Outage Statistics of Hybrid Double-RIS System Assisted by Aerial AF-Relay for Multi-hop Communications

This paper considers single-input single-output (SISO) multi-hop wireless communication system (M-WCS) that consists of two dual-hop re-configurable intelligent surface (RIS)-enabled links that are connected by a unmanned aerial vehicle (UAV)-amplify-and-forward relay (AFR) in order to extend coverage. In particular, probability density function (PDF) $p_{R_{2}^{2}}(\gamma_{tr,2})$ and cumulative distribution function (CDF) $F_{R_{2}^{2}}(\gamma_{tr,2})$ of end-to-end SNR for the hybrid double RIS-enabled communications (RIS-ECs) with a UAV-AFR over dissimilar Rayleigh-Nakagami-m fading channels are derived. Capitalizing on the obtained mathematical expressions the system performance analysis in terms of outage probability (OP) $P_{R_{2}^{2}}(\gamma_{tr,2})$ is further performed, graphically presented and analysed for different number of RIS modules and under various severity conditions. Moreover, we provide comparison between double RIS-ECs link with UAV-AFR and RIS-ECs link without UAVAFR in terms of outage statistics. It is further analysed that the RIS-ECs with UAV-AFR can not only extend the coverage but also can be deployed with sufficiently large number of RIS elements to improve the system performances.