# Design of Wideband FMCW Radar Transceiver System Using Photonic Elements
## 2 Proposed Radar System Design
As can be expected from Equation (2), the distance between the two second-order sidebands is 0.08 nm, which allows the proposed system to generate a 10 GHz signal [9]. The signal generation simulation has been also conducted for the LFM signal which will be applied in the proposed system. Figure 1(d),\(e\) present the simulation results from the OSA and the ESA, respectively, when the input IF LFM signal has 500 MHz bandwidth at 2.5 GHz center frequency. The results demonstrate that the proposed transceiver can generate a quadrupled signal while the fundamental optical carrier and two first-order sidebands are suppressed. Figure 2: _Cont._  
To detect low-RCS targets and obtain high-resolution images when RCS is below 1 m\({}^{2}\), the link budget of the proposed transceiver was calculated when considering the characteristics of the RF electronics and the photonic elements. The parameters and their values are specified in Table 1.  
The maximum detection range of a target depends on the RCS of the target and the peak power of the radar. The maximum detection range can be arranged as  
\[R_{max}=\left(\frac{P_{t}G_{t}G_{r}G_{p}\lambda^{2}\sigma}{\left(4\pi\right)^{ 3}\!\!\!\!\!KTBFL_{T}(\min(S/R))}\right)^{\frac{1}{4}} \tag{3}\]  
where \(\sigma\) and \(B\) refer to the RCS of the target and the instantaneous receiver bandwidth, respectively. The other variables are as described in Table 1. Figure 3a presents maximum \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Quantity** & **Values** \\ \hline \(P_{t}\) & Transmit power & 20 W \\ \(G_{t}\) & Transmit antenna gain & 37 dBi \\ \(G_{r}\) & Receive antenna gain & 37 dBi \\ \(G_{p}\) & Signal processing gain & 21 dB \\ \(F\) & Noise figure & 15.57 dB \\ \(L_{T}\) & Total loss & 13.58 dB \\ \(K\) & [PERSON]’s constant & \(1.38\times 10^{-23}\) J/K \\ \(T\) & Standard temperature & 290 K \\ \(\min(S/R)\) & Minimum SNR & 13 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the proposed radar transceiver. Figure 2: **(a)** Simulation circuit by Lumerical Interconnect. **(b)** Simulation output result from OSA with an input ISF CW signal of 2.5 GHz. **(c)** Simulation output result from ESA with an input IF CW signal of 2.5 GHz. **(d)** Simulation output result from OSA with an input IF LFM signal of 2.5 GHz. **(e)** Simulation output result from ESA with an input IF LFM signal of 2.5 GHz center frequency and 500 MHz bandwidth. detection ranges according to RCS, and the ranges are expected to be 3000 m and 1800 m when RCS is 1 m\({}^{2}\) and 0.1 m\({}^{2}\), respectively, with \(P_{t}\) of 20 W, as indicated by the circles ('o'). The RCS of a target changes every moment according to the movement of the target relative to the radar, resulting in the fluctuation loss. The Swerling model addresses this issue by describing the relationship of the target RCS and the probability density function (PDF) using the chi-square distribution. The Swerling I model was used in this study, and the PDF in this case can be expressed as  
\[P_{d}=\exp(-V_{T}/(1+S/R)) \tag{4}\]  
where \(P_{d}\), \(V_{T}\), and \(S/R\) refer to the probability of detection, detection threshold, and signal to noise ratio, respectively [16]. Here, we assumed the number of integrated pulses is 1. Figure 3: (**a**) Detection range versus RCS plot with changes in transmission power. (**b**) Detection probability versus range plot with changes in RCS. Figure 3b illustrates the detection probability for moving targets when \(P_{d}\) is 0.8 with RCS of 0.1 m\({}^{2}\) and 1 m\({}^{2}\)[17].