Frequency domain interpretation of LMS convergence of a fractionally spaced equalizer

In this letter, we extend results regarding the behavior of a symbol-spaced tapped-delay-line LMS-adapted equalizer in frequency domain terms to a fractionally spaced implementation. These results rely on an eigendecomposition of the autocorrelation matrix of the received signal. In fractionally spaced equalization systems, the output of the analog channel is oversampled, resulting in a cyclostationary signal. We derive its autocorrelation matrix. A symbol-spaced representation of the combined channel, equalizer and downsampling device is formed in the frequency domain, and the convergence rate of the time-domain LMS algorithm is described in the frequency domain.