Convergence and steady state behavior of a phase-splitting fractionally spaced equalizer

The eigenstructure, initial convergence, and steady-state behavior of a phase-splitting fractionally spaced equalizer (PS-FSE) are analyzed. It is shown that the initial convergence rate of a T/3, or in general a T/M, PS-FSE using the least-mean-square (LMS) stochastic gradient adaptive algorithm is half that of a symbol rate equalizer (SRE) or a complex fractionally spaced equalizer (CFSE) with the same time span. The authors also show that the LMS adaptive PS-FSE with symbol rate update converges to a Hilbert transformer followed by a matched filter in cascade with an optimal SRE and thus forms an optimal receiver structure.<>