In the present scenario, mobile communication is ruling the world with advanced technologies. Long Term Evolution (LTE) is one such advanced high-speed technology. Cell search is done using the Primary Synchronization Signal (PSS) and Secondary Synchronization Signal (SSS), in LTE Systems. PSS is generated from frequency domain Zadoff-Chu (ZC) sequence which has zero autocorrelation property. SSS corresponds to a cell-specific scrambling code, given by Pseudo-Noise (PN) sequence. Detection of cell identity in LTE systems is done by using correlation. In this paper, we have proposed detection of the physical layer cell identity group from SSS using linear and circular correlation schemes. We also extended our work to estimate the spectral analysis for the detection of physical layer cell identity group. We have compared probabilistic analysis of correlation schemes with spectral analysis and results are validated and justified.