Research On The Improved Affine Projection-type Adaptive Filtering Algorithms

Adaptive filter is widely used in various kinds of technological applications, suchas system identification, channel equalization, interference cancellation，and linear andnonlinear prediction. The least mean square(LMS) and the recursive least square(RLS)algorithms are the most common adaptive filtering algorithms. LMS algorithm has lowcomputational cost, but it suffers from a slow convergence rate. The performance ofRLS is opposite to the LMS. That is, RLS converges very fast, but it is computationalcomplex. In order to improve the convergence rate of the LMS, Affine projectionalgorithm(APA) is commonly used. However, the standard APA algorithm has two maindrawbacks:1. the APA with a large step size parameter or a small regularization factorcan converge very fast, but it has a poor steady-state performance. On contrast, the APAwith a small step size parameter or a large regularization factor has a low steady-stateperformance, but it converges slowly. Therefore, the standard APA adaptive filteringalgorithm cannot satisfy the requirements for high convergence speed and lowsteady-state performance in technological applications.2. The APA-type algorithmssuffer from severe performance degeneration, when the adaptive system is interfered byimpulsive noise. In other words, the APA-type algorithms are not robust againstimpulsive noise. This thesis carries research on how to improve the robustness andtracking performance of the APA algorithm, which is of great practical significance.First, the standard APA and its improved versions are briefly discussed in thisthesis.Second, aiming at the problem of poor tracking performance of the APA, a novelvariable regularization parameter APA(VR-APA) is proposed. Instead of trying to derivea variable regularization parameter algorithm based on the criterion of setting the aposterior error to zero, like conventional algorithms. A novel variable regularizationexpression is derived via minimizing energy of the noise-free a posterior error vector. Inpractical implementation, the statistical variance of the measurement noise and a moreeasily-controlled exponential scaling factor estimation method are used. Besides, thestability performance of the proposed algorithm is also discussed. Reduced steady-statemisalignment and improved convergence speed as compared to conventional algorithmsare demonstrated in simulations for system identification scenarios. Last, aiming at the problem of poor robustness of the APA caused by the impulsiveinterference, this thesis proposes a convex combination scheme to improve the trackingperformance and the robustness. Simulation results show that the proposed algorithmhas a high convergence rate, a low steady-state error, and is robust against impulsiveinterference.