## 3 Experimental Results and Discussions  
We firstly measured the transmission characteristics of the employed optical backplane. The frequency response of the end-to-end system to the optical transmission path was measured under configurations for both with and without optical backplane as depicted in Figure 6. A N5227B Keysight project network analysis (PNA) network analyzer with a 67 GHz bandwidth was employed in the mentioned measurements. The measured path was between the MZM input port and the PIN output port. The frequency for the 3 dB bandwidth of the transmission system with and without an optical backplane was 18 and 18.15 GHz, respectively. The nominal bandwidth of employed devices in our experiments was specific for the non-return-to-zero (NRZ) modulation signals, which means that the analog bandwidth basically agreed with above mentioned results. The result indicates that the employment of the optical backplane had a slight impact on frequency fading. Due to the short length of the backplane, the dispersion was not the dominant impairment in the above-mentioned system. Figure 4: (**a**) The schematic diagram on the spatial structure of the optical backplane (**b**) the cross-sectional view of the rectangular optical waveguide (ROW). Figure 5: The insertion loss characteristics for each lane of the optical backplane. A detailed investigation into the performance of proposed scheme was performed. To set up a reference baseline for the employed equalization methods, optical back-to-back (OB2B) transmission experiments of the 80 Gb/s PAM-4 signal were firstly performed with the direct decision, and the DFE, MLSE and proposed NN equalization algorithms were employed. During the measurements, the RoP changed from \(-2.5\) to \(-12.5\) dBm with a 1 dB decrement. The BER curves with the mentioned direct decision and DFE equalization algorithms are shown in Figure 7. For both cases, the BER could not be lower than the adopted 7% HD-FEC limit for all measured RoP values. In the DFE case, the training length was 1000, and the tap is 3. As a linear equalizer, DFE got the right optimal tap coefficient through the training sequence. DFE is an essentially linear mapping, which means that it lacks the ability to compensate for the impairment induced by a constrained bandwidth. The BER performance deteriorated as the RoP decreased from \(-8.5\) to \(-12.5\) dBm. However, when the RoP was above \(-8\) dBm and kept increasing, the BER did not decrease, indicating that the impairment of the signal at this bit rate exceeded the compensation limit of DFE. Figure 6: The measured system’s frequency response to the optical transmission path. Figure 7: The curves of the bit error rate (BER) versus the received optical power (RoP) of transmission with decision feedback equalization (DFE), maximum likelihood sequence estimation (MLSE) and the NN equalization scheme for 80 Gb/s. The MLSE case considered all the sequences that may be formed after convolution of effective transmission sequence and channel impulse response, and a sequence with minimum distance from the received signal was found. Here, the memory length used was 4. As displayed in Figure 7, the BER decreased with the increase of the RoP and was even lower than the HD-FEC when the RoP was higher than \(-4.5\) dBm. In addition, for the MLSE case, the BER curve after transmission through the optical backplane was basically the same as the OB2B curve, thus confirming the transmission features as mentioned in Figure 7. In the following measurements, MLSE was used as the reference algorithm for comparison. It is worth mentioning that this paper only discusses the performance of the equalization algorithm at the adopted forward error correction (FEC) threshold due to the fact that the implementation of the FEC can be achieved by special hardware and software. As shown in the performance of the proposed NN algorithm plotted in Figure 7, the BER also decreased with the increase of the RoP at the transmission rate of 80 Gb/s.