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In light of the novel concept of authorized/licensed shared access, in this paper, we consider the spectrum sharing between a colocated multiple-input-multiple-output (MIMO) radar and a full-duplex (FD) MIMO cellular communication system consisting of an FD base station (BS) serving multiple downlink and uplink users simultaneously, without hindering the detection probability of the radar. The main objective is to develop an optimization technique at the cellular system for jointly designing the transceiver for the cellular BS and power allocation vectors for uplink users that can maximize the detection probability of radar, while guaranteeing a pre-defined quality-of-service for each user and power budget for the uplink users and BS. The original problem is non-convex and thus, we convert the non-convex problem into a second-order cone and propose an iterative algorithm to find the optimal solution. Numerical …