## 3 The Signal Adaptive Iterative Optimization Resampling (SAIOR) Algorithm
### Constructing Anti-Jamming Weights  
After estimating the modulation period of the PFM signal in the previous step, the next goal is to identify the interference signal and remove it from the original input signal, completing the anti-jamming operation. Compared to the impact of the high received power of the LEO satellite signal on interference identification, interference spectral line judgment in the noise and PFM interference obtained after signal adaptive iterative elimination is clearly more accurate. Therefore, after autocorrelation, the further optimization sampling of the mixed signal of noise and interference with the removed LEO satellite signal, based on the acquired modulation period \(T_{m}\), can yield a set of resampled data of PFM interference and noise signals. The position of the interference spectral line in the power spectrum is determined by the interference judgment threshold, and the interference set \(I_{j}\) is constructed, along with the construction of anti-jamming weights:  
\[W_{f}=\left\{ \begin{aligned} &=0,k\in I_{j}\\ &=1,else\end{aligned} \right. \tag{17}\]Perform weighted processing on the resampled data obtained from the original input signal after optimization sampling with modulation period \(T_{m}\):  
\[Y(f)=W_{f}X(f) \tag{18}\]  
Apply Inverse Fast Fourier Transform (IFFT) to the weighted spectrum to obtain the time-domain signal after interference suppression. \[y(t)=F^{-1}\{Y(f)\} \tag{19}\]  
At this point, the SAIOR algorithm framework can be summarized as shown in Figure 1, where the changes in the signal power spectrum at key stages of the algorithm framework are illustrated in Figure 2.  
As shown in Figures 1 and 2, the SAIOR algorithm involves four key aspects: (1) From 1 to 2 in Figure 2: An adaptive signal-approximation model is iteratively constructed to estimate the power spectrum of the LEO satellite signal, thereby eliminating its high-power components from the input signal. This isolates the PFM interference, facilitating subsequent estimation of its carrier frequency, modulation period, and other parameters. (2) From 2 to 3 in Figure 2: Leveraging the periodicity of PFM interference, an optimized resampling process is performed to determine the modulation period \(T_{m}\). After removing the LEO satellite signal through adaptive iteration, the remaining mixture of interference and noise is subsampled, generating a resampled dataset where the PFM interference is converted into one or several single-frequency components. An interference detection threshold is then applied to locate the spectral lines of interference in the power spectrum, constructing the anti-jamming weighting coefficients. (3) 4 in Figure 2: The original input signal is similarly resampled at modulation period \(T_{m}\), producing a dataset containing the  
Figure 1: The SAIOR algorithm framework. Figure 2: Signal power spectrum variation in the algorithm. LEO satellite signal, PFM interference, and noise. In this case, the PFM interference is again transformed into single-frequency components, while the energy distribution of the LEO satellite signal and noise remains largely unaffected. (4) From 4 to 5 in Figure 2: The resampled data derived from the original input signal undergo anti-jamming weighting, completing the suppression process. Finally, an IFFT is applied to the weighted spectrum to recover the interference-mitigated time-domain signal. The specific steps of the algorithm are shown in Algorithm 1:  
```
Step 1: Perform FFT on the original received signal \(x(n)\) to obtain the signal power spectrum \(X(f)\); Step 2: Initiate signal adaptive iterative cancellation on the original received signal. Using the gradient descent method, obtain the estimates of parameters a and b by minimizing Equation (12) \(e(a,b)^{2}=\sum\limits_{f=1}^{N}\left(aGs(f)+b-X(f)\right)^{2}\), and substitute them into Equation (10) to obtain the estimated power spectrum \(Y_{e}(f)\) of the LEO satellite signal.