Spectrum sensing is one of key enabling techniques to advanced radio technologies such as cognitive radios and ALOHA. This paper presents a novel non-cooperative spectrum sensing approach that can achieve a good trade-off between latency, reliability and computational complexity. Our major idea is to exploit the first-order cyclostationarity of the primary user's signal to reduce the noise-uncertainty problem inherent in the conventional energy detection approach. It is shown that the proposed approach is suitable for detecting the primary user's activity in the interweave paradigm of cognitive spectrum sharing, while the active primary user is periodically sending training sequence. Computer simulations are carried out for the typical IEEE 802.11g system. It is observed that the proposed approach outperforms both the energy detection and the second-order cyclostationarity approach when the observation period is more than 10 frames corresponding to 0.56 ms.