## 2 A CBS System Model with an EPC  
The most commonly used array configurations for mobile CBS antennas are linear arrays and 2-Dimensional (2D) planar arrays [44]. In the subsequent work, the antenna array utilized for the CBS is a 2D planar array. However, due to the differing polarization modes of each linear array, only one linear array was employed in the experiments. Consequently, the discussion will focus solely on the linear array. A linear array refers to the arrangement where the antenna elements are uniformly distributed along a straight line, known as a Uniform Linear Array (ULA). By controlling the timing of signal transmission and reception, the operation mode of SAR can be simulated, enabling the observation of targets and the acquisition of echoes. Specifically, during the detection process, a signal is emitted by a designated source, and a single element on one side of the ULA is controlled to receive the echo signal, completing one azimuth sample. At the next moment, the signal emitted by the source is received by the subsequent element on the ULA. This process continues, with the timing of signal transmission and reception being manipulated to alter the position of the antenna phase center, simulating the movement of elements and thereby enabling SAR functionality. In the work presented herein, two CBSs are utilized as transmitting and receiving antennas, respectively. In this configuration, one element of the transmitting CBS emits a signal, which is then reflected by the target and received by a ULA at the receiving CBS. This operational mode is equivalent to that of bistatic SAR. To simplify data processing, the Equivalent Phase Center (EPC) principle is employed to represent this configuration as a self-transmitting and self-receiving ULA. The EPC principle refers to the conceptualization of the separated transmitting and receiving elements as a single element shared for both functions, positioned at the central location of the transmitting and receiving elements (further details and limitations regarding the EPC principle can be found in [45]), as shown in Figure 1. T, R, C, and X respectively represent the positions of the transmitter, receiver, EPC, and target, \(R_{TX}\), \(R_{RX}\), and \(R_{CX}\) represent the corresponding slant ranges. During the observation process, the actual echo history can be expressed as follows:  
\[R_{real}=R_{TX}+R_{RX} \tag{1}\]  
The two-way slant range between the EPC and the target is as follows:  
\[R_{EPC}=2R_{CX} \tag{2}\]  
Therefore, the EPC error introduced due to the use of the EPC principle is as follows:  
\[q_{error}=-\frac{2\pi}{\lambda}(R_{TX}+R_{RX}-2R_{CX}) \tag{3}\]  
where \(\lambda\) is the wavelength. The EPC error will cause the phenomenon of \"spurious peaks\" in the azimuth imaging result of the target, resulting in the decrease of SAR image quality [46]. Consequently, during the imaging process, it is crucial to apply phase compensation to the target based on Equation (3) to guarantee the precision of the resulting image. Following the aforementioned equivalence, data processing can be conducted according to the signal model of a ULA positioned at the EPC. Let us assume that the number of elements in the ULA is \(N\) and that the spacing between the elements is \(d\), as illustrated in Figure 2. Thus, the signal model for the ULA can be expressed as follows:  
\[x_{n}(t)=a_{n}(\theta)s(t)+n_{n}(t) \tag{4}\]  
Figure 1: Geometry of the Equivalent Phase Center. where \(s(t)\) is the transmitted signal, \(f\) is the carrier frequency, and \(\theta\) is the incidence angle [47]. Here, \(a_{n}(\theta)\) represents the direction vector of the signal propagation to the \(n\)th element, and can be denoted as follows:  
\[a_{n}(\theta)=e^{-j\omega\tau_{n}}=e^{-j2\pi/\tau_{n}} \tag{5}\]  
where \(\tau_{n}\) is the time delay of the signal propagating to the \(n\)th element, and is denoted as follows:  
\[\tau_{n}=\frac{(n-1)d\sin\theta}{c} \tag{6}\]  
where \(c\) is the light speed and \(n_{n}(t)\) is noise.