# X-Band Photonic-Based Pulsed Radar Architecture with a High Range Resolution
## 2 Principle of the Proposed Architecture
\begin{split} E_{\text{DOBPF}}(t)=E_{\text{c}}J_{2}(m)& [\overbrace{J_{0}(m^{\prime})\cos(\omega_{\text{c}}t+2\omega_{\text{IF}}t)+ jI_{1}(m^{\prime})\cos(\omega_{\text{c}}t+2\omega_{\text{IF}}t+8\pi k \Delta\tau t)}^{\text{Output channel 2 of DOBPF}}\\ &+\overbrace{J_{0}(m^{\prime})\cos(\omega_{\text{c}}t-2\omega_{ \text{IF}}t)+jI_{1}(m^{\prime})\cos(\omega_{\text{c}}t-2\omega_{\text{IF}}t-8 \pi k\Delta\tau t)}^{\text{Output channel 1 of DOBPF}}.\end{split}  \tag{10}\]  
Each of the DOBPF output signals is injected into a BPD, which converts the signals from the optical domain to the electrical domain with suppression of the common-mode noise and reinforcement of the amplitude of signals, to extract the beat frequency, respectively [28]. As shown in (ii) and (iv) of Figure 2, the pulse signal by the MZM is transmitted to detect the target; however, the continuous LFM signal from the DPMZM output is applied to the receiver as the base signal for the de-chirping processing. Therefore, the beat frequency has three frequency components, namely, low-frequency, high-frequency, and time-varying-frequency components due to the frequency differences between the continuous LFM signal and the reflected echo signal. The low- and high-frequency components occur when the received pulse signal exists, however, the time-varying-frequency component is generated when there exists only the base signal. Because only the low-frequency component is valid, in order to eliminate the time-varying frequency component, the beat frequency is extracted with synchronous at the same period as the MZM control signal of the GSG. Furthermore, since the amplitude of the high-frequency component is small enough to negligible, it can be filtered by the ADC without the electrical low-pass filter in contrast to the conventional structure. Therefore, the beat frequency \(\Delta f=4k\Delta\tau\) can be obtained. To evaluate the fundamental performance of the proposed pulsed radar system, it is necessary to measure the range resolution and the cross-range resolution. According to the beat frequency representation in Reference [1], the range resolution, \(R_{\text{rr}}\) is represented as  
\[R_{\text{rr}}=\frac{cT\Delta f_{\text{min}}}{2B}=\frac{c}{2B}, \tag{11}\]  
because the minimum identifiable spectral interval, \(\Delta f_{\text{min}}\), is \(\Delta f_{\text{min}}=1/T\), where \(c\) is the velocity of light, \(T\) and \(B\) are the time period and the bandwidth of the pulse signal, respectively. According to Equation (11), it is clear that a broadband signal is required for obtaining a high range resolution of the target. However, as distinct from the range resolution, the cross-range resolution is determined by the specification of the antenna and the distance to the target. As for considering Fraunhofer distance [29], if the target is in the far-field, the cross-range resolution can be expressed as  
\[R_{\text{cr}}=2R\tan\left(\frac{\theta_{\text{3 dB}}}{2}\right), \tag{12}\]where \(R_{\text{cr}}\) is the cross-range resolution, \(R\) is the distance from the receiving antenna to the target, and \(\theta_{\text{3 dB}}\) is the 3-dB beamwidth of the antenna. If \(\theta_{\text{3 dB}}\) is small enough, the cross range resolution will be simplified as \(R_{\text{cr}}\approx R\theta_{\text{3 dB}}\).