Abstract
Blind deconvolution (equalization) of a multi-input multi-output(MIMO) linear time invariant (LTI) system is a problem ofestimating the vector input with only a set of non-Gaussian vector output measurements distorted by the MIMO LTI system. Tugnait proposed MIMO inverse filter criteria (MIMO-IFC) for blind deconvolution of MIMO systems using second- and third-order cumulants or second- and fourth-order cumulants of inverse filter (equalizer) output. Tugnait's MIMO-IFC achieve perfect equalization as signal-to-noise ratio (SNR) is infinite. However, the performance of MIMO-IFC is unknown as SNR is finite. This thesis extends Tugnait's MIMO-IFC to those using second- and higher-order cumulants and analyzes the performance of the class of the proposed MIMO-IFC for finite SNR. This thesis also proposes a fast blind deconvolution algorithm for obtaining the optimum inverse filter and an algorithm for obtaining the theoretical inverse filter associated with MIMO-IFC. Then two blind equalization lgorithms using signature waveform matched filter output signal and chip waveform matched filter output signal, respectively, for suppression of multiple access interference and intersymbol interference of DS/CDMA systems using the proposed blind deconvolution algorithm are proposed.On the other hand, estimation of a two-dimensional (2-D) linearshift-invariant (LSI) system with only a given 2-D system outputrandom field is a blind system identification (BSI) problem thatis essential in a variety of 2-D statistical signal processingapplications, such as 2-D spectral estimation, texture imagesynthesis, classification and image restoration. The thesisproposed a 2-D FFT-based noise-insensitive BSI algorithm usinghigher-order cumulants with application to texture synthesis. The minimum mean square error (MMSE) equalizer estimate and MMSEsignal enhancement filter estimate can also be obtained using the proposed BSI algorithm.