Equalizers

INTERCONNECT Photonic Integrated Circuits - Circuit 5G Communications

Equalizers are often used to render the frequency response of a communication channel flat from input to output. It estimates the (inverse) response of the transmission channel impulse response by using equalization filters.

In this section, we demonstrate the performances of two types of equalizers, namely the decision feedback equalizer (DFE) and the most likelihood sequence estimate (MLSE) equalizer.

Decision Feedback Equalizer (DFE)

This example demonstrates the performance of a DFE in a fiber transmission system for PAM4 signals.

The modulated signal is distorted by the transmission channel (fiber) with dispersion and attenuation. The following figures show the waveform (partial) at point A (transmitted signal with no channel) and B (transmitted signal after the fiber channel) in the circuit above. The signal is clearly distorted by the fiber and the Q-factor measured at point B is 4.976.

We set the DFE to training mode first and update the adaptive filter coefficients, and then use the coefficients in the DFE to equalize the fiber transmission channel. Here are some key parameters settings for the DFE and their descriptions.

Property	Value	Description
training mode	true	enables training mode
training sequence length	1	training sequence length = 1 (this indicates there is no training in the circuit)
scale factor	1587.3	scales the received signal by 1587.3 times
threshold table	$$ \left[\begin{array}{cc}{1} & {1} \\ {0.8333} & {0 .8333} \\ {0.6666} & {0 .6666} \\ {0.5} & {0.5}\end{array}\right] $$	match the received signal level to the equalized signal level
equalizer type	FFE	feed-forward equalizer
equalizer output	analog	analog output type
feedforward filter coefficient	$$ \left[\begin{array}{cc}{0.659332} & {0} \\ {0.554591} & {0} \\ {-0.152816} & {0} \\ {-0.09430770} & {0} \\ {0.0390265} & {0} \end{array}\right] $$	the estimated feedforward filter coefficient (inverse response of the channel impulse response)

The following figures show the waveform after the DFE (point C) with the output type "quantized", "analog" and "decision", respectively.

The Q-factor measured at point C is 7.751, 7.527 and 10e12 for the three output types, respectively. Following are the eye diagrams at point B and C for analog output. The eye opening effect is visible.

MLSE Equalizer

This example demonstrates the performance of a MLSE equalizer in a simple PAM2 transmission link.

The modulated signal is distorted by the transmission channel (fiber) with dispersion and attenuation. The following figures show the waveform (partial) at point A (signal before transmission) and B (transmitted signal after the fiber channel) in the circuit above. The signal is clearly distorted by the fiber and the Q-factor measured at point B is 14.77.

We set the MLSE modulation type to "2PAM", and set the initial channel coefficients to $ \left[\begin{array}{ll}{0} & {0}\\ {0} & {0} \end{array}\right] $

The following figure shows the waveform after the MLSE (point C), and it shows the recovery of the signal. The Q-factor measured after point C is 22.77e12.