Modeling and Analysis of Uplink Non-Orthogonal Multiple Access (NOMA) in Large-Scale Cellular Networks Using Poisson Cluster Processes

Abstract

Using the theory of Poisson cluster process (PCP), this paper provides a framework to analyze multi-cell uplink non-orthogonal multiple access (NOMA) systems. Specifically, we characterize the rate coverage probability of an NOMA user who is at rank $m$ (in terms of the distance from its serving base station) among all users in a cell and the mean rate coverage probability of all users in a cell. Since the signal-to-interference-plus-noise ratio of the $m$ th user relies on efficient successive interference cancellation (SIC), we consider three scenarios, i.e., perfect SIC (in which the signals of $m-1$ interferers who are stronger than the $m$ th user are decoded successfully), imperfect SIC (in which the signals of $m-1$ interferers who are stronger than the $m$ th user may or may not be decoded successfully), and imperfect worst case SIC (in which the decoding of the signal of the $m$ th user is always unsuccessful whenever the decoding of its relative $m-1$ stronger users is unsuccessful). To derive the rate coverage expressions, we first characterize the Laplace transforms of the intra-cluster interferences in closed-form considering various SIC scenarios. The Laplace transform of the inter-cluster interference is then characterized by exploiting distance distributions from geometric probability. The derived expressions are customized for an equivalent OMA system. Finally, numerical results are presented to validate the derived expressions. The worst case SIC assumption provides remarkable simplifications in the mathematical analysis and is found to be highly accurate for higher user target rate requirements. A comparison of Poisson point process-based and PCP-based modeling is also conducted.