Performance analysis of multi-branch multi-hop wireless relay systems over log-normal channels

In this paper, analytical models are proposed to study the performance of amplify-and-forward (AF) multi-branch multi-hop (MBMH) wireless relay systems (WRS) over log-normal fading channels. The presented analytical models are used to estimate the end-to-end performance of the MBMH WRS with maximal ratio combining (MRC) and selection combining (SC) schemes. In particular, we derive closed-form expressions for the parameters of the end-to-end signal-to-noise ratio (SNR) of an AF multi-hop chain relay link. Further, we characterize the distribution of the end-to-end SNR and derive closed-form expressions for the mean and standard deviation of the end-to- end SNR's natural logarithm for AF MBMH WRS with MRC scheme, and the probability density function (pdf) for the end-to-end SNR of AF MBMH WRS with SC scheme. Then, under MRC and SC schemes, we analyze the diversity gain by adopting asymptotical relative diversity order (ARDO) and develop accurate analytical expressions for average bit error probability, outage probability, and ergodic capacity, respectively. Our analysis reveals that the computational complexity of the proposed models is acceptably low for practical applications. Numerical and Monte Carlo simulation results are presented to substantiate the accuracy of the proposed analytical models.