Abstract
Analytical expressions are developed to describe the dynamic response of the phase detector in multilevel decision feedback equalization (MDFE). First, it is shown that high density recording channels using a 2/3(1,7) run-length code are bandlimited, so that the Nyquist sampling criterion is satisfied. Consequently, the phase-locked loop (PLL) can be analyzed using sin x/x interpolation between samples of the equalized response. Analytical expressions are derived for determining the gain of the phase detector for MDFE, when the PLL uses a stochastic gradient algorithm. However, this approach is not attractive from an implementation standpoint. A simpler strategy in which the timing phase is only updated on certain signal trajectories is presented. The cost of using this simpler phase detector is timing jitter.

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