Massive Uncoordinated Access With Random User Activity

TL;DR

This paper extends the analysis of massive uncoordinated access to scenarios with unknown and random active user counts, deriving bounds that quantify the power efficiency loss and evaluating the optimality of existing schemes.

Contribution

It introduces a new random-access coding framework for Gaussian channels with unknown user activity, providing achievability bounds that account for misdetection and false alarms.

Findings

A small power penalty (0.5-0.7 dB) is needed when user count is unknown.

The derived bounds show some recent schemes are highly suboptimal.

Lack of knowledge of active users causes minimal efficiency loss.

Abstract

We extend the seminal work by Polyanskiy (2017) on massive uncoordinated access to the case where the number of active users is random and unknown a priori. We define a random-access code accounting for both misdetection (MD) and false alarm (FA), and derive a random-coding achievability bound for the Gaussian multiple-access channel. Our bound captures the fundamental trade-off between MD and FA probabilities. The derived bound suggests that, for the scenario considered in Polyanskiy (2017), lack of knowledge of the number of active users entails a small penalty in terms of power efficiency. For example, our bound shows that 0.5-0.7 dB extra power is required to achieve both MD and FA probabilities below 0.1 compared to the case in which the number of active users is known a priori. Taking both MD and FA into account, we show that some of the recently proposed massive random access schemes are highly suboptimal with respect to our bound.