Moderate Deviation Principle Of Eigenvalues Of The Sample Covariance Matrix And Application

This paper mainly studies the principle of modreate deviation and large deviation of eigenvalues of sample covariance matrix,then the relevant results are applied to the Code Division Multiple Access(CMDA)system to compare the advantages and disadvantages of different decoding schemes.The first two chapters mainly introduce the basic knowledge of the sample covariance matrix,large deviation principle and moderate deviation principle,and their corresponding research status.The third chapter focuses on the moderate deviation principle of eigenvalues of sample covariance matrix.First of all,the result of the moderate deviation principle of the eigenvalues of the sample covariance matrix is presented.Then we use the first result to obtain the moderate deviation principle of the maximum and minimum eigenvalues of the sample covariance matrix and the moderate deviation principle of the eigenvalues of Wishart matrix.Finally,the accuracy of the moderate deviation principle of the eigenvalues of the sample covariance matrix is verified by using the method of numerical simulation through python.The fourth chapter is the application of moderate deviation principle in CDMA system.Because the eigenvalues of sample covariance matrix can be used to describe the errors of different decoding schemes in CDMA system,and this model satisfies the requirements of the third chapter,so we can use the results of the third chapter to judge the advantages and disadvantages of different decoding schemes.The last chapter is the summary of this paper and the prospect of the future work.