Joint Antenna and Relay Selection Strategies for Decode-and-Forward Relay Networks

Cooperative diversity systems with optimal and suboptimal antenna and relay selection have been paid significant attention for more than half a decade. However, optimal antenna and relay selection strategies require global channel state information (CSI), which is a cumbersome process. In this paper, we propose a diversity-optimal and three suboptimal transmit–receive antenna and relay selection strategies, named S1, S2, and S3, for decode-and-forward cooperative relaying systems, equipped with
$N_{t}$
and
$N_{r}$
antennas at the source (S) and the destination (D), respectively, and considering a multirelay scenario. Furthermore, we study the symbol error probability (SEP) for these strategies, assuming
$M$
-ary phase-shift keying signaling over Rayleigh fading channels. In addition, we perform diversity order analysis through closed-form asymptotic SEP expressions. Since the proposed suboptimal strategies, i.e., S2 and S3, involve the so-called switch-and-examine combining scheme, we compare the complexity of S1, S2, and S3 in terms of the average number of CSI required at D to select the best transmit–receive antenna pair and relay. From the derived SEP expressions, it can be concluded that all three suboptimal strategies achieve the same diversity order of
$N_{t}N_{r}+N$
, where
$N$
is the number of relays, except for the case when the switching threshold signal-to-noise ratio (SNR) is much lower than the average SNR in S2 and S3. Finally, the diversity-optimal strategy achieves full diversity order of
$N_{t}N_{r}+N\min(N_{t},N_{r})$
.