I found this problem in a book
Consider the series $$y[k] = x[k]+\varepsilon_1[k]$$ where $$x[k] = \phi_1 x[k-1]+\varepsilon_2[k]$$ and $\varepsilon_1[k]$ and $\varepsilon_2[k]$ are both white noise sequences with variances $\sigma^2_{{\varepsilon}_{1}} $, $\sigma^2_{{\varepsilon}_{2}} $. It is given that $|\phi_1|<1$ and $E(x[0]) =0$. Show that the power spectral density is of the form
$$\gamma_{yy}(f) = \frac{\sigma^2\left|1-\theta_1e^{-i2\pi f}\right|^2}{\left|1-\phi_1e^{-i2\pi f}\right|^2} $$
Power spectral density is given by calculating DTFT auto-covariance function of the series. I'm stuck at 'how to calculate auto-covariance function'. Please help.