# Two-Dimensional Interference Estimator with Parallel Structure for Holographic Data Storage Channel
## 5 Simulation and Results  
Firstly, we randomly created the original data \(u[k]\) with a size of 1,440,000 bits and the same probabilities for 0 and 1 (OFF and ON). \(u[k]\) is modulated into a data page of \(1200\times 1200\) bits. We used a spatial light modulator (SLM) to store the original data on the holographic medium. We used one page for the training process to estimate the equalizer and GPR target. During the testing process, ten pages were used to calculate the BERperformance. The channel model of the HDS was characterized using an effective discrete PSF of size 5 \(\times\) 5, as described in Section 4.  
We investigate the effect of the fill factor by varying \(\alpha\) from 0.5 to 1. During the first experiment, we set up an environment with a blur of 1.85, and the \(x\)- and \(y\)-axes misalignments were 0%. The results are presented in Figure 3.  
Figure 3 shows that the BER performance is worse as the fill factor \(\alpha\) is smaller. When \(\alpha\) decreases, the channel interference parameter also decreases because of the smaller intensity, and AWGN becomes the major factor in the received signal. In this article, for easier comparison, we chose \(\alpha=1\) like the previous studies [17; 18].  
Next, we show the BER performance of the output signal from the horizontal SOVA, vertical SOVA, and average function (proposed model).  
The results in Figure 4 indicate that the proposed model achieves the best performance when the horizontal process is combined with the vertical process using the average function. The gain is approximately 2 dB at a BER of \(10^{-5}\).  
In addition, we replace the linear equalizer with the nonlinear equalizers in [19; 20] to estimate the non-linearity in the channel. The results are shown in Figure 5.  
Figure 5 shows that the BER performances of three equalizers are almost the same. This implies that the linearity is the major factor of the HDS channel during the simulation.  
In the next experiment, the channel is affected by a blur grade of 2.0 and the a misalignment of 5%. We compared our proposed model with a decision feedback equalizer [17] and a 2D SOVA [18]. The BER performance according to the SNR is depicted in Figure 6.  
Figure 3: Effect of the fill factor on BER performance of the proposed model.  
Figure 6 shows that our proposed model is better than that of previous studies. This is because our proposed model can estimate and remove the interference to make the SOVA effective. In addition, the average helps the proposed model utilize the information from horizontal and vertical processes.  
Because blur is an important factor affecting HDS, we varied it from 1.9 to 2.1 with an SNR of 20 dB and a misalignment of 5%. Figure 7 shows the BER performance according to the blur grade.  
Figure 4: BER performance of the proposed model.  
Figure 5: BER performance of the proposed model using the linear and nonlinear equalizers.  
From Figure 7, we can observe that the BER performance of the proposed model is sensitive to blur. However, when compared with other methods, the proposed model achieves the best performance.  
To investigate the effect of the ON and OFF ratio, we varied the probability of ON from 0.25 to 0.75 (or the probability of OFF from 0.75 to 0.25) at 15 dB. The results are presented in Figure 8.  
Figure 8 shows that the proposed model performs better when the probability of ON is smaller.  
Figure 6: Comparison of the BER performances.  
Figure 7: BER performance according to blur.