Performance Analysis of Pair-wise Symbol Detection in Uplink NOMA-ISaC Systems

This paper investigates the bit error rate (BER) and outage probability performance of integrated sensing and communication (ISaC) in uplink non-orthogonal multiple access (NOMA) based Internet of Things (IoT) systems. Specifically, we consider an ISaC system where the radar signal is designed to be orthogonal to the communication signal over two symbol periods so that its interference on the communication signal is completely eliminated when detecting the data in pairs of consecutive symbols. This is akin to multi-symbol rate NOMA systems except in this case as the radar bears no data, its waveform is manipulated to be orthogonal to the transmitted communication signal. To eliminate potential decision ambiguity during the pair-wise data detection, a constant phase-offset between adjacent communication symbols is applied at the transmitter. The performance of such a system is analyzed through deriving analytical expressions for the exact BER of zero-forcing (ZF) based receivers. In addition, close-form expressions for the upper BER bound and the outage probability for both ZF and the joint maximum likelihood (JML) receivers are presented. The results show that the derived expressions are perfectly matched with the simulation results. The obtained expressions provide an insight into the performance of this novel ISaC system including demonstrating the impact of various parameters and showing how the ZF receiver provides a useful trade-off between performance and complexity relative to the JML receiver.