In this two-part paper, we investigate synthetic aperture radar (SAR) moving target imaging using planar antenna arrays. For a target moving over a three-dimensional terrain, its accurate localization requires the joint estimation of the motion-induced cross-range shift and the target height. In Part I of this two-part paper, starting from the planar array imaging geometry and the corresponding signal model, we show that these two quantities can be unified into a two-dimensional parameter vector and represented, after two-dimensional discrete Fourier transform (2D-DFT) processing across the planar array, through a natural vector remainder formulation. We first develop a general 2D-DFT matrix modulus framework and show that, in the two-dimensional setting, the associated 2D-DFT matrix modulus affects the propagation of vector remainder errors. Under a fixed array geometry and antenna number constraint, we derive an optimal construction of this matrix modulus and adopt it in the subsequent analysis. Under this construction, a single planar array provides only a folded estimate when the true parameter vector lies outside its unambiguous range. To resolve this ambiguity, we develop a multi-subarray framework in which multiple planar subarrays generate multiple vector remainders with different matrix moduli, and the desired parameter vector is recovered through the multidimensional Chinese remainder theorem (MD-CRT). To account for practical errors introduced by 2D-DFT quantization and additive noise, we further introduce an approximate 2D-DFT peak model for non-integer frequency vectors, incorporate robust MD-CRT, and establish sufficient conditions together with explicit reconstruction error bounds for both noiseless and noisy settings. Numerical results verify that the proposed multi-subarray framework enlarges the unambiguous range compared with a single planar array.

翻译：本两部分论文中，我们研究利用平面天线阵列进行合成孔径雷达（SAR）动目标成像。对于在三维地形上运动的目标，其精确定位需要联合估计运动引起的跨航向偏移和目标高度。在本两部分的论文的第一部分中，从平面阵列成像几何及其对应信号模型出发，我们证明这两个量可以统一为一个二维参数向量，并在对平面阵列进行二维离散傅里叶变换处理后，通过自然向量余数公式表示。首先，我们发展了一个通用二维离散傅里叶变换矩阵模数框架，并论证在二维设定下，关联的二维离散傅里叶变换矩阵模数会影响向量余数误差的传播。在固定阵列几何与天线数量约束下，我们推导出该矩阵模数的最优构造，并将其用于后续分析。在此构造下，当真实参数向量位于单个平面阵列的无模糊范围之外时，仅能得到折叠估计。为解决此模糊性，我们发展了一个多子阵列框架，其中多个平面子阵列生成具有不同矩阵模数的多个向量余数，并通过多维中国剩余定理恢复目标参数向量。为考虑由二维离散傅里叶变换量化和加性噪声引入的实际误差，我们进一步引入针对非整数频率向量的近似二维离散傅里叶变换峰值模型，融入鲁棒多维中国剩余定理，并为无噪声和有噪声情形建立充分条件及显式重建误差界。数值结果验证所提出的多子阵列框架相比单个平面阵列能扩大无模糊范围。