# The Design of a Long-Distance Signal Transmission System in a Bistatic RCS Testing System
## 4 System Application  
The actual structure of the bistatic testing system after integrating the signal transmission system into the entire testing setup is shown in Figure 18. Except for the transmitting antenna and the photodetector in the signal transmission system located at the Transmitting Base, all the other components of the testing system are situated at the Receiving Base. The Core contains the local oscillator clock source and the two agile frequency signal sources. It also performs mixing to obtain the intermediate frequency reference signal, as well as the final sampling, quadrature demodulation, and other processing tasks. Via analysis in conjunction with Figure 2, it can be gleaned that for a series of n frequency incrementation pulses with a carrier frequency of \(f_{i}=f_{0}+k\cdot\Delta f,k=0,1\ldots,\)\(n-1\), the transmission of a specific pulse can be represented as follows:  
\[x(t)=\cos(2\pi f_{i}t+\theta_{1})\quad kT_{2}\leq t\leq kT_{2}+T_{1}, \tag{15}\]  
where \(f_{0}\) is the base frequency, which can be set according to the testing requirements, with the test system covering a frequency range of 1-40 GHz; \(\Delta f\) is the inter-pulse frequency increment, set to 1 MHz; \(T_{1}\) is the pulse width, determined by the maximum size of the target; and \(T_{2}\) is the pulse repetition period, determined by the distance to the target. The target echo signal can be represented as follows:  
\[y(t)=\cos[2\pi f_{i}(t-\tau)+\theta_{1}], \tag{16}\]  
where \(\tau=2R/c\), \(R\) is the target distance, and \(c\) is the speed of light. The signal generated by agile frequency signal source 2 is as follows:  
\[z(t)=[2\pi(f_{i}+f_{1})t+\theta_{2}], \tag{17}\]  
where one path, after mixing with signal \(x(t)\), yields the reference intermediate frequency (IF) signal \(x_{ref}(t)\), while the other path, after mixing with the echo signal \(y(t)\), produces signal \(y^{\prime}(t)\):  
\[\left\{ \begin{array}{l}x_{ref}(t)=\cos(2\pi f_{i}t+\theta_{3})\\ y^{\prime}(t)=\cos(2\pi f_{i}t+2\pi f_{i}\tau+\theta_{2}-\theta_{1})\end{array} \right. \tag{18}\]  
Figure 18: The principle diagram of the dual-station RCS testing system. After undergoing a series of processes including sampling, digital phase locking, quadrature digital down-conversion, and baseband signal post-processing, signals \(y^{\prime}(t)\) and \(x_{ref}(t)\) yield the processed result \(G_{k}\):  
\[\left\{ \begin{array}{l}G_{k}=\cos\psi_{k}+j\sin\psi_{k}\\ \psi_{k}=-2\pi f_{i}\frac{2R}{c}+\beta,\quad\beta=\theta_{3}-\theta_{2}+\theta _{1}\end{array} \right. \tag{19}\]  
Each pulse corresponds to a result, \(G_{k}\), and the system emits 30 pulses per measurement. As a result, a series of 30 echo information samples was obtained. Performing an IDFT on the echo data yielded the target's distance and position information, i.e., the one-dimensional image. Next, the region of interest was centered around the target position, with zero-padding applied before performing a DFT. The frequency domain data were then used to compute the power spectrum of the echo, which allowed for the calculation of the target's RCS value. According to the system specifications, the transmission power of the system needs to reach at least \(P_{0}=21.63\) dBm to meet the testing requirements. Before introducing the long-distance signal transmission system, the system's achieved transmission power was \(P_{t}=27\) dBm. Therefore, as long as the loss introduced by the signal transmission system is within 6.37 dBm, the requirements will be met. As indicated by the previous test results, the system not only did not undergo attenuation but also provided a gain of at least 15 dBm. Thus, its integration would not affect the overall transmission power of the system. Moreover, the results shown in Figure 19 indicate that the positional information in the one-dimensional image is only obscured when the introduced random phase error reaches around 1.6\(\pi\).