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Long term evolution (LTE) is considered to be a key technology for the next generation of cellular telecommunications. In LTE systems, each user equipment (UE) detects the surrounding cells by searching their identities (IDs) in the synchronization channels of the received waveform. Searching and tracking neighboring cells is important for cellular network management, such as handover and base station cooperation. In this paper, we establish a general framework for neighboring cell search (NCS) in LTE systems. In particular, we derive sufficient signal metrics (SSMs) for NCS under various channel conditions, and develop NCS algorithms based on the SSMs, which optimally combine multiple observations over space and/or time. Moreover, we develop a statistical model for NCS using probability analysis. The performance of NCS algorithms is characterized in terms of the number of detected cells and the cell detection probability, and simulation results validate the effectiveness of the proposed algorithms.