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

The eigenstructure, the initial convergence, and the 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 employing 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. It is also shown 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 optional receiver structure. The LMS PS-FSE is computationally more efficient and introduces less system delay than the CFSE