# Analysis on Target Detection and Classification in LTE Based Passive Forward Scattering Radar
## 2 Target Detection in Passive Forward Scattering Radar
### Target Doppler Signature in Passive FSR  
To analyze the feasibility of using LTE signal for passive FSR, an outdoor test with actual LTE signal transmission has been carried out. The aim of the experiment is to capture signal scattered from a moving vehicle crossing the transmitter and receiver baseline in forward scatter mode prior to the classification system. Figure 6 illustrates the outdoor testing scenario and block diagram of the hardware used for the system. Unlike conventional passive radar systems, only one channel is required facing the LTE base station in the proposed passive FSR. This is due to the receiver applies a self-mixing technique by the non-linear element, thus it does not require any synchronization channel. Overall, the receiver system was made of low noise amplifier (LNA), a diode (a non-linear element as amplitude detector), a low pass filter (LPF), a low frequency amplifier and an ADC. When a moving target entering the FS mode, two signals were scattered to the FS receiving antenna; a direct signal from the LTE base station transmission, \(S_{dr}\), (assume phase noise free) and a scattered signal from a moving target, \(S_{sc}\) carrying a Doppler shift, \(\omega_{sc}\)[2,13] as depicted in Equations (1) and (2) respectively. In a simplified manner, the received signal at the input of the passive FSR system \(S_{rx}\) can be expressed as Equation (3):  
\[S_{dr}\left(t\right)=A_{dr}\text{cos}\left(\left(\omega_{o}\right)t\right) \tag{1}\]  
\[S_{sc}\left(t\right)=A_{sc}\text{sin}\left(\left(\omega_{o}+\omega_{sc}\right)t\right) \tag{2}\]  
\[S_{rx}\left(t\right)=S_{dr}\left(t\right)+S_{sc}\left(t\right)\]  
\[S_{rx}\left(t\right)=A_{dr}\text{cos}\left(\left(\omega_{o}\right)t\right)+A_{ sc}\text{sin}\left(\left(\omega_{o}+\omega_{sc}\right)t\right) \tag{3}\]  
where \(A_{dr}\) represents the amplitudes of the direct transmission signal (leakage) and \(A_{sc}\) is the amplitude of the signal scattered from the moving target. As stated earlier, the system uses a non-linear element as its detection mechanism with the transfer characteristics of \(Y_{out}=\left(Y_{in}\right)^{2}\), hence at the output of the non-linear element and in this case the self-mixing between \(S_{dr}\) and \(S_{sc}\), the signal could be represented by:  
\[Y_{out}\left(t\right)=\left(A_{dr}\text{cos}\left(\omega_{o}t\right)+A_{sc} \text{sin}\left(\left(\omega_{o}+\omega_{sc}\right)t\right)\right)^{2} \tag{4}\]  
The LPF is then filtered out the high frequency part at the output signal from the non-linear element, so only two spectral components that contained in \(Y_{out}\); the direct path signal (leakage signal) and the signal with Doppler frequency scattered from the target. The filtered signal is denoted as \(Y_{out\_f}\) and shown in Equation (5):  
\[Y_{out\_f}\left(t\right)=\text{K}\left(\left(\left(A_{dr}\right)^{2}+\left(A_ {sc}\right)^{2}\right)+\left(A_{dr}A_{sc}\text{sin}\left(\omega_{sc}t\right) \right)\right) \tag{5}\]  
Figure 5: Vehicles’ RCS at two different incident angles: (**a**) Cartesian Plot and (**b**) Polar Plot. whereby, K is the conversion coefficient that depends on the type of non-linear device used. The direct signal in Equation (5) can be filtered out by using HPF (the system can use either hardware or software filter), it will then retain only the Doppler component as \(Y_{out\_f}=A_{dr}A_{sc}sin(\omega_{sc}t)\). The total Doppler frequency can be extracted by deriving the phase component of Equation (5): and is given by:  
\[f_{d}=\frac{2v}{\lambda}\text{sin}\alpha \tag{6}\]  
Equation (6) indicates the Doppler shift depends on the target's velocity vector components (in the direction to the receiver) and the carrier frequency, \(\lambda\). The resulted Doppler shift can be used for moving target detection, speed determination and trajectory reconstruction [2]. The Doppler component of the received waveform also contains information about the target silhouette. In this paper, this information was used for vehicle classification and recognition.