# X-Band Photonic-Based Pulsed Radar Architecture with a High Range Resolution
## 2 Principle of the Proposed Architecture
Therefore, only if the applied voltage of the MZM is zero, the output signal of the MZM can be represented as  
\[E_{\text{MZM}}(t)=\alpha E_{\text{c}}J_{2}(m)\left[\cos\left\{2\pi(f_{c}+2f_{ \text{IF}})t\right\}+\cos\left\{2\pi(f_{c}-2f_{\text{IF}})t\right\}\right]. \tag{6}\]  
As can be seen from Equations (3) and (6), if the pulse generating voltage is zero, the output signal of the MZM has two frequency spectrum of \(f_{c}-2f_{\text{IF}}\) and \(f_{c}+2f_{\text{IF}}\), which is the same characteristics of the output signal of the DPMZM. In addition, it is noted that the PRF of the pulsed radar is determined by the applied voltage signal; therefore, by controlling the GSG, the pulse waveform with a various PRF can be generated according to changes in the operating environment as shown in Figure 2. In the extreme case, if the GSG generates only zero voltage for whole operating time, the proposed architecture can operate the same as the conventional photonic-based FMCW radar. The output signal of the MZM is sent to a PD, which converts signals from the optical domain to the electrical domain. The signal converted into the electric domain through the PD has an instantaneous frequency of \(f_{\text{gLFM}}(t)=4f_{\text{IF}}=4(f_{0}+kt)\) and it is confirmed that the center frequency and the bandwidth of the domain-converted signal are quadrupled compared with the center frequency and the bandwidth of the applied IF signal. Finally, the domain-converted signal is transmitted through the antenna to space for detecting a target. If there exists a target, the echo signal reflected by a target is received through the antenna. The received signal enters an RF port of a PM, which modulates the optical signal from the DPMZM output as shown in Figure 1:0 As represented in Equation (3), the output of the DPMZM has two optical carriers at \(f_{\text{c}}-2f_{\text{IF}}\) and \(f_{\text{c}}+2f_{\text{IF}}\) and is modulated by the reflected echo signal, which has a frequency of \(f^{\prime}_{\text{gLFM}}=4\{f_{0}+k(t+\Delta\tau)\}\). Here, \(\Delta\tau\) is the time delay due to target reflection and the PM produces a serial of sidebands at both sides of the optical carrier separated by the amount of frequency of the received echo signal, \(f^{\prime}_{\text{gLFM}}\), and it shifted the phase by \(\pi/2\)[27]. Therefore, the output of the PM, \(E_{\text{PM}}(t)\), is expressed as  
Figure 1:1  
where \(m^{\prime}\) is the phase-modulation index and \(\omega^{\prime}_{\text{gLFM}}\) is angular frequency of the received signal. By applying the Jacobi-Anger expansion, Equation (7) can be rewritten as  
Figure 1:2Considering only the 1 st-order coefficient of the infinity coefficient of the power series, Equation (8) can be simplified as  
\[ \begin{split} E_{\text{PM}}(t)\approx E_{\text{c}}J_{2}(m)& [J_{0}(m^{\prime})\{\cos(\omega_{\text{c}}t-2\omega_{\text{IF}}t)+\cos(\omega_{ \text{c}}t+2\omega_{\text{IF}}t)\}\\ &+jI_{1}(m^{\prime})\{\cos(\omega_{\text{c}}t+6\omega_{\text{IF}}t +8\pi k\Delta\tau t)\\ &+\cos(\omega_{\text{c}}t-2\omega_{\text{IF}}t-8\pi k\Delta\tau t) +\cos(\omega_{\text{c}}t+2\omega_{\text{IF}}t+8\pi k\Delta\tau t)\\ &+\cos(\omega_{\text{c}}t-6\omega_{\text{IF}}t-8\pi k\Delta\tau t )\}].\end{split}  \tag{9}\]  
The output signal of PM is connected to the input of a DOBPF. The purpose of the DOBPF is to extract the frequency spectrum difference from the phase-modulated signal by the reflected echo signal. Therefore, by blocking the other harmonics except for the components with a beat frequency, the output signal of the DOBPF, \(E_{\text{DOBPF}}(t)\), is expressed as  
\[