Ludwig Rota

Parallel deflation with alphabet-based criteria for blind source extraction

Blind source extraction aims at estimating the source signals which appear mixed at the output of a sensor array. A novel approach to blind source extraction is presented in this contribution, which exploits the discrete character (finite alphabet property) of digital modulations in the case where sources with different alphabet exist. An alphabet polynomial fitting (APF) criterion matched to the specific signal constellation is employed to extract, through deflation, the sources with the same modulation. Using the appropriate APF criteria, the sources with different modulations can be extracted in parallel. This new concept, referred to as parallel deflation, presents the potential of reducing both the signal estimation errors that typically accumulate in the conventional deflationary approach and the spatio-temporal diversity required for a satisfactory source extraction. In addition, APF criteria can be optimized through a cost-effective optimal step-size technique that can escape local extrema

Blind equalizers based on polynomial criteria

We describe a family of criteria dedicated to blind SISO equalizers. These criteria are based on alphabet polynomial fitting (APF), and remind us of the well-known constant modulus algorithm (CMA) criterion, and encompass the constant power algorithm (CPA) criterion. Algorithms based on several polynomial criteria have been implemented in block form (including CPA and APF), as well as the CMA and the kurtosis maximization (KMA). Block implementations are indeed more efficient for short data records, and allow the direct computation of the optimal step size in a gradient descent, as shown in the paper. Computational complexities of APF, KMA and CMA are eventually compared, as well as their performance for various digitally modulated inputs.

Blind equalization of MIMO channels

This paper introduces a blind MIMO equalization algorithm for convolutive mixtures. A parametrization of the equalizer is proposed when observations are whitened. From theoretical results, a numerical algorithm is then derived. This algorithm is based on the solution of a polynomial system, which some values of output cumulant multi-correlations enter. Simulations and performance of the numerical algorithm are also included.

Blind MIMO paraunitary equalizer

This paper introduces a new blind source separation algorithm for convolutive mixtures. In addition to separate sources, this algorithm respects the paraunitary property of the model considered, obtained after whitening observations. In order to do this, the equalizer is factorized in a novel manner. After a presentation of theoretical results, a numerical algorithm is then derived. This algorithm is based on the solution of a polynomial system, which some values of output cumulant multi-correlations enter. Simulations and performances of the numerical algorithm are presented in the last section.

Blind paraunitary equalization

In this paper a blind multiple-input/multiple-output (MIMO) space-time equalizer is described, dedicated to convolutive mixtures when observations have been pre-whitened. Filters preserving space-time whiteness are paraunitary; a parameterization of such filters with plane rotations is proposed. Theoretical developments then lead to a numerical algorithm that sweeps all pairs of delayed outputs. This algorithm involves the solution of a polynomial system in two unknowns, whose coefficients depend on the output cumulants. Simulations and performance of the numerical algorithm are reported.