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Abstract-In this letter, we propose a robust beamforming design for non-orthogonal multiple access (NOMA) based multiple-input single-output (MISO) downlink systems. In particular, the robust power minimization problem is studied with imperfect channel state information (CSI), where the beamformers are designed by incorporating norm-bounded channel uncertainties to provide the required quality of service at each user. This robust scheme is developed based on the worst-case performance optimization framework. In terms of beamforming vectors, the original robust design is not convex and therefore, the robust beamformers cannot be obtained directly. To circumvent this non-convex issue, the original intractable problem is reformulated into a convex problem, where the non-convex constraint is converted into a linear matrix inequality (LMI) by exploiting S-Procedure. Finally, simulation results are provided to demonstrate the effectiveness of the proposed robust design.

Abstract-In this paper, we develop various beamforming techniques for downlink transmission for multiple-input single-output (MISO) non-orthogonal multiple access (NOMA) systems. First, a beamforming approach with perfect channel state information (CSI) is investigated to provide the required quality of service (QoS) for all users. Taylor series approximation and semidefinite relaxation (SDR) techniques are employed to reformulate the original non-convex power minimization problem to a tractable one. Further, a fairness-based beamforming approach is proposed through a max-min formulation to maintain fairness between users. Next, we consider a robust scheme by incorporating channel uncertainties, where the transmit power is minimized while satisfying the outage probability requirement at each user. Through exploiting the SDR approach, the original non-convex problem is reformulated in a linear matrix inequality (LMI) form to obtain the optimal solution. Numerical results demonstrate that the robust scheme can achieve better performance compared to the non-robust scheme in terms of the rate satisfaction ratio. Further, simulation results confirm that NOMA consumes a little over half transmit power needed by OMA for the same data rate requirements. Hence, NOMA has the potential to significantly improve the system performance in terms of transmit power consumption in future 5G networks and beyond.Index Terms-Non-orthogonal multiple access (NOMA), Maxmin fairness, Robust beamforming, Outage Probability.

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In this paper, we propose a device to device (D2D) communication scenario underlaying a cellular network where both D2D and cellular users (CUs) are discrete power-rate systems with limited feedback from the receivers. It is assumed that there exists an adversary which wants to eavesdrop on the information transmission from the base station (BS) to CUs. Since D2D communication shares the same spectrum with cellular network, cross interference must be considered. However, when secrecy capacity is considered, the interference caused by D2D communication can help to improve the secrecy communications by confusing the eavesdroppers. Since both systems share the same spectrum, cross interference must be considered. We formulate the proposed resource allocation into an optimization problem whose objective is to maximize the average transmission rate of D2D pair in the presence of the cellular communications under average transmission power constraint. For the cellular network, we require a minimum average achievable secrecy rate in the absence of D2D communication as well as a maximum secrecy outage probability in the presence of D2D communication which should be satisfied. Due to high complexity convex optimization methods, to solve the proposed optimization problem, we apply Particle Swarm Optimization (PSO) which is an evolutionary approach. Moreover, we model and study the error in the feedback channel and the imperfectness of channel distribution information (CDI) using parametric and nonparametric methods. Finally, the impact of different system parameters on the performance of the proposed scheme is investigated through simulations. The performance of the proposed scheme is evaluated using numerical results for different scenarios.