Pilot design for sparse MIMO-OFDM channel estimation with generalized shift invariance property

Compressed sensing (CS) based channel estimation is greatly bound by the measurement matrix according to CS theory. We design pilot patterns by minimizing the mutual coherence of the measurement matrix with the generalized shift invariance property (GSIP). GSIP and a corollary are firstly proposed. Then two pilot pattern design schemes termed pilot design with GSIP (PDGSIP) and tradeoff pilot design with GSIP (TPDGSIP) are put forward to design orthogonal pilot patterns based on GSIP for a multiple-input multiple-output orthogonal frequency division multiplexing system. In PDGSIP, a collection of pilot patterns are firstly obtained and then pilot patterns having large mutual coherence are replaced with new ones generated with optimal pilot patterns. TPDGSIP directly produces new pilot patterns based on GSIP to fully exploit the pilot distance of the obtained pilot pattern as soon as one pilot pattern is obtained. Simulation results have shown that, the proposed pilot pattern design schemes are able to obtain the best pilot patterns in comparison to existing methods from the perspective of mutual coherence. Channel estimation performance using pilot patterns designed by proposed schemes precedes that using pilot patterns designed by existing schemes in terms of normalized mean square error and bit error rate.