## 4 Evaluation
### Testing of Harmonic Interference Suppression Effects  
We conducted harmonic interference suppression tests using the experimental scenario depicted in Figure 10a. Specifically, the reader transmits a carrier signal or command at a frequency of 910 MHz. The reader's receiving end captures the backscattered signals from the tags at a frequency of 934 MHz. Tag 1 modulates the excitation signal with a frequency shift of 8 MHz, while Tag 2 applies a frequency shift of 24 MHz. The aim is to test the impact of the harmonic components generated by Tag 1's frequency shift on the reader's ability to demodulate the backscatter information from Tag 2. According to Equation (1), the spectrum of a standard square wave comprises significant third harmonic components. Therefore, it is theoretically anticipated that Tag 1 employing a standard square wave for frequency shifting will interfere with the reader's identification of Tag 2. However, according to Equation (4), we can mitigate the interference from the third harmonic components by utilizing an adaptive pulse-width square wave with pulse widths of (\(x=\frac{T}{6}\)) and (\(y=\frac{5T}{6}\)). Under this pulse-width configuration, the Fourier series of the third harmonic can be expressed as follows:  
\[ \begin{split} a_{3}&=\frac{e^{-\tilde{n}\frac{ \pi}{6}\frac{\pi}{6}}+e^{-\tilde{n}\frac{11\pi}{6}}-e^{-\tilde{n}\pi}-1}{-2 \tilde{n}\pi\pi}.\\ &=\frac{e^{-j3\pi\frac{\pi}{6}}+e^{-j3\pi\frac{11\pi}{6}}-e^{-j3 \pi\pi}-1}{-2j*3\pi}.\\ &=0.\end{split}  \tag{5}\]  
Figure 11: Frequency shift measurement diagram. Consequently, we conducted a comparative experiment consisting of two groups. In one group, Tag 1 utilized an 8 MHz standard square wave for frequency shifting, while in the other group, Tag 1 implemented an 8 MHz adaptive pulse-width square wave with pulse widths of (\(x=\frac{T}{6}\)) and (\(y=\frac{5T}{6}\)). The objective was to assess the accuracy of the reader in identifying the backscatter information from Tag 2 under both conditions, as illustrated in Figure 12a. We evaluated the effectiveness of harmonic interference suppression by measuring the bit error rate (BER) associated with the reader's identification of the EPC of Tag 2. Additionally, we conducted tests on the harmonic interference suppression effects during frequency shifting using adaptive pulse-width square waves configured with several different pulse widths (i.e., the different value of x and y). We selected adaptive pulse widths of (\(x=0.3T,y=0.7T\)) and (\(x=0.2T,y=0.8T\)) for the comparison. According to Equation (4), it can be inferred that these two adaptive pulse widths theoretically exhibit a weaker suppression effect on the third harmonic components compared to the pulse-width configuration of (\(x=\frac{T}{6}\), \(y=\frac{5T}{6}\)). We analyse the BER of the reader decoding the EPC of Tag 2 under various conditions, as illustrated in Figure 12b. In the figure, \"distance\" represents the distance between Tag 1/Tag 2 and the reader. The results presented in Figure 12a indicate that, compared to the FS (frequency-shifting) backscatter system utilizing standard square waves, our harmonic interference resilient backscatter system, which employs adaptive pulse-width square waves for frequency shifting, achieved a 70% reduction in the BER. Figure 12b illustrates that the adaptive pulse-width square waves, configured with varying pulse widths, exhibit different suppression effects on harmonic interference, leading to variations in the BER during the reader's identification process. Therefore, to enhance the suppression of harmonic interference, it is essential to design the pulse-width distribution of the adaptive pulse-width square waves with precision. In addition, the BER test results with error bars at the specified key distances are illustrated in Figure 13a. The corresponding confidence interval is 95%. Moreover, to better assess the harmonic interference suppression in scenarios with many deployed tags, we added a third tag (Tag 3) with an identical configuration to Tag 1.