Eye Diagram (EYE) - INTERCONNECT Element

Allows observation and analysis of eye diagrams

Keywords

analyzer, electrical, unidirectional, bidirectional

Ports

Properties

General Properties

Standard Properties

Enhanced Properties

Simulation Properties

Display Properties

Results

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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.