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

International audienceThis 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

A new blind signal separation algorithm for instantaneous MIMO system

We address the problem of adaptive blind source separation (BSS) from instantaneous multi-input multi-output (MIMO) channels. In this paper, we propose a new constant modulus (CM)-based algorithm which employ nonlinear function as the de-correlation term. Moreover, it is shown by theoretical analysis that the proposed algorithm has less mean square error (MSE), i.e., better separation performance, in steady state than the cross-correlation and constant modulus algorithm (CC-CMA). Numerical simulations show the effectiveness of the proposed result.<br /

Blind, MIMO system estimation based on PARAFAC decomposition of higher order output tensors

IEEE Transactions on Signal Processing, 54(11): pp. 4156-4168.We present a novel framework for the identification of a multiple-input multiple-output (MIMO) system driven by white, mutually independent unobservable inputs. Samples of the system frequency response are obtained based on parallel factorization (PARAFAC) of three- or four-way tensors constructed based on, respectively, third- or fourth-order cross spectra of the system outputs. The main difficulties in frequency-domain methods are frequency- dependent permutation and filtering ambiguities.We show that the information available in the higher order spectra allows for the ambiguities to be resolved up to a constant scaling and permutation ambiguities and a linear phase ambiguity. Important features of the proposed approach are that it does not require channel length information, needs no phase unwrapping, and unlike the majority of existing methods, needs no prewhitening of the system outputs

Blind channel identification/equalization with applications in wireless communications

Ph.DDOCTOR OF PHILOSOPH

Advanced optimization algorithms for sensor arrays and multi-antenna communications

Optimization problems arise frequently in sensor array and multi-channel signal processing applications. Often, optimization needs to be performed subject to a matrix constraint. In particular, unitary matrices play a crucial role in communications and sensor array signal processing. They are involved in almost all modern multi-antenna transceiver techniques, as well as sensor array applications in biomedicine, machine learning and vision, astronomy and radars. In this thesis, algorithms for optimization under unitary matrix constraint stemming from Riemannian geometry are developed. Steepest descent (SD) and conjugate gradient (CG) algorithms operating on the Lie group of unitary matrices are derived. They have the ability to find the optimal solution in a numerically efficient manner and satisfy the constraint accurately. Novel line search methods specially tailored for this type of optimization are also introduced. The proposed approaches exploit the geometrical properties of the constraint space in order to reduce the computational complexity. Array and multi-channel signal processing techniques are key technologies in wireless communication systems. High capacity and link reliability may be achieved by using multiple transmit and receive antennas. Combining multi-antenna techniques with multicarrier transmission leads to high the spectral efficiency and helps to cope with severe multipath propagation. The problem of channel equalization in MIMO-OFDM systems is also addressed in this thesis. A blind algorithm that optimizes of a combined criterion in order to be cancel both inter-symbol and co-channel interference is proposed. The algorithm local converge properties are established as well

Blind channel estimation for MIMO OFDM communication systems

Ph.DDOCTOR OF PHILOSOPH