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

TL;DR

This paper evaluates the accuracy of using distance-based user ranking instead of instantaneous channel gains in NOMA systems, providing analytical insights into when this approximation is valid under various fading and spatial models.

Contribution

It derives the probability that distance-based ranking matches instantaneous signal power ranking in Nakagami-m fading environments with different user distributions.

Findings

Distance-based ranking can be accurate under certain fading conditions.

The accuracy probability varies with user distribution and fading parameters.

Implications for system analysis and implementation are discussed.

Abstract

We characterize the accuracy of analyzing the performance of a NOMA system where users are ranked according to their distances instead of instantaneous channel gains, i.e., product of distance-based path-loss and fading channel gains. Distance-based ranking 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 in a NOMA system has a direct impact on coverage probability analysis, 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 to instantaneous signal power-based ranking, is acceptable for 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. We illustrate the impact of accuracy probability on uplink and downlink coverage probability.