样本协方差矩阵的特征值的中偏差原理
Moderate Deviation Principle of the Eigenvalues of the Sample Covariance Matrix
DOI: 10.12677/AAM.2021.104145, PDF,    国家自然科学基金支持
作者: 金 鑫, 解永晓*：山东师范大学数学与统计学院，山东 济南
关键词: 样本协方差矩阵；中偏差原理；特征值；码分多址；Sample Covariance Matrix； Moderate Deviation Principle； Eigenvalues； Code Division Multiple Access
摘要: 样本协方差矩阵特征值的大偏差对移动通信领域中比特错误问题的近似计算有非常重要的应用。设矩阵Ckxn的元素Cij独立且满足E[Cij]=0，Var(Cij)=1，则样本协方差矩阵的特征值为，其中x=(x1,x2,...xk)，满足。本文首先给出样本协方差矩阵特征值的中偏差原理，即满足速度为速率函数为的中偏差原理，其中。其次使用数值模拟的方法利用python验证了该定理的准确性，最后利用该中偏差原理来对比CDMA系统中不同解码方案的优劣。
Abstract: The large deviation of eigenvalues of sample covariance matrix has great significance in calculating the bit error probability of Code Division Multiple Access. Throughout the paper, we assume that the i.i.d. real matrix elements of Ckxn satisfy E[Cij]=0, Var(Cij)=1, then the eigenvalue of the sample covariance matrix is , where x is with k coordinates and norm . First of all, we prove that satisfies moderate deviations where speed is and the rate function is , where . Then we use the numerical simulation method to model the theoretical function by python, to verify its reliability. Finally, we use the moderate deviation of sample covariance matrix in the CDMA to compare the advantages and disadvantages of different decoding techniques.
文章引用：金鑫, 解永晓. 样本协方差矩阵的特征值的中偏差原理[J]. 应用数学进展, 2021, 10(4): 1350-1358. https://doi.org/10.12677/AAM.2021.104145

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