Orthogonal frequency division multiplexing (OFDM) has been a widely accepted technology in high rate and multimedia data service systems such as the long term evolution (LTE) in the third generation partnership project (3GPP). The design of a synchronization signal for supporting an efficient cell search in a mobile station (MS) is one of the most important issues in cellular systems. In this thesis, we first propose two cell search methods based on the sequence hopping technology and then compare with the existing LTE scheme. The goal of the proposed schemes is to minimize the receiver complexity while maintaining similar performance with existing scheme. The performance of our proposed schemes is evaluated under various channel environments. The impacts of multipath fading, frequency offset, and vehicular speed on system performance are examined and the average search time performance using the Markov process is analyzed. The complexity of the proposed schemes is also compared with existing scheme. Ideas addressed in this thesis will provide a useful guideline in designing the downlink synchronization signals and the cell search algorithm for future wireless communication systems.