Adaptive methods for blind equalization and signal separation in MIMO systems

This thesis addresses the problems of blind source separation (BSS) and blind and semi-blind communications channel equalization. In blind source separation, signals from multiple sources arrive simultaneously at a sensor array, so that each sensor output contains a mixture of source signals. Sets of sensor outputs are processed to recover the source signals from the mixed observations. The term blind refers to the fact that specific source signal values and accurate parameter values of a mixing model are not known a priori. Application domains for the material in this thesis include communications, biomedical, and sensor array signal processing. The goal of this thesis is development of blind and semi-blind algorithms which require little or no prior information about source signal or mixing system parameter values in order to process the data. We start with the problem of extracting unknown input signals from measured outputs of instantaneous multiple-input multiple-output (I-MIMO) systems with constant parameter values. Suggested solutions are then extended to time-varying I-MIMO systems and also to constant finite impulse response multiple-input multiple-output (FIR-MIMO) systems. Another goal is to find a practical solution for the more challenging case of time-varying FIR-MIMO systems. The source separation techniques proposed in this thesis are based on state-space models and on recursive estimation. Blind separation algorithms based on Kalman filters are proposed. The source signals are treated using low-order autoregressive models. Projections along signal subspace eigenvectors are used to reduce the dimensionality of observations and also for spatial decorrelation of sources. Any changes that occur in the signal subspace can be tracked online. When considering slowly time-varying FIR-MIMO systems, fractional sampling can be used to derive a set of slowly time-varying I-MIMO systems. Thus, the proposed recursive BSS algorithms for I-MIMO systems can be used for blind equalization of slowly time-varying FIR communications channels. The problem of equalization of time-varying FIR MIMO systems is also addressed in this thesis. The proposed solutions involve semi-blind algorithms which work in two stages. First, a channel estimate is derived, and then the observation sequence is equalized. The algorithms estimate the otherwise-unknown noise statistics, and as a result achieve performance close to that of an optimal Kalman-based algorithm. A non-connected decision feedback equalization algorithm is derived for FIR-MIMO systems, using a minimum mean square error criterion. Simulation results show that the algorithm is able to track time and frequency selective channels and also to mitigate intersymbol and interuser interference.