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When the complex least mean-square (CLMS) algorithm is used to estimate a complex sparse system, its convergence rate is relatively slow. To make full use of the sparsity of the unknown system to improve convergence rate, a zero-attracting CLMS (ZA-CLMS) algorithm has recently been proposed. In order to predict the statistical behavior of the complex adaptive filter after converging, this paper analyzes the steady-state mean-square deviation (MSD) performance of ZA-CLMS with circular Gaussian input. For mathematical tractability, in the analysis, the unknown system weights are divided into two sets according to their values and some statistical assumptions are used. The simulation results are provided to show the superior performance of ZA-CLMS for complex sparse system identification and to verify the validity of the theoretical expressions for predicting the steady-state MSD performance.

Steady-State Mean-Square Deviation Analysis of the Zero-Attracting CLMS Algorithm With Circular Gaussian Input