Sparse NLMS adaptive algorithms for multipath wireless channel estimation

Embedding a sparse penalty in conventional Least Mean Square (LMS) adaptive algorithms is an established strategy to enhance the performance and robustness against noise in the estimation of sparse plants, such as wireless mul-tipath channels. In this paper we review the most prominent NLMS-based algorithms with ℓ
_p
-norm constraint, discussing the underlying mechanisms that lead to improvement gains in sparse scenarios. Simulation results validate the analysis and comparative discussion. Given that adaptive algorithms operating in time domain deteriorate with correlated signals, we propose hereby a novel frequency-domain (FD) ℓ
_p
-NLMS that performs in such situations. Simulation results indicate that the proposed method outperforms its time-domain counterparts not only in convergence rate but more importantly in residual misalignment. This important result has not been echoed so far.