Exact and Asymptotic SER of Receive Diversity in Multiple Amplify-And-Forward Relaying

Multiple amplify-and-forward (AF) relays with receive diversity is analyzed over unbalanced hops with independent but not necessarily identically distributed Rayleigh fading. Exact closed-form expressions are derived for the moment generating function of the end-to-end signal-to-noise ratio (SNR) at the destination. Our analysis apply to arbitrary numbers of relays and arbitrary numbers of antennas at the destination. Based on the derived results, we determine the symbol error rate with M-ary phase-shift keying. In addition, we carry out an asymptotic analysis in the high SNR regime. Our results provide fundamental insights into the impact of the number of antennas on the performance of multiple AF relaying. We explicitly reveal that the diversity order is equal to the sum of the number of relays and the number of antennas. Theoretical analysis is verified by simulation.