# Deep Neural Network Equalization for Optical Short Reach Communication
## 3 Experimental Verification and Discussion
### Measurement Results over an Optical Channel with 600 Gb/s/\(\lambda\)
#### 3.2.2 Deep Neural Network Equalizer
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Number** & **Architecture** & **Design** & **Multipliers** \\ \hline
1 & joint I\&Q & \(10|20|30|40|2\) & \((10*20+20*30+30*40+40*2)*2=4160\) \\
2 & Independent I\&Q & \(5|20|30|40|1\) & \((5*20+20*30+30*40+40*1)*2*2=7760\) \\
3 & Independent I\&Q & \(5|20|20|1\) & \((5*20+20*20+20*1)*2*2=2080\) \\
4 & Independent I\&Q & \(5|10|10|10|1\) & \((5*10+10*10+10*10+10*1)*2*2=1040\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: DNN structures. Figure 9: Deep Neural Network Equalizer Architectures. In addition to the learning behavior, Figure 11 shows the altered constellation diagrams of the equalized signal for one polarization during the training of the DNN \(5|10|10|10|1\) NLE. The resulting constellations, such as the one in Figure 11f, differ fundamentally from a classical constellation. The DNN-NLE has the ability of concentrating the constellation points and to reduce the possible outputs (dimensional space) to the target 16 QAM points, in order to reach a low value of the cost function. In combination with the tanh activation function, a square grid constellation occurs, which exhibits non-Gaussian distributed noise. The overall performance of the DNN-Equalizer is shown in Figure 12. On the left hand side, Figure 12a plots the preFEC BER as a function of the OSNR, comparing the best performing general VNLE of 5 th order, the best performing reduced size alternative MP-VNLE of 5 th order and the proposed DNN-NLE structures. On the right hand side, Figure 12b shows the improvements of the base-line curve. The gains in OSNR at the FEC threshold are plotted. The most complex DNN \(5|20|30|40|1\) design, which processes I and Q separately, performs best. This architecture improves the base line curve by 2.81 dB and outperforms the 5 th order VNLE and MP-VNLE by 0.53 dB and 0.80 dB, respectively. The performance losses of the lower complex \(5|20|20|1\) and \(5|10|10|10|1\) designs are very low. The performance is almost identical to the much larger design. The \(10|20|30|40|1\) design with joint processing, performs worst among all DNN structures. The higher number of input nodes together with the equal number of neurons in the hidden layers as the independent I and Q equalizer structure leads to suboptimal projection of the input signal. Figure 10: Learning Process of three different DNN structures. Fair complexity comparisons are not trivial. Given 4 memory taps, a 5 th order MP-VNLE requires 25 kernels, a general VNLE 3905 kernels [8]. However, most of these VNLE kernels can be safely pruned without severe performance reduction [20]. The \(5|10|10|10|1\) DNN-NLE requires 291 trainable parameters (weights, biases), respectively 1040 independent hardware multipliers, which can be pruned considerably, too [21]. Besides the sheer number of trainable parameters, the way of using them for polynomials or activation functions is of course decisive, too. Figure 11: Constellation diagrams during the learning process.