SER of Multiple Fixed Gain Amplify-and-Forward Relays with Receive Diversity

Multiple fixed gain amplify-and-forward (AF) relays with receive diversity is analyzed for the practical case of unbalanced hops with independent but non-identically distributed (i.n.d.) Rayleigh fading channels. We derive a new exact closed-form expression for the moment generating function (mgf) of the end-to-end signal-to-noise ratio (SNR). Our mgf is valid for the general case of arbitrary numbers of relays and arbitrary numbers of antennas at the destination. Based on this, we determine the exact and approximate symbol error rate (SER) for M-ary phase-shift keying. Our results provide new important insights into the joint impacts of the number of relays and the number of receive antennas on the system performance. Theoretical analysis is verified by simulation.