## 1 Introduction
### Potential Function Model
\begin{array}{l}\frac{{\rm d}^{2}\eta_{\rm I}(t)}{{\rm d}t^{2}}=-\frac {{\rm d}U(\imath_{\rm I}(t))}{{\rm d}\alpha_{\rm I}(t)}-\gamma\frac{d\alpha_{ \rm I}(t)}{dt}+s_{\rm I}(t)+n_{\rm I}(t)\\ \frac{{\rm d}^{2}\chi_{\rm Q}(t)}{{\rm d}t^{2}}=-\frac{{\rm d}U(\imath_{\rm Q}(t ))}{{\rm d}\alpha_{\rm Q}(t)}-\gamma\frac{d\chi_{\rm Q}(t)}{dt}+s_{\rm Q}(t)+n_ {\rm Q}(t)\\ \end{array} \right. \tag{7}\]  
\(U(x)\) is the unsaturated potential function; \(\gamma\) is the damping coefficient; the in-phase component of the OFDM baseband complex signal is the input signal for channel I of the system, \(s_{\rm I}(t)\); the quadrature component of the OFDM baseband complex signal is the input signal for channel Q of the system, \(s_{\rm Q}(t)\); the number of subcarriers is \(N\); \(\imath_{k}\) and \(\beta_{k}\) represent the real and imaginary parts of the complex value for OFDM symbol mapping, respectively; and \(f_{k}\) and \(\theta_{k}\) are, respectively, the frequency and phase of the kth subcarrier. \(n_{\rm I}(t)\) and \(n_{\rm Q}(t)\) represent Gaussian white noise with a mean of 0 and a variance of \(\sigma^{2}=2D\), where \(D\) denotes the magnitude of the noise intensity. By substituting Equation (3) into Equation (7), the following equation for the SUUBSR is obtained:  
\[\left\{ \begin{array}{l}\frac{{\rm d}^{2}\imath_{\rm I}(t)}{{\rm d}t^{2}}= \frac{2\imath_{\rm P}}{r^{2}}x_{\rm I}(t)\exp(-\frac{x_{\rm Q}^{2}(t)}{r^{2}} )-ax_{\rm I}(t)-\gamma\frac{dx_{\rm I}(t)}{dt}+s_{\rm I}(t)+n_{\rm I}(t)\\ \frac{{\rm d}^{2}\chi_{\rm Q}(t)}{{\rm d}t^{2}}=\frac{2\imath_{\rm P}}{r^{2}}x_ {\rm Q}(t)\exp(-\frac{x_{\rm Q}^{2}(t)}{r^{2}})-ax_{\rm Q}(t)-\gamma\frac{dx_{ \rm Q}(t)}{dt}+s_{\rm Q}(t)+n_{\rm Q}(t)\\ \end{array} \right. \tag{8}\]  
OFDM Signal Enhancement and Demodulation Model Based on Second-Order Underdamped Unsaturated Stochastic Resonance System  
The OFDM signal detection system model based on the SUUBSR system proposed in this paper is shown in Figure 1. In Figure 1, firstly, the received OFDM signal is segmented according to the symbol period, and the orthogonal transform is performed on the OFDM signal waveform within one symbol period to obtain the I-path signal \(s_{\rm I}(m,n)\) and the Q-path signal \(s_{\rm Q}(m,n)\); secondly, the two signals are input into the PSO algorithm parameter optimization system to obtain the optimal parameter sets for the I- and Q-paths of the SUUBSR system, respectively; then, the signals are input into the optimized SUUBSR system, and the transient influence is removed from the two resonance output signals; finally, the signals, after removing the transient response, are demodulated through serial-to-parallel conversion, FFT, parallel-to-serial conversion, constellation inverse mapping, and other steps. Transient Response Analysis of Second-Order Underdamped Stochastic Resonance System Excited by OFDM Signals  
Based on the mathematical model of the system proposed in the previous section, in order to theoretically demonstrate the feasibility of the system presented in this paper, this section analyzes the performance of the proposed system from three aspects: first passage time of system response, transient response, and steady-state response. Furthermore, a theoretical comparative analysis is conducted on the response of the SUUBSR system and the FUBSR system.