Accuracy of Distance-Based Ranking of Users in the Analysis of NOMA Systems

We characterize the accuracy of analyzing the performance of a non-orthogonal multiple access (NOMA) system where users are ranked according to their distances instead of instantaneous channel gains, i.e., product of their distance-based path-loss and fading channel gains. Distance-based ranking of users is analytically tractable and can lead to important insights. However, it may not be appropriate in a multipath fading environment where a near user suffers from severe fading while a far user experiences weak fading. Since the ranking of users (and in turn interferers) in an NOMA system has a direct impact on coverage probability analysis, the impact of the traditional distance-based ranking, as opposed to instantaneous signal power-based ranking, needs to be understood. This will enable us to identify scenarios where distance-based ranking, which is easier to implement compared with instantaneous signal power-based ranking, is acceptable for the system performance analysis. To this end, in this paper, we derive the probability of the event when distance-based ranking yields the same results as instantaneous signal power-based ranking, which is referred to as the accuracy probability. We characterize the probability of accuracy considering Nakagami-m fading channels and three different spatial distribution models of user locations in NOMA, namely, the Poisson point process (PPP), the Matern cluster process (MCP), and the Thomas cluster process (TCP). For all these models of users' locations, we assume that the spatial locations of the base stations (BSs) follow a homogeneous PPP. We show that the accuracy probability decreases with the increasing number of users and increases with the path-loss exponent. In addition, through examples, we illustrate the impact of accuracy probability on uplink and downlink coverage probabilities. Closed-form expressions are presented for the Rayleigh fading environment. The effects of fading severity and users' pairing on the accuracy probability are also investigated.