## 2 System Description and Simulation Setup  
We propose the following system for short-reach communication. At the transmitter, a digital-to-analog converter (DAC) maps the signal to an OOK modulation format with root-raised cosine (RRC) as pulse shaping. We believe that our method can be easily extended to a PAM-4 modulation format, which will be considered in our future works. The Mach-Zehnder modulator (MZM) is used to modulate the signal. A standard single-mode fiber (SSMF) propagates the signal, and an erbium-doped fiber amplifier (EDFA) amplifies it. At the receiver, an optical band-pass filters the noise outside the signal bandwidth. Before detection, an optical module is used to pre-distort the signal to mitigate the CD. This process will be used to assist the nonlinear digital equalizer. A photodetector (PD) is then used to detect the signal, and an analog-to-digital converter (ADC) converts it to the digital domain. A DSP with NN equalizer and RRC filter are used to equalize the signal. The optical module, PD, and NN equalizer are the proposed hybrid optoelectronic blocks used to mitigate CD for direct detection systems.  
Figure 1 shows the simulation setup used to validate the proposed system. At the transmitter, the DAC is the assumed ideal and an OOK 32-GBd signal is generated with 2\({}^{18}\) symbols, up-sampled to eight samples per symbol and filtered by a RRC filter (roll-off = 0.1). The digital signal is directly mapped onto the optical domain by assuming an ideal linear transformation. The MZM is assumed ideal in order to neglect its nonlinear transfer function as a source of degradation and to focus solely  
on the impact of CD. The CD (\(D=16.4\) ps/nm/km) is the only impairment considered in the optical fiber, and additive white Gaussian noise (AWGN) is used to simulate the pre-amplifier at the Rx point. The noise variance and fiber length (accumulated CD) are swept to meet the target SNR and distance. The signal is then detected by a DD receiver.  
Figure 2 shows different topologies of the receiver that is analyzed in the result section. For all of them, a second-order Gaussian filter (40-GHz bandwidth) is used as a band-pass filter, which reduces the noise-to-noise beating in the PD. Moreover, the RRC filter block (ADC is assumed ideal) is used as a low-pass filter to downsample the signal to one sample per symbol. Receiver (a) is used as a reference. No optical pre-processing or digital equalization is applied. Receivers (b) and (c) show the block diagram for digital equalization with NN and MLSE (more details in Section 2.2), respectively. Receiver (d) shows the block diagram for optical pre-processing using a complete optical module (more details in Section 2.1). Receivers (e) and (f) show the proposed hybrid solution to mitigate CD. The former is based on the complete optical module, together with the NN. The latter is the receiver with the proposed simplified optical module together with an NN, respectively.  
The simulation results firstly show a comparison between the performance of optical equalization and electronic equalization, individually. This results are followed by the complete hybrid module. Secondly, we analyze the requirements of the optical module to mitigate CD in a hybrid system. Thirdly, we compare a simplified hybrid module with the complete hybrid module. Fourthly, we study the tolerance of the simplified and complete hybrid module to CD. And lastly, we investigate the performance of NN in both hybrid systems.  
Figure 1: Simulation setup.  
Figure 2: Receiver configurations.