## 4 Simulation Experiments and Results Analysis
### The Verification of Signals from a Real-World RF Device  
In this part, signals passing through real-world RF are utilized for testing. For the sake of corresponding with the simulation signal experiments, the signals used for testing contain three strong 16 QAM signals and one weak 16 QAM signal. The sampling rate here is 112 MHz. The strong 16 QAMs have the same symbol rate of 2 MHz and their center frequencies are 157 MHz, 162 MHz, and 168 MHz, respectively. The weak one, with a 0.5 MHz symbol rate, is located at 150 MHz. The center frequency of the intermediate frequency sampling is set as 160 MHz and the passband bandwidth is 40 MHz. The order and memory depth of the Hammerstein model employed is set to be the same as those of the simulation signals. From Figure 8b, among the optimized power residuals of each delay, when delay \(\tau\) equals 11, the minimal value is 88.3% of the optimized \(E(\omega,\tau)\) without the best delay. This indicates that nearly 11.7% of power residuals, when mitigation is already finished without the best delay, can still be reduced if best delay searching is carried out. In Figure 8a, the best delay is also decided as 11, which reduces the optimized power residuals in the false-alarm region to almost one third of that without delay. A comparison of the spectrum before and after nonlinearity compensation is shown in Figure 9. As expected, SFDR increases at least 10 dB and the best delay approach can eliminate 3-5 dB more nonlinearities in most parts of the spectrum. Figure 8: Relationships between delay and power residuals after optimization: (**a**) the optimized power residuals in the false-alarm region; and (**b**) the optimized power residuals in the full-spectrum band. Figure 9: Nonlinearity mitigation results of simulation signals including three strong 16 QAM signals and one weak 16 QAM signal: (**a**) distorted signals; and (**b**) signals after nonlinearity mitigation. To verify the improvement of spectrum sensing performance of the proposed mitigation method, the green region in Figure 9 is chosen as the band of interest. Its receiver operating characteristics (ROC) for each case are calculated for the detection of spurious signals. The ED [37] method is utilized as a demonstration where the detection threshold is calculated by:  
\[\gamma=\sigma_{w}^{2}\Big{(}N+\sqrt{2N}Q^{-1}(P_{f})\Big{)} \tag{36}\]  
where \(\sigma_{w}^{2}\) is the noise variance of the sub-band, \(Q^{-1}(\cdot)\) is the inverse function of the normal distribution function, \(N\) is the point used, and \(P_{f}\) is the false-alarm probability which is used as a metric for CR-WSN failing to detect the absence of the primary signal. As shown in Figure 10, \(P_{d}\) denotes the spurious signal detection probability. The curve in red represents the ROC of the distorted signal whose \(P_{d}\) is always one when \(P_{f}\) changes from 0 to 1. This means that, as a result of the existence of intermodulation, the ED method will always detect the green region as busy. This result is acceptable since the intermodulation component's spectrum power is 10 dB higher than the noise floor in Figure 9a. As for the comparison between the mitigation method with and without best delay searching, the pure noise's ROC is treated as a standard whose characteristic conforms to \(P_{d}\approx P_{f}\). Considering that the ROC curve here is in the false-alarm region, \(P_{d}\) indicates the probability of detecting a nonexistent signal. For a fixed probability of \(P_{f}\), the blue curve's \(P_{d}\) is always greater than that of the pure noise, while the purple's curve is always less. This is to say that, by the proposed best delay-based mitigation method, the sensor is less likely to detect a false signal. Consequently, we can draw the conclusion that nonlinearities can be mitigated more effectively when best delay searching is employed and, in that way, the reliability of spectrum sensing is enhanced.