comm.EyeDiagram

(Removed) Display eye diagram of time-domain signals

comm.EyeDiagram has been removed. To display the eye diagram of a signal, use the eyediagram function instead. For more details on the recommended workflow, see Version History.

Description

The comm.EyeDiagram System object™ displays multiple traces of a modulated signal to produce an eye diagram. You can use the object to reveal the modulation characteristics of the signal, such as the effects of pulse shaping or channel distortions. The eye diagram can measure signal characteristics and plot horizontal and vertical bathtub curves when the jitter and noise comply with the dual-Dirac model [1].

To display the eye diagram of an input signal:

Create the comm.EyeDiagram object and set its properties.
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

ed = comm.EyeDiagram

ed = comm.EyeDiagram(Name,Value)

Description

ed = comm.EyeDiagram creates an eye diagram System object with default property values.

ed = comm.EyeDiagram(Name,Value) sets properties using one or more name-value pair argument. Enclose each property name in single quotes. Unspecified properties have default values.

Example: comm.EyeDiagram('SampleRate',2,'DisplayMode','2D color histogram')

example

Properties

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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 eye diagram window
`'Eye Diagram'` (default) | character vector

Title of eye diagram window, specified as a character vector.

Tunable: Yes

Data Types: char

`SampleRate` — Sample rate of input signal
`1` (default) | positive real-valued scalar

Sample rate of the input signal in hertz, specified as a positive real-valued scalar.

Data Types: double

`SamplesPerSymbol` — Number of samples per symbol
`8` (default) | positive integer

Number of samples per symbol, specified as a positive integer.

Tunable: Yes

Data Types: double

`SampleOffset` — Number of samples to skip before plotting the first point
`0` (default) | nonnegative integer

Number of samples to skip before plotting the first point, specified as a nonnegative integer. To avoid irregular behavior, specify the offset to be less than the product of the SamplesPerSymbol and SymbolsPerTrace properties.

Tunable: Yes

Data Types: double

`SymbolsPerTrace` — Number of symbols per trace
`2` (default) | positive integer

Number of symbols per trace, specified as a positive integer. To obtain eye measurements and visualize bathtub curves, use the default value of 2.

Tunable: Yes

Data Types: double

`TracesToDisplay` — Number of traces to display
`40` (default) | positive integer

Number of traces to display, specified as a positive integer.

Tunable: Yes

Dependencies

To enable this property, set DisplayMode property to 'Line plot'.

Data Types: double

`DisplayMode` — Eye diagram display mode
`'Line plot'` (default) | `'2D color histogram'`

Eye diagram display mode, specified as one of these values.

'Line plot' — Overlay traces by plotting one line for each of the last TracesToDisplay traces.
'2D color histogram' — Display a color gradient that shows how often the input matches different time and amplitude values.

Tunable: Yes

Data Types: char

`EnableMeasurements` — Option to enable eye diagram measurements
`false` (default) | `true`

Option to enable eye diagram measurements, specified as true or false. Set this property to true to display the measurement pane and calculations in the eye diagram.

Tunable: Yes

Data Types: logical

`ShowBathtub` — Option to enable visualization of bathtub curves
`'None'` (default) | `'Horizontal'` | `'Vertical'` | `'Both'`

Option to enable visualization of bathtub curves, specified as 'None', 'Horizontal', 'Vertical', or 'Both'.

Tunable: Yes

Dependencies

To enable this property, set the EnableMeasurements property to true.

Data Types: char

`OverlayHistogram` — Histogram overlay
`'None'` (default) | `'Jitter'` | `'Noise'`

Histogram overlay, specified as 'None', 'Jitter', or 'Noise'.

To overlay a horizontal histogram on the eye diagram, set this property to 'Jitter'.
To overlay a vertical histogram on the eye diagram, set this property to 'Noise'.
To display no histogram overlay, set this property to 'None'.

Tunable: Yes

Dependencies

To enable this property, set the DisplayMode property to '2D color histogram' and EnableMeasurements property to true.

Data Types: char

`DecisionBoundary` — Amplitude level threshold
`0` (default) | real-valued scalar

Amplitude level threshold in volts, specified as a real-valued scalar. This property separates the different signaling regions for horizontal (jitter) histograms. Jitter histograms reset when this property changes.

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

Tunable: Yes

Dependencies

To enable this property, set the EnableMeasurements property to true.

Data Types: double

`EyeLevelBoundaries` — Time range for calculating eye levels
`[40 60]` (default) | two-element row vector

Time range for calculating eye levels, specified as a two-element row vector. Specify the vector values as percentages of the symbol duration.

Tunable: Yes

Dependencies

To enable this property, set the EnableMeasurements property to true.

Data Types: double

`RiseFallThresholds` — Amplitude levels of the rise and fall transitions
`[10 90]` (default) | two-element row vector

Amplitude levels of the rise and fall transitions, specified as a two-element row vector. Specify the vector values as percentages of the eye amplitude. The crossing histograms of the rise and fall thresholds reset when this property changes.

Tunable: Yes

Dependencies

To enable this property, set the EnableMeasurements property to true.

Data Types: double

`Hysteresis` — Amplitude tolerance of the horizontal crossings
`0` (default) | real-valued scalar

Amplitude tolerance of the horizontal crossings in volts, specified as a real-valued scalar. Increase this value to provide more tolerance to spurious crossings due to noise. Jitter and the rise and fall histograms reset when this property changes.

Tunable: Yes

Dependencies

To enable this property, set the EnableMeasurements property to true.

Data Types: double

`BERThreshold` — BER used for eye measurements
`1e-12` (default) | scalar in the range [0, 0.5]

Bit error rate (BER) used for eye measurements, specified as a scalar in the range [0, 0.5]. The System object uses this value to measure the random jitter, the total jitter, horizontal eye openings, and vertical eye openings.

Tunable: Yes

Dependencies

To enable this property, set the EnableMeasurements property to true.

Data Types: double

`BathtubBER` — BER values used to calculate openings of bathtub curves
`[0.5 10.^-(1:12)]` (default) | vector

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

Tunable: Yes

Dependencies

To enable this property, set the EnableMeasurements property to true and ShowBathtub property to 'Both', 'Horizontal', or 'Vertical'.

Data Types: double

`MeasurementDelay` — 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.

Dependencies

To enable this property, set the EnableMeasurements property to true.

Data Types: double

`OversamplingMethod` — 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 OversamplingMethod to 'None'. The drawback to not oversampling is that the plots look pixelated when the number of symbols per trace is small.

To create smoother, less-pixelated plots using a small number of symbols per trace, set OversamplingMethod to'Input interpolation' or 'Histogram interpolation'. In this case, 'Input interpolation' is the faster interpolation method and produces good results when the signal-to-noise ratio (SNR) is high. With a low 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

Dependencies

To enable this property, set the DisplayMode property to '2D color histogram'.

Data Types: char

`ColorScale` — Color scale of the histogram
`'Linear'` (default) | `'Logarithmic'`

Color scale of the histogram, specified as 'Linear' or 'Logarithmic'. Change this property if certain areas of the histogram include a disproportionate number of points. Use the 'Logarithmic' option for eye diagrams with sharp peaks, where the signal repetitively matches specific time and amplitude values.

Tunable: Yes

Dependencies

To enable this property, set the DisplayMode property to '2D color histogram'.

Data Types: char

`ColorFading` — Color fading
`false` (default) | `true`

Color fading, specified as true or false. To fade the points in the display as the interval of time after they are first plotted increases, set this property to true. This animation resembles an oscilloscope.

Tunable: Yes

Dependencies

To enable this property, set the DisplayMode property to 'Line plot'.

Data Types: logical

`ShowImaginaryEye` — Show imaginary signal component
`false` (default) | `true`

Show imaginary signal component, specified as true or false. To view the imaginary or quadrature component of the input signal, set this property to true.

Tunable: Yes

Dependencies

To enable this property, set the EnableMeasurements property to false.

Data Types: logical

`YLimits` — Y-axis limits
`[-1.1 1.1]` (default) | two-element row vector

Y-axis limits of the eye diagram in volts, specified as a two-element vector. The first element corresponds to ymin and the second to ymax. The second element must be greater than the first.

Tunable: Yes

Data Types: double

`ShowGrid` — Option to enable grid display
`false` (default) | `true`

Option to enable grid display on the eye diagram, specified as true or false. To display a grid on the eye diagram, set this property to true.

Tunable: Yes

Data Types: logical

`Position` — Scope window position
four-element row vector

Scope window position in pixels, specified as a four-element row vector of the form [left bottom width height].

Tunable: Yes

Data Types: double

Usage

Syntax

ed(x)

Description

ed(x) displays and analyzes input signal x in an eye diagram.

Input Arguments

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`x` — Input signal
vector | matrix

Input signal to be analyzed and displayed in the eye diagram, specified as a vector or matrix. x can be either a real or complex vector, or a real two-column matrix.

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)

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Specific to `comm.EyeDiagram`

`show`	Show scope window
`hide`	Hide scope window
`horizontalBathtub`	(Removed) Horizontal bathtub curve
`verticalBathtub`	(Removed) Vertical bathtub curve
`jitterHistogram`	(Removed) Jitter histogram
`noiseHistogram`	(Removed) Noise histogram
`measurements`	(Removed) Measure eye diagram parameters

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

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Eye Diagram of Filtered QPSK Signal

Specify the sample rate and the number of output samples per symbol parameters.

fs = 1000;
sps = 4;

Create transmit filter and eye diagram objects.

txfilter = comm.RaisedCosineTransmitFilter(...
    'OutputSamplesPerSymbol',sps);
ed = comm.EyeDiagram('SampleRate',fs*sps,'SamplesPerSymbol',sps);

Generate random symbols and apply QPSK modulation. Then filter the modulated signal and display the eye diagram.

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

txSig = txfilter(modSig);
ed(txSig)

Eye diagram of a filtered QPSK signal

More About

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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:

$SNR = \frac{L_{1} - L_{0}}{σ_{1} - σ_{0}},$

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:

$RJ = (Q_{L} + Q_{R}) σ,$

where

$Q = \sqrt{2} {erfc}^{- 1} (2 \frac{B E R}{ρ}) .$

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.

References

[1] Stephens, Ransom. "Jitter analysis: The dual-Dirac model, RJ/DJ, and Q-scale." Agilent Technical Note (2004).

[2] Ou, N., T. Farahmand, A. Kuo, S. Tabatabaei, and A. Ivanov. “Jitter Models for the Design and Test of Gbps-Speed Serial Interconnects.” IEEE Design and Test of Computers 21, no. 4 (July 2004): 302–13. https://doi.org/10.1109/MDT.2004.34.

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 R2016b

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R2022a: `comm.EyeDiagram` has been removed

comm.EyeDiagram has been removed. To display the eye diagram of a signal, use the eyediagram function instead.

comm.EyeDiagram

Description

Creation

Syntax

Description

Properties

Name — Title of eye diagram window 'Eye Diagram' (default) | character vector

SampleRate — Sample rate of input signal 1 (default) | positive real-valued scalar

SamplesPerSymbol — Number of samples per symbol 8 (default) | positive integer

SampleOffset — Number of samples to skip before plotting the first point 0 (default) | nonnegative integer

SymbolsPerTrace — Number of symbols per trace 2 (default) | positive integer

TracesToDisplay — Number of traces to display 40 (default) | positive integer

Dependencies

DisplayMode — Eye diagram display mode 'Line plot' (default) | '2D color histogram'

EnableMeasurements — Option to enable eye diagram measurements false (default) | true

ShowBathtub — Option to enable visualization of bathtub curves 'None' (default) | 'Horizontal' | 'Vertical' | 'Both'

Dependencies

OverlayHistogram — Histogram overlay 'None' (default) | 'Jitter' | 'Noise'

Dependencies

DecisionBoundary — Amplitude level threshold 0 (default) | real-valued scalar

Dependencies

EyeLevelBoundaries — Time range for calculating eye levels [40 60] (default) | two-element row vector

Dependencies

RiseFallThresholds — Amplitude levels of the rise and fall transitions [10 90] (default) | two-element row vector

Dependencies

Hysteresis — Amplitude tolerance of the horizontal crossings 0 (default) | real-valued scalar

Dependencies

BERThreshold — BER used for eye measurements 1e-12 (default) | scalar in the range [0, 0.5]

Dependencies

BathtubBER — BER values used to calculate openings of bathtub curves [0.5 10.^-(1:12)] (default) | vector

Dependencies

MeasurementDelay — Duration of initial data discarded from measurements 0 (default) | nonnegative scalar

Dependencies

OversamplingMethod — Oversampling method 'None' (default) | 'Input interpolation' | 'Histogram interpolation'

Dependencies

ColorScale — Color scale of the histogram 'Linear' (default) | 'Logarithmic'

Dependencies

ColorFading — Color fading false (default) | true

Dependencies

ShowImaginaryEye — Show imaginary signal component false (default) | true

Dependencies

YLimits — Y-axis limits [-1.1 1.1] (default) | two-element row vector

ShowGrid — Option to enable grid display false (default) | true

Position — Scope window position four-element row vector

Usage

Syntax

Description

Input Arguments

x — Input signal vector | matrix

Object Functions

Specific to comm.EyeDiagram

Common to All System Objects

Examples

Eye Diagram of Filtered QPSK Signal

More About

Measurements

References

Extended Capabilities

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

Version History

R2022a: comm.EyeDiagram has been removed

See Also

Objects

Blocks

Functions

`Name` — Title of eye diagram window
`'Eye Diagram'` (default) | character vector

`SampleRate` — Sample rate of input signal
`1` (default) | positive real-valued scalar

`SamplesPerSymbol` — Number of samples per symbol
`8` (default) | positive integer

`SampleOffset` — Number of samples to skip before plotting the first point
`0` (default) | nonnegative integer

`SymbolsPerTrace` — Number of symbols per trace
`2` (default) | positive integer

`TracesToDisplay` — Number of traces to display
`40` (default) | positive integer

`DisplayMode` — Eye diagram display mode
`'Line plot'` (default) | `'2D color histogram'`

`EnableMeasurements` — Option to enable eye diagram measurements
`false` (default) | `true`

`ShowBathtub` — Option to enable visualization of bathtub curves
`'None'` (default) | `'Horizontal'` | `'Vertical'` | `'Both'`

`OverlayHistogram` — Histogram overlay
`'None'` (default) | `'Jitter'` | `'Noise'`

`DecisionBoundary` — Amplitude level threshold
`0` (default) | real-valued scalar

`EyeLevelBoundaries` — Time range for calculating eye levels
`[40 60]` (default) | two-element row vector

`RiseFallThresholds` — Amplitude levels of the rise and fall transitions
`[10 90]` (default) | two-element row vector

`Hysteresis` — Amplitude tolerance of the horizontal crossings
`0` (default) | real-valued scalar

`BERThreshold` — BER used for eye measurements
`1e-12` (default) | scalar in the range [0, 0.5]

`BathtubBER` — BER values used to calculate openings of bathtub curves
`[0.5 10.^-(1:12)]` (default) | vector

`MeasurementDelay` — Duration of initial data discarded from measurements
`0` (default) | nonnegative scalar

`OversamplingMethod` — Oversampling method
`'None'` (default) | `'Input interpolation'` | `'Histogram interpolation'`

`ColorScale` — Color scale of the histogram
`'Linear'` (default) | `'Logarithmic'`

`ColorFading` — Color fading
`false` (default) | `true`

`ShowImaginaryEye` — Show imaginary signal component
`false` (default) | `true`

`YLimits` — Y-axis limits
`[-1.1 1.1]` (default) | two-element row vector

`ShowGrid` — Option to enable grid display
`false` (default) | `true`

`Position` — Scope window position
four-element row vector

`x` — Input signal
vector | matrix

Specific to `comm.EyeDiagram`

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

R2022a: `comm.EyeDiagram` has been removed