The present invention is a demodulator and a method of demodulating burst communications. A demodulator (100, 200) includes a phase angle source (18), coupled to a current received burst communication, which provides a phase angle of the current received burst communication; a comparator (20), coupled to the phase angle source and a source of an estimated phase angle, which provides an output signal representing an angular difference between a phase of the current received burst communication and the estimated phase angle; and a phase lock loop (20), coupled to the output signal, which provides the estimated phase angle. The phase lock loop includes a Doppler accumulator (102) which provides a Doppler output which provides compensation in the estimated phase angle for the Doppler effect produced by relative motion between the demodulator and a source of the burst communications.