Digital Modulation: Quadrature Phase-Shift Keying (QPSK) Signal Constellation and Eye Diagrams

A digitally modulated signal is represented by its equivalent complex low-pass or base-band signal. The real and imaginary parts of this signal are called the quadrature components and . The figure shows the signal constellation in the complex plane and the eye diagrams of the quadrature components for QPSK (quadrature phase-shift keying). The eye diagram shows how the waveforms used to send multiple bits of data can potentially lead to errors in interpretation. You can change the roll-off factor of the base-band pulse-shaping filter to see the effect of an amplitude or phase imbalance of the modulator.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


In a quadrature modulator, is multiplied with and is multiplied with , where is the carrier frequency. An amplitude imbalance corresponds to unequal amplitudes of the local carriers, while a phase imbalance corresponds to a phase shift. The complex low-pass signal is given by .
For ideal modulation, and , and the complex low-pass signal is simply .
J. G. Proakis, Digital Communications, 5th ed., New York: McGraw–Hill, 2008.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2017 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+