## 3 Results and Discussion
### A 28-Gbaud Optical-Fiber Communication System  
This subsection investigates the performance of the proposed equalizer to mitigate the impairments induced at a higher transmission data rate. Particularly, we discuss its performance to mitigate the distortions of an IMDD short-reach fiber communication system operating at a baud rate of 28 Gbaud with optical-fiber length \(L\) ranging from a few meters up to a few tens of kilometers. Such communication systems are widely deployed in typical communication scenarios of varied applications, e.g., data center networks (DCNs) and cloud radio access networks (C-RANs). They can exist as 28 Gbaud serial links or as 4 \(\times\) 28 Gbaud parallel links, implementing a data rate of 100 Gbaud. Note that optical amplifiers are not typically used in these systems due to short transmission distances. Therefore, for all results shown in this subsection, we consider the exact system setup given in Figure 4 excluding the EDFA block, which is not required here.  
In Figure 8, we show the BER performance obtained at a fiber transmission distance \(L=20\) km versus received optical power. The BER achieved using the ANNE-AT[7,6] is compared to the system performance at no equalization, the B2B transmission case, and equalization utilizing the ANNE-ET[7,6]. It is clear that increasing the data rate significantly deteriorates the system performance, resulting in an infeasible transmission in the case of no equalization. However, the ANNE-AT can be utilized to improve dispersion tolerance, extending the feasible transmission distance. Compared to the B2B transmission case, the ANNE-AT is shown to achieve the \(\text{BER}=10^{-3}\) with a 2.1 dB power penalty, whereas the ANNE-ET has a power penalty of 5.9 dB. In other words, the ANNE-AT outperforms the ANNE-ET with a \(\sim\)3.8 dB power benefit to achieve \(\text{BER}=10^{-3}\) in this case.  
To demonstrate efficiency of the ANNE-AT compared to other equalizers, Figure 9 plots the received optical power required to achieve \(\text{BER}=10^{-3}\) versus the fiber transmission distance. The compensation performance of the ANNE-AT[7,6] is compared to the performance of the FFE[7], DFE[4,3], MLSE[7], and MLSE[9], as well as the ANNE-ET[7,6]. As can be seen, the proposed ANNE-AT provides an average power benefit of 1.7 dB and 1.2 dB compared to the ANNE-ET and MLSE[7], respectively, while slightly outperforming the MLSE[9]. Moreover, the ANNE-AT significantly reduces the overhead cost and memory storage required by the MLSE during equalization (see Table 1). A total of 42 multiplication operations per bit are required by the ANNE-AT as opposed to 128 and 512 in cases of the MLSE[7] and MLSE[9], respectively. In addition, the MLSE[7] and MLSE[9] require a memory storage of as high as 128 and 512 floating-point numbers as opposed to only 48 floating-point numbers needed to be stored by the ANNE-AT.  
Although we considered only the case of on-off keying (OOK) modulation format throughout this paper, the proposed ANN equalizer can be easily applied to higher modulation formats, e.g., pulse amplitude modulation (PAM) 4 or PAM 8. For instance, if PAM 4 were considered, the output of the ANN equalizer would apply on symbols, rather than bits, and vary between four states instead of the current two states of the OOK. However, we defer this study to future work.