## 4 Conclusions  
We propose an improved artificial neural network (ANN)-based equalization method. It effectively compensates for the nonlinear impairments associated to the received electrical signal in the short-haul fiber-optic communication systems based on intensity modulation and direct photo-detection. The proposed equalizer consists of a single hidden neural network layer which significantly reduces the overhead computational cost and memory storage requirements of the equalization step. The performance and efficiency of the  
Figure 8: BER performance of the 28 Gbaud optical-fiber communication system versus received optical power. The optical-fiber transmission distance is 20 km. The performance without equalizer, with ANNE-ET[7, 6] and with ANNE-AT[7, 6] are compared to the B2B transmission case.  
Figure 9: Received optical power (RoP) required to achieve \(\mathrm{BER}=10^{-3}\) versus fiber transmission distance for the 28 Gbaud optical-fiber communication system. The equalization at the receiver is performed using the FFE[7], DFE[4,3], ANNE-ET[7,6], MLSE[7], MLSE[9], and ANNE-AT[7,6].  
proposed equalizer are demonstrated through 10- and 28-Gbaud short-haul fiber communication systems. Although the minimum overhead equalization cost and memory usage are achieved by the linear feed-forward equalizer (FFE) and decision feedback equalizer (DFE), they both provide poor compensation performance benefit due to their inability to mitigate nonlinear system distortions. The proposed ANN equalizer, on the other hand, provides the required nonlinear compensation performance benefit with slightly higher computational cost and memory usage. The proposed ANN equalizer with the integrated advanced training scheme also outperforms the maximum likelihood sequence estimator (MLSE), achieving an average power benefit of more than 1 dB, when the same number of taps and memory size is considered. Furthermore, the proposed ANN equalizer requires much less computational cost and memory storage. Its cost and memory usage scale linearly with the number of input nodes \(N\) and with the number of hidden-layer nodes \(m\), whereas the computational cost and memory usage of the MLSE scale exponentially with the channel memory size \(N\). Note that the power consumption of the proposed equalizer is not discussed in this paper. The power consumption scales directly with the computational cost and memory usage of the equalizer. In other words, the ANN equalizer should significantly reduce the high power consumption required by the MLSE as well. It is also worth emphasizing that the proposed ANN equalizer can easily be implemented in a field-programmable gate array (FPGA) integrated circuit/kit and attached to any available/commercial digital signal processing (DSP) unit without any hardware constraints or limitations.  
Conceptualization, S.K. and M.H.B.; software, M.M.T.M. and H.S.; validation, H.S.; formal analysis, S.K. and M.H.B.; investigation, M.M.T.M.; data curation, M.M.T.M.; writing--original draft, M.M.T.M.; writing--review and editing, S.K., M.H.B. and S.M.A.; supervision, S.K. and M.H.B.; funding acquisition, S.M.A. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under Grant RGPIN-2022-04951 and Grant RGPIN-2023-04825.  
Not applicable.  
Data Availability Statement: Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.  
The authors declare no conflict of interest.