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In a cognitive radio network, the secondary users are allowed to utilize the frequency bands of primary users when these bands are not currently being used. To support this spectrum reuse functionality, the secondary users are required to sense the radio frequency environment, and once the primary users are found to be active, the secondary users are required to vacate the channel within a certain amount of time. Therefore, spectrum sensing is of significant importance in cognitive radio networks. There are two parameters associated with spectrum sensing: probability of detection and probability of false alarm. The higher the probability of detection, the better the primary users are protected. However, from the secondary users' perspective, the lower the probability of false alarm, the more chances the channel can be reused when it is available, thus the higher the achievable throughput for the secondary network. In this paper, we study the problem of designing the sensing duration to maximize the achievable throughput for the secondary network under the constraint that the primary users are sufficiently protected. We formulate the sensing-throughput tradeoff problem mathematically, and use energy detection sensing scheme to prove that the formulated problem indeed has one optimal sensing time which yields the highest throughput for the secondary network. Cooperative sensing using multiple mini-slots or multiple secondary users are also studied using the methodology proposed in this paper. Computer simulations have shown that for a 6 MHz channel, when the frame duration is 100 ms, and the signal-to-noise ratio of primary user at the secondary receiver is -20 dB, the optimal sensing time achieving the highest throughput while maintaining 90% detection probability is 14.2 ms. This optimal sensing time decreases when distributed spectrum sensing is applied.