## 4 Simulation and Results  
In this simulation, we set \(M_{m}=N_{m}=1\) for the MLP input sequences, \(M_{w}=1\), \(M_{m}=5\) for the 2D equalizer of width 3 and length 11, and \(N_{g}=1\) for the PR target of length 3. The signal-to-noise ratio (SNR) is defined as 10 log\({}_{10}\)(1/\(\sigma^{2}\)). At each SNR, 810,000 bits for training the MLP and 2,250,000 bits for simulating the proposed detector are used. Figure 3 shows the bit error rate (BER) performance depending on the scaling factor \(\alpha\) when SNR = 16 dB, and one hidden layer with 16 neurons in the MLP is selected. Because the proposed detector demonstrates the minimum BER performance when \(\alpha\) is 0.1, we set \(\alpha\) to 0.1 as the scaling factor.  
Figure 4 presents the BER performance comparisons among the conventional PRML detector, MLP alone, and the proposed detector according to the SNR at a TMR of 0%. In the conventional PRML, the readback signal is detected without the MLP and iteration. In the MLP scheme alone, the readback signal is estimated only by the MLP. As shown in Figure 3, at BER = 10\({}^{-4}\), the proposed detector with one hidden layer with 16 neurons without iteration provides an SNR gain of approximately 2 dB and 1 dB as compared with the conventional PRML detector and MLP alone, respectively. Subsequently, to compare the BER performance based on the number of hidden layers and neurons in the MLP, we apply two types of MLP to the proposed detector. One is a hidden layer with 16 neurons (Case 1)  
Figure 1: Block diagram of proposed bit-patterned media recording (BPMR) system model.  
Figure 2: Multilayer perceptron (MLP) structure.  
and the other is three hidden layers with 128 neurons in each layer (Case 2). Without iteration, the BER performance of Case 2 improves by 1 dB as compared with that of Case 1. Finally, to compare the BER performance with respect to the number of iterations, we simulate the proposed detector iterating numbers from 0 to 2. Even when the number of iterations increases at the BER of \(10^{-4}\), the performance of Case 1 without iteration is similar to that of Case 1 with one and two iterations. However, when the BER is \(10^{-5}\), the BER of Case 2 with two iterations is higher by approximately 0.3 and 0.1 dB as compared with Case 2 without iteration and with one iteration, respectively.  
Figure 5 illustrates the BER performance at SNR of 20 dB when the TMR is varied from 0% to 30%. The proposed detector (Cases 1 and 2) indicates better BER performance as compared with the conventional PRML and MLP alone. Moreover, increasing the number of hidden layers, neurons, and iterations improves the BER performance.  
Figure 4: BER performance comparisons among conventional partial response maximum likelihood (PRML) detector, MLP alone, and proposed detector based on signal-to-noise ratio (SNR) at track misregistration (TMR) of 0%.  
Figure 3: Bit error rate (BER) performance of proposed signal detection scheme based on scaling factor \(\alpha\).  
When the proposed detector is used, the response time is increased as compared with a conventional PRML detector. However, since the proposed detector can cancel the ITI effect from neighboring islands, it shows better BER performance than a conventional PRML and MLP alone. Hence, to use the proposed detector, the trade-off between complexity (or cost) and BER performance should be considered.