Statistical analysis of frequency modulated signals

In the transmission of signals, one of the common models used for transmission is the frequency modulated model. Suppose the original signal is of the form , then the contaminated frequency Modulated signal is given by , where θcis the carrier frequency, θ is the frequency of the original signal, φ and ψ are random phases, each having a uniform distribution over the interval [-π,π], β is a modulation index. Assuming ztis a second order stationary process, we consider the spectral analysis of the process yt. Suppose we have a sample y1,y2.....yn, we consider the (maximum likelihood) estimation of the frequencies θc, θ, β and A on the basis of the sample, under the assumptions (i) {zt} is a Gaussian white noise; (ii) {zt} is a second order stationary Gaussian process.