In cognitive radio networks, previous works almost assume that the primary (licensed) traffic is time-slotted. In time-slotted cognitive radio networks, the secondary (unlicensed) users only need to spend a short time to sense the spectrum because the primary users' states (active or not active) are not changed during the whole secondary frame. However, in realistic cases, the primary traffic is non-time-slotted, which means the primary users can become to be active or not active at any time during the whole secondary frame. Obviously, using the traditional half duplex spectrum sensing scheme, it is impossible for the secondary users to detect the state change in their transmission periods. In this paper, we derive the probability of detection and the probability of false alarm for non-time-slotted cognitive radio networks. We propose the continuous-time Markov chain model to analyze the achievable throughput of primary users and secondary users. To achieve the required primary users' throughput, we develop the full duplex spectrum sensing scheme for non-time-slotted cognitive radio networks. Analyses and numerical results show that using our proposed full duplex spectrum sensing scheme, the primary users can achieve their required throughput and the secondary users' achievable throughput can be increased compared with that of using the half duplex spectrum sensing scheme in non-time-slotted cognitive radio networks.
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