Fading Correlations for Wireless Cooperative Communications: Diversity and Coding Gains

We theoretically analyze outage probabilities of the lossy-forward (LF), decode-and-forward (DF), and adaptive decode-and-forward (ADF) relaying techniques, with the aim of characterizing the impact of the spatial and temporal correlations of the fading variations. First, the exact outage probability expressions are analytically obtained for LF, DF, and ADF relaying assuming each link suffers from statistically independent Rayleigh fading. Then, approximated, yet accurate closed-form expressions of the outage probabilities for the relaying schemes are derived. Based on the expressions, diversity and coding gains are found. The mathematical methodology for the derivation of the explicit outage probability is further extended to the case, where the account is taken of the spatial and temporal correlations of the fading variations. The diversity gains with LF, DF, and ADF are then derived in the presence of the correlations. It is found out that the three techniques can achieve full diversity, as long as the fading variations are not fully correlated. We then investigate the optimal relay location and the optimal power allocation for the three relaying techniques. It is shown that the optimal solutions can be obtained under the framework of convex optimization. It is revealed that in correlated fading, the relay should move close to the destination or allocate more transmit power to the relay for achieving lower outage probabilities, compared with the case in independent fading.