基于高斯化的Gamma-Gamma与Lognormal-Rician湍流信道参数估计
Gaussianization-Based Parameter Estimation for Gamma-Gamma and Lognormal-Rician Turbulence Channels
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中文总结 AI 辅助
针对Gamma-Gamma与Lognormal-Rician湍流信道的参数估计难题，提出分位数变换与Box-Cox两种高斯化估计器，结合物理感知正则化项，可大幅提升参数估计性能。
中文摘要 AI 辅助
大气湍流信道的精确参数估计颇具挑战，因为Gamma-Gamma（GG）与Lognormal-Rician（LR）模型的概率密度函数涉及特殊函数与数值积分。本文针对GG和LR湍流信道提出两种高斯化参数估计器，即分位数变换（QT）估计器与Box-Cox估计器。QT估计器采用双向交叉变换结合高阶统计匹配；Box-Cox估计器通过纳入变换雅可比行列式构建近似似然函数。渐近分析表明，在弱至中等湍流条件下，偏度是偏离高斯性的主导阶偏差，并给出Box-Cox幂参数的渐近表达式。此外，引入基于扩展Rytov理论的正则化项，该正则化项将Rytov方差映射至GG形状参数，以提升参数可识别性。仿真结果显示，两种估计器在无噪与有噪条件下均表现稳健，且在特定湍流场景中，该物理感知正则化项相比迭代矩估计器、矩方法/凸优化估计器，可将参数估计性能提升至少三个数量级。
英文摘要
Accurate parameter estimation for atmospheric turbulence channels is challenging because the probability density functions of the Gamma-Gamma (GG) and Lognormal-Rician (LR) models involve special functions and numerical integrations. This paper proposes two Gaussianization parameter estimators for GG and LR turbulence channels, i.e., the quantile-transformation (QT) estimator and the Box-Cox estimator. The QT estimator employs bidirectional cross-transformation together with higher-order statistical matching, whereas the Box-Cox estimator constructs an approximate likelihood by incorporating the transformation Jacobian. Asymptotic analysis identifies skewness as the leading-order deviation from Gaussianity under weak-to-moderate turbulence and yields asymptotic expressions for the Box-Cox power parameters. In addition, a physics-informed regularizer based on the extended Rytov-theory mapping from the Rytov variance to the GG shape parameters is introduced to improve parameter identifiability. Simulation results demonstrate that both estimators provide robust performance under noiseless and noisy conditions, while the physics-informed regularization term can improve the parameter estimation performance by at least three orders of magnitude compared with the iterative moment-based estimator and the method-of-moments/convex-optimization estimator in specific turbulence scenarios.
