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) systems. Specifically, we consider an ISaC framework where the radar signal is designed to be orthogonal to the communication signal over two symbol periods, ensuring complete interference elimination when decoding consecutive symbol pairs. This approach resembles multi-symbol rate NOMA, except that the radar waveform, carrying no data, is explicitly designed to be orthogonal to the transmitted communication signal. To mitigate potential decision ambiguities during pairwise data detection, a constant phase offset is applied to adjacent communication symbols at the transmitter. We analyze system performance by deriving closed-form expressions for the exact BER using zero-forcing (ZF) receivers. Additionally, we present closed-form upper bound expressions for BER and outage probability for both ZF and joint maximum likelihood (JML) detectors. Furthermore, we evaluate the detection and false alarm probability performance of the radar system, demonstrating that the analytical results align with simulations. The derived expressions offer valuable insights into the performance of this novel ISaC system, highlighting the impact of key parameters and illustrating how the ZF receiver balances performance and complexity compared to the JML receiver under a variety of conditions and system settings.