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

Abstract

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 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.