A Tutorial on Clique Problems in Communications and Signal Processing

Since its first use by Euler on the problem of the seven bridges of K\"onigsberg, graph theory has shown excellent abilities in solving and unveiling the properties of multiple discrete optimization problems. The study of the structure of some integer programs reveals equivalence with graph theory problems making a large body of the literature readily available for solving and characterizing the complexity of these problems. This tutorial presents a framework for utilizing a particular graph theory problem, known as the clique problem, for solving communications and signal processing problems. In particular, the paper aims to illustrate the structural properties of integer programs that can be formulated as clique problems through multiple examples in communications and signal processing. To that end, the first part of the tutorial provides various optimal and heuristic solutions for the maximum clique, maximum weight clique, and $k$-clique problems. The tutorial, further, illustrates the use of the clique formulation through numerous contemporary examples in communications and signal processing, mainly in maximum access for non-orthogonal multiple access networks, throughput maximization using index and instantly decodable network coding, collision-free radio frequency identification networks, and resource allocation in cloud-radio access networks. Finally, the tutorial sheds light on the recent advances of such applications, and provides technical insights on ways of dealing with mixed discrete-continuous optimization problems

Beamforming Techniques for Non-Orthogonal Multiple Access in 5G Cellular Networks

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.Comment: accepted to publish in IEEE Transactions on Vehicular Technolog

Cache-Aided Non-Orthogonal Multiple Access

In this paper, we propose a novel joint caching and non-orthogonal multiple access (NOMA) scheme to facilitate advanced downlink transmission for next generation cellular networks. In addition to reaping the conventional advantages of caching and NOMA transmission, the proposed cache-aided NOMA scheme also exploits cached data for interference cancellation which is not possible with separate caching and NOMA transmission designs. Furthermore, as caching can help to reduce the residual interference power, several decoding orders are feasible at the receivers, and these decoding orders can be flexibly selected for performance optimization. We characterize the achievable rate region of cache-aided NOMA and investigate its benefits for minimizing the time required to complete video file delivery. Our simulation results reveal that, compared to several baseline schemes, the proposed cache-aided NOMA scheme significantly expands the achievable rate region for downlink transmission, which translates into substantially reduced file delivery times.Comment: Accepted for presentation at IEEE ICC 201