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Measure the eye and constellation diagrams for a Quadrature Phase-Shift Keying (QPSK) transceiver circuit.

Minimum product version: 2019a r1

### Contents

Overview

Run and results

Important model settings

Updating the model with your parameters

Taking the model further

Appendix: QPSK transceiver methodology

## Overview

Understand the simulation workflow and key results

Phase-shift keying (PSK) is a digital modulation scheme that conveys message information by modulating the phase of the carrier wave. Quadrature Phase-Shift Keying (QPSK) can encode two bits per symbol by using four different phases. In this example, we will simulate a QPSK transceiver with phase modulation and coherent detection. The phase modulation of the signal is done with an interferometer that contains balanced Mach-Zehnder Modulators (MZM) on each of the arms and a 90 degree phase shifter on one of the arms. Demodulation of the QPSK signal is done with an optical hybrid receiver with local oscillator (LO).

The time domain transient sample mode solver is used to obtain the eye diagram, constellation diagram, and error vector magnitude (EVM) of the transceiver. This circuit uses idealized models for the lasers, photodetectors and amplifiers that don't include noise effects.

## Run and results

Instructions for running the model and discussion of key results

1.Open the simulation file and click the Run button.

2.Results can be explored manually in the Result View window of the analyzers by

right-clicking the result entry and selecting "Visualize" or "Add to visualizer..."

double-clicking the result entry

Eye diagram

An eye diagram is the signal waveform display in which the signal is repetitively sampled and overlaid on top of each other. Some useful system quality criterion can be measured from the eye diagram such as Quality-factor (Q-factor), bit error rate (BER) and time jitter. The following figures show the eye diagrams of the QPSK transceiver real part (I-part) and imaginary part (Q-part), respectively.

### Constellation diagram

The constellation diagram plots the quadrature and in-phase components mapped to the vertical and horizontal directions shown at detection decision points. Some useful system quality criterion such as the EVM can be measured from the constellation diagram. The following figure shows the normalized constellation diagram of the QPSK transceiver.

### Other measurements

Most of the system quality measurements are calculated in the analyzers automatically and can be enabled by setting the "calculate measurements" to "true". The following figures show the measurements in the Eye Diagram element and Vector Signal Analyzer, respectively.

## Important model settings

Description of important objects and settings used in this model

### MZM pi dc/rf voltage

The pi dc voltage is the pi shift voltage for the MZM $$v_pi$$. The driving signal voltage level needs to be set based on this $$v_pi$$ value to get the $$pi$$ phase shift in the modulated signal with the same amplitude. The modulation theory is shown in the figure to the right.

### Local oscillator wavelength

The LO wavelength and phase need to match the Laser source wavelength and phase to have perfect beating between the two signals hence separates the in-phase and quadrature-phase information from the signals.

### Analyzers calculate measurements

User needs to manually enable the "calculate measurements" option in the analyzers to calculate the system quality measurements.

### Time domain settings

The sequence length, sample rate and time window settings are very important for all time domain simulations. Once the bit rate is defined, defining two of these three parameters determines the third one. The default time domain settings in INTERCONNECT will work for most cases, but some special measurements (e.g. to reach a certain digital bit error rate), the settings may need to be adjusted.

## Updating the model with your parameters

Instructions for updating the model based on your device parameters

Set the wavelength of interest in the Laser Source and Local oscillator.

Set the bit rate.

Set the electrical signal level (amplitude) of the non-return to zero Pulse Generator (NRZ).

## Taking the model further

Information and tips for users that want to further customize the model

### Dual-polarization QPSK

This example can be easily scaled to a dual-polarization QPSK (DP-QPSK) transceiver. When the two polarizations orthogonal, the two theoretically interference-free QPSK signals transmit independently, thus the spectral efficiency is doubled with DP-QPSK modulation format compares to QPSK modulation format. To modulate the QPSK signal on different polarizations of the carrier light wave, a polarization beam splitter is needed to separate the two polarizations of the light wave. For more details, please visit the Optical DP-QPSK link in the Additional resources session.

### Circuit with compact models

This example uses primitive elements to build the circuit. For more physical realistic circuits, replace the existing primitive elements models based on real components. For more information on compact model libraries, please visit the Lumerical Compact Model Library link in the Additional resources session.

Additional documentation, examples and training material

Optical QPSK

Optical DP-QPSK

Lumerical Compact Model Library

Related publication: Makovejs, Sergejs. High-speed optical fibre transmission using advanced modulation formats. Diss. UCL (University College London), 2011

## Appendix: QPSK transceiver methodology

QPSK modulation format conveys signal in symbols with two bits per symbol and modulates the phase of the carrier wave. To demodulate the QPSK signal, a 90 degree hybrid is needed in the receiver. The hybrid makes the received signal interfere with a local oscillator (which has the same central frequency and initial phase as the carrier) and then separate to the in-phase part and quadrature phase part, so that the encoded signal information can be retrieved.

Symbol mapping: With two bits per symbol, QPSK modulation format generates 4 different types of symbols in total, the mapping mechanism is shown in the table below. For conventional plotting, the constellation diagram in the example file is rotated for 45 degrees and normalized.

 Symbol mapping Type bit 1 bit 2 Symbol 1 0 0 0 2 0 1 1 3 1 0 2 4 1 1 3

90 degree hybrid: The received signal $$E_{SIG}$$ beats with the LO signal $$E_{LO}$$ and with the 90 degree phase shifter in one branch of the hybrid, the output signals are proportional to the real and imaginary part of the received signal. The hybrid outputs are shown by the equations below:

$$I_1 \sim \mid E_{SIG}\mid ^2 + \mid E_{LO}\mid ^2 + 2Re(E_{SIG}E_{LO}^\ast)$$

$$I_2 \sim \mid E_{SIG}\mid ^2 + \mid E_{LO}\mid ^2 - 2Re(E_{SIG}E_{LO}^\ast)$$

$$I_3 \sim \mid E_{SIG}\mid ^2 + \mid E_{LO}\mid ^2 + 2Im(E_{SIG}E_{LO}^\ast)$$

$$I_4 \sim \mid E_{SIG}\mid ^2 + \mid E_{LO}\mid ^2 - 2Im(E_{SIG}E_{LO}^\ast)$$

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