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In cellular communication systems the mobile station (MS) must be able to perform initial synchronization and search for a base station to set up the downlink access. This process is called the initial cell search. To accomplish the operations, two synchronization signals, the primary synchronization signal (PSS) and the secondary synchronization signal (SSS), are periodically transmitted from the base station in the 3GPP LTE (Long Term Evolution) system. It is announced OFDM signal is applied to downlink transmission in the LTE cellular network. However, OFDM signal is sensitive to synchronization error, such as carrier frequency offset (CFO). CFO, which exists between the transmitter and the receiver, causes loss of orthogonality among subcarriers and inter-carrier interference (ICI), thus degrades the system performance. In this paper all the procedures of synchronization and initial cell search are specified. An innovative processing algorithm for PSS, including the theoretical analysis and deduction, is provided. Most important of all, the proposed scheme is able to evaluate the integer carrier frequency offset (ICFO) more accurately and improve the detection error rate effectively. Comparisons between the proposed scheme and the existing ones are illustrated in the simulation results.