Sparse adaptive L2LP algorithms with mixture norm constraint for multi-path channel estimation

An improved sparse l2 and lp norm error criterion algorithm (L2LP) is carried out by incorporating a p-norm like penalty into the cost function of the L2LP algorithm to fully utilize the prior information of the multi-path fading selective channel. The p-norm-like penalty is split into l0- and l1-norm constraints for large and small channel response coefficients for constructing the l0- and l1-norm constrained L2LP (L0L1-L2LP) algorithm. Two different zero attractors are exerted on the large and small coefficients, respectively. Furthermore, a reweighting factor is incorporated into the L0L1-L2LP algorithm to construct an enhanced algorithm named as reweighted L0L1-L2LP (RL0L1-L2LP) algorithm. The derivations of both sparse L2LP algorithms are introduced in detail. Numerical simulation samples are set up to discuss the channel estimation performance of our proposed L0L1-L2LP and RL0L1-L2LP algorithms. The obtained results give a confirmation that the proposed L0L1-L2LP and RL0L1-L2LP algorithms outperform the L2LP and the related L2LP algorithms in light of the convergence and steady-state performance for handling sparse channel estimation.