Sparsity-aware complex-valued least mean kurtosis algorithms

Complex-valued least mean kurtosis (CLMK) algorithm and its augmented version (ACLMK) have recently become popular as workhorse tools in the processing of complex-valued signals due to their superior performances. Unfortunately, they are not yet suitable for sparse system identification problems. In this paper, combining the well-known sparsity-promoting strategies into the cost function based on the negated kurtosis of the error signal, we introduce a suit of sparsity-aware CLMK algorithms, named /0 0-norm CLMK (/0-CLMK), / 0-CLMK), / 0-ACLMK, zero-attraction CLMK (ZA-CLMK), ZA-ACLMK, reweighted ZA-CLMK (RZA-CLMK), and RZA-ACLMK. Simulation results on synthetic and real-world sparse system identification scenarios in the complex domain show that the proposed algorithms outperform the existing sparsity-aware algorithms in terms of convergence rate, tracking, and steady-state error.