The channel response of data communication over a multipath wireless channel is often required to be known at the receiver. An accurate estimation of channel can greatly increase the throughput of the whole systems. Training-based methods are commonly used to learn the channel response. But the traditional channel estimation doesn't take the characteristics of wireless channel into account. On the other hand, Compressive sensing has recently gained much attention in various areas. In communication, compressive sensing is also been used to estimate the channel response in wireless orthogonal frequency division multiplexing (OFDM) systems. In this paper, we consider the channel estimation of frequency selective wireless channels which is the opposite of time selective wireless. An optimization for channel estimation based on compressed channel sensing is proposed in this paper. The optimization considers the character of channel. We use the delay of the channel to optimize the algorithm of Orthogonal Matching Pursuit. We present the LS and CS estimators and a method for modifications compromising of performance. The bit error number and the normalized mean square error for a 16-QAM system are presented by means of simulation results. Our simulation results demonstrate a significant reduction of the performance of the bite error number and the normalized mean square error. So that, the optimization for channel estimation based on compressed channel sensing achieves the same bit error number with the reduction of pilots by comparing the traditional channel estimation, then, the modified method also increase spectral efficiency.
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