Magnitude-Based Amplitude Estimation of Single Sinusoid in AWGN

Abstract

The structure of the maximum likelihood (ML) amplitude estimator that is based on the received signal magnitudes is derived for a single sinusoid in additive white Gaussian noise. This estimation problem is closely related to the classic open problem of parameter estimation of a Rician distribution. By exploiting tight, exponential, upper and lower bounds on the modified Bessel function of the first kind with order zero, it is shown analytically that the log-likelihood function is bounded by quadratic functions. This insight allows us to develop an efficient and effective numerical method for the implementation of the ML estimator. The simulation results confirm the validity of the theoretical and numerical analysis.