Performance bounds on average error rates using the AM-GM inequality and their applications in relay networks

Novel average bit or symbol error rate (BER/SER) bounds are obtained for systems with instantaneous signal-to-noise ratios (SNRs) given by a sum of O(N\) statistically independent non-negative random variables (RVs). Their tightness is quantified analytically at high SNR by calculating the SNR gap, and shown to be within O(1/N) of the true value. The bounds are most useful when the distribution of the sum is intractable. The bounds are illustrated with the maximum ratio combining (MRC), the combined average performance for amplify-and-forward (AF) relay networks using multiple relays, and AF multiple-input multiple-output (MIMO) single relay systems with beamforming (BF) using multiple antennas at the source, relay, and destination. As a result, the bounds lead us to obtain tight closed-form combined expressions for AF relay networks with multiple relays and with multiple antennas in fast fading, for the first time in the literature. In addition, applicability of the bounds to non-Gaussian noise is addressed. Finally, Monte-Carlo simulations confirm the tightness of the bounds.