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 𝓃ssource antennas, 𝓃Rrelay antennas, and 𝓃Ddestination 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 dAF≤nSnD+nSnRnD/max{nS,nR,nD} with the equality if 2max{nS,nR,nD}≥nS+nR+nD-1. This finding reveals that the number of relay antennas greater than or equal to nS+ nD- 1 is required to achieve the additional diversity order nSnDby scalar-gain AF relaying. We also present the asymptotic SEP as the number of relay antennas tends to infinity.