Analysis of the Frequency Offset Effect on Random Access Signals

Zadoff-Chu (ZC) sequences have been used as random access sequences in modern wireless communication systems, replacing the conventional pseudo-random-noise (PN) sequences due to their superior autocorrelation properties. An analytical framework quantifying the ZC sequence's performance and its fundamental limitation as a random access sequencein the presence of frequency offset between the transmitter and the receiver is introduced. We show that a ZC sequence's perfect autocorrelation properties can be severely impaired by the frequency offset thereby limiting the overall performance of the random access signals formed from these sequences. First, we derive the autocorrelation function of these random access sequences as a function of the frequency offset. Next, we introduce the concept of critical frequency offsets and the spectrum associated with a ZC sequence set to characterize the frequency offset properties of the random access signals. Finally, we demonstrate that the frequency offset immunity of a ZC sequence set can be controlled by shaping the spectrum of the ZC sequence set.