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To mitigate the radar and communication frequency overlapping caused by massive devices access, we propose a novel joint communication and sensing (JCS) system in this paper, where a micro base station (MiBS) can realize target sensing and cooperative communication simultaneously. Concretely, the MiBS, as the sensing equipment, can also serve as a full-duplex (FD) decode-and-forward (DF) relay to assist the end-to-end communication. To further improve the spectrum utilization, non-orthogonal multiple access (NOMA) is adopted such that the communication between the macro base station (MaBS) and the Internet-of-Things (IoT) devices. To facilitate the performance evaluation, the exact and asymptotic outage probabilities, ergodic rates, sensing probability of the system are characterized. Subsequently, two optimal power allocation (OPA) problems of maximizing the received signal-to-interference-plus-noise ratio of sensing signal and maximizing the sum rate for communication are designed that are solved by means of the Lagrangian method and function monotonicity. The simulation results demonstrate that: 1) the proposed JCS NOMA system can accomplish both communication enhancement and sensing function under the premise of the same power consumption as non-cooperative NOMA; 2) the proposed OPA schemes manifest superiorities over a random power allocation scheme.