# TDM-PON PAM Downstream Transmission for 25 Gbit/s and Beyond
## 2 Simulation Setup  
The decoding of the received electrical signal is done with 1, 3, or 7 thresholds for NRZ, PAM4, or PAM8. Rectangular masks are implemented to represent the precision of detection on the receiver. Points falling inside the mask are treated randomly either as above or below the corresponding threshold. The received data are finally compared to the transmitted ones in order to calculate the bit error rate. A loop is implemented in the simulation and the transmission is reiterated until there are at least one hundred errors measured for each Bit Error Rate (BER) value. All the simulations in this paper rely on a model that was first validated based on the actual real-time experimental results of our previous work [10]. The reference experimental setup (see Figure 1) includes a Pulse Pattern Generator (PPG) generating two Pseudo Random Binary Sequences of \(2^{31}-1\) bits (PRBS31); both generated streams are injected into a PAM4 encoder. The encoder is based on a 6 dB electrical attenuator for the Least Significant Bit (LSB) stream, a tunable phase shifter is used on the Most Significant Bit (MSB) stream to align it with the LSB, and then both of the streams are combined with a power divider. The PAM4 electrical signal is amplified with a linear electrical amplifier before modulating the laser. The laser used is a Directly Modulated Laser (DML) emitting at 1311 nm with 10 GHz bandwidth and with 11.8 dBm optical output power at 90 mA bias current. After Standard Single Mode Fiber (SSMF), a Variable Optical Attenuator (VOA) is used to perform the optical budget measurements. The PAM4 ONU is based on an 8 GHz bandwidth Avalanche Photodiode + TransImpedance Amplifier (APD + TIA). A PAM4 decoder consists of three limiting amplifiers, two eXclusive OR (XOR) gates, and a power divider. Also, a clock recovery module and an error detector are in the decoding part of the real-time 25 Gbit/s PAM experimental setup. Our system simulation study aims at validating or disproving the concept for higher-bit-rate transmissions. The simulations were implemented with MATLAB(r) and the main transceiver and transmission system parameters are listed in Table 1. For the sake of simplicity and in contrast with our experimental setup, PAM8 and PAM4 levels were equally spaced. Gbaud rates of 12.5 and 25 were studied here in order to achieve 37.5 Gbit/s and 50 Gbit/s, respectively. \begin{table}
\begin{tabular}{l l} \hline \hline \multicolumn{1}{c}{**Parameter**} & \multicolumn{1}{c}{**Value**} \\ \hline PRBS data sequence length & \(2^{15}-1\) (PRBS15) \\ \hline Modulation formats & PAM4 [PAM8] \\ \hline Laser & \multicolumn{1}{c}{DFB directly modulated} \\ Wavelength & 1311.36 nm \\ Chirp parameter \(\alpha\) & 3 \\ Chirp parameter fc & 2 GHz \\ Bandwidth & 10 GHz [20 GHz] at 90 mA bias \\ Electro-optical conversion efficiency & 0.15 mW/mA \\ Threshold current & 27.8 mA \\ Saturation current & 138 mA \\ RIN & \(-110\) dBm (AWGN) \\ \hline Photodiode + TIA & APD \\ Responsivity & 0.8 A/W \\ Bandwidth & 8.5 GHz [21 GHz] \\ Transimpedance gain & 36 dB \\ \hline Fiber & SMF \\ Length & 0, 10, or 20 km \\ Attenuation & 0.4 dB/km \\ Dispersion & 0 ps/nm/km \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Transceiver and transmission parameters. Figure 1: Original experimental setup. PAM8 has more amplitude levels than PAM4, which will add extra complexity to the encoder and decoder but has the advantage of allowing a 50% increase in the bit rate when using the same bandwidth as a PAM4 signal. Namely, a 12.5 Gbaud PAM8 signal would allow reusing 10 GHz optical components and a lower clock frequency. As far as 50 Gbit/s PAM4 is concerned, four amplitude levels are used and can be decoded following the same principle as that used in the experimental part of our previous work. However, it would require optics and electrical components with bandwidths around 20 GHz, as well as a higher clock reference (25 GHz for 50 Gbit/s). The first step in the simulation is to generate a PRBS with a Linear Feedback Shift Register (LFSR) function.