## 4 Experimental Simulation  
### Detection Simulation of Communication Signal Waveform by FUBSR and SUUBSR  
#### 4.1.1 Detection Simulation of Single-Carrier Signal Waveform by FUBSR and SUUBSR  
Through experimental simulation, the detection effects of SUUBSR and FUBSR systems on single-carrier signal waveforms under high background noise were tested. The simulation parameter settings were as follows: the input signal \(s_{\text{Q}}(t)=Q_{m}\sin(2\pi f_{c}t+\theta_{c})\) was the quadrature component of a single-carrier signal; \(Q_{m}\) was the imaginary part of the complex value mapped by the binary data stream after 16 QAM modulation; carrier frequency \(f_{c}=10\)Hz; carrier phase \(\theta_{c}=\pi/4\); noise intensity \(D=1\); and quantum particle swarm optimization was used to optimize the parameters of the FUBSR system and the SUUBSR system to obtain the optimal parameter combination of \(a=0.7793\), \(v=4.2755\), and \(r=3.4298\); \(a=0.0973\), \(v=0.6391\), \(r=4.8007\), and \(\gamma=0.9030\); sampling frequency \(f_{s}=4.55\)Hz; and sampling step size \(h=1/f_{\text{s}}\). Figure 6 presents the detection results of the FUBSR and SUUBSR systems for the waveform of a faint single-carrier signal, respectively. It can be observed from the figure that both systems can enhance the faint single-carrier signal. The output signal of the SUUBSR system has a higher amplitude value and fewer spikes caused by noise interference, indicating that the SUUBSR system has better noise resistance. From the perspective of the upper envelope curves of the output signals of the two systems, the FUBSR system enters a steady state at 3.38% of the symbol period, while the SUUBSR system enters a steady state within 1.93% of the symbol period, demonstrating that the SUUBSR system has a faster response speed. Figure 5: The relationship graph between the damping coefficient and the steady-state output SNR. Figure 6: Detection of single-carrier waveform by FUBSR and SUUBSR systems. **(a)** Detection of single-carrier waveform by FUBSR. **(b)** Detection of single-carrier waveform by SUUBSR. 1.2 Simulation of Detection of OFDM Signal Waveforms by FUBSR Stochastic Resonance and SUUBSR Systems  
The following is an experimental simulation of the detection effect of FUUBSR and UBSR systems on weak OFDM signals under high background noise. Take the signal \(s_{\text{Q}}(t)=\sum_{k=0}^{K-1}\theta_{k}\sin(2\pi f_{k}t+\theta_{k})\), the number of subcarriers \(K=2\), the carrier spacing \(\Delta f=10\)Hz, individual carrier frequencies \(f_{1,2}=[10,20]\) Hz, individual carrier phases \(\theta_{1,2}=[0,\pi/2]\), and noise intensity \(D=1\). Let the sampling frequency \(f_{s}=4000\)Hz, and the sampling step size \(h=1/f_{s}\), through the use of a quantum particle swarm optimization algorithm to optimize the parameters of the FUBSR system and SUUBSR system, the optimal parameter combination is obtained as \(a=3.51,v=2.8493,r=1.835;a=1.2306,v=0.778,r=1.389,\) and \(\gamma=0.63\). As can be seen from Figure 7,b, the upper envelope line of the FUBSR system output signal reaches the system steady-state value point at 3.516% of the symbol period. The amplitude in the time-frequency domain is significantly improved compared to the original noisy signal, and the output SNR is \(-1.6753\) dB. The irregularity of the upper envelope waveform indicates that the time-domain waveform is still greatly affected by the background noise, and the burrs on the waveform have not been weakened. This shows that the nonsaturation model can effectively enhance the amplitude of weak signals, but it cannot solve the poor anti-noise performance of the first-order system. From Figure 7,b, it can be seen that the SUUBSR system output signal reaches the system steady-state value point at 1.538% of the symbol period with an output SNR of \(-0.0256\) dB. The amplitude in the output time-frequency domain has been significantly enhanced, far higher than the enhancement effect of the FUBSR system on weak OFDM signals.