## 4 Simulation and Discussion  
In this section, simulations based on the MATLAB platform are used to examine the performance of the proposed sensing strategy for SS. The simulation band is conducted at very high frequency (VHF), where the carrier frequency is set as \(f_{\text{c}}=1.0\times 10^{8}\text{Hz}\) and sampling frequency is \(f_{\text{s}}=3.0\times 10^{8}\text{Hz}\). An Orthogonal Frequency Division Multiplexing (OFDM) signal is chosen as the test signal (PU) for its generality and popularity in wireless communication networks. Additionally, the sampling point at the receiving terminal of a CR is \(N=f_{\text{s}}\tau=50\) without special instructions. In the simulation, the OFDM signal is first generated and then white Gaussian noise with mean zero and variance one is added into the OFDM signal. After the sampling and energy normalization of the noise-only case and the signal-plus-noise case, the detection probability and false-alarm probability are calculated by the corresponding energy comparisons with the presupposed threshold. Note that the optimal sensing performance in Figures 1-4 is obtained when the corresponding sensing threshold is used, just as analyzed in (9)-(30). Figure 1: Comparisons between three classical sensing strategies and the proposed sensing strategy when N = 100. In Figure 1, we mainly discuss comparisons among three classical sensing strategies and the proposed strategy when the respective optimal sensing performance is obtained (N = 100). Strategies 1-3, respectively, correspond with the one in [28; 29; 30]. From Figure 1, the false-alarm probability of Sensing Strategy 1 is evidently higher than others while its corresponding throughput is the lowest. Meanwhile, the detection probability of Strategy 2 is dramatically inferior to the other three. Compared with Sensing Strategy 1 and Sensing Strategy 2, Sensing Strategy 3 and the proposed strategy consider both the false-alarm probability and detection probability. These results correspond with the first section of Chapter 3. Figure 4: Throughput comparisons when the sensing performance is optimal. Figure 3: Detection probability comparisons when sensing performance is optimal. Figure 2: False-alarm probability comparisons when sensing performance is optimal. Figure 2 exhibits false-alarm comparisons between classical (strategy 3) and proposed sensing strategies in AWGN, Rayleigh, and Rician channels, when the sensing performance is optimal according to Theorem 1 and Theorem 2. Evidently, the proposed sensing strategy appears to have lower false-alarm scores compared with Sensing Strategy 3, which indicates the spectrum sensing scheme with a novel sensing strategy a greater chance of discovering the idle spectrum. Figure 3 provides detection comparisons between Strategy 3 and the proposed sensing strategy when the sensing performance is optimal. From Figure 3, the detection probability of the spectrum sensing scheme with Sensing Strategy 3 has a greater advantage over the proposed one. This states that the proposed scheme tends to discover a more available idle spectrum, while the classical scheme is specialized in the protection of PU. An available throughput comparison between classical and proposed sensing strategies is shown in Figure 4 in AWGN, Rayleigh and Rician channels when the sensing performance is optimal. From the standpoint of a secondary network, the CR equipment with the proposed sensing strategy has an increasing capability to communicate with its users compared to a classical sensing strategy. Based on (23)-(30), the proposed strategy has a better sensing performance when considering the detection probability, false-alarm probability and available throughput. Note that a delay spread nature exists in the process of SS, even if narrow-band-based SS is considered. For narrow-band-based SS, the delay mainly consists in the sampling duration at the receiver of CR. For wide-band-based SS, the delay of SS is the sum of the scanning time over multiple spectrum bands.