This paper considers spectrum utilization, the probability of detection in cognitive radio (CR) model based on cooperative spectrum sensing with both simultaneous adaptive sensing and transmission at a transmitting secondary user (TSU), and the bit error rate (BER) detection with variation checking at a receiving user (RSU). In this paper, a novel detecting model is proposed in the being considered scenario for the full-duplex TSU's simultaneous sensing and transmitting. A spectrum sensing scheme with an adaptive sensing window is designed to improve the spectrum utilization with a high SNR. At RSU, the BER variation is used further to detect whether a PU is active or not. Data fusion based on the proposed adaptive sensing scheme and the BER detection is processed for better decision on the spectrum holes. Simulation results show that i) simultaneous spectrum sensing with an adaptive window improves the spectrum utilization compared with a periodical sensing; ii) cooperative spectrum sensing with the BER-assisted detection improves the probability of detection and spectrum utilization compared with the single simultaneous sensing at TSU.