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Scatter Plots and Constellation Diagrams

A scatter plot or constellation diagram is used to visualize the constellation of a digitally modulated signal.

To produce a scatter plot from a signal, use the scatterplot function or use the System object. A scatter plot or constellation diagram can be useful when comparing system performance to a published standard, such as 3GPP or DVB.

You create the comm.ConstellationDiagram object in two ways: using a default object or by defining name-value pairs. For more information, see the reference page.

View Signals Using Constellation Diagrams

This example shows how to use constellation diagrams to view QPSK transmitted and received signals which are pulse shaped with a raised cosine filter.

Create a QPSK modulator.

qpsk = comm.QPSKModulator;

Create a raised cosine transmit filter with an upsample rate, Rup, equal to 16.

Rup = 16;
txfilter = comm.RaisedCosineTransmitFilter('Shape','Normal', ...
    'RolloffFactor',0.5, ...
    'FilterSpanInSymbols',10, ...

Generate data symbols and apply QPSK modulation.

data = randi([0 3],200,1);
modData = qpsk(data);

Create a constellation diagram and set the SamplesPerSymbol property to the upsampling rate of the signal. Specify the constellation diagram so that it only displays the last 100 samples. This hides the zero values output by the RRC filter for the first FilterSpanInSymbols samples.

constDiagram = comm.ConstellationDiagram('SamplesPerSymbol',Rup, ...

Pass the modulated data through the raised cosine transmit filter.

txSig = txfilter(modData);

Display the constellation diagram of the transmitted signal.


To match the signal to its reference constellation, normalize the filter by setting its gain to the square root of the OutputSamplesPerSymbol property. This was previously specified as Rup. The filter gain is nontunable so the object must be released prior to changing this value.

txfilter.Gain = sqrt(Rup);

Pass the modulated signal through the normalized filter.

txSig = txfilter(modData);

Display the constellation diagram of the normalized signal. The data points and reference constellation nearly overlap.


To view the transmitted signal more clearly, hide the reference constellation by setting the ShowReferenceConstellation property to false.

constDiagram.ShowReferenceConstellation = false;

Create a noisy signal by Passing txSig through an AWGN channel.

rxSig = awgn(txSig,20,'measured');

Show the reference constellation, and plot the received signal constellation.

constDiagram.ShowReferenceConstellation = true;

Illustrate How RF Impairments Distort Signal

This example simulates RF impairments for a signal that was modulated using differential quaternary phase shift keying (DQPSK). Open the example model by typing doc_receiverimpairments_dqpsk at the MATLAB® command line.

Overview of the Model

The model does the following:

  • Modulates a random signal using DQPSK modulation.

  • Applies impairments to the signal using the blocks from the RF Impairments library.

  • Forks the signal into two paths, and processes one path with an automatic gain control (AGC) to compensate for the free space path loss and the I/Q imbalance.

  • Displays the trajectory of the signal with AGC and the trajectory of the signal without AGC.

  • Demodulates both signals and calculates their error rates.

You can see the effect of the automatic gain by comparing the trajectories of the signals with and without AGC, as shown in the following figure.

Signal With (Left) and Without (Right) AGC

The trajectory of the signal with AGC more closely matches the undistorted trajectory for DQPSK, shown in the following figure, than does than the signal without AGC. Consequently, the error rate for the signal with AGC is much lower than the error rate for the signal without AGC.

In this example, the error rate for the demodulated signal without AGC is primarily caused by free space path loss and I/Q imbalance. The QPSK modulation minimizes the effects of the other impairments.

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