Hi I am trying to derive the autocorrelation matrix and I am unsure about how exactly it works. I can see that the $4\times 1$ matrices result in the Hermitiain and Toeplitz matrix? Surely the only non-zero values in each of these is at $n = 0$ which is the variance?
Any help would be greatly appreciated!
You get a diagonal matrix because the values of $\eta(n)$ at different times (sample indices $n$) are uncorrelated, as shown in your first equation. This means that all off-diagonal elements of the auto-correlation matrix must be zero (they equal $E[\eta(n)\eta(n+m]$ for $m\neq 0$). Only the diagonal elements are non-zero, and they are equal to the variance.
