Blind source separation of convolutive mixtures of non circular linearly modulated signals with unknown baud rates

TL;DR

This paper extends the analysis of blind source separation using the Constant Modulus Algorithm to include BPSK signals with unknown baud rates, proposing a modified cost function to improve separation performance.

Contribution

It introduces a modified Godard cost function that enables separation of BPSK signals with unknown baud rates and carrier frequencies, addressing limitations of previous methods.

Findings

The original CMA fails to separate BPSK signals with identical rates and frequencies.

The modified cost function successfully separates BPSK signals under specified conditions.

Simulations confirm the effectiveness of the proposed approach in realistic scenarios.

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.