## 4 Simulation Results
After introducing 5% media noise (position and size fluctuations), the superiority of the proposed systems over the 1D and 2D conventional systems remained evident. Specifically, Systems II, III, IV, and V achieved gains of 2.7, 3.2, 4.1, and 5.3 dB, respectively, at BER = \(10^{-5}\), over the 1D conventional system, as depicted in Figure 13. Additionally, it is clear that 2D processing can offer better performance compared to the 1D processing technique, which means that the ITI effect can be effectively managed by considering the information from its side tracks through 2D signal processing. Furthermore, Figures 12 and 13 demonstrate that the conventional 2D approach performs better than the proposed HIF, MSI, and BSD methods at lower SNRs. This advantage may stem from the  
Figure 12: BER performance of the proposed systems without position and size fluctuations. fact that all proposed techniques rely on 1D signal processing, whereas 2D signal processing can more effectively manage electronic noise. In a real BPMR channel environment, employing 2D signal processing alongside our proposed techniques would be more effective. However, the proposed MLP technique still provides better BER performance compared with the 2D conventional system. Furthermore, we also evaluated the proposed systems under severe media noise conditions (i.e., 10% media noise), as illustrated in Figure 14. The results reveal that the severity of media noise affects all systems, significantly degrading their BER performance. However, all proposed systems maintained superior BER performance compared to the 1D conventional system. Specifically, at BER = 10\({}^{-4}\), Systems II, III, IV, and V achieved gains of 2.4, 3.9, 4.5, and 5.0 dB, respectively, over the 1D conventional system. The 2D conventional system gains around 2.5 dB over the 1D conventional system at BER = 10\({}^{-4}\), which means that it not only deals with the ITI effect but also copes with the media noise effectively. However, the proposed MLP technique provides the best BER performance. This demonstrates the robustness of our proposed systems even under severe media noise conditions. We also analyzed the system performance using FER versus SNR at an AD of 3.0 Tb/in\({}^{2}\) without media noise, as shown in Figure 15. Each FER point was calculated using as many 4096-bit sectors as were needed to collect 1000 error frames or sectors. The results indicate that our proposed systems outperformed the 1D conventional system. Nearly all of them demonstrated better performance than the 2D conventional system, except for System II-HIF, which performed slightly worse than the 2D conventional system. In particular, at FER = 10\({}^{-3}\), System V can approximately provide gains of 3.1, 2.0, and 1.2 dB over Systems II, III, and IV, respectively, while the 1D conventional system cannot achieve an FER of 10\({}^{-3}\) with an SNR of 20 dB. Among all proposed systems, the MLP-based approach demonstrated the highest performance improvement. Based on these results, all the proposed systems outperformed the 1D conventional system. Notably, System V, utilizing the MLP algorithm, showed superior performance compared with the 2D conventional system. This might be because the MLP demonstrates an ability to understand the characteristics of the readback signals. System IV closely followed, leveraging the LLR for maximum data reliability detection. In this technique, a high LLR  
Figure 13: BER performance of the proposed systems with position and size fluctuations at 5%. signified a high reliability of the data bit, and the BSD technique, which sums LLR mutual data, further enhanced the reliability of detected bits. It is important to note that with the MLP's capability, it could directly process the readback signals without needing to be cascaded after the SOVA detector. It may use the readback signals for MLP training and learning.