## 3 Results and Discussion
### A 10-Gbaud Optical-Fiber Communication System
In other words, a 2.4 dB and 1 dB power benefit is achieved by ANNE-AT, as opposed to ANNE-ET, to obtain a BER of \(10^{-3}\) and \(10^{-9}\), respectively. Comparing Figure 5a,b, we find that at a BER of \(10^{-3}\), the performance benefit provided by the ANNE-AT over ANNE-ET increases at longer distances. That is because at a higher BER and/or longer distances, the impact of noise is more severe, and the advanced training of ANNE-AT under the noisy environment helps to achieve the better performance. Note that for a specific transmission distance, the BER is determined from the following factors: (i) ISI effect due to dispersion, which can be mitigated using the ANNE-AT equalizer provided that the number of taps is larger than the ISI span of the channel, (ii) channel noise that includes shot noise and thermal noise, and (iii) received optical power which depends on the transmitted power and fiber loss. The main purpose of the ANNE-AT equalizer is to mitigate the nonlinear distortions caused by fiber dispersion. The B2B results shown in Figure 5a,b are the minimum BER obtainable for the given received signal power and noise power levels. From these figures, it can be seen that ANNE-AT performance is quite close to the B2B case. To further demonstrate the efficiency of the proposed ANNE-AT, three types of common equalization schemes including feed-forward equalizer (FFE), decision feedback equalizer (DFE), and maximum likelihood sequence estimator (MLSE) are considered for comparative analysis. The received optical power required to achieve BER \(=10^{-3}\) versus a sweep of the fiber transmission distance is shown in Figure 6. Particularly, we compare the BER performance of the ANNE-AT to FFE[7], DFE\(\{4,3\}\), ANNE-ET, MLSE\(\{7\}\), and MLSE\(\{9\}\), where \(\{\cdot\}\) refers to the number of FFE taps or the memory size of the MLSE. In the case of DFE, \(\{\cdot,\cdot\}\) denotes the numbers of its feed-forward and feed-backward taps, respectively. Note that the parameters of the ANNE-AT and ANNE-ET are fixed to \(N=7\) and \(m=6\) for all distance cases shown in Figure 6. For a fair comparison, we use the advanced training scheme to train both the FFE and DFE equalizers. However, the MLSE is trained using the extensive training scheme. Note that the MLSE training process aims to construct a look-up table that considers all the distorted noise-free sequences that may be received after the channel transmission. Once trained, the MLSE estimates the transmitted sequence by comparing the received distorted sequence with all look-up table entries and selects the sequence with highest probability. Therefore, it is impractical to train the MLSE using the advanced training scheme as this will significantly enlarge the size of its look-up table, leading to an infeasible equalization time. As can be seen from Figure 6, the feasible transmission distance is limited to less than 100 km if no equalization is used. The linear equalizers including the FFE and DFE can barely extend the feasible transmission distance to around 100 km. They fail to compensate for the nonlinear distortions at longer transmission distances. However, nonlinear equalizers including the proposed ANNE-AT, the ANNE-ET, and the MLSE can provide a BER performance benefit, significantly extending the transmission distance feasibility. Clearly, the ANNE-AT shows superior BER performance over all other nonlinear equalizers. The power benefit of the ANNE-AT over ANNE-ET ranges from 1.6 dB to 3.3 dB with an average power benefit of 2.3 dB. Owing to the strength of the advanced training scheme, the ANNE-AT also provides a 1.6 dB power benefit, on average, as opposed to the MLSE[7], and a slight power benefit over the MLSE[9]. In terms of the overhead cost and memory usage required for equalization, Table 1 tabulates the computational complexity per symbol and the memory storage requirements of the FFE, DFE, ANNE-ET, and MLSE compared to the proposed ANNE-AT. The minimum overhead equalization cost and memory requirements are achieved by the FFE and DFE.