Multi-relay MIMO Systems With OSTBC Over Nakagami- $m$ Fading Channels

We investigate the performance of a dual-hop amplifyand-forward (AF) multi-relay system over independent and identically distributed (i.i.d.) Nakagami- m fading channels, where all nodes in the system are equipped with multiple antennas, and space-time block codes are used in both transmissions. By assuming that the number of source-relay spatial subchannels is equal to the number of relay-destination subchannels, new analytical expressions for the most important figures of merit, namely, outage probability, symbol error probability (SEP), and average channel capacity, are derived for arbitrary signal-to-noise ratios (SNRs) and for arbitrary values of the m parameter. We also present simplified expressions in the high-SNR regime that enable us to quantify the system performance in terms of diversity order and coding gain. Two different scenarios have been considered. First, each relay and destination combine the received signal, and then, the harmonic mean of the source-relay and relay-destination channels is computed. After that, the relay with the best harmonic mean is selected. In the second scenario, each relay and destination combine the received signal, and then, the relay with the best source-relay SNR is selected. After that, the harmonic mean of the source-to-selected-relay channel and selected-relay-to-destination channel is computed. For both considered scenarios, some special cases of interest (e.g., Nakagami-0.5 and Rayleigh) are examined. Our results explicitly demonstrate that the first scheme has higher diversity order than the second scheme, whereas the coding gain of the second scheme is always greater for the multi-relay case.