Clock Recovery MM

This block is meant to act as a clock recovery, to synchronize to a signal's frequency and phase, so that symbols can be extracted.

The two loop gains are expressed in damping factor (< 1 is underdamped, = 1 is critically damped, > 1 is overdamped) and normalized loop bandwidth (ranges between 0.0 and 0.5, but numbers close to 0.0 are what you want). For symbol clock recovery, one probably want something overdamped, with the damping factor at say 1.0, 1.5, or 2.0.

Specifically, this implements the Mueller and Mueller (M&M) discrete-time error-tracking synchronizer. The peak to peak input signal amplitude must be symmetrical about zero, as the M&M timing error detector (TED) is a decision directed TED, and this block uses a symbol decision slicer referenced at zero. The input signal peak amplitude should be controlled to a consistent level (e.g. +/- 1.0) before this block to achieve consistent results for given gain settings; as the TED's output error signal is directly affected by the input amplitude. The input signal must have peaks in order for the TED to output a correct error signal. If the input signal pulses do not have peaks (e.g. rectangular pulses) the input signal should be conditioned with a matched pulse filter or other appropriate filter to peak the input pulses. For a rectangular base pulse that is N samples wide, the matched filter taps would be [1.0/float(N)]*N, or in other words a moving average over N samples. This block will output samples at a rate of one sample per recovered symbol, and is thus not outputting at a constant rate. Output symbols are not a subset of input, but may be interpolated.

The complex version here is based on: Modified Mueller and Muller clock recovery circuit: G. R. Danesfahani, T.G. Jeans, "Optimisation of modified Mueller and Muller algorithm," Electronics Letters, Vol. 31, no. 13, 22 June 1995, pp. 1032 - 1033.

For more info see [1]

Parameters

(R): Run-time adjustable

Omega (R)

Initial estimate of samples per symbol

Gain Omega (R)

Gain setting for omega update loop

Mu (R)

Initial estimate of phase of sample

Gain Mu (R)

Gain setting for mu update loop

Omega Relative Limit

Limit on omega