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Cramer Rao Bound for DOA Estimation

Hi, everyone!
I try to analytically estimate Cramer-Rao Bound for DOA estimation using the formula for stochastic sygnals and noise:
CRB_uncond = (nose_power/(2*L)) * inv(real( (D'*P_orth*D) .* (Sx*A'*R*A*Sx)' ))
P_orth = eye(N) - A*inv(A'*A)*A'
L - number of samples, R -  spatial correlation matrix estimation,  A - matrix of signals sterring vectors, D - matrix of steering derivatives, Sx - signal correlation matrix.

Then i test that formula in simulation. I estimate Direction-of-Arriva using MUSIC method at the same conditions as CRB. Ansvers i get are very confusing. 
In example, if i use linear antenna array, SNR=-5dB, two singnals with DOAs [-5 12], L = 200 samples. CRB -  

1.0e-05 *
    0.0981         0
         0    0.1017

but variances of MUSIC method are  
1.0e-03 *
    0.1807
    0.1330

The Difference is too big, i think. What do I do wrong.
1
Ilia
11/22/2014 8:29:05 AM
comp.soft-sys.matlab 211266 articles. 22 followers. lunamoonmoon (257) is leader. Post Follow

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