si.MER

Reconstruct MER waveform and estimate MER statistical eye of nonlinear systems

Since R2024b

Description

Use si.MER to perform multiple edge response (MER) waveform reconstruction and estimate the MER statistical eyes of nonlinear systems. You can define the nonlinear system in one of two ways as a set of:

Exhaustive data patterns with the depth of Order+1, where Order is the MER order
Effective step responses

Creation

Syntax

mer = si.MER

mer = si.MER(Name=Value)

Description

mer = si.MER creates an object with reconstructed MER waveform and estimates the statistical eye.

example

mer = si.MER(Name=Value) sets properties using one or more name-value arguments. For example, mer = si.MER('Specification'='Wave','SourceWaves'='SourceWaves','SourceWavesPattern'='SourceWavesPattern') creates an object with reconstructed MER waveform and estimates the statistical eye from the input waveforms defined by 'SourceWaves' and 'SourceWavesPattern'.

Properties

expand all

`Order` — MER order
`1` (default) | integer ≥ 1

MER order, specified as an integer ≥ 1.

Data Types: double

`Modulation` — Number of pulse amplitude modulation symbol levels
`2` (default) | integer ≥ 2

Number of pulse amplitude modulation symbol levels, specified as an integer ≥ 2.

Data Types: double

`SymbolTime` — Time of single symbol duration
`1e-10` (default) | real scalar

Time of a single symbol duration, specified as a real scalar in seconds.

Data Types: double

`SamplesPerSymbol` — Number of samples within single symbol time
`16` (default) | even integer ≥ 4

Number of samples within a single symbol time, specified as an even integer ≥ 4.

Data Types: double

`Specification` — Type of nonlinear system
`'wave'` | `'step'`

Type of nonlinear system, specified as 'wave' or 'step'.

If you set Specification to 'wave', the object defines the system from the values of the SourceWaves and SourceWavesPattern properties.
If you set Specification to 'step', the object defines the system from the values of the SourceEffectiveSteps, SourceEffectiveStepsPattern, and SourceSymbolVoltage properties.

Data Types: char

`SourceWaves` — Input waveform defined by source waves pattern
2-D matrix

Input waveforms defined by SourceWavesPattern, specified as a 2-D matrix.

Each column of the matrix defines the system response to the data pattern specified in each row of SourceWavesPattern. The property must have a uniform time step.

The object uses the SourceWaves property when you set the Specification to 'wave'.

Data Types: double

`SourceWavesPattern` — Symbol pattern
matrix

Symbol patterns, specified as a matrix whose elements are integers ranging from 0 to (Modulation − 1). This matrix defines SourceWaves.

Each row of the matrix represents a distinct pattern. There are Modulation^{(Order +
1)} number of rows and Order + 1 number of columns.

To be functional, SourceWaves and SourceWavesPattern must contain all patterns from 0 to Modulation^(Order+1) expressed in base Modulation integers. The base Modulation integers range from [0 0 ... 0] to [n n ... n], where n is (Modulation − 1).

The object uses the SourceWavesPattern property when you set the Specification to 'wave'.

Data Types: double

`SourceDelay` — Channel delay
integer

Channel delay, specified as an integer in samples. The object uses the SourceDelay property to correctly express the channel delay in the step responses calculated from SourceWaves.

The object uses the SourceDelay property when you set the Specification to 'wave'.

Data Types: double

`SourceEffectiveSteps` — Input MER step responses
matrix

Input MER step responses calculated outside the MER object, specified as a matrix.

The object uses the SourceEffectiveSteps property when you set Specification to 'step'. The property must have a uniform time step.

Data Types: double

`SourceEffectiveStepsPattern` — Input MER step responses patterns
matrix

Step response patterns of the input MER step responses, specified as a matrix.

The object uses the SourceEffectiveStepsPattern property when you set Specification to 'step'.

Data Types: double

`SourceSymbolVoltage` — Input symbol voltage
real scalar

Input symbol voltage for the input MER step responses, specified as a real scalar.

The object uses the SourceSymbolVoltage property when you set Specification to 'step'.

Data Types: double

`ReferenceWave` — Reference waveform to use to validate reconstructed MER waveform
matrix

Reference waveform to use to validate the reconstructed time-domain MER waveform, specified as a matrix.

Data Types: double

`ReferenceWavePattern` — Data pattern of reference waveform
vector of integers in the range [0, (`Modulation` -1)]

Data pattern of the reference waveform, specified as a vector of integers in the range [0, (Modulation−1)].

Data Types: double

`PlotAxis` — Unit of measurement for axes in plot
`'UI'` | `'Seconds'`

Unit of measurement for axes in plot, specified as 'UI' or 'Seconds'.

Data Types: char

`SourceWaveLabel` — Labels for input source waveforms
string

This property is read-only.

Labels for input source waveforms, returned as a text string.

`EffectiveSteps` — Output MER step responses
matrix

This property is read-only.

Calculated MER step responses, returned as a matrix.

`EffectiveStepsPattern` — Calculated MER step responses patterns
matrix

This property is read-only.

Calculated MER step response patterns, returned as a matrix.

`EffectiveStepsLabel` — Label for output MER step responses
string

This property is read-only.

Labels for output MER step responses, returned as a text string.

`SymbolVoltages` — PAM symbol voltage levels
vector

This property is read-only.

PAM symbol voltage levels of the system, returned as a vector.

`VoltageReference` — Threshold between symbol voltage levels
vector

This property is read-only.

Threshold between symbol voltage levels, returned as a vector.

`SampleInterval` — Uniform time step of waveform
real scalar

This property is read-only.

Uniform time step of output waveforms, returned as a scalar.

`Wave` — Symbol pattern of output waveform
matrix

This property is read-only.

Symbol pattern of output waveform created by makWave, returned as a matrix.

`Stateye` — Estimated statistical eye
matrix

This property is read-only.

Estimated statistical eye, returned as a matrix.

`VEye` — Voltage data of statistical eye
vector

This property is read-only.

Voltage data of the statistical eye matrix along the vertical axis, returned as a vector.

`TEye` — Time data of statistical eye
vector

This property is read-only.

Time data of the statistical eye matrix along the horizontal axis, returned as a vector.

`ZkPDF` — Symbol transition probability distribution functions
matrix

This property is read-only.

Symbol transition probability distribution functions (PDFs), returned as a matrix.

`ZkPDFPattern` — Patterns of symbol transition PDFs
matrix

This property is read-only.

Patterns of the symbol transition PDFs, returned as a matrix.

`ZkPDFLabel` — Labels of symbol transition PDFs
string

This property is read-only.

Labels of the symbol transition PDFs, returned as a string.

`StatEyeInfo` — Statistical eye diagram information
structure

This property is read-only.

Statistical eye diagram information, returned as a structure.

`WaveAligned` — Aligned validation waveform
matrix

This property is read-only.

Aligned validation waveform, returned as a matrix

`WaveDifference` — Difference between aligned and reference waveforms
matrix

This property is read-only.

Difference between the aligned and reference waveforms, returned as a matrix.

`ValidationResults` — Validation metrics
structure

This property is read-only.

Validation metrics, returned as a structure. This value helps you to determine if the MER order is sufficient to model the nonlinear system.

`ReferenceWaveEyeInfo` — Reference waveform eye diagram information
structure

This property is read-only.

Reference waveform eye diagram information, returned as a structure.

`AlignedWaveEyeInfo` — Aligned waveform eye diagram information
structure

This property is read-only.

Aligned waveform eye diagram information, returned as a structure. The MER wave is aligned with the reference wave.

`WaveEyeInfo` — Aligned waveform eye diagram information
structure

This property is read-only.

Reconstructed MER waveform eye diagram information, returned as a struct.

Object Functions

`makeWave`	Create symbol pattern waveform
`estimateStateye`	Generate statistical eye from effective step responses
`validateWave`	Compare MER waveform to reference waveform
`plotInputs`	Plot input waveforms and MER effective step responses
`plotValidation`	Plot reconstructed, reference, and error waveforms
`plotStateye`	Plot statistical eye of reconstructed MER waveform
`plotPDFs`	Plot PDFs of MER waveforms

Examples

collapse all

Use Multiple-Edge Responses to Create Statistical Eye

Open Live Script

Define the order and modulation of the nonlinear system.

Order = 1;        % For this example, you can vary the value of order between 1 to 4.
Modulation = 2;   % For this example, you can vary the value of modulation between 1 to 4.

Load the MAT files containing the simulation parameters.

matfilename = sprintf('MERExampleOrder%iModulation%i.mat',Order,Modulation);
load(matfilename)

Create the si.MER object.

mer = si.MER(...
    'Order', MERorder,...
    'Modulation', Modulation,...
    'SamplesPerSymbol', SamplesPerSymbol,...
    'PlotAxis', 'Seconds',...
    'SymbolTime', SymbolTime,...
    'Specification', 'Wave',...
    'SourceWaves', SourceWaves,...
    'SourceWavesPattern', SourceWavesPattern,...
    'SourceDelay', SourceDelay);

Visualize the inputs to the MER analysis by plotting them.

figure,plotInputs(mer)

$Figure contains 2 axes objects. Axes object 1 with title Source waveforms, xlabel ns, ylabel V contains 4 objects of type line. These objects represent y^{00}, y^{01}, y^{10}, y^{11}. Axes object 2 with title MER step responses, xlabel ns, ylabel V contains 2 objects of type line. These objects represent S^{01}, S^{10}.$

Ensure the generated waveforms are accurate by validating them against a reference wave.

figure,mer.validateWave(ReferenceWave,DataPattern,'plot','on')

Plot the statistical eye.

figure,plotStateye(mer)

Figure contains an axes object. The axes object with title MER Statistical NRZ Eye, MER order = 1, xlabel Seconds, ylabel Volts contains an object of type image.

Plot the PDFs.

figure,plotPDFs(mer)

You can change the modulation level and MER orders to better reflect your nonlinear systems. For example, in a PAM3 modulation scheme and an MER of order 1, the input waveforms look as shown in this plot.

And the PDFs and estimated statistical eye looks as shown in these diagrams.

References

[1] Chou, Chiu-Chih, Sheng-Yun Hsu, and Tzong-Lin Wu. “Estimation Method for Statistical Eye Diagram in a Nonlinear Digital Channel.” IEEE Transactions on Electromagnetic Compatibility 57, no. 6 (December 2015): 1655–64. https://doi.org/10.1109/TEMC.2015.2457928.

[2] Ren, JiHong, and Kyung Suk Oh. "Multiple edge responses for fast and accurate system simulations." IEEE Transactions on Advanced Packaging 31, no. 4 (2008): 741–748.

Version History

Introduced in R2024b

si.MER

Description

Creation

Syntax

Description

Properties

Order — MER order 1 (default) | integer ≥ 1

Modulation — Number of pulse amplitude modulation symbol levels 2 (default) | integer ≥ 2

SymbolTime — Time of single symbol duration 1e-10 (default) | real scalar

SamplesPerSymbol — Number of samples within single symbol time 16 (default) | even integer ≥ 4

Specification — Type of nonlinear system 'wave' | 'step'

SourceWaves — Input waveform defined by source waves pattern 2-D matrix

SourceWavesPattern — Symbol pattern matrix

SourceDelay — Channel delay integer

SourceEffectiveSteps — Input MER step responses matrix

SourceEffectiveStepsPattern — Input MER step responses patterns matrix

SourceSymbolVoltage — Input symbol voltage real scalar

ReferenceWave — Reference waveform to use to validate reconstructed MER waveform matrix

ReferenceWavePattern — Data pattern of reference waveform vector of integers in the range [0, (Modulation -1)]

PlotAxis — Unit of measurement for axes in plot 'UI' | 'Seconds'

SourceWaveLabel — Labels for input source waveforms string

EffectiveSteps — Output MER step responses matrix

EffectiveStepsPattern — Calculated MER step responses patterns matrix

EffectiveStepsLabel — Label for output MER step responses string

SymbolVoltages — PAM symbol voltage levels vector

VoltageReference — Threshold between symbol voltage levels vector

SampleInterval — Uniform time step of waveform real scalar

Wave — Symbol pattern of output waveform matrix

Stateye — Estimated statistical eye matrix

VEye — Voltage data of statistical eye vector

TEye — Time data of statistical eye vector

ZkPDF — Symbol transition probability distribution functions matrix

ZkPDFPattern — Patterns of symbol transition PDFs matrix

ZkPDFLabel — Labels of symbol transition PDFs string

StatEyeInfo — Statistical eye diagram information structure

WaveAligned — Aligned validation waveform matrix

WaveDifference — Difference between aligned and reference waveforms matrix

ValidationResults — Validation metrics structure

ReferenceWaveEyeInfo — Reference waveform eye diagram information structure

AlignedWaveEyeInfo — Aligned waveform eye diagram information structure

WaveEyeInfo — Aligned waveform eye diagram information structure

Object Functions

Examples

Use Multiple-Edge Responses to Create Statistical Eye

References

Version History

See Also

WeChat

`Order` — MER order
`1` (default) | integer ≥ 1

`Modulation` — Number of pulse amplitude modulation symbol levels
`2` (default) | integer ≥ 2

`SymbolTime` — Time of single symbol duration
`1e-10` (default) | real scalar

`SamplesPerSymbol` — Number of samples within single symbol time
`16` (default) | even integer ≥ 4

`Specification` — Type of nonlinear system
`'wave'` | `'step'`

`SourceWaves` — Input waveform defined by source waves pattern
2-D matrix

`SourceWavesPattern` — Symbol pattern
matrix

`SourceDelay` — Channel delay
integer

`SourceEffectiveSteps` — Input MER step responses
matrix

`SourceEffectiveStepsPattern` — Input MER step responses patterns
matrix

`SourceSymbolVoltage` — Input symbol voltage
real scalar

`ReferenceWave` — Reference waveform to use to validate reconstructed MER waveform
matrix

`ReferenceWavePattern` — Data pattern of reference waveform
vector of integers in the range [0, (`Modulation` -1)]

`PlotAxis` — Unit of measurement for axes in plot
`'UI'` | `'Seconds'`

`SourceWaveLabel` — Labels for input source waveforms
string

`EffectiveSteps` — Output MER step responses
matrix

`EffectiveStepsPattern` — Calculated MER step responses patterns
matrix

`EffectiveStepsLabel` — Label for output MER step responses
string

`SymbolVoltages` — PAM symbol voltage levels
vector

`VoltageReference` — Threshold between symbol voltage levels
vector

`SampleInterval` — Uniform time step of waveform
real scalar

`Wave` — Symbol pattern of output waveform
matrix

`Stateye` — Estimated statistical eye
matrix

`VEye` — Voltage data of statistical eye
vector

`TEye` — Time data of statistical eye
vector

`ZkPDF` — Symbol transition probability distribution functions
matrix

`ZkPDFPattern` — Patterns of symbol transition PDFs
matrix

`ZkPDFLabel` — Labels of symbol transition PDFs
string

`StatEyeInfo` — Statistical eye diagram information
structure

`WaveAligned` — Aligned validation waveform
matrix

`WaveDifference` — Difference between aligned and reference waveforms
matrix

`ValidationResults` — Validation metrics
structure

`ReferenceWaveEyeInfo` — Reference waveform eye diagram information
structure

`AlignedWaveEyeInfo` — Aligned waveform eye diagram information
structure

`WaveEyeInfo` — Aligned waveform eye diagram information
structure