Covert Communication in Uplink NOMA Systems Against a Two-Phase Detector

In this paper, we investigate the covert communications in uplink nonorthogonal multiple access (NOMA) systems with the random power allocation and multi-carrier modulation scheme to confront a two-phase detector. In the NOMA system, a covert user (CU) and a reliable user (RU) transmit messages to Bob, in the presence of a warden (Willie) who tries to detect CU's transmission behavior. A two-phase detector, i.e., energy detection and similarity detection phases, is designed to improve the detection performance. In addition, we propose a random power allocation and multi-carrier modulation scheme to cover CU's transmissions. For the proposed scheme, the expected minimum detection error probability (EMDEP) and connection outage probabilities (COPs) at RU and CU are derived in closed-form expressions. The maximum expected covert rate (ECR) is analyzed under covertness and reliability constraints. Numerical results show that the proposed two-phase detector has a lower EMDEP, and the multi-carrier modulation scheme improves the covertness performance.