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On the performance of massive grant-free NOMA

Many uplink grant-free non-orthogonal multiple access (NOMA) schemes have been recently proposed to solve the massive access problem of M2M communications. However, little has been done on characterizing the performance bounds for such systems. In this paper, we take a step forward in this direction. We consider an uncoordinated NOMA scheme where devices have strict latencies and no retransmission opportunities are available. Devices choose pilot sequences from a predetermined set uniformly at random. Then, each device encodes its data using the pilot as the signature and transmits its selected pilot and data simultaneously with the rest of the devices. A collision occurs when two or more devices choose the same pilot sequence. Collisions are regarded as interference to the remaining set of transmitting devices. We first show that this interference can be well-approximated by a PPP. Then, we derive the average system throughput under joint decoding and massive access for a Rayleigh fading and path loss channel model. Our numerical results verify the accuracy of our derived analytical expressions. Finally, we investigate the impact of finite block lengths on the system throughput, i.e., when the decoding error probability is strictly non-zero. We show that we can support more than 10 packets per slot when the pilot sequences are large enough.