negative eigenvalues in sample covariance matrix

Question

yasser 2014-10-10

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/158144-negative-eigenvalues-in-sample-covariance-matrix

回答： Matt J 2014-10-10

clc; clear;

N=10; taps=2; snr=0; noise_var=0.05;

h1r=randn(1,taps)/sqrt(2); h1i=randn(1,taps)/sqrt(2); h1=complex(h1r,h1i); h1=h1/norm(h1);

h2r=randn(1,taps)/sqrt(2); h2i=randn(1,taps)/sqrt(2); h2=complex(h2r,h2i); h2=h2/norm(h2);

c1=[h1(1);zeros(1,N-1)']; r1=[h1 zeros(1,N-1)]; H1=toeplitz(c1,r1);

c2=[h2(1);zeros(1,N-1)']; r2=[h2 zeros(1,N-1)]; H2=toeplitz(c2,r2);

H=[H1;H2];

order=64; k=log2(order); n=(taps+N-1)*k; x = randi([0 1],n,1); hMod = comm.RectangularQAMModulator(order); hBitToInt = comm.BitToInteger(k);% Convert the bits in x into k-bit symbols. xsym = step(hBitToInt,x); D = modulate(modem.qammod(order),xsym);

X=awgn(H*D,snr,'measured');

% noise1=sqrt(noise_var/2)*(randn(1,size(H1*D,1))+i*randn(1,size(H1*D,2))); % noise2=sqrt(noise_var/2)*(randn(1,size(H2*D,1))+i*randn(1,size(H2*D,2))); % noise=[noise1.';noise2.']; % % X=H*D+noise;

R=X*X'/size(X,2);

[Q ,eig_val]=eig (R);

the problem is that matrix of eig_val has negative values and this can't happen for sample covariance matrix R any help please

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Answer 1

Matt J 2014-10-10

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/158144-negative-eigenvalues-in-sample-covariance-matrix#answer_154716

I can't run your code, because you haven't provided all variables needed to run it. However, you can expect small magnitude negative eigenvalues due to floating point errors, if your true covariance matrix ix close to singular.