comm.ConstellationDiagram

Display and analyze input signals in IQ-plane

Description

The comm.ConstellationDiagram System object™ displays real- and complex-valued floating- and fixed-point signals in the IQ plane. Specifically, the IQ-plane displays the in-phase and quadrature components of modulated signals on the real and imaginary axis of an xy-plot. Use this System object to perform qualitative and quantitative analysis on modulated single-carrier signals.

In the Constellation Diagram window, you can:

• Input and plot multiple signals on a single constellation diagram. To define a reference constellation for each input signal, use the ReferenceConstellation property.

• Select signals in the legend to toggle visibility of individual channels. To display the legend, use the ShowLegend property. For a multichannel signal, specify the input as a matrix with individual signals defined in the columns of the matrix.

• Display calculated error vector magnitude (EVM) and modulation error ratio (MER) measurements for individual signals. To view and configure the measurements, select EVM/MER on the Measurements tab. When multiple signals are input, you can select which signal to use for measurements in the Channel section.

To display constellation diagrams for input signals:

1. Create the comm.ConstellationDiagram object and set its properties.

2. Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

Creation

Syntax

constdiag = comm.ConstellationDiagram

constdiag = comm.ConstellationDiagram(Name,Value)

Description

constdiag = comm.ConstellationDiagram returns a constellation diagram System object that displays real- and complex-valued floating- and fixed-point signals in the IQ plane.

constdiag = comm.ConstellationDiagram(Name,Value) sets properties using one or more name-value arguments. For example, 'SamplesPerSymbol',10 specifies 10 samples for each plotted symbol.

Properties

Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

Name — Title of Constellation Diagram window

'Constellation Diagram' (default) | character vector | string scalar

Title of the Constellation Diagram window, specified as a character vector or string scalar.

Tunable: Yes

Data Types: char | string

ShowTrajectory — Option to plot signal trajectory

false or 0 (default) | true or 1

Option to plot the signal trajectory, specified as a logical 0 (false) or 1 (true). Setting this property to true displays the trajectory between constellation points for the plotted signals. To view the signal trajectory, select Trajectory on the Plot tab.

Tunable: Yes

Data Types: logical

ShowReferenceConstellation — Option to display reference constellation

true or 1 (default) | false or 0

Option to display the reference constellation, specified as a logical 1 (true) or 0 (false).

Tunable: Yes

Data Types: logical

EnableMeasurements — Option to calculate and display EVM and MER measurements

false or 0 (default) | true or 1

Option to calculate and display the EVM and MER measurements, specified as a logical 0 (false) or 1 (true).

Tunable: Yes

Data Types: logical

NumInputPorts — Number of input signals

1 (default) | integer in the range [1, 20]

Number of input signals, specified as an integer in the range [1, 20]. Each input signal, whether it is a multichannel signal or a single channel signal, becomes a separate channel in the scope.

The total number of channels cannot exceed 20. When you specify multichannel input signals, the maximum number of input signals is limited by the total number of input channels that you define.

When you call the object, the number of inputs that you specify must equal the value of this property.

Tips

To define ReferenceConstellation values for multiple input signals, you must first set the NumInputPorts value.

Data Types: double

Symbol configuration

SamplesPerSymbol — Number of samples used to represent each symbol

1 (default) | positive integer

Number of samples used to represent each symbol, specified as a positive integer. The signal is downsampled by the value of this property before it is plotted.

Tunable: Yes

Data Types: double

SampleOffset — Number of samples to skip before plotting points

0 (default) | nonnegative integer

Number of samples to skip before plotting points, specified as a nonnegative integer less than the SamplesPerSymbol property value. This value specifies the number of samples to skip when SamplesPerSymbol is greater than 1.

Tunable: Yes

Data Types: double

SymbolsToDisplaySource — Source of symbols to display

'Input frame length' (default) | 'Property'

Source of symbols to display, specified as one of these values.

• 'Input frame length' — The number of symbols to display is equal to the input frame length divided by the SamplesPerSymbol property value.

• 'Property' — The SymbolsToDisplay property specifies the maximum number of symbols to display.

Tunable: Yes

Data Types: char | string

SymbolsToDisplay — Maximum number of symbols to display

256 (default) | positive integer

Maximum number of symbols to display, specified as a positive integer. Use this property to limit the maximum number of symbols that the constellation diagram displays when you input long signals. The object plots the most recently received symbols.

Tunable: Yes

Dependencies

To enable this property, set SymbolsToDisplaySource to 'Property'.

Data Types: double

Display configuration

ColorFading — Option to add color fading effect

false or 0 (default) | true or 1

Option to add color fading effect, specified as a logical 0 (false) or 1 (true). When you set this property to true, the points in the display fade as the interval of time after they are first plotted increases. This animation resembles an oscilloscope display.

Tunable: Yes

Data Types: logical

XLimits — x-axis limits

[-1.375 1.375] (default) | two-element row vector

x-axis limits, specified as a two-element row vector of the form [xmin xmax]. The first element is the minimum x-axis value, and the second element is the maximum x-axis value.

Tunable: Yes

Data Types: double

YLimits — y-axis limits

[-1.375 1.375] (default) | two-element row vector

y-axis limits, specified as a two-element row vector of the form [ymin ymax]. The first element is the minimum y-axis value, and the second element is the maximum y-axis value.

Tunable: Yes

Data Types: double

XLabel — x-axis label

'In-phase Amplitude' (default) | character vector | string scalar

x-axis label, specified as a character vector or string scalar.

Tunable: Yes

Data Types: char | string

YLabel — y-axis label

'Quadrature Amplitude' (default) | character vector | string scalar

y-axis label, specified as a character vector or string scalar.

Tunable: Yes

Data Types: char | string

Title — Plot title

'' (default) | character vector | string scalar

Plot title, specified as a character vector or string scalar.

Tunable: Yes

Data Types: char | string

ShowLegend — Option to display legend

false or 0 (default) | true or 1

Option to display the legend, specified as a logical 0 (false) or 1 (true). The names listed in the legend are the signal names specified by the ChannelNames property. The legend does not display until you call the object with an input signal.

In the scope legend, click a signal name to toggle the signal visibility in the scope.

Tunable: Yes

Data Types: logical

ChannelNames — Names for input channels

{''} (default) | cell array of strings or character vectors

Names for the input channels, specified as a cell array of strings or character vectors. If you do not specify names, the object labels the channels as Channel 1, Channel 2, etc.

These names appear in the legend, the Measurements tab, and the Measurements Setting pane.

Example: {'8-QAM','8-PSK'} specifies the names for two input channels to 8-QAM and 8-PSK.

Tunable: Yes

Data Types: cell

ShowGrid — Option to show grid

true or 1 (default) | false or 0

Option to show grid on the constellation diagram, specified as a logical 1 (true) or 0 (false).

Tunable: Yes

Data Types: logical

ShowTicks — Option to show tick labels

false or 0 (default) | true or 1

Option to show tick labels on the constellation diagram axes, specified as a logical 0 (false) or 1 (true).

Tunable: Yes

Data Types: logical

Position — Scope window position and size

600-by-600 pixel window at center of screen (default) | four-element row vector

Scope window position and size in pixels, specified as a four-element row vector of the form [left bottom width height]. The first two elements in the vector indicate the location of the lower-left corner, and the second elements two specify the size of the window. The default value for the location depends on the screen resolution.

Tunable: Yes

Data Types: double

Reference constellation

ReferenceConstellation — Reference constellations

[0.7071+0.7071i -0.7071+0.7071i -0.7071-0.7071i 0.7070-0.7071i] (default) | row vector | cell array

Reference constellations for the input signals, specified as a row vector or cell array of vectors defining the ideal constellation points for each input signal. Input signals can be single channel or multichannel. You can define one reference constellation for each input signal.

• When you specify a row vector, the values apply for all input signals.

• When you specify a cell array, you can specify individual reference constellations for each input signal.

The EVM and MER measurements use the specified reference constellation to calculate the signal quality of the modulated input signal. For more information about the signal quality measurements, see EVM and MER Measurements.

Tunable: Yes

Dependencies

To define ReferenceConstellation values for multiple input signals, you must first set the NumInputPorts value.

Data Types: double
Complex Number Support: Yes

ReferenceColor — Color for reference display constellation

[1 0 0] (red) (default) | three-element row vector | cell array

Color for reference display constellation, specified as a three-element row vector indicating RGB component colors or as a cell array containing RGB component colors for each input signal.

Tunable: Yes

Data Types: double

ReferenceMarker — Marker for reference constellation display

'+' (default) | 'o' | '*' | '.' | 'x' | ...

Marker for the reference constellation display, specified as one of the values listed in this table.

Marker	Description	Resulting Marker
"o"	Circle
"+"	Plus sign
"*"	Asterisk
"."	Point
"x"	Cross
"_"	Horizontal line
"|"	Vertical line
"square"	Square
"diamond"	Diamond
"^"	Upward-pointing triangle
"v"	Downward-pointing triangle
">"	Right-pointing triangle
"<"	Left-pointing triangle
"pentagram"	Pentagram
"hexagram"	Hexagram
"none"	No markers	Not applicable

Tunable: Yes

Measurement settings

MeasurementInterval — Window length for EVM and MER measurements

'Current display' (default) | 'All displays' | ...

Window length for the EVM and MER measurements, specified as 'Current display', 'All displays', or an integer in the range [2, SymbolsToDisplay].

For more information, see EVM and MER Measurements.

Tunable: Yes

Data Types: char | string | double

EVMNormalization — EVM normalization method

'Average constellation power' (default) | 'Peak constellation power'

EVM normalization method, specified as 'Average constellation power' or 'Peak constellation power'. For more information, see EVM and MER Measurements.

Tunable: Yes

Usage

Syntax

constdiag(signal1, ..., signalN)

Description

constdiag(signal1, ..., signalN) displays up to N signals in one constellation diagram, where N is the NumInputPorts property value.

Input Arguments

signal1, ..., signalN — Signals (as separate arguments)

column vectors | matrices

Signals, specified as separate arguments of N_sym-by-1 column vectors or N_sym-by-N_channel matrices. N_sym is the number of symbols, and N_channel is the number of input signal channels. Signals can have different data types and dimensions.

You must specify N input arguments, where N is the NumInputPorts property value. You can visualize up to 20 individual or collective signal channels in the constellation diagram. For example, if you create a two-channel signal for every input, then you can define up to 10 input arguments.

Example: [sig1_1,sig1_2],sig2 specifies two signals, provided that sig1_1, sig1_2, and sig2 are single channel column vector signals. The first, [sig1_1,sig1_2], specifies a two-channel signal (constructed by concatenating two column vectors into a matrix). The second signal, sig2, specifies a single channel.

Data Types: double
Complex Number Support: Yes

Object Functions

To use an object function, specify the System object as the first input argument. For example, to release system resources of a System object named obj, use this syntax:

release(obj)

Specific to Scopes

show	Show scope window
hide	Hide scope window
isVisible	Determine visibility of scope window

Common to All System Objects

step	Run System object algorithm
release	Release resources and allow changes to System object property values and input characteristics
reset	Reset internal states of System object

Examples

Display Amplitude-Imbalanced QPSK Constellation

QPSK-modulate random data symbols and apply an amplitude imbalance to the signal. Pass the signal through a noisy channel. Display the resultant constellation.

Create a constellation diagram System object. Because the default reference constellation for the object is QPSK, setting additional properties is not necessary.

constDiagram = comm.ConstellationDiagram;

Generate random data symbols, and then apply QPSK modulation.

data = randi([0 3],1000,1);
modData = pskmod(data,4,pi/4);

Apply an amplitude imbalance to the modulated signal.

txSig = iqimbal(modData,5);

Pass the transmitted signal through an AWGN channel, and then display the constellation diagram. The data points shift from their ideal locations.

rxSig = awgn(txSig,20);
constDiagram(rxSig)

Display 16-QAM Constellation

Apply 16-QAM modulation, transmit data using an AWGN channel, and display the signal constellation.

Create a 16-QAM reference constellation.

M = 16;
refC = qammod(0:M-1,M);

Create a constellation diagram System object, specifying the constellation reference points and axes limits.

constDiagram = comm.ConstellationDiagram('ReferenceConstellation',refC, ...
    'XLimits',[-4 4],'YLimits',[-4 4]);

Generate random 16-ary data symbols.

data = randi([0 M-1],1000,1);

Apply 16-QAM modulation.

sym = qammod(data,M);

Pass the modulated signal through an AWGN channel.

rcv = awgn(sym,15);

Display the constellation diagram.

constDiagram(rcv)

Display Constellation of Multi-Input Signals

Display the constellation of multi-input and multichannel modulated signals. Plot a multichannel signal with two 16-QAM signals for the first input and one 8-PSK signal for the second input.

Create a 16-QAM and an 8-PSK reference constellation.

M = 16;
refQAM = qammod(0:M-1,M);
S = 8;
refPSK = pskmod(0:S-1,S,pi/8);

Create a constellation diagram System object, specifying reference constellations for the two input signals. The object applies a single reference constellation for all the channels of an individual multichannel signal input, but separate input signals can specify separate reference constellations.

constDiag = comm.ConstellationDiagram(2, ...
    'ReferenceConstellation',{refQAM,refPSK}, ...
    'ShowLegend',true, ...
    'XLimits',[-6 6],'YLimits',[-6 6], ...
    'ChannelNames', ...
    {'16-QAM, SNR 10 dB','16-QAM, SNR 20 dB','8-PSK'});

Generate random data symbols, modulate the symbols, and add AWGN with two different SNRs to yield two received signals. Use SNR values of 10 and 20 dB.

d = randi([0 M-1],1000,1);
dQAM = qammod(d,M);
rcv1_1 = awgn(dQAM,10);
rcv1_2 = awgn(dQAM,20);
d = randi([0 S-1],1000,1);
dPSK = pskmod(d,S,pi/8);
rcv2 = awgn(dPSK,20);

For the first input, create a multichannel signal by concatenating the two received 16-QAM signals. For the second input uses a single channel 8-PSK signal.

Display the constellation diagram of the multi-input and multichannel signals.

constDiag([rcv1_1,rcv1_2],rcv2);

More About

EVM and MER Measurements

The Measurements pane displays the EVM and MER signal quality measurement settings and the calculation results for the specified signal channel.

• EVM — An error vector is a vector in the IQ plane from the ideal constellation point to the actual point at the receiver. The EVM calculations include root mean square (RMS), peak, and average values.

  You can normalize the EVM_RMS and EVM_Average calculations by the average or peak constellation power method as computed using these algorithms.

  EVM Normalization Method	Algorithm
  Average constellation power	$$EV{M}_k=100\sqrt{\frac{e_k}{P_{\text{avg}}}}$$ EVMRMS, in percent, for average constellation power normalization: $$EV{M}_{\text{RMS}}(\text{\%})=100\sqrt{\frac{\frac{1}{N}{\displaystyle \sum _{k=1}^N(e_k)}}{P_{\text{avg}}}}$$
  Peak constellation power	$$EV{M}_k=100\sqrt{\frac{e_k}{P_{\text{max}}}}$$ EVMRMS, in percent, for peak constellation power normalization: $$EV{M}_{\text{RMS}}(\text{\%})=100\sqrt{\frac{\frac{1}{N}{\displaystyle \sum _{k=1}^N(e_k)}}{P_{\text{max}}}}$$

  The Measurements pane shows the RMS and peak EVM in percent and the average and peak EVM decibels for the selected input channel. The EVM in decibels is computed as EVM (dB) = 10 ‑ log10(EVM_MS) = 20 ‑ log10(EVM_RMS), where:

  • $$e_k={(I_k-{\tilde{I}}_k)}^2+{(Q_k-{\tilde{Q}}_k)}^2$$

  • I_k is the in-phase value of the kth symbol in the input vector.

  • Q_k is the quadrature phase value of the kth symbol in the input vector.

  • I_k and Q_k represent ideal (reference) symbol values. $${\tilde{I}}_k$$ and $${\tilde{Q}}_k$$ represent measured (received) symbol values.

  • N is the input vector length.

  • P_avg is the value for average constellation power.

  • P_max is the value for peak constellation power.

  • $$EV{M}_{\text{RMS}}=\sqrt{EV{M}_{\text{MS}}}$$

  The maximum EVM value in a vector is $$EV{M}_{\text{max}}=\underset{k\in [1,\mathrm{...},N]}{\text{max}}\left\{EV{M}_k\right\}\text{,}$$ where k is the kth symbol in a vector of length N.

• MER — MER is the ratio of the average power of the transmitted signal to the average power of the error vector. The Measurements pane indicates average MER measurement result in decibels for the selected signal channel.

  MER is a measure of the SNR in a modulated signal, calculated in dB. The MER over N symbols is

  $$MER=10\times \text{}{\log }_{10}\left(\frac{{\displaystyle \sum _{k=1}^N\left(I_k^2+Q_k^2\right)}}{{\displaystyle \sum _{k=1}^N\left(e_k\right)}}\right)\text{dB,}$$

  where:

  • $$e_k={(I_k-{\tilde{I}}_k)}^2+{(Q_k-{\tilde{Q}}_k)}^2$$

  • I_k is the in-phase value of the kth symbol in the input vector.

  • Q_k is the quadrature phase value of the kth symbol in the input vector.

  • I_k and Q_k represent ideal (reference) values. $${\tilde{I}}_k$$ and $${\tilde{Q}}_k$$ represent measured (received) symbols.

Tips

• To capture a simple signal constellation snapshot, use the scatterplot function.

• To calculate signal quality, show signal trajectory, capture constellations for multiple signals, or maintain state between calls, use a comm.ConstellationDiagram System object.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• Supports MEX code generation by treating the calls to the object as extrinsic. Does not support code generation for standalone applications.

• See System Objects in MATLAB Code Generation (MATLAB Coder).

Version History

Introduced in R2013a

R2023a: Variable-size support

This support enables you to vary the length of input signal each time you call the object.