## 4 Simulation Experiments and Results Analysis
### The Verification of Simulation Signals  
The simulation signals are comprised of two strong 16 Quadrature Amplitude modulation (16 QAM) signals and a weak one. Both of the strong signals are generated with the same amplitude of \(-45\) dBFS and the same symbol rate of 2 MHz. Their center frequencies are 125 MHz and 130 MHz, respectively. The weak one located in the polluted region is at 119 MHz with \(-97\) dBFS, and its symbol rate is 0.5 MHz. Their baseband signals are obtained by carrying out DDC. Hence, from the distorted spectrum in Figure 5a, unwanted nonlinearities cover the weak 16 QAM's spectrum and distort it seriously so that its signal to interference plus noise ratio (SINR) inevitably decreases. In addition, the green region affected by intermodulation is originally supposed to be a vacant spectrum. Therefore, false-alarm probability in this region rises and spectrum efficiency degrades. Figure 6b provides the relationship between the delay and optimized power residuals in the full-spectrum band. When \(\tau\) equals 10, the optimized residuals reach the minimum value compared to the others. Therefore, 10 is chosen as the best delay. In Figure 5b, the blue spectrum indicates the mitigation performance when best delay searching is employed, while the red spectrum shows the compensation result without the best delay. The nonlinear behavior model adopted here is the Hammerstein model in Equation (20) and the model orders are 1, 3, and 5 with the same memory depth of 20. By carrying out mitigation methods, SFDR in the full band rises by 10-15 dB. In Figure 5b, it seems that both the proposed mitigation methods have achieved satisfactory results, while the apparent differences between them are only focused on the adjacent channels of strong 16 QAMs. However, these differences are crucial evidence for explaining the advantage of the best delay-based method. In Figure 5a, there mainly exist two kinds of intermodulation products. The first kind is generated when one strong 16 QAM is modulated by another. In Figure 5a, they are located at the center of 120 MHz and 135 MHz and have a 9 MHz bandwidth, since the roll-off factor is 0.5. The second is caused by the strong signal itself and is located in an adjacent channel to the strong 16 QAM. In the first adjacent channels of the strong 16 QAMs, different kinds of distortions are vector overlapped in the frequency domain. For the first type of intermodulation product, both mitigation  
Figure 5: Nonlinearity mitigation results of simulation signals including two strong 16 QAM signals and one weak 16 QAM signal: (**a**) distorted signals; and (**b**) signals after nonlinearity mitigation. Figure 6: Relationships between delay and power residuals after optimization: (**a**) optimized power residuals in false-alarm region; and (**b**) optimized power residuals in full spectrum band. methods have a significant improvement while, for the second one, the best delay-based mitigation method outperforms the mitigation-only method. In particular, in the marked false-alarm region ranging from 127 MHz to 128 MHz, the spectrum after mitigation at the best delay is about \(-110\) dBFS, which is close to the background noise level and 5 dB lower than that without the best delay. If the black line of \(-108\) dBFS is used as the ED threshold, the red spectrum will always be detected as occupied so that SUs would miss a transmission opportunity. This is also proved by Figure 6a, which shows the relationship between the delay and optimized power residuals in the false-alarm region. The best delay of 10 corresponds to its minimal optimized power residuals. Consequently, we conclude that when the best delay is determined, the nonlinear behavior model can provide better outputs to deal with the more complicated situation where different kinds of nonlinearities simultaneously exist. Figure 7 shows the constellations of the weak 16 QAM in Figure 5 before and after mitigation.