Improved smoothed LO reconstruction algorithm for ISI sparse channel estimation

In this paper, the problem of inter symbol interference (ISI) sparse channel estimation in wireless communication with the application of compressed sensing is investigated. However, smoothed L0 norm algorithm (SL0) has ‘notched effect’ due to the negative iterative gradient direction. Moreover, the property of continuous function in SL0 is not steep enough, which results in inaccurate estimations and low convergence. Afterwards, we propose the Lagrange multipliers as well as Newton method to optimize SL0 algorithm in order to obtain a more rapid and efficient signal reconstruction algorithm, improved smoothed L0 (ISL0). ISI channel estimation will have a direct effect on the performance of ISI equalizer at the receiver. So, we design a pre-filter model which with no considerable loss of optimality and do analyses of the equalization methods of the sparse multi-path channel. Real-time simulation results clearly show that the ISL0 algorithm can estimate the ISI sparse channel much better in both signal noise ratio (SNR) and compression levels. In the same channel conditions, ISL0 algorithm has been greatly improved when compared with the SL0 algorithm and other compressed-sensing algorithms.