# Performance Tradeoff Analysis of Hybrid Signaling SWIPT Systems with Nonlinear Power Amplifiers
## 5 Numerical Results and Discussion  
This section presents numerical results based on the above analysis. The default values of parameters used in this section are set as follows. The maximum amplitude of linear amplification \(r_{\text{max}}\) is set to be 3, the ideal amplification gain coefficient of PA \(A\) is 10, the effective IBO ranges from \(-5\) dB to 15 dB. The power of the information signal is set to be constant, the power ratio of the energy signal to the information signal \(P_{E}/P_{1}\) ranges from 4 to 256, and the noise power \(\sigma_{v}^{2}\) is set to \(-100\) dB. Complex Gaussian signals are used to approximate the multi-carrier information signal and multitone energy signal. In some figures, theoretical results and simulation results are presented for comparison purposes. The theoretical results are obtained from numerical computation of closed-form or semi-closed-form equations, while the simulation results are obtained from Monte Carlo simulations and sample-based numerical evaluation. The presented results are statistically averaged over 50 trials. Figure 5 compares the PA efficiency of Class A and Class B PAs as a function of the effective IBO. Results for both the Saleh model and polynomial model are shown. The theoretical and simulation results are calculated based on Equations (17) and (15), respectively, which are shown to agree well. As expected, the efficiency of PA generally decreases with the increase in IBO. The efficiency of Class B exceeds that of Class A, with a gain ranging from 10 dB to 40 dB. The efficiency differences are more significant at smaller values of IBO. Moreover, the efficiency given by the polynomial model is slightly better than that of the Saleh model. This is because the polynomial model exhibits a slightly higher AM-AM curve, as shown in Figure 4. Such difference diminishes with increasing IBO. Figure 5 successfully establishes the relationship between PA efficiency and IBO. The next step is to link IBO with SNDR, such that we can use IBO as an intermediate parameter to characterize the tradeoff between PA efficiency and SNDR. Figure 6 shows the relationship between effective IBO and SNDR under different energy-to-information signal power ratios. Results are shown for the two different cases discussed in Section 4. Case I refers to the case where we have the same amplification coefficients, while Case II denotes the case with different coefficients. For Case I, we can have both theoretical and simulation results based on the equations presented in Section 4.1. For Case II, we can only have simulation results based on Equation (34). For notation simplicity, the SNDR values obtained by Case I theory, Case I simulation, and Case II simulation are denoted as I(1), I(2), and II(2) in the figure legend, respectively. In Figure 6, SNDR values are shown to increase almost linearly with increasing IBO (both in dB values). The SNDR difference between Case I and Case II is not very significant, only reaching a maximum value of 2 dB when the IBO is 15 dB. Moreover, the SNDR given by the polynomial model is slightly better than the Saleh model. This is because the memoryless polynomial model in (9) assumes no AM-PM distortion. Another finding presented in Figure 6 is that the SNDR decreases with increasing \(P_{E}/P_{1}\) power ratio. This  
Figure 5: The efficiency of Class A and Class B PAs as a function of the effective IBO (Class A and Class B PAs, Saleh, and polynomial models). is expected because a higher-power energy signal will generate more interference with the information signal. Figure 6 establishes the relationship between SNDR and IBO. Building on the results shown in Figures 5-7 show the tradeoff between SNDR and PA efficiency with different PA classes and different PA models. The power ratio is fixed at 64. We can see that, given a targeted SNDR value, the two PA classes contribute to the most significant efficiency difference at around 20 dB. The two different PA models also lead to a small difference of less than 5 dB.