Parameters estimation of noise amplitude modulation signal

This study proposes a maximum likelihood (ML) estimator for parameter estimation for a complex noise amplitude modulation (NAM) signal. The NAM signal is a general expansion of the exponential signal in which the noise is not circularly symmetric. In the proposed estimator, a non-parametric modified interpolation on Fourier coefficients method is first applied to produce a coarse estimation. Then, a gradient descent method is applied to refine the parameters. The modulation noise to complex additive white Gaussian noise ratio, which is an implicit unknown parameter, is calculated and refreshed at each iteration. For signal-to-noise ratios above the threshold, the variances of the coarse estimation are derived and shown to be independent of the modulation index. The probabilities of a divergence in different gradient descent methods are derived; the pure Newton's method is adopted based on the consideration of both computational complexity and practical applications. Monte Carlo simulations verify the variances and the threshold effect of the coarse estimation; the variances of the ML estimator are demonstrated to asymptotically approach the Cramer-Rao bounds.