Research On Affine Projection P-Norm Algorithm

Digital Signal Processing Technology has been developed a lot in modern society. Filtering is a kind of signal processing technology; after processing the input signals, the output signal contains the useful content. Filter is one of representative digital signal processing system which could be divided into time invariant system and time variable system. The filtering is one kind of time variable system. Least Mean square algorithm is widely used for the simply structure, low compute complex. While the input of high correlated would worsen the algorithm convergence speed. The affine projection algorithm (APA) can be a very good solution to the above problem. The AP algorithm reusing the input signal improves the convergence speed with the high correlated input signal. However, to a certain extent the least mean mixed norm (LMMN) algorithm and the least mean p-order (LMP) algorithm can reduce the steady-state mean square error of the algorithm.This paper mainly includes the following aspects: 1. Learn to know Affine Projection algorithm and the source of it. The relationship of different parameters about convergence speed and AP steady state condition of adaptive algorithm. Utilizing Matlab simulation to compare AP algorithm with NLMS adaptive algorithm on the convergence speed. 2. Base on the reuse of formal AP’S input signal and combine the methods of LMMN and LMP adaptive algorithms to propose APMN adaptive algorithm and APP adaptive algorithm. And respectively deduce weight vector expression of APMN and APP. Meanwhile, analyze the steady state error of APMN and APP. Then, deduce the expression of steady-state mean square error. 3. According to their weight vector update expressions and steady-state mean square error, verified and analyzed the relationship between the use of Matlab simulation convergence of APMN adaptive algorithm and APP algorithm, the steady-state error and different parameters, and the adaptive algorithm are compared between the theoretical results and simulation and comparison the gap between the theoretical analysis results are verified.