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This letter introduces a new frequency domain approach for either MIMO System Identification or Source Separation of convolutive mixtures in cyclostationary context. We apply the joint diagonalization algorithm to a set of cyclic spectral density matrices of the measurements to identify the mixing system at each frequency up to permutation and phase ambiguity matrices. An efficient algorithm to overcome the frequency dependent permutations and to recover the phase, even for non-minimum-phase channels, based on cyclostationarity is also presented. The new approach exploits the fact that each input has a different and specific cyclic frequency. A comparison with an existing MIMO method is proposed.

In many real-world situations, man-made
signals such as those encountered in rotating machines, communications,
telemetry, radar, and sonar systems are nonstationary and very often
cyclostationary [

The method offered in this letter is a frequency
domain technique that exploits the cyclic spectral density matrices of the
measurements to identify the mixing channel and separate convolved
cyclostationary sources with different cyclic frequencies. The organization of
this letter is as follows. The problem statement including the set of required
assumptions is presented in Section

We consider

Let us introduce the SCD of the source
vector [

We conclude from (

The singular value decomposition (SVD) of

Let us introduce the SCD matrix of the measurements
[

The SCD matrices of the whitened processes at
different cyclic frequencies

An interesting property of cyclostationary signals is their spectral redundancy. In our case, the cyclic spectra of signals will not overlap because they have distinct cyclic frequencies. This is the property that we seek to exploit in our effort to derive a new algorithm for the correction of permutations across all the frequency bins. More precisely, our approach makes use of the cyclic cepstrum of the estimated signals which are permuted.

Let us first consider the estimating sources:

The phase retrieval of single-input single-output (SISO) systems, excited by
cyclostationary inputs, has been studied in several papers [

Actually, we have no knowledge on the true order of

As the processes
of estimating the MIMO system's magnitude and phase are disconnected, the
correspondence between channel magnitude and phase is missed. This can be seen
by taking the absolute value of the relationship (

We provide here
a comparison between the proposed approach against the method of [

Let

Figure

Comparison of the proposed method with the method of [

The spectral redundancy allowed us to apply the AJD
algorithm to a set of SCD matrices for every frequency. A robust algorithm to
overcome the frequency-dependent permutations and to remove the phase ambiguity,
based on cyclostationarity, was presented. The performance of the new algorithm
was demonstrated, it is apparent, therefore, that the proposed method performs
better than [

The authors gratefully thank the financial support from the Region Rhone Alpes.