# MUSIC Algorithm

1. Dec 1, 2011

### elibj123

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.

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:
$$S=APA*+\lambda S_{0}$$

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.

Last edited by a moderator: Dec 1, 2011
2. Dec 2, 2011

### MisterX

What's the name of the Schmidt paper?