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Cognitive radio has attracted an increasing amount of interest over the past few years as an effective method of alleviating the spectrum scarcity problem in wireless communications. One of the most promising approaches in cognitive radio is the opportunistic spectrum access, which enables unlicensed users to access licensed frequency bands that are detected to be idle. In this paper, we propose a novel cognitive radio system that exhibits improved throughput and spectrum sensing capabilities compared to the conventional opportunistic spectrum access cognitive radio systems studied so far. More specifically, we study the average achievable throughput of the proposed cognitive radio system under a single high target detection probability constraint, as well as its ergodic throughput under average transmit and interference power constraints, and propose an algorithm that acquires the optimal power allocation strategy and target detection probability, which under the imposed average interference power constraint becomes an additional optimization variable in the ergodic throughput maximization problem. Finally, we provide simulation results, in order to compare the achievable throughput of the proposed cognitive radio system with the respective throughput of the conventional cognitive radio systems and discuss the effects of the optimal power allocation and target detection probability on the ergodic throughput of the proposed cognitive radio system.