# 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
First, the ECA is used to suppress clutter in both cases, and the difference between them in clutter suppression is evaluated using the clutter suppression factor (CSF), which is defined as:

\[\gamma=10\log(\|\mathbf{S}_{\text{sur}}\|_{2}^{2}/\|\mathbf{S}_{\text{err}}\|_ {2}^{2})(\text{dB}) \tag{41}\]

where \(y\) stands for the CSF, and the bigger, the better. The values of the CSF for those two target methods are shown in Figure 3. From Figure 3, it can be observed that, regardless of whether the reference signal is pure or not, the values of the CSFs of the two methods are \begin{table}
\begin{tabular}{c c c} \hline \hline
**Description** & **Parameter** & **Value** \\ \hline Data length & \(L\) & 200,000 \\ Maximum range cell & \(R\) & 200 \\ Maximum Doppler cell & \(L\) & 2000 \\ Clutter suppression order & \(K\) & 100 \\ Pairwise matching gate & \(\Delta R\) & \(1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: System parameters of target detection. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Description** & **Range Cell** & **Doppler (Hz)** & **Pure Case** & **Impure Case** \\ \hline Clutter & 1 & 0 & \(\surd\) & \(\surd\) \\ Target 1 & 73 & 89 & \(\times\) & \(\surd\) \\ Target 2 & 38 & \(-\)70 & \(\times\) & \(\surd\) \\ Noise & Following a Gaussian distribution & \(\surd\) & \(\surd\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Reference signal parameters. Figure 2: Flowchart of the proposed target detection. almost equivalent, and the value of the proposed method is slightly higher. The main reason for this difference is the additional target term in (9). On the other hand, it is further shown that in the surveillance signal, the energy of the targets is almost negligible compared to that of the clutter. Then, the RDCC processing results of the traditional target detection method in the pure case and the impure case are given in Figure 4a,b, respectively. As is apparent, more suspected real targets can be observed clearly in Figure 4b and the energy of the real target, whose range cell is 73, is also weakened, thus verifying the negative benefit of the impure reference signals on target detection. Furthermore, the unit average detection method is applied to detect the targets, and the detection results are shown in Figure 5a,b. By comparison, it is not difficult to see that more false targets will be detected in the impure case, among which, in addition to real targets, some of them are random false targets, and the rest are false targets derived from the real target. There is no doubt that the existence of more false targets will bring more interference to the localization and tracking of real targets. Figure 3: Values of the CSF of traditional target detection in pure case and impure case. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Description** & **Range Cell** & **Doppler (Hz)** & **Pure Case** & **Impure Case** \\ \hline Clutter 1 & 1 & 0 & \(\surd\) & \(\surd\) \\ Clutter 2 & 10 & 0 & \(\surd\) & \(\surd\) \\ Clutter 3 & 25 & 0 & \(\surd\) & \(\surd\) \\ Clutter 4 & 40 & 0 & \(\surd\) & \(\surd\) \\ Clutter 5 & 56 & 0 & \(\surd\) & \(\surd\) \\ Clutter 6 & 78 & 0 & \(\surd\) & \(\surd\) \\ Target 1 & 73 & 89 & \(\surd\) & \(\surd\) \\ Target 2 & 38 & \(-\)70 & \(\surd\) & \(\surd\) \\ Target 3 & 102 & 33 & \(\surd\) & \(\surd\) \\ Noise & Following a Gaussian distribution & \(\surd\) & \(\surd\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Surveillance signal parameters. (2) Effectiveness of the proposed target detection method: In this subsection, based on the impure reference signal and the surveillance signal, the proposed method and the traditional method are utilized to detect the three targets in the surveillance signal, respectively.