Unequal Power Allocation and Generalized ESE for ODMA-Based Unsourced Random Access

Abstract

On-off division multiple access (ODMA) has emerged as a state-of-the-art unsourced random access (URA) scheme for massive machine-type communications. However, its performance is constrained by equal power allocation, which lacks a natural decoding order for successive interference cancellation, and by the elementary signal estimator (ESE) that relies on a Gaussian approximation for multiuser interference. To address these issues, we first propose a heuristic unequal power allocation where pattern vectors are assigned powers following an exponential distribution with a single tilt factor $\alpha$, and a Lloyd-Max quantizer is employed to produce a few discrete power steps, reducing interference randomness while preserving the SIC hierarchy. Second, we develop a generalized ESE (GESE) that selects up to $Q$ dominant interferers and exactly marginalizes over their discrete symbol combinations. Simulation results show that unequal power allocation noticeably improves the per-user probability of error (PUPE) under perfect active user detection, GESE with $Q=2$ or 3 already captures most of the gain, and the joint scheme achieves over 70% PUPE reduction in practical scenarios, with moderate complexity.