Allows observation and analysis of eye diagrams

## Keywords

analyzer, electrical, unidirectional, bidirectional

## Ports

Name | Type |
---|---|

reference | Electrical Signal |

input | Electrical Signal |

## Properties

### General Properties

Name | Default value | Default unit | Range |
---|---|---|---|

Defines the name of the element. |
Eye Diagram | - | - |

Defines whether or not to display annotations on the schematic editor. |
true | - | [true, false] |

Defines whether or not the element is enabled. |
true | - | [true, false] |

Defines the element unique type (read only). |
Eye Diagram | - | - |

A brief description of the elements functionality. |
Allows observation and analysis of eye diagrams | - | - |

Defines the element name prefix. |
EYE | - | - |

Defines the element model name. |
- | - | - |

Defines the element location or source in the library (custom or design kit). |
- | - | - |

Defines the local path or working folder $LOCAL for the element. |
- | - | - |

An optional URL address pointing to the element online help. |
- | - | - |

Defines the icon or element symbol view option. |
small | - | [small, medium |

### Standard Properties

Name | Default value | Default unit | Range |
---|---|---|---|

Defines whether or not to enable the bit pattern input port. The bit pattern input port allows for clock recovery of the input signal. |
false | - | [true, false] |

Defines the input signal bitrate. |
%bitrate% | bits/s | [1, +∞) |

Defines whether or not to enable the signal reference input port. The reference input port allows for automatic delay compensation of the input signal. |
true | - | [true, false] |

The number of periods displayed in the eye diagram. |
1.5 | bit period | [1, +∞) |

The number of consecutive bits at the begging of the signal waveform to be excluded from the eye diagram. |
8 | - | [0, +∞) |

The number of consecutive bits at the end of the signal waveform to be excluded from the eye diagram. |
8 | - | [0, +∞) |

Defines whether or not to use the automatic synchronization delay. |
automatic | - | [automatic, user defined |

The time delay to apply to the input signal. |
0 | s | (-∞, +∞) |

Enables setting the time range( start/stop) of the analysis. |
false | - | [true, false] |

Time instant to start the signal analysis. |
0 | s | [0, +∞) |

Time instant to stop the signal analysis. |
1 | s | [0, +∞) |

### Enhanced Properties

Name | Default value | Default unit | Range |
---|---|---|---|

Defines whether or not to enable color grading. It allows to color code the eye to display the frequency (histogram) at which a certain point in the eye is reached |
true | - | [true, false] |

The number of vertical and horizontal bins used to calculate the histogram required to generate the color grading. |
500 | - | [0, +∞) |

The number of samples used to smooth the color grading effect. It is equivalent to a average moving filter applied to each signal trace. |
10 | - | [0, +∞) |

Defines whether or not to enable random sampling effect. It is used to create realistic displays of measured eye diagrams. |
false | - | [true, false] |

Defines the time unit to plot the analyzer results. |
s | - | [s, bit period |

Defines the icon or element symbol view option. |
2 | - | [2, +∞) |

Defines whether or not to automatically determine the optimum decision point for eye measurements. |
automatic | - | [automatic, user defined |

Defines the decision instant for eye measurements. |
20e-012 | s | (-∞, +∞) |

Defines the decision amplitude for eye measurements. |
0.5 | a.u. | - |

Defines type of algorithm used for BER estimation. |
Gaussian | - | [Gaussian, measured |

Defines whether or not to calculate eye measurements. Measurements include 'BER', 'Q factor', 'jitter', etc. |
false | - | [true, false] |

Defines whether or not to calculate eye graphs. Graphs include 'min BER vs. time', 'Q factor vs. time', etc. |
false | - | [true, false] |

Defines whether the eye opening tolerance, used to estimate the calculation range where the eye is considered open. |
0 | ratio | [0, 1] |

Defines whether or not to plot waveforms. Waveforms include 'signal input', 'signal reference', 'bit pattern', etc. |
false | - | [true, false] |

The minimum detectable amplitude (real and imag) value. |
0 | - | [0, +∞) |

### Simulation Properties

Name | Default value | Default unit | Range |
---|---|---|---|

Input signal selection option. |
last | - | [last, index |

The signal index to analyzed. |
1 | - | [1, +∞) |

Defines whether inserted delays should be included as part of the signal or not. |
false | - | [true, false] |

### Display Properties

Name | Default value | Default unit | Range |
---|---|---|---|

Defines whether or not to update display and annotations during the simulation. |
true | - | [true, false] |

Defines how ofter to update the element. This is the minimum number of new data values available at the element input port that will trigger the element update. |
8192 | - | [0, +∞) |

Defines whether or not to limit the number of values displayed in the element display. |
true | - | [true, false] |

This is the number of data values used to update the display and annotations during the simulation. |
2048 | - | [2, +∞) |

## Results

Name | Description |
---|---|

eye diagram | The eye diagram is constructed from the input signal waveform by overlapping the parts of the waveform corresponding to each individual bit into a single graph with signal amplitude on the vertical axis and time on horizontal axis. |

waveform/reference | The reference signal waveform used for delay compensation of the input signal. |

waveform/correlation | The correlation between the input and the reference signal waveform. |

waveform/input | The input signal waveform after delay compensation. |

waveform/bit pattern | The digital signal after the detection of 'ones' and 'zeros' levels. |

measurement/decision instant | The decision instant used to calculate the eye measurements.If 'automatic' decision point is selected, this is the decision instant at the minimum BER. |

measurement/threshold | The threshold value used to calculate the eye measurements.If 'automatic' decision point is selected, this is the threshold at the minimum BER. |

measurement/level zero mean | The mean value of 'zero' levels (μ) at the measured decision instant and threshold._{0} |

measurement/level zero sigma | The standard deviation of 'zero' levels (σ) at the measured decision instant and threshold._{0} |

measurement/level one mean | The mean value of 'one' levels (μ) at the measured decision instant and threshold._{1} |

measurement/level one sigma | The standard deviation of 'one' levels (σ) at the measured decision instant and threshold._{1} |

measurement/BER | The BER at the measured decision instant and threshold. |

measurement/log of BER | The log of BER at the measured decision instant and threshold. |

measurement/Q factor | The Q factor at the measured decision instant. |

measurement/height | The eye height (E) at the measured decision instant and threshold._{H}=μ_{1}-μ_{0}-3(σ_{1}+σ_{0}) |

measurement/amplitude | The eye amplitude (E) at the measured decision instant and threshold._{A}=μ_{1}-μ_{0}) |

measurement/extinction ratio | The extinction ratio (E) at the measured decision instant and threshold._{r}=μ_{1}/μ_{0} |

measurement/opening factor | The eye opening factor (E) at the measured decision instant and threshold._{O}=(μ_{1}-μ_{0}-(σ_{1}+σ_{0}))/E_{A} |

measurement/width | The eye width (E) at the measured threshold._{W}=μ_{T1}-μ_{T0}-3(σ_{T1}-σ_{T0}) |

measurement/pulse width | The pulse width (μ
_{T1}-μ_{T0}) at the measured threshold. |

measurement/jitter RMS | The RMS jitter (σ) at the measured threshold._{T1}-σ_{T0} |

measurement/peak to peak jitter | The peak to peak jitter (T) at the measured threshold._{1max}-T_{0min}) |

measurement/rise time | The rise time (μ) at the measured decision instant._{T0[10%-90%]} |

measurement/fall time | The fall time (μ) at the measured decision instant._{T1[90%-10%]} |

graph/threshold at min BER | The threshold at the the minimum BER value vs.the decision instant. |

graph/min BER | The minimum BER vs.the decision instant. |

graph/min log of BER | The minimum BER vs.the decision instant. |

graph/Q factor | The Q factor vs.the decision instant. |

graph/level zero mean | The mean value of 'zero' levels (μ) vs.the decision instant._{0} |

graph/level zero sigma | The standard deviation of 'zero' levels (σ) vs.the decision instant._{0} |

graph/level one mean | The mean value of 'one' levels (μ) vs.the decision instant._{1} |

graph/level one sigma | The standard deviation of 'one' levels (σ) vs.the decision instant._{1} |

graph/height | The eye height (E) vs.the decision instant._{H} |

graph/amplitude | The eye amplitude (E) vs.the decision instant._{A} |

graph/extinction ratio | The extinction ratio (E) vs.the decision instant._{r} |

graph/opening factor | The eye opening factor (E) vs.the decision instant._{O} |

====================================

## Implementation Details

Please see Optical PAM-4 in Advanced Modulation Format Transceivers for detailed information.

Please see also the example file [[4PAM_Symbol_Map.icp]].

### BER calculation

When "calculate measurements" is turned on, the EYE Diagram elements will generate some signal measurements like Quality-factor (Q-factor) and Bit Error Rate (BER) based on the signal eye diagram. The "BER estimation" has two options: Gaussian and measured.

**Gaussian BER estimation:**

For the case of Additive White Gaussian Noise (AWGN) channels, the optimum BER of the system can be estimated by the parametric Gaussian probability density function (pdf). The estimation is based on statistical properties of the received signal, which is also how Q-factor is calculated.

For AWGN signal, we assume that:

- There is an equal probability of transmitting 1s and 0s
- The likelihood of receiving a signal at some level S is given by a Gaussian distribution (with mean V+ or V-)

The optimum Q factor and the BER are calculated as:

$$Q_{op}=\frac{\mu_{1}-\mu_{0}}{\sigma_{1}+\sigma_{0}}$$

$$B E R=0.5 * P_{1} * \operatorname{erfc}\left(\frac{\mu_{1}-\mu_{t h}}{\sqrt{2} \sigma_{1}}\right)+0.5 * P_{0} * \operatorname{erfc}\left(\frac{\mu_{t h}-\mu_{0}}{\sqrt{2} \sigma_{0}}\right)$$

where

\(\mu_1\): received signal level 1 mean

\(\mu_0\): received signal level 0 mean

\(\mu_{th}\): received signal threshold level

\(\sigma_1\): received signal level 1 standard deviation

\(\sigma_0\): received signal level 0 standard deviation

\(P_1\): ratio of '1' bits to total number of bits

\(P_0\): ratio of '0' bits to total number of bits

If the **number of levels** is more than two, the Q factor and BER are calculated for each pair of levels using the above equations, then averaged together to get the total Q factor and BER, weighted by the number of symbols at each level. For example, with PAM4 modulation (**number of levels** = 4), the Q factor and BER are calculated with the following equations:

$$Q = \frac{(P_0 + P_1)Q_{01} + (P_1 + P_2)Q_{12} + (P_2 + P_3)Q_{23}}{P_0+2P_1+2P_2+P_3}$$

$$BER = \frac{BER_{01} + BER_{12} + BER_{23}}{P_0+2P_1+2P_2+P_3}$$

where

\(Q_{ij}\): Q factor between level \(i\) and \(j\), calculated with the two level Q factor equation above

\(P_i\): ratio of bits at the \(i\) level to total number of bits

\(BER_{ij}\): BER between level \(i\) and \(j\), calculated with the two level BER equation above

Since the statistical properties are retrieved from the received signal inputs to the EYE Diagram element, using the Gaussian estimation of BER calculation doesn't require the reference signal nor the bit pattern input.

**Measured BER estimation:**

For a more accurate BER calculation method, the "measured" BER estimation option compares the received bits (the bits recovered from the input signal to the EYE Diagram element) to the original bit pattern that feeds into the transmitter for the error bits, then calculate the BER by:

$$BER=\frac{number\: of\: error\: bits}{total\: number\: of\: bits} $$

Hence for this calculation to work, the reference signal or the bit pattern input is required:

**with only the input signal**: with no information of the original bits, BER = 0 (incorrect)

**with only reference signal**: retrieve the bit pattern from the reference signal and calculate BER based on this bit pattern

**with bit pattern input**: calculate BER based on the provided bit pattern (recommend)

Note that the received bits are retrieved from the samples on the decision point.

### Signal recovery

The Eye Diagram element can also be used as a decoder when the reference signal/bit pattern is provided. Note that in this case, the Eye Diagram element will recover the signal based on the input bit pattern, so it is possible to recover level one signal in a lower power level than the level zero signal when the modulator swaps the signal levels in modulation.