  Zadoff-Chu (ZC) sequences have been used as synchronization sequences in
modern wireless communication systems, replacing the conventional pseudo-random
noise (PN) sequences due to their perfect autocorrelation properties. We first
study the ambiguity problem between a timing offset and a frequency offset when
a ZC sequence is used as a synchronization signal. We show how a frequency
offset can impair the timing property of a ZC sequence, causing irreducible
timing errors. An analytical framework is developed, which completely
characterizes a ZC sequence's timing behavior and its fundamental limitation as
a synchronization sequence in the presence of a frequency offset between the
transmitter and the receiver.
