Abstract: An apparatus and accompanying method for demodulating with baseband Doppler frequency shift compensation. An RF section (20) down-converts received data communication signals (12) to baseband. A/D converters (24, 26) digitize I, Q quadrature baseband signal components. Phase (32) and frequency (50) tracking loops reside on a common digital ASIC substrate (28). A complex multiplier (30) rotates digitized baseband signals by a digitized oscillation signal, producing Doppler shift compensated signals. The phase tracking loop (32) estimates data and generates a pure phase error signal from which data modulation and Doppler shift compensation influences have been removed, which drives a frequency discriminator (52) that identifies either clockwise or counterclockwise phase rotation for each symbol (18). An integrator (54) combines identification results over a burst and a numerically controlled oscillator (56) adjusts the digitized oscillation signal frequency in a constant frequency step.