_n\exp \left(j{}_n\right)\stackrel{\_}{Y_n}\right]$ where G.sub.n is a vector composed of the complex gains of each of the complex weights of the vector of complex weights at the time n, and where .sub.n is the vector composed of the complex delays of each of the complex weights of the vector of complex weights at the time n, and where .sub.g and .sub. are the iterative steps chosen for the update of the gains and phases of each of the complex weights and where the operator is defined as performing the multiplication of two vectors, component by component, the resultant being a vector.

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

7. A motor vehicle comprising a radio receiver as claimed in claim 6.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) An aspect of the invention will be better understood on reading the following description, which is given solely by way of example, and with reference to the appended drawing which shows, in the FIGURE, a block diagram of a method for cancelling out multi-path radio signals.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

(2) 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 be implemented in any other technical field, and in particular in any type of FM radio receiver.

(3) An aspect of the present invention proposes to introduce an adaptive temporal model, in order to take into account the temporal correlation that exists, from the physical point of view, between the multi-path FM radio signals received by the antenna of the radio receiver in question.

(4) 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 are however not transposable as such to the field of FM radio reception.

(5) The adaptive temporal model implemented in the world of radars is in fact 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:

(6) 0$Wn=\left[\begin{array}{c}\exp \left(j2F_{d}0T\right)\\ \exp \left(j2F_{d}1T\right)\\ \mathrm{.Math.}\\ \mathrm{.Math.}\\ \exp \left(j2F_d\left(K-1\right)T\right)\end{array}\right]$

(7) 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 traveled by the radio wave, said distance not being a linear frequency-dependent function, contrary to the case of radar reception.

(8) According to an aspect of the invention, the complex weights of the temporal adaptive model are thus stated in polar coordinates, so as to introduce, into the system, a strong temporal correlation between said complex weights, while taking into account the respective gain of each of the received multi-path signals. The vector of complex weights, which forms an adaptive filter to be applied to the received radio signal, is therefore written:

(9) $Wn=\left[\begin{array}{c}{g}_o\exp \left(j{}_o\right)\\ g_1\exp \left(j{}_1\right)\\ \mathrm{.Math.}\\ \mathrm{.Math.}\\ g_{K-1}\exp \left(j{}_{K-1}\right)\end{array}\right]$

(10) Hence, according to an aspect of the invention, an iterative algorithm is implemented to determine the values g.sub.k and .sub.k able to minimize the following cost function:
J.sub.CMA=E{(|z.sub.n|.sup.2R.sup.2).sup.2}

(11) where R is a constant to be determined, corresponding to the modulus of the envelope of the FM radio signal, for example able to be obtained by averaging the power of the combined received signal.

(12) The computation of the instantaneous gradient of this cost function leads to:

(13) $\begin{array}{c}{J}_{CMA}=2\left({.Math.z_n.Math.}^2-R^2\right){.Math.z_n.Math.}^2\\ =2\left({.Math.z_n.Math.}^2-R^2\right)\left(z_n{\stackrel{\_}{z}}_n\right)\\ =2\left({.Math.z_n.Math.}^2-R^2\right)\left(z_n{\stackrel{\_}{z}}_n+{\stackrel{\_}{z}}_n{z}_n\right)\end{array}$

(14) Differently to the prior art, the model of the FM radio signals received is then written:

(15) $z_n=W_n^T{Y}_n=\underset{k=0}{\overset{K-1}{.Math.}}\stackrel{\_}{w_{\left(k\right)}}{y}_{\left(n-k\right)}=\underset{k=0}{\overset{K-1}{.Math.}}\stackrel{\_}{g_{\left(k\right)}\exp \left(j{}_{\left(k\right)}\right)}{y}_{\left(n-k\right)}$

(16) where K is the number of complex weights, i.e. the number of coefficients of the adaptive filter to be applied to the received radio signal.

(17) Therefore, writing the instantaneous gradient makes it possible to obtain:

(18) ${\stackrel{\_}{z}}_n=\frac{{\stackrel{\_}{z}}_n}{Wn}=\left[\begin{array}{c}\exp \left(j{}_n\right)\stackrel{\_}{Y_n}\\ j{G}_n\exp \left(j{}_n\right)\stackrel{\_}{Y_n}\end{array}\right]$

(19) and

(20) $z_n=\frac{z_n}{Wn}=\left[\begin{array}{c}\exp \left(-j{}_n\right)Y_n\\ -j{G}_n\exp \left(-j{}_n\right)Y_n\end{array}\right]$

(21) where G.sub.n is a vector composed of the complex gains of each of the complex weights of the vector of complex weights at the time n, .sub.n is the vector composed of the complex delays of each of the complex weights of the vector of complex weights at the time n and the operator is defined as performing the multiplication of two vectors, component by component, the resultant being a vector.

(22) The following expression of the gradient of the cost function is obtained therefrom:

(23) $J_{CMA}=2\left({.Math.z_n.Math.}^2-R^2\right)\left[\begin{array}{c}2\mathrm{Re}\left[z_n\exp \left(j{}_n\right)\stackrel{\_}{Y_n}\right]\\ -2\mathrm{Im}\left[z_n{G}_n\exp \left(j{}_n\right)\stackrel{\_}{Y_n}\right]\end{array}\right]$

(24) The gains and phases of each of the complex weights to be determined are therefore updated over time by virtue of the following formulae:

(25) $\{\begin{array}{c}{G}_{n+1}=G_n-{}_g\left({.Math.z_n.Math.}^2-R^2\right)\mathrm{Re}\left[z_n\exp \left(j{}_n\right)\stackrel{\_}{Y_n}\right]\\ {}_{n+1}={}_n+{}_{}\left({.Math.z_n.Math.}^2-R^2\right)\mathrm{Im}\left[z_n{G}_n\exp \left(j{}_n\right)\stackrel{\_}{Y_n}\right]\end{array}$

(26) where .sub.h and .sub. are iterative steps chosen for the update of the gains and phases of each of the complex weights. It is known to those skilled in the art that the larger the size of the iterative steps p, the faster the algorithms converge, but with a lower precision. In contrast, for iterative steps p of small size, the convergence of the algorithms is slow, but with a higher precision. In practice, the final choice as to the value of the iterative steps p is often made in the field, empirically during campaigns of trials.

(27) The strong interdependency between the real and imaginary parts of the complex weights to be determined will be evident from these formulae.

(28) The implementation of iterative 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 temporal correlation introduced above induces 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.

(29) 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.

(30) The implementation of the method according to an aspect of the invention, via an impulse response filter FIR, therefore allows secondary signals produced by the multi-path effect to be removed with a better stability than in the prior art.

(31) It is furthermore specified that aspects of the present invention are 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 indeed be implemented.