elibj123
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I'm studying the MUSIC algorithm in order to implement it in some project of mine, but I have some difficulties understanding the mathematical derivations done in the original Schmidt paper.
For those of you who have access to this paper, I'll appreciate your time and help.
The author begins with a vector x=Af+w, which's derivation is pretty clear to me. Then he proceeds to define the auto-correlation matrix S=xx*
The first result is understandable:
S=Aff*A*+ww*
But then he defines S as:
[tex]S=APA*+\lambda S_{0}[/tex]
Now, there are some points later that I don't understand, but this seems to be the core problem:
How does he arrive at the factorization of Lambda and S0?
In the summary of the algorithm, the second step is to calculate the eigenvalues (the Lambda's) of S in the metric of S0. So more specifically: how do I calculate S0 from my model of noise?
In other papers that summarize MUSIC the algorithm was to simply calculate eigenvalues of S (in the euclidean metric). I've ran some MATLAB simulations and it worked fine, but I guess that a Gaussian white noise model really coincides with S0=I.
For those of you who have access to this paper, I'll appreciate your time and help.
The author begins with a vector x=Af+w, which's derivation is pretty clear to me. Then he proceeds to define the auto-correlation matrix S=xx*
The first result is understandable:
S=Aff*A*+ww*
But then he defines S as:
[tex]S=APA*+\lambda S_{0}[/tex]
Now, there are some points later that I don't understand, but this seems to be the core problem:
How does he arrive at the factorization of Lambda and S0?
In the summary of the algorithm, the second step is to calculate the eigenvalues (the Lambda's) of S in the metric of S0. So more specifically: how do I calculate S0 from my model of noise?
In other papers that summarize MUSIC the algorithm was to simply calculate eigenvalues of S (in the euclidean metric). I've ran some MATLAB simulations and it worked fine, but I guess that a Gaussian white noise model really coincides with S0=I.
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