A cellular communications system comprising: at least one cellular base station and a plurality of mobile cellular communications devices (22a-22n) for communicating therewith; said at least one cellular base station and said mobile cellular communications devices (22a-22n) each comprising an encoder for generating a binary digital information signal, a modulator for generating a modulated waveform based upon the binary digital information signal, a carrier signal having a frequency and phase associated therewith, and a plurality of carrier phase reference symbols, said modulator comprising an offset circuit so that the modulated waveform comprises a carrier frequency indicator, and said offset circuit biasing the binary digital information signal by changing values thereof, wherein the carrier frequency indicator is based upon the bias of the information signal, and a transmitter for transmitting the modulated waveform; wherein each of said mobile cellular communications devices (22a-22n) and said at least one cellular base station further comprises: a front end for receiving a modulated waveform; a carrier reconstructor for determining the phase of the carrier signal associated with the received modulated waveform based upon the phase reference symbols, and for determining the frequency of the carrier signal based upon the carrier frequency indicator; said carrier reconstructor comprises a phase symbol correlator adapted to correlate the phase reference symbols by performing a complex multiplication of the phase reference symbols plus noise with local phase symbols; and a phase/frequency estimator adapted to determine the phase and frequency of the carrier signal based upon output of the phase symbol correlator and the carrier frequency indicator. at least one cellular base station and a plurality of mobile cellular communications devices (22a-22n) for communicating therewith; said at least one cellular base station and said mobile cellular communications devices (22a-22n) each comprising an encoder for generating a binary digital information signal, a modulator for generating a modulated waveform based upon the binary digital information signal, a carrier signal having a frequency and phase associated therewith, and a plurality of carrier phase reference symbols, said modulator comprising an offset circuit so that the modulated waveform comprises a carrier frequency indicator, and said offset circuit biasing the binary digital information signal by changing values thereof, wherein the carrier frequency indicator is based upon the bias of the information signal, and a transmitter for transmitting the modulated waveform; an encoder for generating a binary digital information signal, a modulator for generating a modulated waveform based upon the binary digital information signal, a carrier signal having a frequency and phase associated therewith, and a plurality of carrier phase reference symbols, said modulator comprising an offset circuit so that the modulated waveform comprises a carrier frequency indicator, and said offset circuit biasing the binary digital information signal by changing values thereof, wherein the carrier frequency indicator is based upon the bias of the information signal, and a transmitter for transmitting the modulated waveform; wherein each of said mobile cellular communications devices (22a-22n) and said at least one cellular base station further comprises: a front end for receiving a modulated waveform; a carrier reconstructor for determining the phase of the carrier signal associated with the received modulated waveform based upon the phase reference symbols, and for determining the frequency of the carrier signal based upon the carrier frequency indicator; said carrier reconstructor comprises a phase symbol correlator adapted to correlate the phase reference symbols by performing a complex multiplication of the phase reference symbols plus noise with local phase symbols; and a phase/frequency estimator adapted to determine the phase and frequency of the carrier signal based upon output of the phase symbol correlator and the carrier frequency indicator. a front end for receiving a modulated waveform; a carrier reconstructor for determining the phase of the carrier signal associated with the received modulated waveform based upon the phase reference symbols, and for determining the frequency of the carrier signal based upon the carrier frequency indicator; said carrier reconstructor comprises a phase symbol correlator adapted to correlate the phase reference symbols by performing a complex multiplication of the phase reference symbols plus noise with local phase symbols; and a phase/frequency estimator adapted to determine the phase and frequency of the carrier signal based upon output of the phase symbol correlator and the carrier frequency indicator.