We study the performance of differential orthogonal space-time block codes over independent and semi-identically distributed Rayleigh fading channels. In this semi-identically distributed 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 are 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 orthogonal space-time block codes exist. For two transmit antennas, explicit and closed-form BEP expressions are obtained. A Chernoff bound on the BEP of optimal detection for any number of transmit antennas is also derived.
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