On-Off Random Access Channels: A Compressed Sensing Framework

TL;DR

This paper models on-off random multiple access channels using compressed sensing, demonstrating that sparse signal detection algorithms like OMP can effectively identify active users, with new algorithms improving high SNR performance.

Contribution

It introduces a compressed sensing framework for on-off random access channels and proposes sequential OMP, enhancing multiuser detection performance at high SNRs.

Findings

OMP and lasso outperform single-user detection

Sequential OMP improves high SNR capacity

Power shaping enhances detection performance

Abstract

This paper considers a simple on-off random multiple access channel, where n users communicate simultaneously to a single receiver over m degrees of freedom. Each user transmits with probability lambda, where typically lambda n < m << n, and the receiver must detect which users transmitted. We show that when the codebook has i.i.d. Gaussian entries, detecting which users transmitted is mathematically equivalent to a certain sparsity detection problem considered in compressed sensing. Using recent sparsity results, we derive upper and lower bounds on the capacities of these channels. We show that common sparsity detection algorithms, such as lasso and orthogonal matching pursuit (OMP), can be used as tractable multiuser detection schemes and have significantly better performance than single-user detection. These methods do achieve some near-far resistance but--at high signal-to-noise ratios (SNRs)--may achieve capacities far below optimal maximum likelihood detection. We then present a new algorithm, called sequential OMP, that illustrates that iterative detection combined with power ordering or power shaping can significantly improve the high SNR performance. Sequential OMP is analogous to successive interference cancellation in the classic multiple access channel. Our results thereby provide insight into the roles of power control and multiuser detection on random-access signalling.