A Novel Analytical Framework for Massive Grant-Free NOMA

In this paper, we consider a massive grant-free non-orthogonal multiple access (GF-NOMA) scheme, where devices have strict latency requirements and no retransmission opportunities are available. Each device chooses a pilot sequence from a predetermined set as its signature and transmits its selected pilot and data simultaneously. A collision occurs when two or more devices choose the same pilot sequence. Existing GF-NOMA schemes assume that a collision of at least one pair of users entails a collision for all simultaneously transmitting users, which is sub-optimal in terms of individual outage and system throughput. For that, we propose a novel framework, where collisions are treated as interference to the remaining received signals. With the aid of Poisson point processes and ordered statistics, we derive simplified expressions that can well approximate the outage probability and throughput of the system for both successive joint decoding (SJD) and successive interference cancellation (SIC). Numerical results verify the accuracy of our analytical expressions. For low data rate transmissions, results show that the performance of SIC is close to that of SJD in terms of outage probability, for packet arrival rates up to 10 packets per slot. However, SJD can achieve almost double the throughput of SIC and is, thus, far more superior.