Nerd Pool: Clock and Data Recovery

Lee, Hae-Chang. An estimation approach to clock and data recovery. Diss. Stanford University, 2007.

Section 2.1.1 Linear Phase Detector, gives a great overview of the Hogge phase detector, how it works (Creates two pulses that cancel each other out when zero phase difference), why it was popular (linear PD are easy to analyze), it's downsides (if the CDR is digital you need to convert output from analog to digital).
KPD (loop gain) is define as the slope of the transfer function at 0.
Section 2.2, Benefits of digital loop filter

"Additional benefits of this architecture deriving from the digital loop filter are reduced pattern dependent jitter caused by leakage currents in the loop filter in the presence of CID, reduced phase offset error caused by charge pump current mismatch, reduced sensitivity to supply noise, and finally loop dynamics that are not affected by process, voltage and temperature variations."

"KPD (loop gain) is difficult to define as the slope of the curve through the zero crossing is infinite (Figure 2.8 (b)). A method to approximate KPD exists and will be explored in a later section.

Also swept reference offset as part of the JTOL testing of the CDR
"The first order CDR can only take corrective action after the error has occurred. For this reason, a time lag exists between the TX data transitions and the recovered clock in steady state which in turn offsets the data sampling point from its optimum.
"The second order CDR learns the phase offset ramp rate (frequency offset) from past bits and takes predictive correction on the deterministic phase offset trajectory. This allows the second order CDR to drive the average steady state phase estimation error to zero.

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