## 6 Results
### Information and Power Trade-off  
From the previous results, it is shown that the balanced pre-equalizer with \(p=0.1\) provides the maximal normalized PCE for multisine PSK modulated SWIPT and the balanced pre-equalizer with \(p=0.5\) provides capacity approaching the maximum value for both modulation schemes. In this subsection, we further compare the SWIPT performance of the proposed multisine PSK modulation with the QAM-OFDM scheme, by investigating the trade-off between information and power transfer. We apply the balanced pre-equalizer with \(p=0.1,0.5\). The proposed WPT pre-equalizer from [23] and the pre-equalizer maximizing capacity are also considered as a baseline for evaluating performance of power and information transfer. Figure 11 shows the normalized PCE-capacity boundary when varying the power splitting factor from 0.1 to 1. The multisine based SWIPT experiences a frequency-selective channel with normalized gain one. It is shown for the multisine PSK based SWIPT that the balanced equalizer with \(p=0.1\) leads to the largest PCE-capacity region, while the pre-equalizer \(\mathbf{w}_{|\mathbf{h}|^{3}\angle\mathbf{h}^{*}}\)[23] leads to the smallest region. Nevertheless, for QAM based SWIPT, the pre-equalizer \(\mathbf{w}_{|\mathbf{h}|^{3}\angle\mathbf{h}^{*}}\) provides the highest normalized PCE and \(\mathbf{w}_{\mathrm{C}}\) still provides the lowest PCE and the highest capacity. It is noted that when the power-splitting factor is higher than 0.9, the water-filling algorithm tends to allocate no power to the bad channels which also lowers the power transfer performance. In addition, by comparing the two modulation schemes, it is shown the maximum normalized PCE improves up to 140% by applying multisine PSK when the power splitting coefficient is 1. As can be seen from Figure 9, the received power achieves the highest value by using pre-equalizer \(\mathbf{w}_{|\mathbf{h}|^{3}\angle\mathbf{h}^{*}}\) compared to the other pre-equalizers. Besides, as expected, the PAPR of the signal applying complex normal symbol input is much lower than the PAPR of the signal applying the multisine PSK scheme, as can be seen in Figure 10.  
To give more insight in the interplay between the wireless channel and the modulation strategy, we further discuss the impact of the number of tones on the SWIPT performance for multisine PSK and QAM. Figure 12 shows the capacity with increasing number of tones in the multisine based SWIPT when applying multisine PSK modulation and complex normal input symbols at fixed BW. It is shown that the capacity is almost flat with increasing number of tones when the balanced pre-equalizers are applied in the multisine PSK SWIPT. This is because when the signal BW is fixed, the total capacity  
Figure 10: PAPR of the received signals using multisine PSK modulation and QAM modulation using the proposed pre-equalizers of an 8-tone based SWIPT of bandwidth 1 MHz. \(C\simeq B\log_{2}(\frac{4\pi\frac{\tilde{P}_{l}}{N_{l}}}{e})\) which mainly depends on the variance of \(\log_{2}(\frac{4\pi}{e}\frac{\tilde{P}_{l}}{N})\) that only decreases in a small range with increasing \(N_{l}\). The pre-equalizer \(\mathbf{w}_{\|h\|^{3}\Delta\mathbf{h}}\), assigns major power to the good sub-channels and loses the information in the other sub-channels. In addition, for QAM modulation, more capacity is gained when it is possible to exploit the channel statistics and apply water-filling, but this improvement saturates when the number of tones is large enough since the SNR of each sub-channel also decreases. The normalized PCE increases with the number of tones as shown in Figure 13. Looking at Figure 15, it is shown that the balanced pre-equalizers \(p=0.1,p=0.5\), and \(\mathbf{w}_{\|h\|^{3}\Delta\mathbf{h}}\), improve the received power with increasing number of tones, while the pre-equalizer \(\mathbf{w}_{maxC}\) results in a slightly decreased power with increasing number of tones.