## Module 14

### Dual Polarization CO-OFDM Systems

(1) **Use the Existing Modules** / Components for Your Research Papers, Research Projects, Theses and Lab Simulation Experiments.

(2) **Modify** the Modules / Components to the Next Level for Your Research Papers, Research Projects and Theses.

(3) **Integrate** Different Modules / Components in the OCSim Package to Realize Your Own Fiber Optic Communication Systems.

(4) **Modify** the Modules for Co-Simulations with the Third Party Commercial Optical Communication Systems Softwares.

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#### Source Code: **ofdm_qam_vec.m**

Simulation of a FIBER OPTIC QAM-M coherent OFDM system with dual polarization and PMD compensation. This module takes into account (1) dispersion, (2) nonlinearity, (3) PMD and (4) random coupling between polarizations in the fibers.

**This source code calls the following functions:**

(1) qam_ofdm_transmitter_vec.m : Models the **dual polarization** OFDM transmitter.

(2) power_meter.m : Calculates the average optical power in dBm units.

**(3) fiber_prop_vec.m : **Propagation of **dual polarization** signal in OPTICAL FIBER. The model takes into account the (1) dispersion, (2) nonlinearity, (3) PMD and (4) random coupling between polarizations in the fibers.

(4) amp_vec.m : Multiplies the input signal by gain factor and adds noise (the amount of noise is controlled by ).

(5) opt_rect_filt.m : Optical ideal band pass filter to truncate the spectrum.

(6) AtoD_convert.m : Analog to digital converter. The resolution should be specified.

(7) DtoA_convert.m : Digital to analog converter. The resolution should be specified.

(8) ofdm_receiver_vec : Models the **dual polarization** OFDM receiver.

(9) ber_calc_qam_ofdm.m : Calculates the symbol error rate.

(10) const_diagram_ofdm.m : This function plots the constellation diagram for optical OFDM. FFT is performed on the OFDM symbol in each frame before plotting the constellation diagram.

(11) const_diagram_ofdm_direct.m : This function plots the constellation diagram for optical OFDM without taking FFT of each frame.

(12) mzm_iq.m : Calculates outputs of IQ modulators (MZM-I and MZM-Q Mach-Zehnder modulators) in OFDM.

**Explore Further this Module:
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**14.1** For fiber optic DP-QAM-16 Coherent OFDM,** Keep** the symbol rate fixed at 12.5 GBaud, number of subcarriers = 256 and average power = -3 dBm. **Choose **the second order dispersion as 17 ps/nm/km (or -21 ps.ps/km) and set the *nonlinear coefficient* to zero. **Calculate** the symbol error rate as the number of samples in the guard interval (which is proportional to the duration of guard interval) changes from 16 to 48. **Observe** that the symbol error rate decreases as the duration of the guard interval increases. This is because the OFDM symbols in the neighboring frames interfere due to dispersion and the large guard intervals helps to mitigate the ISI due to dispersion. **Plot** the symbol error rate as a function of the duration of guard interval.

**14.2** For fiber optic DP-QAM-16 Coherent OFDM**, Keep** the symbol rate fixed at 12.5 GBaud, number of subcarriers = 256 and number of samples in the guard interval = 32. **Choose** the second order dispersion as 17 ps/nm/km (or -21 ps.ps/km) and set the *nonlinear coefficient* to zero. **Change** the launch power from -8 dBm to 1 dBm at a step of 1 dBm and **plot** the symbol error rate SER (or bit error rate) as a function of launch power. **Observe** that the SER decreases as the launch power increases due to the fact that the OSNR increases with the launch power.

**14.3** **Repeat** **14.2** with the *nonlinear coefficient* = 1.1e-3. **Change** the launch power from -8 dBm to 1 dBm at a step of 1 dBm and **plot** the symbol error rate SER (or bit error rate) as a function of launch power. **Now observe** that the SER decreases initially (in the linear regime). However, at higher launch powers (nonlinear regime), SER increases due to distortions caused by the fiber nonlinearity.

**14.4** For fiber optic DP-QAM-16 Coherent OFDM**, Keep** the symbol rate fixed at 12.5 GBaud, number of subcarriers = 256 and number of samples in the guard interval = 32. Launch power = -3dBm. **Choose** the second order dispersion as 17 ps/nm/km (or -21 ps.ps/km) and set the *nonlinear coefficient* to zero. **Change** the *PMD parameter* Dpp from 0.1 ps/sqrt(km) to 3 ps/sqrt(km) and plot the symbol error rate as a function of the *PMD parameter*. **Observe** that the SER without equalization is very large. However, after the *PMD equalization*, the SER is nearly constant (or a slight increase) showing that the equalizer effectively removes the degradations caused by *PMD*.

**14.5** **Repeat** 14.1, 14.2, 14.3 and 14.4 with number of segments to 2, 4, 6, 8, 10, 12, 14, …. and **observe** the constellation diagrams at Rx. One segment is equal to 80km of fiber length.

**14.6** **Simulate** fiber optic DP-QAM-M OFDM systems for other QAM-M modulations eg., QAM-2 (BPSK), QAM-4 (QPSK), QAM-8, QAM-32, QAM-64, QAM-128, QAM-256, …… .

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**Selected Simulated Results**

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