# Target Detection of Passive Bistatic Radar under the Condition of Impure Reference Signal
## 3 Proposed Target Detection Method under the Condition of Impure Reference Signal
### Target Detection Method Based on Impure Reference Signal  
Combined with the localization and reconstruction methods proposed above, the flowchart of the target detection method under the condition of an impure reference signal is shown in Figure 2, while the detailed steps of the proposed method are summarized in Algorithm 1. ```
1 Input: Original reference signal \(\mathbf{S}_{\text{ref}}\), surveillance signal \(\mathbf{S}_{\text{sur}}\). Initialization: Set the maximum range cell \(R\), the maximum Doppler cell \(F\), the pairwise matching gate \(\Delta R\) and other related parameters. 3 Clutter suppression: Apply ECA on \(\mathbf{S}_{\text{ref}}\) and \(\mathbf{S}_{\text{sur}}\) to obtain the residual signal \(\mathbf{S}_{\text{err}}\) and weight coefficients \(\mathbf{W}\). RDCC: Exploiting (10) to calculate the two \(-\) dimensional range \(-\) Doppler matrix to be detected \(\mathbf{\xi}[r,p]\). Points detection: Go through each \(p\) channel in \([1,F]\) with interval 1 to achieve all the points exceeding the detection threshold. For\(p=1,2,\,\ldots,F\)do
5 Each cell is detected in turn as follows: \(\mathbf{\xi}[r,p]= \begin{cases}1,&\mathbf{\xi}[r,p]\geq\tau_{p}\\ 0,&\text{other}\end{cases} \)
6 Weights analysis: Sort the weight coefficients of \(\mathbf{W}\), and save the corresponding range cells \(l_{1}\) and \(l_{2}\) of the two coefficients with the largest values. Points matching: Based on \(\overline{\mathbf{\xi}}[r,p]\), go through each \(p\) channel in \([1,F]\) with interval 1 to distinguish between real and false targets, while saving real targets information, which is performed as For\(p=1,2,\,\ldots,F\)do
7 Pairwise matching is conducted for range cells with a value of one within the channel as follows If \(\left||r_{i}-r_{j}\right|-\left|l_{2}-l_{1}\right|\right|\leq\Delta R\) (suppose \(r_{i}<r_{j}\) ), \(\overline{\mathbf{\xi}}[r,p]\)\(=1\), otherwise, \(\overline{\mathbf{\xi}}[r,p]\)\(=0\). end
8 Purify verification: Based on \(\overline{\mathbf{\xi}}[r,p]\), go through each \(p\) channel in \([1,F]\) with interval 1 to determine whether the reference signal is pure. 9 For\(p=1,2,\,\ldots,F\)do
10 If \(\overline{\mathbf{\xi}}[r,p]\)\(=1\), record the corresponding range cell \(r\) and Doppler cell \(p\), and pass them to next step; otherwise, enter the next loop. end
11 Reconstruction: Based on the saved \(r\) and \(p\), the target signal in the reference signal is reconstructed via (20). 12 Purification: The reference signal is purified via (21). Target detection: Based on the purified reference signal and surveillance signal, go back to step 3, 4, and 5 to obtain the updated \(\overline{\mathbf{\xi}}\) Output: Save the detection result matrix \(\overline{\mathbf{\xi}}\) and then output it for subsequent signal processing. ## 4 Simulations and Analysis

In this section, the effectiveness of the proposed method is validated and analyzed by using both it and a traditional method to process the simulated data. In the experiments, the FM signal is utilized as the transmitting signal of the PBR. The key system parameters used for simulated data are listed in Table 1 and the detailed parameters of the reference signal and surveillance signal are described in Tables 2 and 3, respectively. From Tables 2 and 3, it can be seen that the only difference between the pure case and the impure case is whether the surveillance signal is included in the reference signal. Next, the proposed target detection method and conclusions of the theoretical analysis are verified from two aspects. (1) Validation of the impact of impure reference signals on target detection performance: In this subsection, the traditional target detection method is employed for target detection in the pure case and the impure case.