## 3 Results and Discussion
### A 10-Gbaud Optical-Fiber Communication System
However, as can be seen from Figure 6, both the FFE and DFE provide poor compensation performance benefit because of their limited ability against nonlinear system distortions. Particularly, the computation cost per symbol of the FFE\(\{N\}\) and DFE\(\{N_{1},N_{2}\}\) scales linearly as \(\sim\)\(N\) and \(\sim\)\((N_{1}+N_{2})\), where \(N\) is the number of FFE taps, and \(N_{1}\) and \(N_{2}\) are the numbers of feed-forward and feed-backward taps of the DFE, respectively [36]. During equalization, both the FFE and DFE also need to store the values of their tap weights, where the number of FFE and DFE weight parameters is equal to their total number of taps [36]. The memory requirements of the FFE\(\{N\}\) and DFE\(\{N_{1},N_{2}\}\) therefore scale as \(\sim\)\(N\) and \(\sim\)\((N_{1}+N_{2})\) floating-point numbers, respectively. The computational complexity per symbol and memory storage requirements of the ANNE-AT (as well as the ANNE-ET) scale as \(\sim\)\(mN\) and \(\sim\)\(m(N+1)\), respectively. However, the computational cost of the MLSE scales exponentially as \(\sim\)\(2^{N}\) per symbol, where \(N\) is the memory size of the MLSE [36]. In addition, the MLSE requires huge memory storage during the equalization process, because it needs to store all entries of its look-up table to compare them with the received distorted sequence and determine the most probable transmitted sequence [36]. It thus follows that the memory usage requirements of the MLSE scale as high as the size of its look-up table, i.e., \(\sim\)\(2^{N}\) floating-point numbers. Figure 6: Received optical power (RoP) required to achieve BER = \(10^{-3}\) versus fiber transmission distance for the 10 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]. From Table 1, to obtain the results provided in Figure 6, the FFE[7], DFE[3; 4], MLSE[7], and MLSE[9] particularly require 7, 7, 128, and 512 multiplication operations per bit, respectively, whereas the ANNE-AT[7; 6] and ANNE-ET[7; 6] need only 42 multiplication operations per bit. During the equalization process, the ANNE-AT[7; 6] and ANNE-ET[7; 6] also require a memory storage of 48 floating-point numbers, as opposed to 7, 7, 128, and 512 floating-point numbers needed to be stored by the FFE[7], DFE[3; 4], MLSE[7], and MLSE[9], respectively. Hence, among all tested nonlinear equalizers that provide the required performance benefit, the ANNE-AT is the most efficient equalizer from the performance, computation complexity, and memory requirement points of view. So far, we have assumed a noise-free EDFA. However, in addition to amplifying the optical signal, actual EDFAs add optical noise to the signal due to spontaneous emission effect [1; 2]. The interaction between this added optical noise with the fiber dispersion and square-law detection of the DD results in further BER performance degradation. To investigate this degradation, we consider the 140 km communication scenario with a noisy EDFA having a noise figure \(N_{f}=4.77\) dB. The ANNE-AT model used to obtain the results of Figure 5a is re-trained to include the effect of the EDFA optical noise. Figure 7 plots the BER performance of the overall system including the EDFA noise effect versus the received optical power. We compare the BER performance achieved using the ANNE-AT[7; 6] with that obtained in the no-equalization case, equalization using the ANNE-ET[7; 6], and the zero-dispersion transmission case. Notice that the minimum BER that can be achieved in this case is not the BER performance of the B2B transmission case, which does not include the effect of the EDFA optical noise. Rather, the reference BER that we seek to converge to, in this case, is the BER performance of the 140 km transmission over a non-dispersive (i.e., \(\beta_{2}=0\) ps\({}^{2}\)/km) optical-fiber link, i.e., the zero-dispersion transmission case ('crosses' in Figure 7).