## 5 Experimental Results and Discussions
### Accuracy Comparison  
In each scenario, we compare the performance of our method to four alternative methods commonly used for CSI preprocessing techniques. As the first alternative, we select a statistical method that takes a median value for each \(a_{c,i}(t)\)s in \(X_{c}\)\((\forall i\in[1,S])\) to smooth the temporal dynamics inherent in the measured CSI. Using the median of the measured CSIs is a representative method using statistical measures in the time domain, and it has been used in [15] and the references presented in Table 1 of [15]. Henceforth, we will call this method _Median_. The second comparison target is a signal processing method that takes the FFT on each \(a_{c,i}(t)\)s in \(X_{c}\) and filters out high-frequency components of the \(a_{c,i}(t)\)s. This approach has been used in [28]. We will name the method that removes the upper half of the high-frequency components from the CSI frequency components as _FFT_. The third alternative method, which we will call _PCA_, is a dimension reduction method using PCA [32]. For each subcarrier \(i\) (\(i\in[1,S]\)) in \(X_{c}(t:t+h)\), PCA is applied to \(\{a_{c,i}(t),\ldots,a_{c,i}(t+h)\}\) and obtains its \(k\) principal components. Therefore, the _PCA_ method decreases the dimension of \(X_{c}(t:t=h)\) from \(S\times h\) to \(S\times k\) (in general, \(k<<h\)). In the experiments, we set \(k\) to two values: two and four. CNN is famous for its image classification capability. To exploit the capability of the CNN, a set of measured data is often regarded as a gray image [36]. We further divide the one-dimensional CSI amplitude value per each subcarrier to three-dimensional color values. Thus, to show the validity of the proposed method, we also present the accuracy of CNN when a set of measured CSI amplitudes is used as a gray image (i.e., \(X_{c}(t:t+h)\)). Hereafter, we will call this case _Gray Image_. In Figure 5, we compare the CSI preprocessing methods in terms of the overall IOD accuracy of the CNN in various measurement scenarios when the input to the CNN is prepared by each method. If we denote the total number of tests for the \(i\)-th experiment as \(n_{i}\), and the number of times the Wi-Fi sensing system accurately determines the number of people as \(m_{i}\), then the overall IOD accuracy becomes \(m_{i}/n_{i}\). We repeat the same experiments with different test datasets for ten iterations and depict box plots for \(m_{i}/n_{i}\) to compare not only the overall average prediction accuracy but also the variation in the overall prediction accuracy across various test datasets. In this figure, we observe that the relative efficacy of the conventional methods is contingent upon the specific Wi-Fi sensing environments. For example, in the TTW scenario, the median IOD accuracy is the highest with the \(PCA\) method with the two principle components method. However, in the other two scenarios, our method outperforms in terms of the IOD accuracy. We observe that Q1 (i.e., 25 percentile) of the IOD accuracy when our method is applied is higher than the Q3 (i.e., 75 percentile) obtained by other methods. To analyze the influence of the proposed method on the prediction accuracy for each number of people, we scrutinize the confusion matrices in Figure 6. A confusion matrix is a table used to evaluate the performance of a classification algorithm. It is particularly useful in supervised learning, where the goal is to predict labels for a set of instances. The confusion matrix allows us to see how well a Wi-Fi sensing system is performing by comparing the predicted labels to the actual labels (i.e., the number of people). Specifically, an element \(A(i,j)\) located in the \(i\)-th row and the \(j\)-th column of a confusion matrix represents the proportion of cases where the actual label is \(i\) but the Wi-Fi sensing system predicts \(j\) during the experiments. Figure 5: Impact of each CSI preprocessing method on people counting.