# 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
### Localization of Impure Terms in the Reference Signal  
As discussed in the previous section, when the reference signal is perturbed by target echoes, resulting in signal impurity, the presence of false targets originating from real targets becomes apparent. These false targets share the same Doppler shifts as their corresponding real targets, while their range cells exhibit a pseudo-random distribution influenced by clutter suppression coefficients. That is to say, in this case, there will be several sparsely distributed points exceeding the detection threshold in a certain Doppler channel of the Range-Doppler detection plane. These points comprise a mixture of real and false targets, presenting challenges for direct identification. However, exploiting the relative positions of these points, which are associated with clutter suppression weights, enables the distinction and localization of real and false targets. To illustrate this concept, we consider a scenario where the direct path and multipath clutters in the surveillance signal occur on the 1 st, 8 th, and 19 th range cells. Consequently, during the projection process of clutter suppression, the projection coefficients will have peaks on the 1 st, 8 th, and 19 th cells, while the remaining range cells demonstrate negligible projection coefficients due to the absence of significant clutter. By building upon this quantitative analysis, (9) can be further expanded as:  
\[\begin{array}{l}\mathbf{S}_{\mathrm{err}}[l]=\Psi_{c}[l]+\Psi^{1}_{T_{s}}[l ]+\Psi^{1}_{T_{f}}[l]+\Psi^{2}_{T_{f}}[l]+\Psi^{2}_{T_{s}}[l]+\Psi_{z}[l]\\ =\sum\limits_{c=1}^{N_{s}}a_{c}\mathbf{d}[l-\tau_{c}f_{s}]-\mathbf{W}[1]a_{ \mathrm{ref}}\mathbf{d}[l]-\mathbf{W}[8]a_{\mathrm{ref}}\mathbf{d}[l-7]- \mathbf{W}[19]a_{\mathrm{ref}}\mathbf{d}[l-18]\\ +(\overline{b}_{1}-\mathbf{W}[1]b_{1})\mathbf{d}[l-\tau_{1}f_{s}]e^{j2\pi f_{ \mathrm{aff}}a^{1/f_{s}}t/f_{s}}\\ -\mathbf{W}[8]\Big{\{}b_{1}\mathbf{d}[l-(\tau_{1}f_{s}+7)]e^{j2\pi f_{\mathrm{ dif}}a^{1/f_{s}}t/f_{s}}-j14\pi f_{\mathrm{aff}}/f_{s}\Big{\}}\\ -\mathbf{W}[19]\Big{\{}b_{1}\mathbf{d}[l-(\tau_{1}f_{s}+18)]e^{j2\pi f_{ \mathrm{di}}1/f_{s}}e^{-j6\pi f_{\mathrm{di}}1/f_{s}}\Big{\}}\\ +\overline{b}_{2}\mathbf{d}[l-\tau_{2}f_{s}]e^{j2\pi f_{\mathrm{d}}2^{1/f_{s} }t/f_{s}}+\boldsymbol{\varphi}_{2}[l]\end{array} \tag{33}\]  
From (33), it is not difficult to deduce that four targets will be generated after the RDCC, among which \(\Psi^{1}_{T_{s}}\) and \(\Psi^{2}_{T_{s}}\) are real targets, while \(\Psi^{1}_{T_{f}}\) and \(\Psi^{2}_{T_{f}}\) are false. Moreover, the range cells of the two false targets are located at \(\tau_{1}f_{s}+7\) and \(\tau_{1}f_{s}+18\), respectively. That is, the relative distances between the real target \(\Psi^{1}_{T_{s}}\) and the two false targets are 7 and 18 range cells, respectively. Therefore, the positions where the false targets appear are related to the peak values of the projection weight coefficients of the clutter suppression. Employing the prior information, the impure terms in the reference signal introduced by the target echo can be located.