Adaptive Filter Theory Based On Cumulant And Its Application

The theory and technology of adaptive signal processing have become a popular topic insignal processing field, and have been widely used in signal processing practices, such assystem identification,echo cancellation,adaptive line enhancement,adaptive channelequalization,speech signal linear prediction,predictive deconvolution,signal detection,adaptive noise cancelling and adaptive beamforming etc. Research for adaptive filteringalgorithms is one of the most active research topics in adaptive signal processing. Signalstatistics are of major importance in adaptive signl processing. Cumulant is one of theimportant statistics. The dissertation is to focus on the research of cumulant-based adaptivefiltering algorithms and their application in system identification and echo cancellation. Firstly, the author of the dissertation discusses about some variable step size adaptivefiltering algorithms based on second-order cumulant (self-relation,cross-relation), andestablishes another non-linear functional relationship between μ and e(n);which is notonly simple, but also has the property of slight change e(n) near to zero. On the basis of thefunctional relationship, the author presents a new variable step size LMS adaptive filteringalgorithm, and analyzes the algorithm with various α and β . Besides good convergenceproperties, the algorithm has less computational complexity than other variable step sizeadaptive filtering algorithm, such as SSVLMS algorithm,SV-LMS algorithm,L.E-LMSalgorithm,. Secondly, the author improves CDLMS algorithm based on error criteria J1 (n) andHOS4-MSEA algorithm based on error criteria J2 (n) by linear searching optimum afterdiscussing about cumulant domain adaptive filtering principle ,error criteria and adaptivefiltering algorithms. He also presents CDEFWLMS algorithm by using descent method onerror criteria J3 (n) from which the CDRLS algorithm was derived. Then he defines a newcumulant domain error criteria J (n)and presents CDSWLMS algorithm based on J(n).Thirdly, the author discusses about Gauss noise insensitive MSE criteria and adaptivefiltering algorithm, and re-derives CLMS algorithm and CRLS algorithm on the basis of allhigh-order cumulant-based error criteria and Wiener-Hopf equation.Fourthly, After analyzing the problem in second-order cumulant-based multichannelacoustic echo cancellation and introducing multichannel acoustic echo cancellationalgorithms, the author improves two channel Extend LMS algorithm and adaptive filteringalgorithm with rotating factor for miltichannel echo cancellation. He also presents athird-order cumulant-based two channel echo cancellation algorithm by applying cumulantdomain adaptive filtering principle to multichannel acoustic echo cancellation.Lastly,The author discusses correlation function adaptive filtering algorithms(thesecond-order cumulant domain adaptive filtering algorithm) and their application in echocancellation, and then presents a correlation function recursive least squares algorithm andanalyzes convergence of the algorithm. The correlation function adaptive filtering algorithmsare based on the processing of correlation function of the input signal, instead of theprocessing of input signal itself. In echo cancellation. The correlation function adaptivefiltering algorithms can continue the tap adaptations under double-talk conditions.