Research On Improvement And Application Of Least Mean Square Algorithm

The adaptive signal processing is an important branch of digital signal processing,besides having the advantages of the stability, repetition and the good adaptability of thedigital signal processing, it has still advantages of predictability and no phase shift. Adaptivefiltering algorithm is a kind of algorithm which can automatically adjust the parameters offilter performance, and it is also the most important part of adaptive filtering processing. TheLMS algorithm (Least Mean Square) has simple principle, less parameters and goodconvergence speed, it is the most widely used algorithm in the adaptive filtering algorithm.But in some application environment like echo cancellation, the standard LMS algorithmdon’t make effective use of the specific properties of these system response. We propose somemodifications and improve the performance based on the LMS algorithm and its relatedforms.First, through the research of the LMS algorithm based on the penalty factor, takingadvantage of the sparse characteristic of system, this algorithm updates the weight coefficientby linear adding fixed disturbance quantity in criterion function and keeps the weightcoefficient in a best level. After the analysis of ZA–LMS and RZA–LMS, we propose a newLMS algorithm based on the penalty factor by introducing the variable stepsize thought intoRZA–LMS. The new algorithm dynamic adjusts the convergence standard of RZA–LMSalgorithm to control the attractive degree, it has a better robustness.Second, this paper analyses the advantages and disadvantages of the several existedcoefficient proportional adaptive algorithm and presents a series of the improved algorithm. Inthe IPNLMS algorithm, its convergence speed is closely related to the sparse degree of system,if the sparse degree of system changes by time, its performance will decrease. We introducean approximate L0norm and sparse degree to adjust the parameters in IPNLMS algorithm,the new algorithm gets a considerable performance in the system with different sparse degree.In the MPNLMS algorithm, although it pointed out the optimal distribution of step sizeaccording to the filter weight coefficient, it has a faster convergence speed, but the steadystate performance is still be affected by the global step, we propose the variable-stepcoefficient proportional adaptive algorithm, setting a large global step size at first and smallglobal step size when the algorithm closed to convergence. This variable-step coefficientproportional adaptive algorithm can get a good convergence speed and a low steady stateerror.Third, a compare between the proposed related LMS adaptive algorithms and severalother adaptive filtering algorithm was made, respectively through system identification and echo cancellation experimental simulation comparison. The experiment results show that theproposed related algorithms can get better performance requirements in convergence andsteady-state error.