Analysis of Differential Orthogonal Space-Time Block Codes over Semi-Identical MIMO Fading Channels

We study the performance of differential orthogonal space-time block codes (OSTBC) over independent and semi-identically distributed block Rayleigh fading channels. In this semi-identical fading model, the channel gains from different transmit antennas to a common receive antenna are identically distributed, but the gains associated with different receive antennas are non-identically distributed. Arbitrary fluctuation rates of the fading processes from one transmission block to another is considered. We first derive the optimal symbol-by-symbol differential detector, and show that the conventional differential detector is suboptimal. We then derive expressions of exact bit error probabilities (BEP) for both the optimal and suboptimal detectors. The results are applicable for any number of receive antennas, and any number of transmit antennas for which OSTBCs exist. For two transmit antennas, explicit and closed-form BEP expressions are obtained. For an arbitrary number of transmit antennas, a Chernoff bound on the BEP for the optimal detector is also derived. Our results show that the semiidentical channel statistics degrade the error performance of differential OSTBC compared with the identical case. Also, the proposed optimal detector substantially outperforms the conventional detector when the channel fluctuates rapidly. But in near-static fading channels the two detectors have similar performances.