Complex-Valued Sparse Channel Estimation via Least Mean Fractional Lp-norm Method

An adaptive least mean fractional Lp-norm method for complex-valued channel estimation is put forward in this paper. This method utilizes the fractional Lp-norm of the instantaneous channel estimation error as the cost function to avoid the problem in the L1-norm least mean squares (LMS) penalized method that the sub gradient of the L1-norm of complex-valued channel coefficients is not well defined. The mathematical derivation and convergence analysis are carried out. Simulation results show that the proposed complex-valued sparse channel estimation method has faster convergence rate and smaller steady-state error than the complex LMS method. The channel equalizer estimated by the proposed method outperforms the one estimated by the complex LMS method.