Eye Diagram Scope

Display eye diagram of time-domain signal

• Library:

• Communications Toolbox / Comm Sinks

  Communications Toolbox HDL Support / Comm Sinks

  Mixed-Signal Blockset / Utilities

  SerDes Toolbox / Utilities

• 

Description

The Eye Diagram block displays multiple traces of a modulated signal to produce an eye diagram. You can use the block to reveal the modulation characteristics of the signal, such as the effects of pulse shaping or channel distortions. For more information, see Eye Diagram Analysis.

The Eye Diagram block has one input port. This block accepts a column vector or scalar input signal. The block accepts a signal with the following data types: double, single, base integer, and fixed point. All data types are cast as double before the block displays results.

To modify the eye diagram display, select View > Configuration Properties or click the Configuration Properties button (). Then select the Main, 2D color histogram, Axes, or Export tabs and modify the settings.

Ports

Input

In — Input signal

scalar | column vector

Input signal, specified as a scalar or column vector.

Data Types: double

Parameters

Main Tab

Display mode — Display mode

Line plot (default) | 2D color Histogram

Display mode of the eye diagram, specified as Line plot or 2D color histogram. Selecting 2D color histogram makes the histogram tab available.

Tunable: Yes

Enable measurements — Enable measurements

off (default) | on

Select this check box to enable eye measurements of the input signal.

Show horizontal (jitter) histogram — Display jitter histogram

off (default) | on

Select this radio button to display the jitter histogram. This can also be accessed by using the histogram button drop down on the toolbar.

Dependencies

This parameter is available when Display mode is 2D color histogram and Enable measurements is selected.

Show vertical (noise) histogram — Display noise histogram

off (default) | on

Select this radio button to display the noise histogram. This can also be accessed by using the histogram button drop down on the toolbar.

Dependencies

This parameter is available when Display mode is 2D color histogram and Enable measurements is selected.

Do not show horizontal or vertical histogram — Do not show horizontal or vertical histogram

on (default) | off

Select this radio button to display neither the histogram noise nor the histogram jitter.

Dependencies

This parameter is available when Display mode is 2D color histogram and Enable measurements is selected.

Show horizontal bathtub curve — Show horizontal bathtub curve

off (default) | on

Select this check box to display the horizontal bathtub curve. This can also be accessed by using the bathtub curve button on the toolbar.

Dependencies

This parameter is available when Enable measurements is selected.

Show vertical bathtub curve — Show vertical bathtub curve

off (default) | on

Select this check box to display the vertical bathtub curve. This can also be accessed by using the bathtub curve button on the toolbar.

Dependencies

This parameter is available when Enable measurements is selected.

Eye diagram to display — Eye diagram to display

Real only (default) | Real and imaginary

Select either Real only or Real and imaginary to display one or both eye diagrams. To make eye measurements, this parameter must be Real only.

Tunable: Yes

Color fading — Color fading

off (default) | on

Select this check box to fade the points in the display as the interval of time after they are first plotted increases.

Tunable: Yes

Dependencies

This parameter is available only when the Display mode is Line plot.

Samples per symbol — Samples per symbol

8 (default) | positive integer

Number of samples per symbol, specified as a positive integer. Use with Symbols per trace to determine the number of samples per trace.

Tunable: Yes

Sample offset — Sample offset

0 (default) | nonnegative integer

Sample offset, specified as a nonnegative integer smaller than the product of Samples per symbol and Symbols per trace. The offset provides the number of samples to omit before plotting the first point.

Tunable: Yes

Symbols per trace — Symbols per trace

2 (default) | positive integer

Number of symbols plotted per trace, specified as a positive integer.

Tunable: Yes

Traces to display — Number of traces to display

40 (default) | positive integer

Number of traces plotted, specified as a positive integer.

Tunable: Yes

Dependencies

This parameter is available only when the Display mode is Line plot

Axes Tab

Title — Title label

None (default)

Label that appears above the eye diagram plot.

Tunable: Yes

Show grid — Toggle scope grid

on (default) | off

Toggle this check box to turn the grid on and off.

Tunable: Yes

Y-limits (Minimum) — Lower limit of y-axis

-1.1 (default) | scalar

Minimum value of the y-axis.

Tunable: Yes

Y-limits (Maximum) — Upper limit of y-axis

1.1 (default) | scalar

Maximum value of the y-axis.

Tunable: Yes

Real axis label — Real axis label

Real Amplitude (default)

Text that the scope displays along the real axis.

Tunable: Yes

Imaginary axis label — Imaginary axis label

Imaginary Amplitude (default)

Text that the scope displays along the imaginary axis.

Tunable: Yes

2D Histogram Tab

The 2D histogram tab is available when you click the histogram button or when the display mode is set to 2D color histogram.

Oversampling method — Oversampling method

None (default) | Input interpolation | Histogram interpolation

Oversampling method, specified as None, Input interpolation, or Histogram interpolation.

To plot eye diagrams as quickly as possible, set the Oversampling method to None. The drawback to not oversampling is that the plots look pixelated when the number of samples per trace is small. To create smoother, less-pixelated plots using a small number of samples per trace, set the Oversampling method to Input interpolation or Histogram interpolation. Input interpolation is the faster of the two interpolation methods and produces good results when the signal-to-noise ratio (SNR) is high. With a lower SNR, this oversampling method is not recommended because it introduces a bias to the centers of the histogram ranges. Histogram interpolation is not as fast as the other techniques, but it provides good results even when the SNR is low.

Tunable: Yes

Color scale — Color scale

Linear (default) | Logarithmic

Color scale of the histogram plot, specified as either Linear or Logarithmic. Set Color scale to Logarithmic if certain areas of the eye diagram include a disproportionate number of points.

Tunable: Yes

The toolbar contains a histogram reset button , which resets the internal histogram buffers and clears the display. This button is not available when the display mode is set to Line plot.

Export Tab

Export measurements, histograms and bathtub curves — Export measurements, histograms and bathtub curves

Off (default) | off

Select this check box export the eye diagram measurements to the MATLAB^® workspace.

Tunable: Yes

Variable name — Variable name

EyeData (default)

Specify the name of the variable to which the eye diagram measurements are saved. The data is saved as a structure having these fields:

• MeasurementSettings

• Measurements

• JitterHistogram

• NoiseHistogram

• HorizontalBathtub

• VerticalBathtub

• BlockName

Tunable: Yes

Style Dialog Box

In the Style dialog box, you can customize the style of the active display. You can change the color of the figure containing the displays, the background and foreground colors of display axes, and properties of lines in a display. To open this dialog box, select View > Style.

Figure color — Figure color

black (default)

Specify the background color of the scope figure.

Axes colors — Axes colors

black | gray (default)

Specify the fill and line colors for the axes.

Line — Line style, thickness and color for line plots

continuous | 0.5 | yellow (default)

Specify the line style, line width, and line color for the displayed signal.

Dependencies

This parameter is available only when the Display mode is Line plot.

Marker — Data point marker

None (default) | ...

Data point marker for the selected signal, specified as one of the choices in this table data point markers. This parameter is similar to the Marker property for MATLAB Handle Graphics^® plot objects.

Specifier	Marker Type
none	No marker (default)
	Circle
	Square
	Cross
	Point
	Plus sign
	Asterisk
	Diamond
	Downward-pointing triangle
	Upward-pointing triangle
	Left-pointing triangle
	Right-pointing triangle
	Five-pointed star (pentagram)
	Six-pointed star (hexagram)

Dependencies

This parameter is available only when the Display mode is Line plot.

Colormap — Colormap for histograms

Hot (default) | Parula | Jet | HSV | Cool | SpringSummer | Autumn | Winter | Gray | Bone | Copper | Pink | Lines | Custom

Specify the colormap of the histogram plots as one of these schemes: Parula, Jet, HSV, Hot, Cool, Spring, Summer, Autumn, Winter, Gray, Bone, Copper, Pink, Lines, or Custom. If you select Custom, a dialog box pops up from which you can enter code to specify your own colormap.

Dependencies

This parameter is available only when the Display mode is 2D color histogram.

Measurement Settings Pane

To change measurement settings, first select Enable measurements. Then, in the Eye Measurements pane, click the arrow next to Settings. You can control these measurement settings.

Eye level boundaries — Time range for calculating eye levels

[40 60] (default) | two-element vector

Time range for calculating eye levels, specified as a two-element vector. These values are expressed as a percentage of the symbol duration.

Tunable: Yes

Decision boundary — Amplitude level threshold

0 (default) | scalar

Amplitude level threshold in V, specified as a scalar. This parameter separates the different signaling regions for horizontal (jitter) histograms. This parameter is tunable, but the jitter histograms reset when the parameter changes.

For non-return-to-zero (NRZ) signals, set Decision boundary to 0. For return-to-zero (RZ) signals, set Decision boundary to half the maximum amplitude.

Tunable: Yes

Rise/Fall thresholds — Amplitude levels of the rise and fall transitions

[10 90] (default) | two-element vector

Amplitude levels of the rise and fall transitions, specified as a two-element vector. These values are expressed as a percentage of the eye amplitude. This parameter is tunable, but the crossing histograms of the rise and fall thresholds reset when the parameter changes.

Tunable: Yes

Hysteresis — Amplitude tolerance of the horizontal crossings

0 (default) | scalar

Amplitude tolerance of the horizontal crossings in V, specified as a scalar. Increase hysteresis to provide more tolerance to spurious crossings due to noise. This parameter is tunable, but the jitter and the rise and fall histograms reset when the parameter changes.

Tunable: Yes

BER threshold — BER used for eye measurements

1e-12 (default) | nonnegative scalar from 0 to 0.5

BER used for eye measurements, specified as a nonnegative scalar from 0 to 0.5. The value is used to make measurements of random jitter, total jitter, horizontal eye openings, and vertical eye openings.

Tunable: Yes

Bathtub BERs — BER values used to calculate openings of bathtub curves

[0.5 0.1 0.01 0.001 0.0001 1e-05 1e-06 1e-07 1e-08 1e-09 1e-10 1e-11 1e-12] (default) | vector

BER values used to calculate openings of bathtub curves, specified as a vector whose elements range from 0 to 0.5. Horizontal and vertical eye openings are calculated for each of the values specified by this parameter.

Tunable: Yes

Dependencies

To enable this parameter, select Show horizontal bathtub curve, Show vertical bathtub curve, or both.

Measurement delay — Duration of initial data discarded from measurements

0 (default) | nonnegative scalar

Duration of initial data discarded from measurements, in seconds, specified as a nonnegative scalar.

Model Examples

Visualize Random and Deterministic Jitter

The doc_visualize_jitter model generates bipolar data, adds deterministic and random jitter, applies white noise, and displays the resulting eye diagram.

Block Characteristics

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

More About

Using Eye Diagram in Conditionally Executed Subsystems

When an Eye Diagram block is placed in a conditionally executed subsystem, for example in a triggered or enabled subsystem:

• Input size must be an integer multiple of SamplesPerSymbol * SymbolsPerTrace

• Sample offset must be zero

• The rightmost part of the display is intentionally omitted. This figure compares typical eye diagram display when placed in a normal system versus one placed in a conditionally executed subsystem.

  Eye Diagram Plot in Normal System	Eye Diagram Plot in Conditionally Executed Subsystem
  In a regular Eye Diagram,​ the rightmost part is a line between the last sample of a trace and the first sample of the next trace.	In conditionally executed subsystems,​ these traces may be non-contiguous,​ thus this rightmost segment could corrupt the display and is omitted.

Measurements

Measurements assume that the eye diagram object has valid data. A valid eye diagram has two distinct eye crossing points and two distinct eye levels.

To open the measurements pane, click on the Eye Measurements button or select Tools > Measurements > Eye Measurements from the toolbar menu.

Note

• For amplitude measurements, at least one bin per vertical histogram must reach 10 hits before the measurement is taken, ensuring higher accuracy.

• For time measurements, at least one bin per horizontal histogram must reach 10 hits before the measurement is taken.

• When an eye crossing time measurement falls within the [-0.5/Fs, 0) seconds interval, the time measurement wraps to the end of the eye diagram, i.e., the measurement wraps by 2×T_s seconds (where T_s is the symbol time). For a complex signal case, the analyze method issues a warning if the crossing time measurement of the in-phase branch wraps while that of the quadrature branch does not (or vice versa). To avoid time-wrapping or a warning, add a half-symbol duration delay to the current value in the MeasurementDelay property of the eye diagram object. This additional delay repositions the eye in the approximate center of the scope.

Eye Levels - Amplitude level used to represent data bits

Eye level is the amplitude level used to represent data bits. For the displayed NRZ signal, the levels are –1 V and +1 V. The eye levels are calculated by averaging the 2-D histogram within the eye level boundaries. For example, when the EyeLevelBoundaries property is set to [40 60], that is, 40% and 60% of the symbol duration, the eye levels are calculated by estimating the mean value of the vertical histogram in this window marked by the eye level boundaries.

Eye Amplitude - Distance between eye levels

Eye amplitude is the distance in V between the mean value of two eye levels.

Eye Height - Statistical minimum distance between eye levels

Eye height is the distance between μ – 3σ of the upper eye level and μ + 3σ of the lower eye level. μ is the mean of the eye level, and σ is the standard deviation.

Vertical Opening - Distance between BER threshold points

The vertical opening is the distance between the two points that correspond to the BERThreshold property. For example, for a BER threshold of 10^–12, these points correspond to the 7σ distance from each eye level.

Eye SNR - Signal-to-noise ratio

The eye SNR is the ratio of the eye level difference to the difference of the vertical standard deviations corresponding to each eye level:

$$\text{SNR}=\frac{L_1-L_0}{{\sigma }_1-{\sigma }_0},$$

where L₁ and L₀ represent the means of the upper and lower eye levels and σ₁ and σ₀ represent their standard deviations.

Q Factor - Quality factor

The Q factor is the quality factor and is calculated using the same formula as the eye SNR. However, the standard deviations of the vertical histograms are replaced with those computed with the dual-Dirac analysis.

Crossing Levels - Amplitude levels for eye crossings

The crossing levels are the amplitude levels at which the eye crossings occur.

The level at which the input signal crosses the amplitude value is specified by the DecisionBoundary property.

Crossing Times - Times for which crossings occur

The crossing times are the times at which the crossings occur. The times are computed as the mean values of the horizontal (jitter) histograms.

Eye Delay - Mean time between eye crossings

Eye delay is the midpoint between the two crossing times.

Eye Width - Statistical minimum time between eye crossings

Eye width is the horizontal distance between μ + 3σ of the left crossing time and μ – 3σ of the right crossing time. μ is the mean of the jitter histogram, and σ is the standard deviation.

Horizontal Opening - Time between BER threshold points

The horizontal opening is the distance between the two points that correspond to the BERThreshold property. For example, for a 10^–12 BER, these two points correspond to the 7σ distance from each crossing time.

Rise Time - Time to transition from low to high

Rise time is the mean time between the low and high rise/fall thresholds defined in the eye diagram. The default thresholds are 10% and 90% of the eye amplitude.

Fall Time - Time to transition from high to low

Fall time is the mean time between the high and low rise/fall thresholds defined in the eye diagram. The default thresholds are 10% and 90% of the eye amplitude.

Deterministic Jitter - Deterministic deviation from ideal signal timing

Jitter is the deviation of a signal’s timing event from its intended (ideal) occurrence in time [2]. Jitter can be represented with a dual-Dirac model. A dual-Dirac model assumes that the jitter has two components: deterministic jitter (DJ) and random jitter (RJ).

DJ is the distance between the two peaks of the dual-Dirac histograms. The probability density function (PDF) of DJ is composed of two delta functions.

Random Jitter - Random deviation from ideal signal timing

RJ is the Gaussian unbounded jitter component. The random component of jitter is modeled as a zero-mean Gaussian random variable with a specified standard-deviation of σ. The RJ is computed as:

$$\text{RJ}=(Q_L+Q_R)\sigma ,$$

where

$$Q=\sqrt{2}{\mathrm{erfc}}^{-1}\left(2\frac{BER}{\rho }\right).$$

BER is the specified BER threshold. ρ is the amplitude of the left and right Dirac function, which is determined from the bin counts of the jitter histograms.

Total Jitter - Deviation from ideal signal timing

Total jitter (TJ) is the sum of the deterministic and random jitter, such that TJ = DJ + RJ.

The total jitter PDF is the convolution of the DJ PDF and the RJ PDF.

RMS Jitter - Standard deviation of jitter

RMS jitter is the standard deviation of the jitter calculated in the horizontal (jitter) histogram at the decision boundary.

Peak-to-Peak Jitter - Distance between extreme data points of histogram

Peak-to-peak jitter is the maximum horizontal distance between the left and right nonzero values in the horizontal histogram of each crossing time.

View Eye Diagram

Display the eye diagram of a filtered QPSK signal using the Eye Diagram block.

Load the doc_eye_diagram_scope model from the MATLAB command prompt.

doc_eye_diagram_scope

Run the model and observe that two symbols are displayed.

Open the configuration parameters dialog box. Change the Symbols per trace parameter to 4. Run the simulation and observe that four symbols are displayed.

Try changing the Raised Cosine Transmit Filter parameters or changing additional Eye Diagram parameters to see their effects on the eye diagram.

Histogram Plots

Display histogram plots of a noisy GMSK signal.

Load the doc_eye_diagram_gmsk model from the MATLAB command prompt.

doc_eye_diagram_gmsk

Run the model. The eye diagram is configured to show a histogram without interpolation.

The lack of interpolation results in a plot having piecewise-continuous behavior.

Open the 2D Histogram tab of the Configuration Properties dialog box. Set the Oversampling method to Input interpolation. Run the model.

The interpolation smooths the eye diagram.

On the AWGN Channel block, change SNR (dB) from 25 to 10. Run the model.

Observe that vertical striping is present in the eye diagram. This striping is the result of input interpolation, which has limited accuracy in low-SNR conditions.

Set the Oversampling method to Histogram interpolation. Run the model.

The eye diagram plot now renders accurately because the histogram interpolation method works for all SNR values. This method is not as fast as the other techniques and results in increased execution time.

Programmatic Configuration

You can programmatically configure the scope properties with callbacks or within scripts by using a scope configuration object as describe 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.