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Cell search and synchronization in the Third-Generation Partnership Project (3GPP) Long-Term Evolution (LTE) system is performed in each user equipment (UE) by using the primary synchronization signal (PSS) and secondary synchronization signal (SSS). The overall synchronization performance is heavily dominated by robust PSS detection, which can be achieved in the conventional noncoherent detector by exploiting the essential near-perfect autocorrelation and cross-correlation properties of Zadoff-Chu (ZC) sequences. However, a relatively high computational complexity is observed in conventional algorithms. As compared with them, two new detectors, i.e., almost-half-complexity (AHC) and central-self-correlation (CSC) detectors, are proposed in this paper to achieve reliable PSS detection with much lower complexity by exploiting the central-symmetric property of ZC sequences. The complexity of the proposed CSC detector is only 50% that of the AHC detector, which achieves exactly the same PSS detection accuracy as that of the conventional detector with one half of complexity being saved. An improvement of CSC, i.e., CSCIns, is also proposed in this paper to combat the large-frequency offset. The performance of the CSCIns detector is independent of the frequency offset, and numerical results show that the 90% PSS acquisition time of CSCIns can be well within an 80-ms duration, even in a heavy intercell-interference environment with a signal-to-noise ratio (SNR) of -10 dB.