The Research And Application Of LMS Algorithm In Adaptive Filter

The adaptive filter automatically adjusts its own parameters by iteration, to meet a certain criteria, in order to achieve optimal filtering. In the design process of adaptive filter, the adaptive filtering algorithm is the most important part. Developed based on the Wiener filter, the least mean square algorithm (LMS algorithm), has been widely used because of its simple structure, easy to implement, stable performance, and low computational complexity.However, LMS algorithm has drawbacks, such as slow convergence, which seriously affect those applications which require a higher convergence rate. Therefore, the researchers seek more ways to study how to better enhance the performance of the LMS algorithm, thus making many branches of the LMS algorithm appear. The paper mainly researches the two branches of the LMS algorithm-proportionate adaptive algorithm and affine projection sign algorithm. For adaptive filtering algorithm, performance indicators to measure algorithm contain convergence speed, steady-state error and computational complexity. The paper is focused on research to improve the convergence speed and reduce the complexity of the two branches. The specific study contents are as follows:The branch of LMS algorithm-proportionate adaptive algorithm is studied deeply. On the basis of summing the existing several proportionate adaptive algorithms, the paper proposed to improve the convergence speed of the IMPNLMS algorithm by using the improving coefficient μ, and completed the simulation under network echo cancellation model. At the same time, the improvement can also be incorporated into or used in the MMIPAPA algorithm, and the corresponding simulation was also completed. In addition, the paper also proposed a relatively simple and easy way to derive the MPNLMS algorithm, and introduced briefly several ways to reduce the computational complexity of the proportionate adaptive algorithm, such as, reduce the normalized, partially updated and so on, and took the simulation for the reduction of the normalized.The branch of LMS algorithm-affine projection sign algorithm is studied deeply. On the basis of summing the existing several affine projection sign algorithms, the paper used a variable step size to improve the convergence speed of the APSA algorithm, and completed the simulation under system identification model. In addition, the paper also completed the optimization of the APSA algorithm by using the "history" of proportionate step control matrix G(n) and recursive method, which making the multiplication complexity of Q(n) drop to N times from p×N times at each iteration, and the corresponding simulation was completed.