Detection and Estimation of Randomly Phase Modulated Signals

The design of detectors for weak sinusoidal signals with random varying phase and frequency has been studied for many decades and continues to be a topic of significant theoretical and practical interest. For a random process, the likelihood ratio detector is known to have an estimator-correlator structure that requires generation of the causal minimum mean square error (MMSE) estimate of the random signal, which generally is very challenging for non-Gaussian signals. In this paper we present methods to project an infinite dimensional solution to the stochastic differential equations generating the required MMSE estimate onto a finite dimensional space, closely approximating the exact solution. Simulations of our proposed detectors are presented and compared with existing approaches, specifically optimized quadratic detectors and extended Kalman filter based methods.