# X-Band Photonic-Based Pulsed Radar Architecture with a High Range Resolution
## 2 Principle of the Proposed Architecture
Therefore, the output signals of the \(90^{\circ}\) hybrid coupler are \(\cos\{2\pi(f_{0}+kt)t\}\) and \(\cos\{2\pi(f_{0}+kt)t+\pi/2\}\), respectively. In the expression of a \(90^{\circ}\) hybrid coupler outputs, \(k\) is the chirp rate of the LFM signal. The output signals of a \(90^{\circ}\) hybrid coupler are applied to a DPMZM and modulated by the optical signal. Figure 3 shows the principle of the quadrupled signal generation through a DPMZM using two signals which have a \(90^{\circ}\) phase difference. As shown in Figure 3, the DPMZM consists of three sub-MZMs, which are placed in two sub-MZMs (MZM-I and MZM-Q) on each arm of the main MZM (MZM-m). The output signals with a \(90^{\circ}\) phase difference are applied to MZM-I and MZM-Q, respectively. If the operation points of the two sub-MZMs (MZM-I and MZM-Q) are both at the full-bias point, the outputs of the sub-MZMs produce the optical carrier and even-order sidebands with a \(180^{\circ}\) phase difference ((2) and (3) of Figure 3). In contrast, MZM-m should be biased at the null-bias point to minimize the signal amplitude at the carrier frequency ((4) and (5) in Figure 3) [25]. Therefore, the optical signal of the DPMZM output can be expressed as  
\[E_{\text{DPMZM}}(t)=E_{c}\left[\sum_{n=1}^{\infty}J_{4n-2}(m)\left\{\cos(2\pi( f_{c}+(4n-2)f_{\text{IF}})t)+\cos(2\pi(f_{c}-(4n-2)f_{\text{IF}})t)\right\} \right], \tag{2}\]  
where \(m\) is the modulation index of the two sub-MZMs as \(m=\pi V_{\text{IF}}/V_{\pi}\), \(f_{\text{IF}}(t)\) is the instantaneous frequency as \(f_{\text{IF}}(t)=f_{0}+kt\), and \(J_{4n-2}\) means the \((4n-2)\)th-order Bessel function of the first kind. If the harmonics are higher than the 2 nd-order under the conditions of the appropriate modulation index for generating a quadrupled signal, it can be negligible due to the relatively low amplitudes and Equation (2) can be simplified as  
\[E_{\text{DPMZM}}(t)\approx E_{c}J_{2}(m)\left[\cos\left\{2\pi(f_{c}+2f_{\text{ IF}})t\right\}+\cos\left\{2\pi(f_{c}-2f_{\text{IF}})t\right\}\right]. \tag{3}\]  
The DPMZM output signal is branched through an OC for use in the transmitter and the receiver of the proposed architecture. One of the two-branched signals is used as a base signal for the de-chirping process in the receiver, and the other signal is transmitted to an MZM, which makes the conventional photonic-based FMCW radar as a pulsed radar. An MZM is an intensity modulator, which has a characteristic in which the intensity of the output optical signal varies depending on the applied voltage. Thus, by controlling the applied voltage of an MZM, the pulse-type output signal can be  
Figure 3: Principle of quadrupled signal generation through a DPMZM. BW: Bandwidth of IF signal. generated even though the applied optical signal is continuous. The output signal of an MZM, \(E_{\text{MZM}}(t)\), by a time-dependent applied voltage is  
\[E_{\text{MZM}}(t)=\frac{1}{2}\alpha E_{\text{in}}\left[\exp\left\{j\frac{\pi V_ {1}(t)}{V_{\pi}}\right\}+\exp\left\{j\frac{\pi V_{2}(t)}{V_{\pi}}\right\} \right], \tag{4}\]  
where \(\alpha\) is the insertion loss of the MZM, \(E_{\text{in}}\) is the applied optical signal, \(V_{\pi}\) is the half-wave voltage of the modulator, \(V_{1}(t)\), and \(V_{2}(t)\) are the applied voltage to each arms of the MZM, respectively [26]. The pulse generating voltage, \(V(t)\), to the MZM can be expressed as \(V(t)=V_{1}(t)-V_{2}(t)\), if \(V(t)=V_{1}(t)\) and \(V_{2}(t)=0\) is satisfied, Equation (4) can be denoted as  
\[E_{\text{MZM}}(t)=\frac{1}{2}\alpha E_{\text{in}}\left[\exp\left\{j\frac{\pi V (t)}{V_{\pi}}\right\}+1\right]. \tag{5}\]  
According to Equation (5), if the pulse generating voltage is set to zero, the output signal of an MZM becomes \(\alpha E_{\text{in}}\). However, if the pulse generating voltage is changed to \(V_{\pi}\), the MZM output signal is zero. Using this characteristic, a signal for a pulsed radar, which is known as the gated LFM signal, can be generated by the control of the applied voltage of an MZM, which produces by a GSG.