Sparse NOMA: An Achievable Region via Random Coordinate Transformations

In the quest for efficient multiple access schemes for future wireless systems, sparse code-domain non-orthogonal multiple access (NOMA) has gained considerable interest, potentially achieving significant performance enhancement in overloaded settings at feasible complexity. This paper revisits an uplink model with two classes of users distinguished by their received powers, each employing regular sparse code-domain NOMA (where a fixed and finite number of orthogonal resources is occupied by each user and vice versa). Introducing random coordinate transformations, the achievable ergodic class throughput region is analytically specified in the large system limit, and shown to strictly contain the achievable region with randomly spread dense code-domain NOMA, while closing the gap to the Cover-Wyner capacity region. Furthermore, harnessing tools from free probability theory, an exact closed form expression is derived for the total achievable sum-rate, which has been so far characterized in analogous settings by means of lower and upper bounds. The analysis significantly broadens the information theoretic perspective on code-domain NOMA applications, and establishes key tools for generalizing the results to more complex models for future systems.