Constellation diagram

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A constellation diagram is a representation of a signal modulated by a digital modulation scheme such as quadrature amplitude modulation or phase-shift keying.^[1] It displays the signal as a two-dimensional xy-plane scatter diagram in the complex plane at symbol sampling instants. In a manner similar to that of a phasor diagram, the angle of a point, measured counterclockwise from the horizontal axis, represents the phase shift of the carrier wave from a reference phase; the distance of a point from the origin represents a measure of the amplitude or power of the signal. It could be considered a heat map of I/Q data.

In a digital modulation system, information is transmitted as a series of samples, each occupying a uniform time slot. During each sample, the carrier wave has a constant amplitude and phase, which is restricted to one of a finite number of values. So each sample encodes one of a finite number of "symbols", which in turn represent one or more binary digits (bits) of information. Each symbol is encoded as a different combination of amplitude and phase of the carrier, so each symbol is represented by a point on the constellation diagram, called a constellation point. The constellation diagram shows all the possible symbols that can be transmitted by the system as a collection of points. In a frequency or phase modulated signal, the signal amplitude is constant, so the points lie on a circle around the origin.

The carrier representing each symbol can be created by adding together different amounts of a cosine wave representing the "I" or in-phase carrier, and a sine wave, shifted by 90° from the I carrier called the "Q" or quadrature carrier. Thus each symbol can be represented by a complex number, and the constellation diagram can be regarded as a complex plane, with the horizontal real axis representing the I component and the vertical imaginary axis representing the Q component. A coherent detector is able to independently demodulate these carriers. This principle of using two independently modulated carriers is the foundation of quadrature modulation. In pure phase modulation, the phase of the modulating symbol is the phase of the carrier itself and this is the best representation of the modulated signal.

A 'signal space diagram' is an ideal constellation diagram showing the correct position of the point representing each symbol. After passing through a communication channel, due to electronic noise or distortion added to the signal, the amplitude and phase received by the demodulator may differ from the correct value for the symbol. When plotted on a constellation diagram the point representing that received sample will be offset from the correct position for that symbol. An electronic test instrument called a vector signal analyzer can display the constellation diagram of a digital signal by sampling the signal and plotting each received symbol as a point. The result is a 'ball' or 'cloud' of points surrounding each symbol position. Measured constellation diagrams can be used to recognize the type of interference and distortion in a signal.