### Mean-Square Performance Analysis of Variable Step-Size l0-NLMS Algorithm

#### Abstract

Wireless communication systems often require accurate Channel State Information (CSI) at the receiver side. Typically, the CSI can be obtained from Channel Impulse Response (CIR). Measurements have shown that the CIR of wideband channels are often sparse. To this end, the Least Mean Square (LMS)-based algorithms have been used to estimate the CIR at the receiver side, which unfortunately is not able to accurately estimate sparse channels. In this paper, we propose a variable step-size *l*_{0}-norm Normalised LMS (NLMS) algorithm. The step-size is varied with respect to changes in the mean square error (MSE), allowing the filter to track changes in the system as well as produce smaller steady-state errors. We present simulation results and compare the performance of the new algorithm with the Invariable Step-Size NLMS (ISS-NLMS), Variable Step-Size NLMS (VSS-NLMS) and the Invariable Step-Size *l*_{0}-NLMS (ISS-L0-NLMS) algorithms. The results show that the proposed algorithm performs admirably to improve the identification of sparse systems, especially at SNR of 10 dB.

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