Use the minimum-variance method to estimate the PSD of \(L=256\) samples of the following signal:

\[y(n)=\sin \frac{\pi}{2} n+x_{1}(n)\]

where

\[x_{1}(n)=-0.8 x_{1}(n-1)+x_{2}(n) \text {, }\]

with \(x_{2}(n)\) being a white Gaussian noise with variance \(\sigma_{X_{2}}^{2}=0.36\).