Constellation Diagram

Display and analyze input signals in IQ-plane

Libraries:
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.

Constellation diagram displaying QPSK,16-QAM, and 8-DPSK signals, and signal quality measurements.

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.

Examples

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View Constellation Diagram

This example uses:

Open Model

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

A random signal is M-PSK modulated, filtered through an AWGN channel, and passed into a Constellation Diagram to be plotted.

Run the slex_constellation_diagram model and observe the 8-PSK constellation. The received data points are shown in yellow while the red ‘+’ symbols represent the ideal constellation locations.

After running the simulation the constellation diagram shows the noisy constellation points.

You can select the Show Signal Trajectory button to display the signal trajectory of the modulated signal.

Plot Noisy QPSK Constellation

This example uses:

Open Model

Apply QPSK modulation to a signal of random data. Pass the modulated signal through an additive white Gaussian noise (AWGN) channel. Plot the signal constellation.

The doc_qpsk_mod model generates QPSK data, applies the AWGN, and displays the resulting constellation diagram.

Run the model with the Eb/N0 of the AWGN Channel block set to 15 dB. The constellation diagram shows the QPSK symbol samples with AWGN.

Change the Eb/N0 from 15 dB to 10 dB. The noise level increases as shown by the greater distance between the samples in the constellation diagram.

View Multi-Input Constellation Diagram

This example uses:

Open Model

This example shows how to use the Constellation Diagram block to visualize the constellation of multi-input and multichannel modulated signals.

Pass two random 16-QAM signals through the first input port and a random 8-PSK signal through the second input port. One reference constellation can be defined for each input port. Since a single reference constellation is applied for all multichannel signals through one input port, use the Vector Concatenate (Simulink) block to concatenate multiple signals of the same data type and same reference constellation. In the case where all input signals are single channel input, then they can be directly fed in the Constellation Diagram.

Filter three signals through the AWGN channel and pass them to a Constellation Diagram.

Run Example Model to Explore Its Constellation

After running the simulation, the constellation diagram shows the noisy constellation points for the input signals. The received data points shown in yellow and blue represent the two 16-QAM input signals, and the received data points shown in red represent the 8-PSK signal. The red ‘+’ symbols represent the ideal constellation locations for 16-QAM modulated signals, and the white ‘+’ symbols represent the ideal constellation locations for 8-PSK modulated signal.

The trajectory trace is shown for each signal below.

Further Exploration

Use the Trace Selection pane to display measurements for the channel of interest.
Consider modifying the model to change the current modulation order.

Extended Examples

Impact of RF Effects on Communication System Performance

Model thermal noise, phase noise, and nonlinearity impairments of an RF transceiver in Simulink^®.

Open Script

Ports

Input

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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

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To edit block parameters interactively, use the Property Inspector. From the Simulink Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.

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

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.

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.

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

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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	$E V M_{k} = 100 \sqrt{\frac{e_{k}}{P_{avg}}}$ EVM_RMS, in percent, for average constellation power normalization: $E V M_{RMS} (%) = 100 \sqrt{\frac{\frac{1}{N} \sum_{k = 1}^{N} (e_{k})}{P_{avg}}}$
Peak constellation power	$E V M_{k} = 100 \sqrt{\frac{e_{k}}{P_{max}}}$ EVM_RMS, in percent, for peak constellation power normalization: $E V M_{RMS} (%) = 100 \sqrt{\frac{\frac{1}{N} \sum_{k = 1}^{N} (e_{k})}{P_{max}}}$

EVM Normalization Method

Algorithm

Average constellation power

$E V M_{k} = 100 \sqrt{\frac{e_{k}}{P_{avg}}}$

EVM_RMS, in percent, for average constellation power normalization:

$E V M_{RMS} (%) = 100 \sqrt{\frac{\frac{1}{N} \sum_{k = 1}^{N} (e_{k})}{P_{avg}}}$

Peak constellation power

$E V M_{k} = 100 \sqrt{\frac{e_{k}}{P_{max}}}$

EVM_RMS, in percent, for peak constellation power normalization:

$E V M_{RMS} (%) = 100 \sqrt{\frac{\frac{1}{N} \sum_{k = 1}^{N} (e_{k})}{P_{max}}}$

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.
$E V M_{RMS} = \sqrt{E V M_{MS}}$

The maximum EVM value in a vector is $E V M_{max} = max_{k \in [1, ..., N]} {E V M_{k}},$ 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
$M E R = 10 \times \log_{10} (\frac{\sum_{k = 1}^{N} (I_{k}^{2} + Q_{k}^{2})}{\sum_{k = 1}^{N} (e_{k})}) dB,$
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 VHDL, Verilog and SystemVerilog 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

Constellation Diagram

Description

Examples

View Constellation Diagram

Plot Noisy QPSK Constellation

View Multi-Input Constellation Diagram

Extended Examples

Impact of RF Effects on Communication System Performance

Ports

Input

In_1, ..., In_N — Signals (as separate ports) column vectors | matrices

Parameters

Plot

Settings — Constellation diagram settings button

Number of input ports — Number of input ports on scope block 1 (default) | integer in the range [1, 20]

Samples per symbol — Number of samples used to represent each symbol 1 (default) | positive integer

Offset — Number of samples to skip before plotting points 0 (default) | nonnegative integer

Symbols to display — Maximum number of symbols to display Input frame length (default) | positive integer

Reference Constellation — Reference constellation configuration button

Show reference constellations — Option to display reference constellations on (default) | off

Input — Select input port 1 (default) | positive integer

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

Custom value — Input reference constellation [0.7071+0.7071i -0.7071+0.7071i -0.7071-0.7071i 0.7070-0.7071i] (default) | vector

Dependencies

Constellation normalization — Normalization method Average power (default) | Minimum distance | Peak power

Dependencies

Average reference power — Average power of reference constellation 1 (default) | positive scalar

Dependencies

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

Dependencies

Legend — Option to display legend button

Trajectory — Option to display signal trajectory button

Measurements

Channel — Active input channel name of first channel in first port (default) | list of channels

Measurement Interval — Duration of EVM and MER measurement Current display (default) | All displays | positive integer

EVM Normalization — Normalization method Average constellation power (default) | Peak constellation power

Reference Constellation — Reference constellation configuration button

EVM/MER — Option to display signal quality measurements pane button

Block Characteristics

More About

EVM and MER Measurements

Programmatic Configuration

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

HDL Code Generation Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

Version History

See Also

Blocks

Objects

Functions

Topics

In_1, ..., In_N — Signals (as separate ports)
column vectors | matrices

Settings — Constellation diagram settings
button

Number of input ports — Number of input ports on scope block
`1` (default) | integer in the range [1, 20]

Samples per symbol — Number of samples used to represent each symbol
`1` (default) | positive integer

Offset — Number of samples to skip before plotting points
`0` (default) | nonnegative integer

Symbols to display — Maximum number of symbols to display
`Input frame length` (default) | positive integer

Reference Constellation — Reference constellation configuration
button

Show reference constellations — Option to display reference constellations
`on` (default) | `off`

Input — Select input port
1 (default) | positive integer

Reference constellation — Reference constellation
`Custom` (default) | `BPSK` | `8-PSK` | `16-QAM` | `64-QAM` | `256-QAM`

Custom value — Input reference constellation
`[0.7071+0.7071i -0.7071+0.7071i -0.7071-0.7071i 0.7070-0.7071i]` (default) | vector

Constellation normalization — Normalization method
`Average power` (default) | `Minimum distance` | `Peak power`

Average reference power — Average power of reference constellation
`1` (default) | positive scalar

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

Legend — Option to display legend
button

Trajectory — Option to display signal trajectory
button

Channel — Active input channel
name of first channel in first port (default) | list of channels

Measurement Interval — Duration of EVM and MER measurement
`Current display` (default) | `All displays` | positive integer

EVM Normalization — Normalization method
`Average constellation power` (default) | `Peak constellation power`

Reference Constellation — Reference constellation configuration
button

EVM/MER — Option to display signal quality measurements pane
button

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

HDL Code Generation
Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.