# An Adjusted Frequency-Domain Algorithm for Arc Array Bistatic SAR Data with One-Moving Transmitter
## 1 Introduction  
As one of the most distinctive inventions in the 20 th century, the helicopter has greatly expanded the application range of aircraft, it can achieve vertical taking-off, landing and hovering at a low altitude. However, the low-altitude environment is complex and changeable, which will affect the ability of the helicopter to observe the surrounding environment directly [1]. In the low-altitude complex environment, whether the helicopter and other airborne craft can perceive the surrounding targets in real-time and detect threats accurately has become a prerequisite for safe flight. The perception equipment for the helicopter is very important for the safe flight, cruise, take-off and landing of the helicopter. Therefore, it is of great significance to study the sensing equipment with real-time sensing and accurate detection of threats. Arc array synthetic aperture radar (AA-SAR) [2; 3; 4] is a special imaging system proposed in recent years, which can achieve range high resolution by transmitting bandwidth signals, and realizes wide azimuth observation by arc array antenna. Compared with linear array SAR (LA-SAR) [6; 7], AA-SAR can quickly image and sense the scene with a wide view angle [4], and can realize the dynamic monitoring and rapid imaging of the surrounding environment. Therefore, AA-SAR imaging system can improve the safe flight of helicopters and has important development potential in military reconnaissance, disaster relief and other fields. Arc array bistatic SAR (AA-BiSAR) [8] is a new type of variant bistatic SAR system, with the transmitter and receiver deployed on different platforms. Compared with AA-SAR,AA-BiSAR can observe the target from different angles and can obtain front-view or back-view area imaging. Furthermore, the receiver can be designed as a passive system, which can reduce the costs and improve the concealment of the system at the same time. Different configurations of AA-BiSAR can be applied to further enhance the imaging abilities of the system, such as AA-BiSAR with one-moving transmitter. AA-BiSAR with one-moving transmitter can be applied to improve the ability of the helicopter to perceive and detect the surrounding targets, since the transmitter can move, multiple low-cost receivers can share the same transmitter to reduce the system cost. AA-BiSAR with one-moving transmitter has the characteristics of wide observation, good concealment, and especially when the transmitter is moving, it can be used as a mobile tower to assist helicopter flight at the designated point, which improves the flexibility of the system and expands the working area. According to the characteristics, AA-BiSAR with one-moving transmitter can be applied in the helicopter's auxiliary landing and emergency rescue. When the helicopter is flying, the AA-BiSAR system can ensure the safety of the helicopter with wide observation and high resolution. However, due to the special configuration of AA-BiSAR with one-moving transmitter, the raw signal is more challenging to process than the conventional bistatic SAR (BiSAR) [9; 10; 11] system. On the one hand, different from the traditional invariant BiSAR, the doppler frequency of AA-BiSAR with one-moving transmitter varies not only with the range of target, but also with its azimuth position, which makes the subsequent range cell migration correction (RCMC) [12] more complicated. On the other hand, since the AA-BiSAR system samples at equal angular intervals in the azimuth direction, there will be a trigonometric function under the double root of its slant range equation, so it is difficult to use the principle of stationary phase (POSP) to derive the two-dimensional frequency spectrum directly. In recent years, more and more interest has been devoted to the imaging algorithm of BiSAR with different configurations. For example, an improved nonlinear frequency modulation imaging algorithm is proposed focusing on one-stationary BiSAR, which is combined with motion error compensation to solve the spatial variability of the target point [13].