Method and apparatus for demodulation in a system having known frequency offsets. First and second signals from two users occupy substantially the same bandwidth and use substantially the same carrier frequency, while the relative frequencies of the signals on different transmit antennas associated with a base station are adjusted to have known, specific frequency offsets. These known frequency offsets are used at the receiver to aid in estimating any known frequency errors and to demodulate the multiple transmitted signals. In addition to being useful for demodulation, known frequency offsets can be assigned to each of a plurality of base stations to facilitate identification of a particular base station. The approach can be used for any type of time domain multiple access (TDMA) system, including Global System for Mobile (GSM), or for code division multiple access (CDMA) systems.