Performance of Cooperative Multi-Hop Wireless Systems over Log-Normal Fading Channels

In recent years, there has been a growing interest in antenna sharing systems, and many analytical frameworks have been developed to analyze the performance of various relying protocols in a variety of propagation environments. However, among the different propagation scenarios, the less investigated are those characterized by log-normal fading. Motivated by this consideration, we propose a comprehensive framework for performance analysis of multi-hop multi-branch wireless systems over log-normal fading channels. More specifically, the developed framework allows to estimate the performance of amplify and forward (AF) relay methods for both channel state information (CSI-) assisted analog relays, and semi-blind and blind analog relays. In particular, the contribution of the paper is twofold: i) first of all, by relying on the Gauss quadrature rule (GQR) representation of the moment generation function (MGF) for a log-normal distribution, we develop very accurate formulas for important performance indexes; ii) then, in order to simplify the computational burden of the former framework for some system setups, we also propose an approximation, which is based on the improved Schwartz-Yeh (I-SY) method. We show with numerical and simulation results that the proposed approximation provides a good trade-off between accuracy and complexity.