A unified approach for the fading statistics of heterogeneous compound channels in transparent relay transmissions

In this paper, we address the challenging issue of multi-hop cooperative relaying over heterogeneous compound channels, where constituent channels can incorporate topographical variations and respective distribution changes (due to environmental factors). Existing methods in the literature address various issues pertinent to receiver design by assuming a homogeneous framework. Since real-time signal level monitoring at the relay node is impractical in transparent relaying, statistical knowledge of the end-to-end channel is critical for an energy-efficient system design. As the received signal quality and hence the signal-to-noise ratio (SNR) depend on the channel condition, an exact characterisation of the end-to-end compound channel is essential for the implementation of transparent relay networks in a particular coverage area. This demands a realistic heterogeneous compound channel model, having distinct component distributions, that can accommodate variations in per-hop channel distribution. Exact probability density function and cumulative distribution function of the end-to-end compound channel are derived in closed form, through an inverse Mellin transform approach. As there can be many combinations of heterogeneous channels, we propose a unified approach for deriving statistical properties of interest. Two typical cases of heterogeneous channels, Nakagami×Weibull and Rayleigh×Weibull, are considered to validate the proposed generic analytical approach. Based on the derived exact statistics of these models, performance metrics, such as coefficient of variation, average SNR, outage probability, and average SER, are evaluated. Through appropriate use of these metrics, optimal power boosting at the relays and quality stream selection for arbitrary diversity combiner units can be done. The pertinent analytical results are also validated through simulation studies to demonstrate the accuracy and applications of the results.