Quasi-Optimal Demodulation of Pulse-Frequency Modulation Systems

Novel demodulator structures are derived using a theory for the quasi-optimal on-line demodulation of pulse-frequency modulated (PFM) signals in the presence of white Gaussian channel noise. The basic demodulator consists of a phase-locked loop with time-varying gain elements. Furthermore, its integrators are appropriately reset as each new pulse is received. This modulator may be augmented with additional integrators and gain elements to achieve quasi-optimal demodulation with delay. The quasi-optimal demodulation approaches optimal demodulation, in the minimum mean-square-error sense, as the signal-to-noise ratio increases. The various quasi-optimal receivers are derived by application of the extended Kalman filter theory to a state-space signal model.