autocorrelation - Why use $chi^2$ test to determine the presence of white noise?

I want to test for the presence of broadband noise in a snapshot 1000 complex baseband samples recorded by a software defined radio.

As a follow-up to this post, why was the $\chi^2$ test used? How many degrees of freedom should be used?

Also, how would one extend this approach to complex baseband data? I would assume that I and Q are iid Gaussian random variables. The magnitude of the complex data would then be Rayleigh distributed not Gaussian. Is there a generalization of the $\chi^2$ test for Rayleigh random variables? Or, would I just pick I or Q to operate on?

Update: I was able to find a paper: A test for whiteness. The author outlines a similar process.