Engee documentation

Signalling constellations

See also:

Transmitter Model

Constellation diagram (or constellation diagram) is a graphical method of representing modulated signals in digital communications. It is used to visualise the symbols transmitted in a modulated signal and helps to analyse the quality of data transmission and detect distortions.

In a constellation diagram, each point (or symbol) represents the complex value of the modulated signal, where the axis represents the real part of the signal and the axis represents the imaginary part. The points are located in grid nodes that correspond to different combinations of signal phases and amplitudes.

To plot a signal constellation in Engee in the graph window stateflow graphs button, move the mouse cursor over the graph window toolbox, in the Signal Menu signal menu 1 and change the view of the graph display to Constellation diagram signal constellation:

signal const main

Axes of the graph:

  • Quadrature Amplitude (quadrature amplitude) - the projection of the signal on the axis . Responsible for the in-phase component of the signal. In-phase component means that this component is modulated by a sine wave that is the same phase as the carrier frequency.

  • In-phase Amplitude (amplitude in phase) - the projection of the signal on the axis . Responsible for the quadrature component of the signal. The quadrature component means that this component is modulated by a sinusoid that is shifted in phase by 90 degrees with respect to the carrier frequency (at which the signal is transmitted).

The main features of the signal constellation are:

  • The positions of the points in the diagram are determined by the selected modulation scheme (e.g., QPSK, 16-QAM). Each point corresponds to a specific combination of bits.

  • Deviations of points from their ideal positions may indicate the presence of noise or distortion in the transmission channel. The closer the points are to their ideal positions, the better the signal quality.

  • The constellation diagram allows you to quickly and clearly assess the effect of noise and distortion on the modulated signal.

Constellation diagrams are useful for visualising the effect of different types of distortion and noise on the transmitted signal:

  • Gaussian noise - when white Gaussian noise is added to the signal, the points on the constellation diagram begin to "blur" around their ideal positions. This blurring indicates a decrease in signal-to-noise ratio (SNR).

  • Phase noise - causes the points along the circles to oscillate around their ideal positions, indicating that the phase of the signal is unstable.

  • Interference - mutual interference (interference) can shift points in different directions, causing additional distortion.

  • Inter-Symbol Interference (ISI) - causes constellation diagram points to "spread out", especially if the symbols influence each other.

Example

Build a model from blocks:

Enable signal recording signal logging 1 on the output of block QPSK Modulator Baseband. The model will look like this:

signal const ex 1

For the Random Integer Generator block, set the Set size parameters to 4. Leave the rest of the block parameters and model settings by default. In the graph window stateflow graphs button click Signal Menu signal menu 1 and change the view of the chart display to Constellation diagram signal constellation. Then go to Settings:

signal const settings 1

In the tab. Signals set:

  • Number of points to visualise to 100 for better visualisation.

  • Reference constellation in QPSK as the block QPSK Modulator Baseband is selected as the modulation source.

    To achieve the most optimal values, it is recommended that the modulation source and the selected modulation of the signalling constellation match.

    This results in the following settings:

    signal const settings

After running the simulation start simulation button a graph will be obtained:

signal const ex 2

The model simulation shows no deviations in modulation - this means that all points hit the expected region and the graph shows clean modulation without noise.

For clarity, add a Gaussian noise source to the model - block AWGN Channel and enable recording for its output signal:

signal const ex 3

Block parameters and model settings remain by default. In the graph window, select a new signal and, as shown earlier, set the same values for the number of points and the reference constellation. The result will be a graph:

signal const ex 4

The graph shows that noise has appeared in the modulation - the symbols have moved away from the reference points.

  1. Graphs