A Comparison of Two MIMO Relaying Protocols in Nakagami- $m$ Fading

Transmit antenna selection with receive maximal-ratio combining (TAS/MRC) and transmit antenna selection with receive selection combining (TAS/SC) are two attractive multiple-input-multiple-output (MIMO) protocols. In this paper, we present a framework for the comparative analysis of TAS/MRC and TAS/SC in a two-hop amplify-and-forward relay network. In doing so, we derive exact and asymptotic expressions for the symbol error rate (SER) in Nakagami-m fading. Using the asymptotic expressions, the SNR gap between the two protocols is quantified. Given that the two protocols maintain the same diversity order, we show that the SNR gap is entirely dependent on the array gain. Motivated by this, we derive the SNR gap as a simple ratio of the respective array gains of the two protocols. This ratio explicitly takes into account the impact of the number of antennas and the fading severity parameter . In addition, we address the fundamental question of “How to allocate the total transmit power between the source and the relay in such a way that the SER is minimized?” Our answer is given in the form of new compact expressions for the power allocation factor, which is a practical design tool that optimally distributes the total transmit power in the network.