# Feasibility Study of Passive Bistatic Radar Based on Phased Array Radar Signals
## 3 Direct Wave Signal Parameter Estimation Method Based on Template Matching
### Proposed Method  
Figure 6 shows the flow chart of the direct wave parameter estimation method. Firstly, the double threshold detection method is used to detect the LFM signal and to roughly estimate the PW and TOA; then, by matching with the PW template, the precise estimation of the PW can be obtained. Secondly, the BW is accurately estimated by the dechirp method, and the CF is roughly estimated, then the precise estimation of CF is obtained by matching with the CF template. Finally, the accurate PW, BW, and CF are used to reconstruct a reference signal so as to accurately estimate the TOA by means of matched filtering. Next, we will introduce the process of direct wave parameter estimation step by step. **Step 1**. In order to detect the LFM signal, it is necessary to determine the detection threshold. Since the signal-to-noise ratio (SNR) of a direct wave signal is generally high, after calculating the noise energy \(\sigma^{2}\), set a threshold \(V_{T}\) that is slightly larger than \(\sigma^{2}\). Using the double threshold detection method, it is considered that the pulse has arrived only when the signal amplitude continuously exceeds the threshold for \(p\) times. Similarly, the pulse is considered to be ended only when the amplitude is continuously below the threshold for \(q\) times, wherein the values of \(p\) and \(q\) are determined by the SNR of the direct wave signal. After that, the preliminary estimated arrival time \(\widehat{T}_{s}\), end time \(\widehat{T}_{e}\), and preliminary estimated PW \(\widehat{\tau}\) are obtained. **Step 2**. Comparing \(\widehat{\tau}\) with the PW template library \(\left\{\tau^{(k)}|\mathbf{k}=1,2,\ldots,N_{\tau}\right\}\), choose \(\tau_{0}\) which is closest to \(\widehat{\tau}\) in the PW template library; then, \(\tau_{0}\) is the precise estimation of PW. Thus, the PW estimation error is \(\varepsilon=\widehat{\tau}-\tau_{0}\), and the arrival time and end time are compensated, which can be expressed as  
\[\widehat{T}_{start}=\widehat{T}_{s}+\varepsilon/2\,\ \widehat{T}_{end}= \widehat{T}_{e}+\varepsilon/2 \tag{5}\]  
**Step 3**. Combined with the BW template library, the dechirp method is used to accurately estimate the BW and to preliminarily estimate the CF of the direct wave signal. Firstly, intercept the signal \(s_{p}\) of interval \(\left[\widehat{T}_{start},\widehat{T}_{end}\right]\); \(s_{p}\) contains a total of \(M=\tau_{0}\cdot F_{s}\) points, where \(F_{s}\) is the sampling rate of the signal. As the BW template library is \(\left\{B^{(k)}|\mathbf{k}=1,2,\ldots,N_{B}\right\}\), the possible chirp rate of the signal can be  
\[k_{1}=\frac{B^{(1)}}{\tau_{0}},k_{2}=\frac{B^{(2)}}{\tau_{0}},\cdots,k_{N_{B} }=\frac{B^{(N_{B})}}{\tau_{0}} \tag{6}\]  
Then, construct reference signals with different chirp rates, which can be expressed as  
Figure 6: Flow chart of direct wave parameter estimation method. \[ \begin{split}& s_{ref1}=e^{-j\pi k_{1}\left(i/F_{s}\right)^{2}},i=1,2,...,M\\ & s_{ref2}=e^{-j\pi k_{2}\left(i/F_{s}\right)^{2}},i=1,2,...,M\\ &\cdots\\ & s_{refN_{B}}=e^{-j\pi k_{N_{B}}\left(i/F_{s}\right)^{2}},i=1,2,...,M\\ \end{split}  \tag{7}\]  
Multiply \(s_{p}\) with different reference signals \(s_{ref1},s_{ref2},\cdots,s_{refN_{B}}\) to obtain the dechirped signal \(s_{dcl},s_{dcl2},...,s_{dclN_{B}}\), and then, perform a fixed-point FFT on the signal to obtain the spectrum \(S_{dcl1},S_{dcl2},...,S_{dclN_{B}}\). Measuring and comparing the peak value of \(S_{dcl1},S_{dcl2},...,S_{dclN_{B}}\), the chirp rate \(k_{\max}\) corresponding to the spectrum with the largest peak value is the chirp rate of the signal, and then, the accurate BW can be calculated as \(B_{0}=k_{max}\cdot\tau_{0}\). At the same time, the frequency position corresponding to the peak value in the spectrum is the preliminary estimation of CF of the signal, noted as \(\hat{f}_{c}\).