Sparse NOMA: A Closed-Form Characterization

TL;DR

This paper derives a closed-form expression for the spectral efficiency of regular sparse NOMA in large systems, showing it outperforms RS-CDMA and approaches fundamental bounds, thus advancing understanding of future cellular system limits.

Contribution

It provides the first rigorous closed-form analytical characterization of spectral efficiency for regular sparse NOMA, extending classical formulas and demonstrating its superior efficiency.

Findings

Regular sparse NOMA is more spectrally efficient than RS-CDMA.

The derived formulas extend Verdú-Shamai results to sparse NOMA.

Sparse NOMA approaches fundamental capacity bounds in overloaded systems.

Abstract

Understanding fundamental limits of the various technologies suggested for future 5G and beyond cellular systems is crucial for developing efficient state-of-the-art designs. A leading technology of major interest is non-orthogonal multiple-access (NOMA). In this paper, we derive an explicit rigorous closed-form analytical expression for the optimum spectral efficiency in the large-system limit of regular sparse NOMA, where only a fixed and finite number of orthogonal resources are allocated to any designated user, and vice versa. The basic Verd\'u-Shamai formula for (dense) randomly-spread code-division multiple-access (RS-CDMA) turns out to coincide with the limit of the derived expression, when the number of orthogonal resources per user grows large. Furthermore, regular sparse NOMA is rigorously shown to be spectrally more efficient than RS-CDMA across the entire system load range. It may therefore serve as an efficient means for reducing the throughput gap to orthogonal transmission in the underloaded regime, and to the ultimate Cover-Wyner bound in overloaded systems. The results analytically reinforce preliminary conclusions in [1], which mostly relied on heuristics and numerical observations. The spectral efficiency is also derived in closed form for the suboptimal linear minimum-mean-square-error (LMMSE) receiver, which again extends the corresponding Verd\'u-Shamai LMMSE formula to regular sparse NOMA.