Constellation Diagram

Display constellation diagram for input signals

• Library:

• Communications Toolbox / Comm Sinks

Description

The Constellation Diagram block displays real and complex-valued floating and fixed-point signals in the I/Q plane. Use this block to perform qualitative and quantitative analysis on modulated single-carrier signals.

In the constellation diagram window you can:

• Choose which channels are displayed by selecting signals in the legend. Use Show legend to display the legend. To create a multichannel signal, use the Matrix Concatenate block to concatenate input signals of the same data type.

• Display the EVM / MER Measurements panel, which displays calculated error vector magnitude (EVM) and modulation error ratio (MER) measurements. When a multichannel signal is input, use Trace Selection to choose the signal being measured.

Ports

Input

Port 1 — IQ input signal

column vector | matrix

IQ input signal, specified as a column vector or matrix.

Example: [-1 + 1i; -1 - 1i; 1 + 1i; 1 - 1i]

Parameters

File

From the Constellation Diagram window, select File to view the options available.

Open at Start of Simulation — Open constellation diagram at start of simulation

on (default) | off

Select to open constellation diagram window at start of simulation. Deselect to prevent constellation diagram window from opening at start of simulation.

Tools > Axes Scaling Properties

From the Constellation Diagram window, select Tools > Axes Scaling Properties to open the Axes Scaling Properties: Constellation Diagram dialog box. In this dialog box, you can customize the graphical properties of the axes.

Properties

Axes scaling — Axes scaling options

Manual (default) | Auto | After N Updates

Axes scaling options, specified as:

• Manual — Applies the x and y axes limits specified in the Visuals – Constellation Properties: Constellation Diagram dialog box.

• Auto — Scales the axes limits as needed during and after simulation.

• After N Updates — Scales the axes limits after the specified Number of updates.

Tunable: Yes

Number of updates — Number of updates after which to scale the axes

10 (default) | positive integer

Number of updates after which to scale the axes, specified as a positive integer.

Tunable: Yes

Dependencies

This parameter appears when Axes scaling is set to After N Updates.

Scale axes limits at stop — Option to scale axes at end of simulation

off (default) | on

Select to scale axes at end of the simulation to the data range percentage limits specified by X-axis Data range (%) and Y-axis Data range (%).

X-axis Data range (%) — Percentage of x-axis used to display data

80 (default) | scalar from 1 to 100

Percentage of x-axis used to display data.

Example: 100 scales the x-axis range to the maximum value of the in-phase amplitude component of the input signal.

Tunable: Yes

X-axis Align — Align data along x-axis

Center (default) | Left | Right

Align data along x-axis, specified as Center, Left, or Right.

Example: Right aligns the maximum value of the in-phase amplitude component of the input signal toward the upper x-axis limit.

Tunable: Yes

Y-axis Data range (%) — Percentage of y-axis used to display data

80 (default) | scalar from 1 to 100

Percentage of y-axis used to display data.

Example: 30 scales the y-axis range so that the maximum value of the quadrature amplitude component of the signal occupies 30% of the y-axis range.

Tunable: Yes

Y-axis Align — Align data along y-axis

Center (default) | Top | Bottom

Align data along y-axis, specified as Center, Top, or Bottom.

Example: Bottom aligns the maximum value of the quadrature amplitude component of the signal toward the lower y-axis limit.

Tunable: Yes

Tools > Measurements

From the Constellation Diagram window, select options under Tools > Measurements to display the Trace Selection and Signal Quality panes. By default these panes are docked in the Constellation Diagram window when displayed.

The Signal Quality pane contains the Settings and EVM / MER subpanes. Both subpanes can be independently expanded or collapsed.

For more information about the signal quality measurements, see EVM / MER Measurements.

Trace Selection — Signal trace used to compute measurements

list of signals

Select the signal trace used to compute measurements from the list of available signals. This parameter lists the signals input to the block.

Tunable: Yes

Dependencies

To set this parameter, the Trace Selection pane must be visible. The Trace Selection pane automatically appears when you plot multichannel signals on the Constellation Diagram window. To hide or display the Trace Selection pane, select Tools > Measurements > Trace Selection from the Constellation Diagram window.

EVM / MER Settings Pane

Measurement interval — Duration of EVM or MER measurement

Current Display (default) | All displays | positive integer

Duration of the EVM or MER measurement in symbols, specified as Current Display, All displays, or a positive integer. To specify a positive integer, select and then replace <user-defined> with your desired value. The value must be positive and less than or equal to Symbols to display. The measurement is computed after the number of input data samples exceeds the measurement interval.

Tunable: Yes

EVM normalization — Normalization method used for EVM calculation

Average constellation power (default) | Peak constellation power

Normalization method used for EVM calculation, specified as Average constellation power or Peak constellation power. The comm.EVM System object™ computes the EVM.

Tunable: Yes

Reference constellation — Reference constellation

QPSK (default) | BPSK | 8-PSK | 16-QAM | 64-QAM | 256-QAM | vector

Reference constellation, specified as BPSK, QPSK, 8-PSK, 16-QAM, 64-QAM, 256-QAM, or vector. To specify a vector, select and then replace <user-defined> with your desired value. When defined by the user, the reference constellation values can be specified as a vector, function call, or variable defined in the workspace.

To obtain the EVM/MER measurements, you must set Reference constellation to a valid value corresponding to the modulation of the input signal.

Tunable: Yes

Average reference power — Average power of reference constellation

1 (default) | positive scalar

Average power of the reference constellation in watts, specified as a positive scalar and referenced to a one-ohm load.

Tunable: Yes

Reference phase offset (rad) — Phase offset of reference constellation

pi/4 (default) | scalar

Phase offset of the reference constellation in radians, specified as a scalar.

Tunable: Yes

View > Configuration Properties

From the Constellation Diagram window, select View > Configuration Properties to open the Visuals – Constellation Properties: Constellation Diagram dialog box. In this dialog box, you can customize the graphical properties of the plotted signals.

Main

Samples per symbol — 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. When Samples per symbol is greater than 1, the signal is downsampled before it is plotted.

Tunable: Yes

Offset (samples) — 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 Samples per symbol. This parameter specifies the number of samples to skip when downsampling the input signal.

Tunable: Yes

Symbols to display — Maximum number of symbols to display

Input frame length (default) | positive integer

Maximum number of symbols to display, specified as Input frame length or a positive integer. To specify a positive integer, select and then replace <user-defined> with your desired value.

Use Symbols to display to limit the maximum number of symbols displayed when long signals are input. Symbols plotted are the most recent symbols received.

Tunable: Yes

Display

Show grid — Display plot grid lines

on (default) | off

Select to display plot grid lines.

Tunable: Yes

Show legend — Display plot legend

off (default) | on

Select to display plot legend. The names listed in the legend are the signal names from the model.

From the legend, you can control which signals are plotted. This control is equivalent to changing the visibility in the View > Style dialog box. In the scope legend, click a signal name to hide the signal in the scope. To show the signal, click the signal name again. To show only one signal and hide all other signals, right-click the signal name. To show all signals, press Esc.

Tunable: Yes

Show signal trajectory — Display signal trajectory

off (default) | on

Select to display the trajectory between constellation points for the plotted signals.

Tunable: Yes

Color fading — Option to add color fading effect

off (default) | on

When you select Color fading, the points in the display fade as the interval of time after they are first plotted increases. Color fading is for animation that resembles an oscilloscope.

Tunable: Yes

X-limits (Minimum) — Minimum x-axis value

-1.375 (default) | scalar

Minimum x-axis value, specified as a scalar.

Tunable: Yes

X-limits (Maximum) — Maximum x-axis value

1.375 (default) | scalar

Maximum x-axis value, specified as a scalar.

Tunable: Yes

Y-limits (Minimum) — Minimum y-axis value

-1.375 (default) | scalar

Minimum y-axis value, specified as a scalar.

Tunable: Yes

Y-limits (Maximum) — Maximum y-axis value

1.375 (default) | scalar

Maximum y-axis value, specified as a scalar.

Tunable: Yes

Title — Title on plot

blank (default) | character vector | string

Title on plot, specified as a character vector or string.

Tunable: Yes

X-axis label — x-axis label

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

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

Tunable: Yes

Y-axis label — y-axis label

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

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

Tunable: Yes

Reference constellation

Show reference constellation — Select to display reference constellation

on (default) | off

Select to display the reference constellation.

Tunable: Yes

Reference constellation — Reference constellation

QPSK (default) | BPSK | 8-PSK | 16-QAM | 64-QAM | 256-QAM | vector

Reference constellation, specified as BPSK, QPSK, 8-PSK, 16-QAM, 64-QAM, 256-QAM, or vector. To specify a vector, select and then replace <user-defined> with your desired value. When defined by the user, the reference constellation values can be specified as a vector, function call, or variable defined in the workspace.

To obtain the EVM/MER measurements, you must set Reference constellation to a valid value corresponding to the modulation of the input signal.

Tunable: Yes

Average reference power — Average power of reference constellation

1 (default) | positive scalar

Average power of the reference constellation in watts, specified as a positive scalar and referenced to a one-ohm load.

Tunable: Yes

Reference phase offset (rad) — Phase offset of reference constellation

pi/4 (default) | scalar

Phase offset of the reference constellation in radians, specified as a scalar.

Tunable: Yes

View > Style

From the Constellation Diagram, select View > Style to open the Constellation Diagram - Style dialog box. In this dialog box, you can customize the graphical properties of the components in the Constellation Diagram window.

Figure color — Select background color

gray (default)

Select the background color within the Constellation Diagram window and outside the scope axes.

Axes colors — Select colors of plot and measurement panes

black (default for background) | gray (default for axes)

Select colors of plot and measurement panes. The first color option specifies the background color of the plot figure and the measurement panes. The second option specifies the color of the plot figure axes (ticks, labels, and grid lines) and the text. For more a description of the measurement panes, see in the Tools > Measurements.

Tunable: Yes

Properties for channel — View or change graphical properties of channel

Channel 1 (default)

Select a channel to view or change its graphical properties.

Bring To Front — Bring channel to front

button

Bring the active channel, as indicated by Properties for channel, to the front.

Visible — Option to hide channel

on (default) | off

Clear to hide the active channel. Use Properties for channel to select the active channel. The setting is synchronized with actions in the interactive legend, see Show legend.

Symbols — Set properties of symbols

symbol properties

Set graphical properties of the symbols for the active channel. Adjust style, size, line width, and color of the marker. Use Properties for channel to select the active channel.

Dependencies

To set marker shape to none, Show signal trajectory must be selected.

Signal trajectory — Select properties of signal trajectory

no line (default) | trajectory properties

Set graphical properties for the signal trajectory of the active channel. Adjust style, width, and color of the line. Use Properties for channel to select the active channel.

Dependencies

To adjust signal trajectory properties, Show signal trajectory must be selected. When Show signal trajectory is selected, the Signal trajectory line style cannot be set to no line.

Reference constellation — Select properties of reference constellation symbols

symbol properties

Select the graphical properties for the symbols of the reference constellation. Adjust the style, size, line width, and color of the marker.

Dependencies

To adjust reference constellation graphical properties, Show reference constellation must be selected.

Model Examples

View Constellation Diagram

Use the Constellation Diagram block to visualize the constellation of a modulated signal.

Open Model

View Multichannel Constellation Diagram

Use the Constellation Diagram block to visualize the constellation of a multichannel modulated signal.

Open Script

Add RF Impairments to DQPSK Signal

This model applies RF impairments to a signal modulated by differential quadrature phase shift keying (DQPSK). To demonstrate and visualize the RF impairments, levels applied in this model are exaggerated and not representative of typical levels for modern radios.

Open Script

Block Characteristics

Data Types	double | single | Boolean | base integer | fixed point | enumerated
Direct Feedthrough	No
Multidimensional Signals	No
Variable-Size Signals	Yes
Zero-Crossing Detection	No

More About

EVM / MER Measurements

The EVM / MER signal quality pane displays the measurement settings, and error vector magnitude (EVM) and modulation error ratio (MER) measurement calculation results for the specified trace selection.

• EVM — An error vector is a vector in the IQ plane from the ideal constellation point to the actual point at the receiver. The root mean square error vector magnitude, EVM_RMS, is measured for the average and peak constellation power.

  On the constellation diagram, you can display the EVM_RMS measurements normalized by either the Average constellation power or Peak constellation power method as computed using these algorithms.

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

  The EVM / MER pane shows the average and peak EVM_RMS in both percent and decibels for the selected trace. The EVM reported 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.

  • 

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

  For more information, see comm.EVM.

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

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

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

  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.

  For more information, see comm.MER.

Extended Capabilities

C/C++ Code Generation

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

This block is excluded from the generated code when code generation is performed on a system containing this block.

HDL Code Generation

Generate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

This block can be used for simulation visibility in subsystems that generate HDL code, but is not included in the hardware implementation.