Massive Uncoordinated Access With Random User Activity

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. It suggests that lack of knowledge of the number of active users entails a small penalty in power efficiency. For a typical scenario, to achieve both MD and FA probabilities below 0.1, the required energy per bit predicted by our bound is 0.5–0.7 dB higher than that predicted by the bound in Polyanskiy (2017) for a known number of active users. Taking both MD and FA into account, we use our bound to benchmark the energy efficiency of some recently proposed massive random access schemes.