In this letter, we proved a matrix identity of Hankel matrices that seems unrevealed before, generated from the moments of Gaussian distributions. In particular, we derived the Cholesky decompositions of the Hankel matrices in closed-forms, and showed some interesting connections between them. The results have potential applications in such as optimizing a nonlinear (NL) distortion function that maximizes the receiving gain in wireless communication systems.

翻译：本文证明了一个由高斯分布矩生成的、此前似乎未曾揭示的Hankel矩阵恒等式。特别地，我们推导了该Hankel矩阵的闭式Cholesky分解，并展示了它们之间一些有趣的联系。该结果在无线通信系统中优化非线性失真函数以最大化接收增益等领域具有潜在应用前景。