Constellation Diagram

Display and analyze input signals in IQ-plane

• Library:

• Communications Toolbox / Comm Sinks

  Communications Toolbox HDL Support / Comm Sinks

• 

Description

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

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 Reference Constellation parameter.

• Select signals in the legend to toggle visibility of individual channels. To display the legend, use the Legend parameter on the Plot tab. 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.

Ports

Input

In_1, ..., In_N — Signals (as separate ports)

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 ports, where N is the Number of input ports parameter 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 ports.

Example: [-1 + 1i; -1 - 1i; 1 + 1i; 1 - 1i] specifies a four-symbol input signal.

Data Types: double
Complex Number Support: Yes

Parameters

Plot

In the Plot tab, you can adjust settings of the constellation diagram configuration, simulate the model, take a snapshot of the plot, copy the display, and print the figure. Parameters unique to the constellation diagram scope are described.

Settings — Constellation diagram settings

button

On the Plot tab, click Settings to open the Configuration Plot Settings window. This window includes parameter subsections to configure the data and axes, labels, and color and styling. Parameters unique to the constellation diagram are described on this page.

Number of input ports — Number of input ports on scope block

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

Specify the number of input ports on the scope block as an integer in the range [1, 20].

The total number of input signal channels cannot exceed 20. When you specify multichannel input signals, the total number of input signal channels limits the maximum number of input ports.

Samples per symbol — Number of samples used to represent each symbol

1 (default) | positive integer

Specify the number of samples used to represent each symbol as a positive integer. The signal is downsampled by the value of this parameter before it is plotted.

Offset — Number of samples to skip before plotting points

0 (default) | nonnegative integer

Specify the number of samples to skip before plotting points as a nonnegative integer less than the Samples per symbol parameter value. This value specifies the number of samples to skip when Samples per symbol is greater than 1.

Symbols to display — Maximum number of symbols to display

Input frame length (default) | positive integer

Specify the maximum number of symbols to display by selecting Input frame length or specifying a positive integer. To specify a positive integer, select and then replace <user-defined> with your desired value. Use this parameter to limit the maximum number of symbols that the constellation diagram displays when you input long signals. The block plots the most recently received symbols.

Reference Constellation — Reference constellation configuration

button

On the Plot tab or Measurements tab, click Reference Constellation, to open the Reference Constellation window. This window includes parameters to configure the reference constellation for each input port.

Show reference constellations — Option to display reference constellations

on (default) | off

Select this parameter to show reference constellations on the plot.

Input — Select input port

1 (default) | positive integer

Configure the reference constellation parameters for the specified input port.

Each input port has its own reference constellation. For a multichannel input signal, the block applies a single reference constellation for all signals in that input port.

Reference constellation — Reference constellation

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

Specify the reference constellation by selecting Custom, BPSK, QPSK, 8-PSK, 16-QAM, 64-QAM, or 256-QAM. To specify a custom value, first select Custom. Then in the Custom value parameter, replace the entry with your custom vector of symbol values.

Each input port had its own reference constellation. For a multichannel input signal, the block applies a single reference constellation for all signals in that input port.

The EVM/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.

Custom value — Input reference constellation

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

Specify the reference constellation for an input as a vector that defines symbol values for the custom modulation scheme.

Dependencies

To enable this parameter, set the Reference constellation parameter to Custom Reference Constellation.

Data Types: char | double
Complex Number Support: Yes

Constellation normalization — Normalization method

Average power (default) | Minimum distance | Peak power

Specify the normalization method that the block uses for the constellation diagram by selecting Average power, Minimum distance, or Peak power.

Dependencies

To enable this parameter, set the Reference constellation parameter to 16-QAM, 64-QAM, or 256-QAM.

Average reference power — Average power of reference constellation

1 (default) | positive scalar

Specify the average power of the reference constellation as a positive scalar. The average power is referenced to a one-ohm load. Units are in watts.

Dependencies

To enable this parameter, set the Reference constellation parameter to BPSK, QPSK, 8-PSK, 16-QAM, 64-QAM, or 256-QAM.

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

scalar

Specify the phase offset of the reference constellation as a scalar. Units are in radians.

Dependencies

To enable this parameter, set the Reference constellation parameter to BPSK, QPSK, 8-PSK, 16-QAM, 64-QAM, or 256-QAM.

• The default value is 0 for BPSK, 16-QAM, 64-QAM, and 256-QAM.

• The default value is pi/4 for 8-PSK.

• The default value is pi/8 for QPSK.

Legend — Option to display legend

button

On the Plot tab, click Legend to toggle the display of the legend. The names listed in the legend are the names for signals connected to input ports as specified in the model. The legend does not display until the model runs with an input signal.

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

Trajectory — Option to display signal trajectory

button

On the Plot tab, click Trajectory to toggle the display of the trajectory. Select this parameter to display the trajectory between constellation points for the plotted signals.

Measurements

In the Measurements tab, you can select the active channel, configure the signal quality measurements, and toggle the Measurements pane.

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

Channel

Channel — Active input channel

name of first channel in first port (default) | list of channels

Select the active input channel for measurements from the list of input channels. Click EVM/MER to display the signal quality measurements for the active channel.

The total number of input signal channels cannot exceed 20. When you specify multichannel input signals, the total number of input signal channels limits the maximum permitted value for the Number of input ports parameter.

Measurements

Measurement Interval — Duration of EVM and MER measurement

Current display (default) | All displays | positive integer

Specify the duration of the EVM and MER measurement in symbols by selecting Current Display, or All displays or by specifying a positive integer. To specify a positive integer, select and then replace <user-defined> with your desired value. The value must be a positive value in the range [1, Symbols to display). The block computes measurements after the number of input data samples exceeds the measurement interval.

EVM Normalization — Normalization method

Average constellation power (default) | Peak constellation power

Specify the normalization method that the block uses for the EVM normalization by selecting Average constellation power or Peak constellation power.

Reference Constellation — Reference constellation configuration

button

On the Plot tab or Measurements tab, click Reference Constellation, to open the Reference Constellation window. This window includes parameters to configure the reference constellation for each input port. For parameter descriptions, see the Reference Constellation parameter in the Plot section.

EVM/MER — Option to display signal quality measurements pane

button

On the Measurements tab, click EVM/MER to toggle display the signal quality measurements pane. For more information, see EVM and MER Measurements.

Model Examples

View Constellation Diagram

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

Open Model

View Multi-Input Constellation Diagram

Use the Constellation Diagram block to visualize the constellation of multi-input and multichannel modulated signals.

Open Model

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	Boolean | double | enumerated | fixed point | integer | single
Direct Feedthrough	no
Multidimensional Signals	no
Variable-Size Signals	yes
Zero-Crossing Detection	no

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.

Programmatic Configuration

You can programmatically configure the scope properties with callbacks or within scripts by using a scope configuration object as described in Control Scope Blocks Programmatically (Simulink).

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.

Version History

Introduced in R2013b