In this article, we investigate to perform spectrum sensing in two stages for a target long-term evolution (LTE) signal where the main objective is enabling co-existence of LTE femtocells with other LTE femto and macrocells. In the first stage, it is required to perform the sensing as fast as possible and with an acceptable performance under different channel conditions. Toward that end, we first propose sensing the whole LTE signal bandwidth using the fast wavelet transform (FWT) algorithm and compare it to the fast Fourier transform-based algorithm in terms of complexity and performance. Then, we use FWT to go even deeper in the LTE signal band to sense at multiples of a resource block resolution. A new algorithm is proposed that provides an intelligent stopping criterion for the FWT sensing to further reduce its complexity. In the second stage, it is required to perform a finer sensing on the vacant channels to reduce the probability of collision with the primary user. Two algorithms have been proposed for this task; one of them uses the OFDM cyclic prefix for LTE signal detection while the other one uses the primary synchronization signal. The two algorithms were compared in terms of both performance and complexity.