Fundamental Limits of Random Access Communication with Retransmissions

We consider a single cell wireless uplink in which randomly arriving devices transmit their payload to a receiver. We study the following problem. Given SNR, target outage rate, payload size per user, total symbol resources N, due to a stringent latency constraint over a fixed total available bandwidth, the resources are partitioned into B bins and maximum number of retransmission attempts M of N=(MB) resources each per retransmission attempt, we characterize the maximum average rate or number of Poisson arrivals that can successfully complete the random access procedure such that the probability of outage is sufficiently small. We analyze the proposed setting for two different regimes: i) noise limited regime with small SNR and ii) interference limited regime with large SNR. We show that i) in the noise limited regime B = M = 1, in which all devices share the resources, and ii) in the interference limited regime, B scales with the number of resource symbols such that devices do not experience any interference, and M that can be determined as a function of the outage constraint. We also study the same random access problem by incorporating Rayleigh fading to model the channel power gain distribution. Although the variability of the channel causes a drop in the number of arrivals that can successfully complete the random access phase, we show that similar scaling results extend to the Rayleigh fading case. Index Terms-IoT, machine-to-machine communications, random access, latency constraint, resource allocation.