Fourier-Analysis of Stationary Random Signals
assuming ergodicity...

ACF:

$$\begin{align}
R_x[k] &amp;= \lim_{N \to \infty} \tfrac{1}{2N+1} \sum\limits_{n=-N}^{N} x[n] \, x[n+k] \\
  &amp;= \mathbb{E}\Big\{ x[n] \, x[n+k]  \Big\} \\
  &amp;= \sigma_x^2 \ \delta[k] \\
  &amp;= 1\  \delta[k] \\
\end{align}$$

PSD:

$$ S_x(e^{j\omega}) = \sum\limits_{n=-\infty}^{\infty} R_x[n] \, e^{-j \omega n} $$