Approximations for the Random Coding Exponent of Correlated Fading Channels with Differential Detection

We formulate the random coding exponent for single and multiple antennae systems on a flatfading additive white Gaussian noise (AWGN) channel with differential encoding and multiple-symbol differential detection (MSDD). Noting the intractability of the computation of the exponent for code lengths of interest, we propose the use of an approximated channel model based on the fact that the observation window of the MSDD metric is usually chosen to be much smaller than the coherence time of the fade. This approximation allows a drastic reduction in complexity. We achieve further simplifications by using a block-fading model that is equivalent, in terms of the coding exponent, to the true continuous fading process. We then apply this optimized algorithm to investigate the relative contributions of spatial and temporal fading diversity in improving channel reliability for moderate code lengths. Index Terms Random coding exponent, fading channel, differential encoding, multiple-symbol differential detection (MSDD), differential space-time modulation (DSTM), diversity. † Corresponding author SUBMITTED AS CORRESPONDENCE TO THE IEEE TRANSACTIONS ON INFORMATION THEORY, SEPTEMBER, 2006. 2