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Existing works design the pilot based on the mutual coherence criterion or total coherence criterion alone. However, using the mutual coherence criterion or total coherence criterion alone to design the pilot will yield the sensing matrix which corresponds to a certain pilot with a large total coherence or mutual coherence. However, the sensing matrix with a large mutual coherence or total coherence will deteriorate the sparse recovery performance and is not optimal from the perspective of the sparse recovery. Therefore, in this paper, we jointly design the pilot based on both the mutual coherence criterion and the total coherence criterion for sparse channel estimation in orthogonal frequency division multiplexing (OFDM) systems. We first prove that the optimal pilot pattern with respect to the total coherence criterion is the cyclic difference set and given a pilot pattern, the pilot power allocation can be cast as a second order cone programming problem with respect to the total coherence criterion. A joint mutual coherence and total coherence pilot design algorithm is proposed to design the pilot jointly while cyclic difference set does not exist for practical OFDM systems. The proposed algorithm first optimizes the pilot pattern with the mutual coherence criterion assuming that the pilot power is equal. After obtaining the pilot pattern, the pilot power is allocated with the total coherence criterion. Simulation results have shown that the proposed pilot design algorithm can achieve the best performance in terms of normalized mean square error and bit error rate in comparison with existing pilot design methods.

Joint Mutual Coherence and Total Coherence Pilot Design for OFDM Channel Estimation