Effects of Non-Identical Rayleigh Fading on Differential Unitary Space-Time Modulation

Non-identical fading distribution in a multiple-input multiple-output (MIMO) channel, including unequal average channel gains and fade rates, often occurs when antennas are not co-located. In this paper, we present an analytical study of the effects of non-identical Rayleigh fading on the error performance of differential unitary space-time modulation (DUSTM). The fading processes for different transmit-receive antenna pairs are assumed to be independent and time-variant. We find that the maximum-likelihood (ML) differential detector of DUSTM over such channels is involved except for differential cyclic group codes. The conventional detector is proved to be asymptotically optimal in the limit of high signal-to-noise ratio (SNR) over static fading channels. Applying the distribution of quadratic forms of Gaussian vectors, we then derive closed-form expressions for the exact error probabilities of two specific unitary classes, namely, cyclic group codes and orthogonal codes. Simple and useful asymptotic bounds on error probabilities are also obtained. Our analysis leads to the following general findings: (1) equal power allocation is asymptotically optimal, and (2) non-identical channel gain distribution degrades the error performance. Finally, we also introduce a water-filling based power allocation to exploit the transmit non-identical fading statistics.