the present invention generates exponents of elements of a zadoff - chu sequence representing a preamble for uplink synchronization of mobile stations or a mobile station reference signal by first obtaining a preamble index defining the zadoff - chu sequence . then it determines 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 . finally it determines exponents of the remaining elements in the zad - off - chu sequence from the initial first difference and the initial exponent in an iterative procedure that avoids multiplication operations .