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# 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.

### DETAILS

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.

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