Probability of SNR gain by dual-hop MIMO relaying over single-hop Alamouti transmission

In this paper, we address the end-to-end signal-to-noise ratio (SNR) gain by dual-hop multiple-input multiple-output (MIMO) relaying over the single-hop Alamouti transmission in Rayleigh fading channels. We deal with MIMO decode-and-forward (DF) relaying as well as MIMO decouple-and-forward (DCF) relaying that does not need decoding at the relay. To quantify the SNR gain, closed-form expressions of the probability of SNR gain are developed for both relaying schemes. The probability of SNR gain results in an explicit function of an average power ratio of the per-hop channel in dual-hop relaying to the single-hop channel. Numerical examples are used to verify the accuracy of our analysis and to show the impact of the power ratio, the relaying strategy and the relay location on the SNR gain, respectively.