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This paper is focused on analyzing the effects of primary user (PU) signal arrival in the sensing interval on the local spectrum sensing performance. The probability for signal arrival at a sample in the sensing time is uniformly distributed. In this case, the performance degradation of the conventional energy detection (CED) method is analyzed. Furthermore, in order to enhance performance, an approach of estimating the signal arrival time is proposed to cooperate with the composite energy detection. The mathematical analysis and numerical simulation are employed to investigate and show the resulted spectrum sensing performance.