Multi-pass phase tracking loop with rewind of current waveform in digital communication systems

A communication receiver using a demodulator demodulating a modulated signal waveform from a transmission channel which is encoded by a sequence of codewords, comprising:

• a down converter which generates a succession of baseband signal samples of said input modulated signal including an in-phase component and a quadrature-phase component;
• a first converter which converts said succession of baseband signal samples of said input modulated signal from a rectangular form into a pair of polar coordinates having an incoming phase;
• a phase tracking loop which estimates the phase of said input modulated signal, said phase locked loop comprising:
• a comparator which generates a phase difference of said incoming phase of said input modulated signal and an estimated phase;
• a second converter which converts said polar coordinates having said phase difference into a set of vector pairs of phase stabilized observables in said rectangular form;
• a first block decoder which decodes said set of vector pairs of phase stabilized observables in said rectangular form at a decode rate to generate associated codewords;
• and
• a loop filter which filters said phase error estimate from said block decoder to yield an update of said estimated phase at each codeword,
• wherein a group of data symbols consisting of the first data symbols of the modulated signal waveform are run backwards through the phase tracking loop and a second block decoder which receives the associated codewords generated by said inner block decoder and which utilizes and corrects only codewords associated with symbols after and including the group of data symbols consisting of the first data symbols of modulated signal waveform.