Joint Impact of Hardware Impairments and Imperfect Channel State Information on Multi-Relay Networks

In this paper, we investigate the performance of dual-hop (DH) decode-and-forward (DF) multi-relay networks, for which two practical deleterious factors are taken into account, namely hardware impairments (HIs) and imperfect channel state information (ICSI). The communication between the source and the destination is realized with the aid of DF multi-relays, where both hops are assumed to be independent but non-identically distributed alpha-mu fading. Aiming at improving the system performance, three representative relay selection strategies are considered, in which the best relay is selected according to the link quality of source-to-relay and/or relay-to-destination. To characterize the performance of the proposed strategies, two key performance metrics, namely outage probability (OP) and ergodic capacity (EC), are analyzed insightfully. We first derive closed-form expressions for both exact and asymptotic OPs. Utilizing the derived results, diversity orders achieved at the destinations are obtained. We demonstrate that the OPs of considered networks are limited by HIs and ICSI, and the diversity orders are zeros due to the presence of ICSI. Then, we study the ECs of the proposed relay selection schemes, and upper bounds for the EC and asymptotic expressions for the EC in the high signal-to-noise ratio (SNR) regime are derived. To obtain more insights, the affine expansions for the EC are involved by two metrics of high-SNR slope and high-SNR power offset. It is shown that there are rate ceilings for the EC due to HIs and ICSI, which result in zero high-SNR slopes and finite high-SNR power offsets.