A Novel Convergence Accelerator for the LMS Adaptive Filter

Abstract

Due to its ease of implementation, the least mean square (LMS) algorithm is one of the most well-known algorithms for mobile communication systems. However, the main limitation of this approach is its relatively slow convergence rate. This paper proposes a booster using the Markov chain concept to speed up the convergence rate of LMS algorithms. The nature of Markov chains makes it possible to exploit past information in the updating process. According to the central limit theorem, the transition matrix has a smaller variance than that of the weight itself. As a result, the weight transition matrix converges faster than the weight itself. Therefore, the proposed Markov-chain based booster is able to track variations in signal characteristics and simultaneously accelerate the rate of convergence for LMS algorithms. Simulation results show that the Markov-chain based booster allows an LMS algorithm to effectively increase the convergence rate and further approach the Wiener solution. This approach also markedly reduces the mean square error while improving the convergence rate.