In this paper, we analyze the performance of spectrum sensing based on energy detection. We do not assume the exact noise variance is known a priori. Instead, an estimated noise variance is used to calculate the threshold used in the spectrum sensing based on energy detection. We propose a new analytical model to evaluate the statistical performance of the energy detection. We claim some characteristics of this model, and analyze how these characteristics affect the performance of spectrum sensing. The analytical results are verified through numerical examples and simulations. Through these examples, we demonstrate the effectiveness of our analytical model: we show how it can be used to set the appropriate threshold such that more spectrum sharing can be facilitated, especially when combined with cooperative spectrum sensing method.