Demodulation of PM Signal in the Presence of White Gaussian Noise

The maximum likelihood estimates of all the parameters of a PM signal, when the baseband signal is a harmonic process and the PM signal observed is contaminated by an independent Gaussian white noise, are derived. The sampling distribution of the maximum likelihood estimates of the parameters and the demodulated signal are also investigated. Alternative estimates for the carrier frequency and the modulating frequency, together with their sampling properties, are also studied. The methods are illustrated with two examples and in each case the demodulated signal is compared to the true baseband signal. Some comments about the performance of the demodulated signals are also included.