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We propose a low complexity synchronization method for the 3rd Generation Partnership Project (3GPP) long term evolution (LTE) mobile communication systems. A low complexity detection window, synchronization state machine, and two-stage detection are used to lower the computational complexity. The positions of the detection window and received samples are recorded, and the position and length of the detection window are controlled by the state machine. The positions are compared to decide if the received sample is useful for synchronization signal detection. Such techniques avoid unnecessary computations especially when implementing a receiver on a software defined radio (SDR) platform with general-purpose processors. We analyze the computational complexity of the proposed method and evaluate its performance based on simulations and using a Universal Software Radio Peripheral (USRP)-based SDR platform. The evaluation shows that the proposed method provides reliable and real-time synchronization signals on the considered SDR platform.