Constellation diagram

Lore & Background

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, restricted to one of a finite number of values. Each sample encodes one of a finite number of symbols, which in turn represent one or more 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.

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.

Reader's Guide

The constellation diagram is significant because it provides a visual means to assess the performance and integrity of a digital modulation system. The number of constellation points determines the size of the symbol alphabet and thus the number of bits transmitted per symbol, which is usually a power of 2. After passing through a communication channel, the demodulator classifies each sample as a symbol; the set of sample values classified as a given symbol can be represented by a region in the plane drawn around each constellation point. If noise causes the point representing a sample to stray into the region representing another symbol, a symbol error occurs. Most demodulators choose the constellation point closest in Euclidean distance to the received sample, called maximum likelihood detection. On the constellation diagram, these detection regions can be represented by dividing the plane by lines equidistant from each adjacent pair of points. One half the distance between each pair of neighboring points is the amplitude of additive noise or distortion required to cause a symbol error. Therefore, the further the points are separated, the greater the noise immunity. Practical modulation systems are designed to maximize the minimum noise needed to cause a symbol error, meaning the distance between each pair of adjacent points is equal. The received signal quality can be analyzed by displaying the constellation diagram on a vector signal analyzer. Different types of distortion show as characteristic patterns: Gaussian noise causes random balls around each point; non-coherent single frequency interference shows as circles; phase noise spreads points into arcs centered on the origin; amplifier compression moves corner points toward the center. The constellation diagram visualises phenomena similar to those an eye pattern does for one-dimensional signals.

Did You Know?

• An 8-PSK constellation has 8 points, each representing 3 bits of data, with phase shifts of 0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315°.
• In a frequency or phase modulated signal, the amplitude is constant, so constellation points lie on a circle around the origin.
• The distance between adjacent constellation points determines the noise immunity of the modulation scheme.
• A vector signal analyzer can display a constellation diagram, showing received symbols as a cloud of points around each ideal position.