Cognitive LTE system, such as LTE-U, has received tremendous interest from almost all research disciplines in wireless communications. In Cognitive LTE systems, spectrum sensing is the key enabling technology to realize dynamic spectrum access. In this paper, an error decision probability is proposed to solve the trade-off problem between detection and false alarm probability with the constraint region requirement. The closed-form expression for the error decision probability, satisfied Signal-to-Noise ratio value, number of samples, and primary users' spectrum utilization ratio are derived for in both fixed and adaptive threshold setting algorithms. By implementing both Welch and wavelet-based energy detectors, the adaptive threshold setting algorithm demonstrates a more reliable and robust sensing result for both primary users and secondary users in comparison with the conventional fixed one. Furthermore, the wavelet denoising method is applied to improve the sensing performance when there are insufficient number of samples.