Performance Analysis of Dual-Hop Multi-Relaying with Max-Mini Relay Selection over Composite Fading Channels

In dual-hop multi-relaying wireless systems, the non-closed form expression in log-normal probability distributions and high varying standard deviations makes it impossible to effectively execute performance analyses of outage probability and bit-error-rate (BER) performance levels; thus, an analysis framework was proposed for use in a composite (Rayleigh plus log-normal) fading channel. Developing analytical derivations involved generalizing the standard approaches for the probability density function (PDF) and the cumulative density function (CDF) of a composite fading channel at a conditioned constraint; that is, the signalto-noise power (SNR) of relay hop segments is relatively high to the targeted threshold when the max-mini relay selection scenario is adopted. The analytical deviations of outage probability and BER performance levels are closed-form expressions that are corroborated using Monte Carlo simulations and exact expression (integral form), yielding consistent results. Thus, the proposed analysis framework provides a simple and efficient approach for evaluating the influence of the shadowing effect and diversity order in system design applications. Index Terms –amplify-and-forward (AF) relay, bit-error-rate (BER), cumulative density function (CDF), dual-hop multirelaying, log-normal fading, moment generation function (MGF), outage probability, probability density function (PDF), Rayleigh fading, standard deviation.