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In this paper, we investigate the resource allocation problem for a full-duplex (FD) massive multiple-input-multiple-output (mMIMO) multi-carrier (MC) decode and forward (DF) relay system which serves multiple MC single-antenna half-duplex (HD) nodes. In addition to the prior studies focusing on maximizing the sum-rate and energy efficiency, we focus on minimizing the overall delivery time for a given set of communication tasks to the user terminals. As our system is an FD MC system, we consider the impact of hardware distortions resulting in residual self-interference and inter-carrier leakage. We also consider that only limited channel state information is available. A joint power and sub-carrier allocation problem to maximize the sum-rate of the system is then formulated. Due to the intractable nature of the underlying problem, an iterative solution is proposed, employing the successive inner approximation (SIA) framework, with guaranteed convergence to the point that satisfies the Karush-Kuhn-Tucker (KKT) conditions. For the energy efficiency maximization problem, a two-stage iterative algorithm which follows the SIA and Dinkelbach algorithm is proposed. The operation of an FD mMIMO MC DF relay system is evaluated for different system parameters using numerical simulations. We also show the importance of considering delivery time minimization rather than sum-rate maximization, i.e., maximizing the sum-rate of the system does not necessarily minimize the overall delivery time. Numerical results show the significance of distortion-aware design for such systems and also the significant gain in terms of different objectives such as sum-rate, energy efficiency, and delivery time compared to its HD counterpart.
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