NOMA-Aided Distributed Massive MIMO—A Graph-Theoretic Approach

A graph-theoretic framework is proposed to efficiently solve the sum rate maximization problems for non-orthogonal multiple-access (NOMA) aided distributed millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems. We reveal that this sum rate maximization problem can be decoupled into two sub-problems, namely a user-access point (AP) association/clustering sub-problem and a pilot resource allocation sub-problem. This decoupling reduces the computational complexity compared to the optimal solution, which can only be attained via an exhaustive search having a factorial-time complexity. In the first sub-problem, the APs optimally select a set of users possessing the highest average channel power gains. Thereby, the analog precoders are designed at each AP by exploiting the angular information of the selected set of users. In the second sub-problem, a set of limited orthogonal pilots is optimally reused/assigned among concurrently served users such that the pilot contamination is minimized. We propose a graph-theoretic solution to find practically-viable and computationally-efficient solutions to both these sub-problems having an overall polynomial-time complexity. We model the joint user-AP association and pilot resource allocation sub-problems as a bipartite graph matching problem and a vertex coloring problem, respectively. Thereby, we propose an algorithm to compute the minimum number of orthogonal pilots required for a given user-AP association/clustering. If the size of available pilot set is larger than the minimum required number of pilots, then it is always possible to assign pilots such that no two users, which are associated with the same AP, share the same pilot. Otherwise, the users, which have been assigned to same beam, are allowed share the pilots. By leveraging the benefits of graph-theoretic approach, we propose a pragmatic solution to the coexistence of NOMA and orthogonal multiple-access schemes to boost the achievable sum rate of distributed mmWave massive MIMO NOMA systems.