Analysis of a maximum likelihood digital receiver using a time-frequency transform

This paper presents an analysis of a novel synchronization algorithm that jointly estimates amplitude, phase and delay parameters and performs data demodulation in a passband digital communication channel. The scheme is based on a Maximum Likelihood (ML) iterative estimator that was presented in [1] and applies to a variety of linear modulation formats and shaping pulses. The algorithm uses an expansion of the received signal on a time-frequency (rr) localized basis. The analysis shows that in the limit of large observation time and signal to noise ratio (SNR) the algorithm converges to a fixed point at the true parameters and it achieves global maximization of the likelihood function. In addition, a gradient descent Version of the algorithm is developed that allows joint parameter tracking and data recovery in a time varying environment.