A method and an apparatus relating to an OFDM data communications system where the sub-carriers are modulated using differential quadrature phase-shift keying (DQPSK). The multi-carrier transmitted signal is directly generated using a summation of pre-computed sample points. As part of the multi-carrier signal generation, a signal for the guard interval is established. In an acoustic application of this approach, direct radiation of the sub-carrier approach is facilitated. Symbol synchronization in the receiver is based on signal correlation with the missed sub-carrier. Separation of the sub-carriers in the receiver uses a correlation of the received signal and reference signals that are derived from a table of pre-computed values. Optimal non-coherent processing of the sub-carriers without any phase tracking procedures is achieved.