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 n(S) source antennas, n(R) relay antennas, and n(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 2 max {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.