Adaptive blind deconvolution using third-order moments exploiting asymmetry

Abstract: This thesis focuses on the use of third-order statistics in adaptive blind deconvolution of asymmetric impulsive signals. Traditional methods are typically based on fourthorder moments, which can discriminate signals with heavy-tailed probability functions (i.e. `spiky' signals) from corresponding filtered versions. The work herein demonstrates that, by using third-order central moments, asymmetry in such signals (e.g. only positive `spikes') can be exploited to achieve faster convergence of algorithms and increased robustness to noise. The reasons for these benefits lie mainly in the use of error functions with lower polynomial orders, which leads to simpler gradient equations, improving the convergence rate. The increased robustness to noise is due to the fact that all odd-order statistics of symmetric signals (e.g. Gaussian noise) are zero. A previously known computationally simple, norm-constrained algorithm for gradient search is also examined. It is demonstrated that this algorithm accomplishes third-order moment maximization by gradient ascent, without the undesired e ect of increasing filter norm. Norm-constrained optimization is commonly achieved using periodic normalization of the filter vector, involving costly divides and square-root operations. The investigated algorithm requires significantly fewer operations, and uses only multiplications and additions, making it well suited for implementation on fixed-point digital signal processors. Numerical experiments, demonstrating the usefulness of the proposed methods, include blind deconvolution of sound from a diesel engine, and blind equalization of a synthetic ultra-wideband (UWB) communication channel.