# An Adjusted Frequency-Domain Algorithm for Arc Array Bistatic SAR Data with One-Moving Transmitter
## 2 Arc Array Bistatic SAR System  
AA-SAR as a special form of SAR has the advantage of wide azimuth observation. However, since the transmitter and receiver are deployed on the same platform, the concealment of the system is poor. On the contrary, one-stationary bistatic SAR (OS-BiSAR) has the advantage of good concealment, and it does not have the ability of full azimuth observation. In order to obtain a wide azimuth observation, meanwhile, and improve the concealment of the system, AA-BiSAR with one-moving transmitter is proposed in this paper. AA-BiSAR with one-moving transmitter both has advantages of AA-SAR and OS-BiSAR, which can be applied to the field of helicopter assisted landing and emergency rescue.  
Shown in Figure 1, is the three-dimensional structure diagram of the arc array antenna. A series of antenna array elements are uniformly arranged along the arc direction. The antenna elements are staggered and distributed evenly at equal intervals, and the direction is always from the center of the circle toward the outside of the circle. It can be seen from the structure diagram, \(\Delta\theta_{\text{interval}}\) is the angular interval between adjacent equivalent sampling points, \(\theta_{0}\) denotes the synthetic aperture angle of the arc array antenna. Let \(R_{\text{arc}}\) denotes the radius of the arc array antenna, the synthetic aperture angle and the arc array radius will affect the resolution of the system.  
Figure 2 is the work mode of AA-BiSAR with one-moving transmitter. In a large-scale imaging scene, the helicopters are equipped with arc array antenna, and the transmitter platform moves like a mobile tower, waiting to help the helicopters. In order to obtain accurate ground information, the helicopter first sends a request signal to the transmitter, after receiving the request signal, the transmitter moves to the designated location and transmits a high-power chirp signal to the target area. Then, the arc array antennas are turned on in turn to receive the reflected signal of the target, and finally, the ground target information is obtained through imaging processing. In this process, high resolution in azimuth is achieved by synthetic arc aperture, and high resolution in range is achieved by using the transmitted chirp signal. After completing the mission of location A, the transmitter moves to another area to continue assisting other helicopters, which not only ensures the safety of helicopters but also reduces the cost of the system.  
Figure 1: The structure of arc array antenna.  
Figure 2: The work mode of AA-BiSAR with one-moving transmitter.  
The general imaging geometry of AA-BiSAR with one-moving transmitter is shown in Figure 3. The transmitter moves with a constant velocity \(v\) along the Y axis, and \(t_{a}\) denotes the azimuth time variable. When \(t_{a}=0\), the initial position of the transmitter is \(P_{t}(\theta_{t},R_{t},H_{t})\), where \(\theta_{t}\) is the azimuth angle of the transmitter, \(R_{t}\) stands for the ground distance from the transmitter to the center of the scene, and \(H_{t}\) is the height of the transmitter platform. The equivalent sampling point coordinates of the receiver arc array antenna is \(P_{r}(\theta_{r},R_{\mathrm{arc}},H_{r})\), where \(\theta_{r}\) is the azimuth angle of the equivalent sampling point, \(R_{\mathrm{arc}}\) is the antenna radius, and \(H_{\mathrm{r}}\) represents the height of the receiver platform. Let the coordinates of any point target in the scene be \(P_{n}(\theta_{n},R_{n},H_{n})\), where \(\theta_{n}\) stands for the azimuth angle of the point target, \(R_{n}\) denotes the distance from the point target to the center of the scene, and \(H_{n}\) is the height of the point target. Let \(\rho\) be the distance from the center of arc array antenna to the point target \(P_{n}\), \(\beta_{r}\) represents the angle between the ground and \(O^{{}^{\prime}}P_{n}\).