Joint Optimization Framework for User Clustering, Downlink Beamforming, and Power Allocation in MIMO NOMA Systems

In this paper, we investigate the application of downlink beamforming along with non-orthogonal multiple access (NOMA) in a multi-user multiple-input multiple-output (MIMO) system. The joint optimization framework for user clustering, downlink beamforming and power allocation scheme is formulated as a novel mixed-integer non-linear program (MINLP), where the aim is to minimize the total transmission power while satisfying quality-of-service (QoS), user clustering and power constraints. Owing to the non-convexity and combinatorial nature of the problem, obtaining an optimal solution is challenging. To tackle this issue, we first develop an algorithm based on branch-and-bound (BB), whereby the feasible space is successively partitioned and searched by means of lower and upper bounds on the objective function. While this algorithm is shown to return an
$\epsilon $
-optimal solution within a finite number of iterations, it entails high computational complexity. Considering this limitation, we then reformulate the original problem into a more tractable form and conceive a low-complexity algorithm for its solution based on the penalty dual-decomposition technique. The proposed joint design algorithms for MIMO NOMA are evaluated by means of simulations over mmWave channels. Results show significant improvements in terms of total transmit power and spectral efficiency compared to benchmark approaches.