A variable step size constant modulus algorithm based on l0-norm for sparse channel equalization

In order to improve the convergence rate of the blind equalizer for sparse multipath channel, a l0-norm constraint blind sparse adaptive algorithm for sparse channel equalization is proposed in this paper. The constant modulus characteristics of multiple phase shift keying (MPSK) signal and the sparse property of equalizer are firstly taken into consideration to construct a new blind equalization cost function with the l0-norm penalty on the equalizer tap coefficients. Then the update formula of the tap coefficients is derived according to the gradient descent algorithm. Moreover, the iteration step is updated adaptively by drawing upon the normalized proportionate factor. Theoretical analysis and simulation results show that the proposed algorithm outperforms the existing blind equalization algorithms for sparse channel in reducing the residual inter-symbol interference (ISI) and improving convergence rate.