Design and analysis of reward-punishment based variable step size LMS algorithm in Rayleigh faded channel estimation

Channel estimation in wireless communication system using various supervised learning algorithms traditionally involves two very popular algorithms namely Least Mean Square (LMS) and Recursive Least Square (RLS). The concept of variable step size adaptive algorithms came into picture later on to achieve a trade-off between convergence speed and mathematical complexity of these two algorithms (LMS and RLS). The family of variable step size least mean square (VSSLMS) algorithms consists of various members depending on their separate step size adaptation rule. In this paper, a new modified variable step size algorithm is proposed employing a simple mathematical adaptation strategy- the “reward-punishment” rule. The performance of the newly developed algorithm is analyzed in estimating an unknown time varying Rayleigh faded channel and compared with the performance of existing algorithms. The computer simulation shows that the “reward-punishment based variable step size least mean square” algorithm exhibits faster convergence rate compared to LMS and other competitors from VSSLMS family of algorithms and consequently acts as better trade-off between LMS and RLS algorithm. The mathematical complexity measured in terms of CPU time usage also indicates betterment over existing VSSLMS algorithms.