# Robust Anti-Jamming Algorithm Based on Transmit/Receive Time-Sharing Technology
## 3 Influence Analysis of Time-Domain Anti-Jamming on Burst Signal  
Convergence time and data loss are essential parameters for evaluating the influence of time-domain anti-jamming on burst signals in the satellite-ground link [20]. In the non-convergence interval, the carrier-to-noise ratio (CNR) cannot satisfy the receiver acquisition sensitivity, resulting in unavailable navigation data. Receiver convergence time and data loss depend on receiver sensitivity [38]. In traditional BeiDou navigation receivers, the time-domain anti-jamming filter presents the characteristics of repeated convergence. The navigation receiver stops working in the non-receiving time slot, and the anti-jamming filter stops iterating and transfers to the initial state. When the receiver enters the following T/R time-sharing period, the filter converges again from the initial weight vector. Figure 4 shows that the convergence time required for the filter weight vector to stabilize is about 5 ms. The time-domain filter order is set to 33, the original CNR is set to 50 dB\(\cdot\)Hz, the jamming-to-signal ratio (JSR) is set to 50 dB, and the interference bandwidth is 2 MHz. All subsequent description simulations are completed with the above conditions (Figures 4-6 are based on this). Figure 4: The convergence of the traditional algorithm. Figure 5: The estimated CNR of the traditional algorithm. The carrier-to-noise ratio is an important parameter to evaluate whether the navigation signal can be calculated. The CNR without interference is the ratio of the average power of the navigation signal to the noise signal [39]:  
\[\left[C/N\right]_{0}=\frac{C}{N}\cdot B_{N}=\frac{\int_{-\infty}^{\infty}S_{s}(f )df}{\int_{-\infty}^{\infty}S_{n}(f)df}\cdot B_{n} \tag{9}\]  
The estimated CNR after anti-jamming is a vital indicator for estimating the interference suppression performance, which can be expressed as:  
\[\left[C/N\right]_{\text{ajm}}=\frac{\int_{-\infty}^{\infty}\left|H(f)\right|^{ 2}S_{s}(f)df}{\int_{-\infty}^{\infty}S_{y}(f)df-\int_{-\infty}^{\infty}\left|H( f)\right|^{2}S_{s}(f)df} \tag{10}\]  
where \(S_{s}(f)\) and \(S_{n}(f)\) are the power spectral densities of the IF signal and noise, respectively. When the CNR loss of the output signal is less than the performance requirement, the actual convergence time of the navigation receiver can be calculated:  
\[T_{\text{conv}}=T\Big{|}\left[C/N\right]_{0}-\left[C/N\right]_{\text{ajm}}<\delta \tag{11}\]  
where \(\delta\) is the maximum CNR loss satisfying the acquisition sensitivity of the navigation receiver. Figure 5 illustrates the output CNR variation trend in the interference suppression process. When the CNR loss does not satisfy the receiver sensitivity, no navigation signal can be processed solved in the acquisition and tracking module, and the critical timing and positioning information cannot be calculated. As the filter converges, the data length of the output signal increases, and the estimated CNR gradually approaches the original CNR, unaffected by interference, and tends to be stable. When the receiver does not converge, the residual interference of the output signal exceeds the anti-interference margin of the receiver, so no data solution is valid in the acquisition and tracking module. Therefore, the repeated convergence of the receiver will cause information loss in each T/R time-sharing period, and the data loss can be expressed as the signal rate within the convergence time [40]:  
\[Q_{loss}=T_{\text{conv}}R_{\text{code}} \tag{12}\]  
where, \(R_{\text{code}}\) is the code rate, which is 50 bits per second (50 bps). Figure 6: The effect of CNR loss margin on convergence. The actual convergence performance of the anti-jamming filter under different interference suppression margin requirements is shown in Figure 6. When the CNR loss decreases to less than 1 dB\(\cdot\)Hz, the filter converges after approximately 10.31 ms. When the CNR loss margin is 4 dB\(\cdot\)Hz, only 2.66 ms is required.