Analysis of impact of integer frequency offset on acquisition of PSS in LTE cellular networks

A base station (BS) in an LTE cellular network, transmits primary synchronization signal (PSS) in every frame to facilitate synchronization. PSS are derived from Zadoff-Chu (ZC) sequences. User equipment (UE) determines physical layer identity and frame timing of BS transmissions, by PSS acquisition. The techniques to detect PSS are typically based on cross-correlating the received signal with local copies of the PSS. In this work, we analyze the shift in cross-correlation peaks in the presence of integer frequency offset (IFO). We derive explicit mathematical relationship between the symbol timing error, cross-correlation peak magnitude, IFO and FFT-size. These expressions can be used to optimize system resources towards LTE frame boundary acquisition. Further, our analysis reveals that the probability of detecting a BS under noisy conditions depends on the root index of its PSS, when IFO is non-zero. Simulation results and numerical examples are provided to support the theoretical findings.