Joint Power and Data Allocation in Multi-Carrier Full-Duplex Relaying Networks Operating With Finite Blocklength Codes

Abstract

In this paper, we study a full-duplex (FD) relaying network operating with finite blocklength (FBL) codes. Based on Polyanskiy’s FBL model, we characterize the FBL reliability of the relaying network under both decode-and-forward (DF) and amplify-and-forward (AF) relaying schemes. Based on the characterisation, we provide reliability-optimal designs via optimal power allocation for both schemes in a single-carrier scenario. In particular, we prove that under the FD DF relaying scheme the (tightly approximated) overall error probability is convex in the transmit power at the relay. In addition, we show that minimizing the overall error probability of the FD AF relaying is equivalent to maximizing the overall signal to interference plus noise ratio (SINR), which is further proved to be pseudo-concave. Then, the designs for a single-carrier scenario are further extended to a multi-carrier scenario with a joint power and data allocation among carriers. In particular, for either the FD DF or FD AF relaying scheme, a joint optimization problem is reformulated to a single problem maximizing the reliability via finding and achieving the optimal SINRs, while auxiliary variables are introduced in FD AF relaying to facilitate the reformulation. Based on mathematical analysis, we respectively construct convex approximations and subsequently propose iterative algorithms, with which the error probability is reduced iteratively until an eventual convergence to an efficient suboptimal value. Hence, a corresponding suboptimal data and power allocation solution can be constructed for the multi-carrier scenario. Via numerical analysis, we validate our analytical model and the proposed allocation algorithms. The FD DF and FD AF relaying schemes are compared with direct transmission in both single-carrier and multi-carrier scenarios, and the benefits of applying FD relaying schemes and joint optimization among multiple carriers are observed.