单边相关格拉姆矩阵逆矩的解析推导及应用
Analytical Derivation of the Inverse Moments of One-sided Correlated Gram Matrices with Applications
摘要：
本文讨论了发展的分析工具，用于计算随机格拉姆矩阵的矩与一侧相关。这样的问题主要是由信号处理和无线通信中的应用驱动的，其中这样的矩阵自然出现。特别是，我们推导出封闭形式的表达式的逆矩，并表明所获得的结果可以帮助近似几个性能指标，如平均估计误差对应的最佳线性无偏估计（BLUE）和线性最小均方误差LMMSE或其他损失函数用于衡量协方差矩阵估计的准确性。
英文摘要：
This paper addresses the development of analytical tools for the computation of the moments of random Gram matrices with one side correlation. Such a question is mainly driven by applications in signal processing and wireless communications wherein such matrices naturally arise. In particular, we derive closed-form expressions for the inverse moments and show that the obtained results can help approximate several performance metrics such as the average estimation error corresponding to the Best Linear Unbiased Estimator (BLUE) and the Linear Minimum Mean Square Error LMMSE or also other loss functions used to measure the accuracy of covariance matrix estimates.
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