# TDM-PON PAM Downstream Transmission for 25 Gbit/s and Beyond
## 2 Simulation Setup
Then, the PAM4 or PAM8 sequence is built up using two or three versions of the original PRBS sequence, delayed with respect to one another so as to allow proper decorrelation. While opting for Gray encoding would result in a simpler receiver structure, it would be at the cost of a more complicated transmitter in a laboratory implementation. Furthermore, it has been shown that the OB gain when substituting Gray for binary encoding for PAM4 remains small--lower than 0.2 dB at a Bit Error Rate (BER) of 1.10-3 [19]. Here, we decided to study the binary encoding for PAM4 and PAM8, which is closer to our reference study [11]. The combined binary streams are converted into electrical symbols with 32 samples. A low-pass filter is used to simulate the 15 ps rising and falling times (10-90%) of the signal coming from electrical generators used in the reference experimental setup. The 5 Vpp signal then directly drives a virtual Distributed FeedBack laser (DFB) having identical characteristics to that used in the experimentation (see Table 1 for its parameters) and emitting 11.8 dBm mean optical power. The laser signal modeling is based the DFB PI response. A polynomial approximation of the reference experimental curve is generated first, and then the electrical signal is applied on the laser model. Relative Intensity Noise (RIN) is added as an Additive White Gaussian Noise (AWGN). The frequency deviation generated by the chirp is applied following the model depicted in [20]. The 8 GHz cut-off frequency of the photodiode used is lower than the relaxation oscillation frequency of the DFB laser in our experimental setup. So, the equivalent electrical frequency responses of the laser and the photodiode are simulated with a single Butterworth low-pass filter positioned after the optical-electrical conversion, and its \(-3\) dB bandwidth is equal to the smallest bandwidth of both, i.e., 8 GHz. The signal propagation in the optical fiber is modeled using the Slowly Varying Envelope Approximation (SVEA) [21]. Indeed, this relatively simple model can be adopted without loss of generality since optical nonlinear effects are expected to be negligible considering the relatively low optical power launched into the fiber and the short distances in single-channel access networks. A 0.4 dB/km fiber attenuation was applied and no chromatic dispersion was added since the laser emits at 1311.36 nm (in the O band), near the zero-dispersion wavelength for the SSMF. In the following analysis, different fiber lengths are considered up to 20 km, which is the typical range of currently deployed access networks. Longer segments would bring no degradation other than attenuation at the tested wavelength. A VOA was simulated to perform OB measurements. The photodiode model mimics the experimental Avalanche PhotoDiode + Transimpedance Amplifier (APD + TIA) used (see Table 1). Both shot noise and thermal noise were simulated, according to [21]. The homemade decoder of the reference experimental setup generates an additional noise that is added to the model as a Gaussian noise whose standard deviation, expressed in arbitrary amplitude units (a.a.u. ), varies as depicted in Figure 2. It should be noted that the realistic noise distribution is slightly broader from the higher levels to the lower ones of the PAM signals due to the differences in optical power. Here, the same noise distribution is implemented for all levels.