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In a paper Multiple emitter location and signal parameter estimation, the well-known MUSIC algorithm starts by calculating covariance (autocorrelation, whatever) matrix with:

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where overlines stand for expectation operation, i.e., $\overline{XX^H}\triangleq E\left[XX^H\right]$. As I understand, the MUSIC algorithm needs to observe signals multiple times to get $S$, i.e., $S=\frac{1}{N}\sum_{i}^{N}{X_{i}X_{i}^{H}}$

On the other hand, when I googled implementations of the MUSIC algorithm, most of them does not perform expectation operation. I mean, they just observe signals only one time and perform the remaining process of the algorithm, i.e., $S=XX^H$

Is there a reasonable explanation that the MUSIC algorithm does not need to observe signals multiple times, but only need to observe signals only once?

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  • $\begingroup$ Self answer: diva-portal.org/smash/… claims that sample autocorrelation (what I've said in the original question) needs to be performed. $\endgroup$ – Jeon Oct 13 '16 at 13:36
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This question is very much related to this answer.

The issue is that the expectation operator to get the auto-correlation (auto-covariance) is generally replaced in signal processing with the sample auto-correlation.

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