Derivation of Probability Distribution Function for Noisy Signal

Abstract

The work in this paper produces mathematically derivation for Probability density function (PDF) of proposed noisy signal model. Two types of noise are considered: zero mean Gaussian multiplicative noise and phase noise. Cramer-Rao bound (CRB) expression of frequency estimator for single tone sinusoidal signal under zero mean Gaussian multiplicative noise and additive Gaussian noise (AWGN) are derived. The obtained simulation results support investigating mathematical and comparative study.