# Partial Pre-Emphasis for Pluggable 400 G Short-Reach Coherent Systems
## 3 Pre-Emphasis in Layer-0 Optical Systems  
Pre-emphasis filter is commonly used in optical communication systems to pre-compensate for part of or the entire channel inter-symbol interference (ISI), such that the noise enhancement associated with Rx equalization is alleviated. Nonetheless, the pre-emphasis filter applied to the signal at the Tx also burdens the AWG used to generate the RF signal due to increased signal PAPR. This leads to lower signal root-mean-square (RMS), and equivalently lower signal power out from the AWG, thus degrading the signal SNR when the power of the quantization noise, the thermal noise, as well as the harmonic noise are relatively stable. In this section, we present a simulation model to investigate the impact of the pre-emphasis filter on the signal SNR out from the AWG. Figure 2 shows the simulation setup. The digital signal, \(S(\Omega)\), is generated and filtered by a root raised cosine (RRC) pulse shaper, \(\sqrt{N(\Omega)}\), with a roll-off factor of 0.125, followed by a digital pre-emphasis (DPE) filter. The AWG frequency response is modelled as a 3 rd order Bessel filter with 14 GHz of 3 dB BW operating at 64 GSa/s. If we ignore clipping, the quantization noise, \(n_{q}(\Omega)\), can be approximated as white noise, and the noise variance is given as \(\Delta^{2}\)/12, with \(\Delta\) being the quantization step size. If the input to the DAC after pre-emphasis filter is \(X(\Omega)\), we can derive  
\[\Delta=\frac{x_{max}}{2^{ENOB-1}-1}=\frac{\sqrt{\sigma_{x}^{2}\cdot 10^{PAPR/10}} }{2^{ENOB-1}-1} \tag{1}\]  
where PAPR is in dB and \(\sigma_{x}^{2}\) is variance of signal fed into the DAC, \(X(\Omega)\). So, this quantization step size, \(\Delta\), depends on signal PAPR and ENoB. For the purpose of simplifying the comparison between different cases, we consider the nominal ENoB. An additional AWGN noise, \(\text{n}_{\text{add}}(\Omega)\), is added along with the quantization noise to better match the practical AWG [18]. This noise is related to the SNR within the AWG module, and, as shown in reference [18], this model shows considerable match with measurements and numerical simulation. The DPE is calculated using least mean square (LMS) algorithm considering only the limited bandwidth of the AWG at the beginning and then used for all other results. Figure 1: Simulated and measured electro-optics (EO) response at 4 V reverse bias for a 4 mm MZM [9]. Figure 3 shows the frequency response of the complete and partial-pre-emphasis filters created based on the full pre-emphasis filter. Here, by \"complete pre-emphasis\" we mean LMS-based pre-emphasis filter that pre-compensates for the frequency response of the transmitter, and thus the transmitted spectrum right after the AWG is equal to set pulse shaping. For partial pre-emphasis, we multiply this complete pre-emphasis filter via an attenuation function. This attenuation function is a linear function with a certain amount of attenuation at a fixed frequency. The partial-pre-emphasis filter shown in Figure 3 has a 3 dB reduction of frequency response at 20 GHz. In the rest of the simulation, the partial pre-emphasis filters are obtained by reducing the frequency response at 20 GHz to different extent. As we stated earlier by doing the complete pre-emphasis, we increase the signal PAPR degrading the signal SNR at the output of the modulator. Figure 4 plots the PAPR of transmitting signal into the AWG as a function of the magnitude loss at 20 GHz. It is seen that the PAPR decreases almost linearly with the frequency loss and there is 1.3 dB reduction of the PAPR for a 4 dB loss at 20 GHz. This reduction in PAPR increases the signal SNR. To calculate the transmitted signal SNR, we use a matched filter followed by an 11-tap feed-forward equalizer (FFE) at the receiver. The FFE removes the ISI caused by partial pre-emphasis. Figure 5 plots the change of the signal SNR out of the AWG versus different losses at 20 GHz when the ENoB varies from 4 to 6 bits.