# Performance Tradeoff Analysis of Hybrid Signaling SWIPT Systems with Nonlinear Power Amplifiers
## 5 Numerical Results and Discussion
The two different cases of SNDR definition give almost identical curves. A slightly concave-shaped tradeoff relationship is observed for SNDR and efficiency. Similar to Figure 7, Figure 8 shows the relationship between SNDR and PA efficiency with different power ratios. We can see that increasing the power ratio in an exponential fashion has a similar effect as shifting the tradeoff curve horizontally towards the left-hand side along the X-axis. This implies a negative linear relationship between the power ratio (in dB) and the SNDR. Again, the differences caused by using the Saleh and polynomial models are limited to 5 dB. Figure 6: The SNDR as a function of the effective IBO with varying power ratios (Class B PA, Saleh, and polynomial models). Figure 7: The tradeoff relationship between SNDR and PA efficiency (\(P_{E}/P_{I}=64\), Class A and Class B PAs, Saleh, and polynomial models). To pinpoint the results more accurately, Table 1 shows the efficiency of different PAs with different values of SNDR and power ratios. We can see that as the energy-to-information signal power ratio increases, the corresponding SNDR under the same efficiency is significantly reduced. In the literature of nonlinear PA analysis, it is a common practice to measure the nonlinear distortion effect by observing the power spectral density (PSD) of signals after a nonlinear PA. In the frequency domain, nonlinear distortion is manifested as power leakage into the adjacent bands. The adjacent channel power ratio (ACPR) is defined as the ratio of the signal power at the central frequency versus the power at an adjacent frequency (i.e., frequency offset). Similar to SNDR, ACPR is also a metric for nonlinear distortion. Figure 9 aims to show the correlation between these two commonly used metrics. A simulation is performed to measure the ACPR and SNDR. The information signal is taken as an OFDM signal with a bandwidth of 5 MHz, while the energy signal is a multitone sine signal. In Figure 9, when the SNDR is measured to be 10 dB, 20 dB, and 30 dB, the corresponding ACPR values at the 5 MHz offset are roughly \(-25\) dB, \(-34\) dB, and \(-41\) dB, respectively. This means that the variations in the theoretically calculated SNDR are mirrored by ACPR in the simulations. This further validates the practical value of the SNDR metrics. From the above discussion, we can see that maximizing SNDR and PA efficiency represents two conflicting objectives in a SWIPT system. The performance of a hybrid signaling SWIPT system is fundamentally characterized by the tradeoff relationship between SNDR and PA efficiency. In practice, an appropriate SNDR efficiency operational point should be carefully chosen for a targeted application. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Class A**} & \multicolumn{4}{c}{**Class B**} \\ \cline{2-11}  & \multicolumn{2}{c}{**Saleh PA**} & \multicolumn{2}{c}{**Polynomial PA**} & \multicolumn{4}{c}{**Saleh PA**} & \multicolumn{4}{c}{**Polynomial PA**} \\ \cline{2-11}
**Power Ratio** & \multicolumn{4}{c}{**SNDR (dB)**} \\ \cline{2-11}  & **10** & **20** & **10** & **20** & **10** & **20** & **30** & **10** & **20** & **30** \\ \hline
4 & & 14.4 & 4.5 & 20.7 & 8.1 & 45.9 & 26.1 & 14.2 & 54.3 & 34.8 & 20.1 \\
16 & & 7.8 & 2.4 & 12.3 & 4.7 & 35.1 & 19.4 & 10.9 & 42.9 & 26.6 & 15.1 \\
64 & & 4.2 & 1.2 & 6.8 & 2.3 & 24.9 & 13.6 & - & 32.5 & 18.9 & - \\
256 & & 1.9 & - & 3.6 & 1.0 & 17.1 & - & - & 23.7 & 13.8 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Efficiency of different PAs with different values of SNDR and power ratios. Figure 8: The tradeoff relationship between SNDR and PA efficiency with varying power ratios (Class B PA, Case I(1), Saleh, and polynomial models.