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I'm still confused on the N^2/N, because you're using the same data multiple times when you're overlapping. Like, you're using the same noise to smooth out.. noise. But I do understand that it's like a normalizer, but I swear you are absolutely correlating the noise by using it multiple times.
It's taking a sum of two RVs. One of is correlated across elements (the signal - because a signal hits every element) and the other is not correlated across elements (the noise) so when you sum up a large beam, the noise never increases, but the signal does. So that's the central limit theorem, the noise just goes into
I was asking my boss a question because I didn't understand how using overlapping virtual aperture arrays is of any use. He answered my question with "the central limit theorom, N^2/N is bigger" and I said I didn't understand and then told me, "It's okay. you don't need to understand this." Yeeeuupp thank you for recon