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This paper introduces a full duplex single secondary user multiple-input multiple-output (FD-SSU-MIMO) cognitive radio network, where secondary user (SU) opportunistically accesses the authorized spectrum unoccupied by primary user (PU) and transmits data based on FD-MIMO mode. Then we study the network achievable average sum-rate maximization problem under sum transmit power budget constraint at SU communication nodes. In order to solve the trade-off problem between SU’s sensing time and data transmission time based on opportunistic spectrum access (OSA) and the power allocation problem based on FD-MIMO transmit mode, we propose a simple trisection algorithm to obtain the optimal sensing time and apply an alternating optimization (AO) algorithm to tackle the FD-MIMO based network achievable sum-rate maximization problem. Simulation results show that our proposed sensing time optimization and AO-based optimal power allocation strategies obtain a higher achievable average sum-rate than sequential convex approximations for matrix-variable programming (SCAMP)-based power allocation for the FD transmission mode, as well as equal power allocation for the half duplex (HD) transmission mode.