Due to the conceptual simplicity, the linear filtering framework, notably the autoregressive (AR) process, has a long history in simulating clutter sequences with specified probability density functions (PDFs) and autocorrelation functions (ACFs). However, linear filtering inevitably distorts the input distribution, which may lead to inaccurate PDF reproduction or restrict applicability to very simple ACFs. To address these challenges, this study proposes a series-based analytic continuation strategy that revitalizes AR process clutter simulation by accurately precomputing the input pre-distortion required to compensate for AR filtering. First, the moments and cumulants of the AR input are derived based on the input-output relationship of the AR process, facilitating the moment and cumulant expansions of the Laplace transform (LT) and the logarithmic LT around zero, respectively. Second, both series expansions are analytically continued via the Padé approximation (PA) to recover the LT over the full complex plane. Notably, the PA-based continuation of the moment expansion, a conventional choice, can be highly inaccurate when the LT exhibits strong oscillations. By contrast, given the logarithmic LT generally has a simpler structure, the continuation of the cumulant expansion provides a more stable and accurate alternative. Third, the LT recovered from the cumulant expansion facilitates fast simulation of the AR input non-Gaussian white sequence via a random variable transformation method, thereby enabling an efficient AR process. Finally, simulations demonstrate that the proposed strategy enables accurate and fast simulation of non-Gaussian correlated clutter sequences.

翻译：由于概念简洁性，线性滤波框架（特别是自回归过程）在模拟具有指定概率密度函数和自相关函数的杂波序列方面具有悠久历史。然而，线性滤波不可避免地会扭曲输入分布，可能导致概率密度函数重建不准确或限制其仅适用于非常简单的自相关函数。为应对这些挑战，本研究提出一种基于级数的解析延拓策略，通过精确预计算补偿自回归滤波所需的输入预畸变，从而革新自回归过程杂波模拟方法。首先，基于自回归过程的输入输出关系推导自回归输入量的矩和累积量，分别构建拉普拉斯变换及其对数变换在零点附近的矩展开式和累积量展开式。其次，通过帕德近似对两种级数展开进行解析延拓，以恢复整个复平面上的拉普拉斯变换。值得注意的是，基于帕德近似的矩展开延拓（传统选择方案）在拉普拉斯变换呈现强烈振荡时可能产生显著误差。相比之下，由于对数拉普拉斯变换通常具有更简洁的结构，累积量展开的延拓提供了更稳定、更精确的替代方案。第三，通过累积量展开恢复的拉普拉斯变换，借助随机变量变换方法可实现自回归输入非高斯白序列的快速模拟，从而构建高效的自回归过程。最终，仿真实验表明所提策略能够实现非高斯相关杂波序列的精确快速模拟。