Should I observe a signal multiple times for MUSIC algorithm?

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

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?

• Self answer: diva-portal.org/smash/… claims that sample autocorrelation (what I've said in the original question) needs to be performed.
– Jeon
Oct 13, 2016 at 13:36