The present application discloses methods and apparatus for generating a Zadoff-Chu sequence for use by a mobile station. One embodiment discloses generating exponents oof elements of a Zadoff-Chu sequence representing a preamble for uplink synchronization of a mobile station or a mobile station reference signal by first obtaining a preamble index defining the Zadoff-Chu sequence. Then an initial exponent of the first element in the Zadoff-Chu sequence and an initial first difference between exponents of consecutive elements of the Zadoff-Chu sequence are determined. Finally the embodiment discloses determining exponents of the remaining elements in the Zadoff-Chu sequence from the initial first difference and the initial exponent in an iterative procedure that avoids multiplication operations.