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This paper investigates the outage probability and rate performance of multi-hop full duplex (FD) and half duplex (HD) decode-and-forward (DF)-based relay networks. First of all, we derive new closed form equation for the end-to-end outage probability of multi-hop FDR system taking into account the inter-relay interference (IRI), i.e., interference caused by simultaneous transmissions by the nodes in non-orthogonal frequency bands, and the residual self-interference (RSI) present at the full duplex relay (FDR) nodes, in independent non-identical Nakagami-m fading channels. We also derive an approximate expression for the outage probability which is found to be highly accurate. Further, we provide an asymptotic expression as well, for Rayleigh fading channels. Furthermore, we derive exact and approximate expression for the outage probability of multi-hop spectral efficient HDR network that employ two-phase relaying. We then consider optimal power allocation (OPA) for multi-hop FDR and HDR networks that maximizes the end-to-end transmission rate with individual peak power constraint at the nodes. Since the optimization problem is non-convex, we develop an efficient, low-complex and fast-converging iterative algorithm for power allocation based on sequential convex programming. Secondly, we consider OPA for multi-hop FDR and HDR networks that minimizes the end-to-end outage probability with individual peak power constraints at the nodes. We devise geometric programming (GP) to obtain the OPA vector. The results demonstrate that OPA can significantly improve the outage and end-to-end rate performance of both FDR and HDR networks as compared to uniform power allocation policy. The results from the analytical model are validated by extensive Monte Carlo simulations.

Outage probability analysis and optimal transmit power allocation for multi-hop full duplex relay network over Nakagami-m fading channels