OOK Devices

Use this module to simulate On-Off Keying modulation optical systems.

>>> import opticomlib.ook as ook

Functions

THRESHOLD_EST(eye_obj)

Threshold estimator

DSP(input[, BW])

On-Off Keying Digital Signal Processing

BER_analizer(mode, **kargs)

BER Analizer

theory_BER(mu1, s0, s1)

Calculates the theoretical bit error probability for an OOK system.
opticomlib.ook.THRESHOLD_EST(eye_obj: eye)[source]

Threshold estimator

Estimates the decision threshold for OOK from the means and standard deviations of the eye diagram.

Parameters:

eye_obj (eye) – Object with the parameters of the eye diagram.

Returns:

Decision threshold for OOK.

Return type:

float

Notes

The decision threshold is estimated as the value of amplitud that minimizes the probability of error given the means and standard deviations of the eye diagram. This is done by minimizing the probability function [th]:

\[f(r) = \frac{1}{2} Q\left(\frac{\mu_1 - r}{\sigma_1}\right) + \frac{1}{2} Q\left(\frac{r - \mu_0}{\sigma_0}\right)\]

where \(\mu_0\) and \(\mu_1\) are the means of the eye diagram, \(\sigma_0\) and \(\sigma_1\) are the standard deviations and Q() is the Q-function.

References

[th]

Armando Palacio Romeu, “Comunicaciones ópticas entre satélites LEO y GEO”, chapter 2.4. link: https://ricabib.cab.cnea.gov.ar/1143/1/1Palacio_Romeu.pdf

opticomlib.ook.DSP(input: electrical_signal, BW: float = None)[source]

On-Off Keying Digital Signal Processing

Performs the decision task of the photodetected electrical signal.

  1. If BW is provided bessel filter will be applied to the signal (opticomlib.devices.LPF())

  2. eye diagram parameters are estimated from the input electrical signal with function opticomlib.devices.GET_EYE().

  3. it subsamples the electrical signal to 1 sample per bit using function opticomlib.devices.SAMPLER().

  4. Then, it compares the amplitude of the subsampled signal with optimal threshold. The optimal threshold is obtained from function opticomlib.ook.THRESHOLD_EST().

  5. Finally, it returns the received binary sequence, eye object and optimal threshold.

Parameters:

  • input (electrical_signal) – Photodetected electrical signal.

  • BW (float, optional) – Bandwidth of DSP filter. If not specified, signal won’t be filtered.

Returns:

  • output (binary_sequence) – Received bits.

  • eye_obj (eye) – Eye diagram parameters.

  • rth (float) – Decision threshold for OOK.

Examples

from opticomlib.devices import DAC, gv
from opticomlib.ook import DSP

import numpy as np
import matplotlib.pyplot as plt

gv(sps=64, R=1e9)

x = DAC('01000100100000', 1, pulse_shape='gaussian')
x.noise = np.random.normal(0, 0.1, x.len())

y, eye_, xth = DSP(x)

x.plot('y', label='Photodetected signal')
DAC(y).plot(c='r', lw=2, label='Received sequence')
plt.axhline(xth, color='b', linestyle='--', label='Threshold')
plt.legend(loc='upper right')
plt.show()

(Source code, png, hires.png, pdf)

DSP OOK
opticomlib.ook.BER_analizer(mode: Literal['counter', 'estimator'], **kargs)[source]

BER Analizer

Calculates the bit error rate (BER), either by error counting (comparing the received sequence with the transmitted one) or by estimation (using estimated means and variances from the eye diagram and substituting those values into the theoretical expressions).

Parameters:

  • mode (str) – Mode in which the Bit Error Rate (BER) will be determined.

  • Tx (binary_sequence, optional) – Transmitted binary sequence. Required if mode=’counter’.

  • Rx (binary_sequence, optional) – Received binary sequence. Required if mode=’counter’.

  • eye_obj (eye, optional) – eye object with the estimated parameters of the eye diagram. Required if mode=’estimator’.

Returns:

BER.

Return type:

float

Examples

from opticomlib.devices import DAC, gv, binary_sequence
from opticomlib.ook import DSP, BER_analizer

import numpy as np

gv(sps=64, R=1e9)

tx = binary_sequence('01000100100000')
x = DAC(tx, pulse_shape='gaussian')
x.noise = np.random.normal(0, 0.1, x.len())

rx, eye_, xth = DSP(x)
BER_count = BER_analizer('counter', Tx=tx, Rx=rx)
BER_est = BER_analizer('estimator', eye_obj=eye_)

print(f'BER by counting: {BER_count:.1e}')
print(f'BER by estimation: {BER_est:.1e}')

Output:

BER by counting: 0.0e+00
BER by estimation: 3.7e-07
opticomlib.ook.theory_BER(mu1: int | ndarray, s0: int | ndarray, s1: int | ndarray)[source]

Calculates the theoretical bit error probability for an OOK system.

Parameters:

  • mu1 (float) – Average current (or voltage) value of the signal corresponding to a bit 1.

  • s0 (float) – Standard deviation of current (or voltage) of the signal corresponding to a bit 0.

  • s1 (float) – Standard deviation of current (or voltage) of the signal corresponding to a bit 1.

Returns:

Theoretical bit error probability (BER).

Return type:

float

Notes

The theoretical bit error probability is calculated using the following expression:

\[P_e = \frac{1}{2} \left[Q\left(\frac{\mu_1 - r_{th}}{\sigma_1}\right) + Q\left(\frac{r_{th}}{\sigma_0}\right)\right]\]

Examples

>>> from opticomlib.ook import theory_BER
>>> theory_BER(mu1=1, s0=0.1, s1=0.1)
2.8674468224390994e-07