Pilot Design for Block Compressed Sensing-Based MIMO-OFDM Channel Estimation with Joint Criterion

This paper studies the pilot design for compressed sensing (CS)-based sparse channel estimation in multi-input–multi-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. To improve the performance of estimating multiple jointly sparse channels, based on the assumption that the modulus of the pilot symbol at each pilot carrier position is equal to a constant, the pilot is currently allocated by means of lowering the sensing matrix’s total coherence (TC). However, according to the block compressed sensing (BCS) theory, the recovery ability of the sensing matrix is determined by the block coherence (BC) and subblock coherence (SC), which should be as small as possible. Therefore, we propose a novel scheme, which designs the pilot by simultaneously minimizing the TC, BC, and SC of the sensing matrix to improve the channel estimation accuracy. We first formulate the jointly sparse channel estimation as a block sparse signal recovery problem, and the pilot allocation problem is comprised of allocating the pilot index for each transmitter and allocating the pilot symbol at each carrier. Then, we derive the error bound of BCS-based channel estimation, where the pilot symbols bear any value. Finally, a novel sequential joint criterion design (SJCD) method is proposed to design pilots with a joint criterion, where the pilot pattern and pilot power are designed by BC and TC, respectively. Simulation results show that, compared with existing algorithms, the proposed algorithm can achieve a better channel estimation performance in terms of normalized mean square error (NMSE) and bit error rate (BER).