Performance Analysis of Dual-Hop AF Relaying Systems over Mixed $\eta{-}\mu$ and $\kappa{-} \mu$ Fading Channels

Abstract

This paper investigates the end-to-end performance of a dual-hop amplify-and-forward (AF) relaying communication system where the source-to-relay and the relay-to-destination channels are subject to different fading conditions. The relay is assumed to either possess perfect channel state information (CSI) or have a fixed gain. We consider the case where the one hop's channel is subject to <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\eta$</tex></formula> – <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\mu$</tex></formula> fading, whereas the other hop's channel is subject to <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\kappa$</tex></formula> – <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\mu$</tex> </formula> fading. This mixed fading propagation channel is capable of accurately modeling various practical dual-hop transmissions. Examples of such environments are encountered in micro-/macrocellular systems and/or hybrid satellite/terrestrial wireless communication systems, where typically, only the one hop's channel has a line-of-sight (LOS) component. For both CSI-assisted and fixed-gain relaying and for integer-valued fading parameters, exact analytical expressions in the form of rapidly convergent infinite series for the outage probability (OP) and average bit error probability (ABEP) of several modulation schemes are derived. Moreover, for CSI-assisted relaying and arbitrary-valued fading parameters, closed-form lower bounds [tight for high values of the signal-to-noise ratio (SNR)] for the OP and ABEP performance are obtained. The analysis is also substantiated by obtaining previously published equivalent performance expressions as special cases of our generic fading models, namely, those available for Nakagami- <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$m$</tex></formula> and Rice fading channels. In addition, the derived analytical expressions have been numerically evaluated, and the performance evaluation results have been further validated by comparing them with equivalent results that have been obtained by means of Monte Carlo computer simulations.