Abstract
This paper addresses the problem of blind separation of convolutive mixtures of BPSK and circular linearly modulated signals with unknown (and possibly different) baud rates and carrier frequencies. In previous works, we established that the Constant Modulus Algorithm (CMA) is able to extract a source from a convolutive mixture of circular linearly modulated signals. We extend the analysis of the extraction capabilities of the CMA when the mixing also contains BPSK signals. We prove that if the various source signals do not share any non-zero cyclic frequency nor any non-conjugate cyclic frequencies, the local minima of the constant modulus cost function are separating filters. Unfortunately, the minimization of the Godard cost function generally fails when considering BPSK signals that have the same rates and the same carrier frequencies. This failure is due to the existence of non-separating local minima of the Godard cost function. In order to achieve the separation, we propose a simple modification of the Godard cost function which only requires knowledge of the BPSK sources frequency offsets at the receiver side. We provide various simulations of realistic digital communications scenarios that support our theoretical statements.
Highlights
The blind source separation of convolutive mixtures of linearly modulated signals has mainly been studied in the case where the signals share the same known baud rate, and when the sampling frequency of the multivariate received signal coincides with this baud-rate
We investigated the separation of convolutive mixtures of second order circular linearly modulated signals and BPSK signals in the context of passive listening
We considered only deflation approaches coupled with the minimization of the Constant Modulus Algorithm (CMA) cost function
Summary
The blind source separation of convolutive mixtures of linearly modulated signals has mainly been studied in the case where the signals share the same known baud rate, and when the sampling frequency of the multivariate received signal coincides with this baud-rate In this context, to be referred to in the sequel as the stationary case, the discrete-time received signal coincides with the output of an unknown MIMO filter driven by the sequences of symbols sent by the various transmitters. We show that it is possible to modify the Godard cost function in order to achieve source separation of K non circular BPSK modulated signals sharing the same known (or well estimated) carrier frequency. A square integrable function fa is an element of F (B) if and only if its Fourier transform fa(ν) is zero outside B
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