MIMO Cooperative Diversity with Scalar-Gain Amplify-and-Forward Relaying

We analyze diversity performance of scalar fixed- gain amplify-and-forward (AF) cooperation in multiple-input multiple-output (MIMO) relay channels with s source antennas, R relay antennas, and D destination antennas. We first derive the exact symbol error probability (SEP) for maximum likelihood decoding of orthogonal space-time block codes with M-ary phase-shift keying modulation over such channels and then characterize the effect of MIMO cooperative diversity on SEP behavior in a high signal-to-noise ratio regime. We show that the simple scalar-gain AF cooperation can create the diversity order d AF ≤n S n D +n S n R n D /max{n S ,n R ,n D } with the equality if 2max{n S ,n R ,n D }≥n S +n R +n D -1. This finding reveals that the number of relay antennas greater than or equal to n S + n D - 1 is required to achieve the additional diversity order n S n D by scalar-gain AF relaying. We also present the asymptotic SEP as the number of relay antennas tends to infinity.