  In this paper, we study the prediction of a circularly symmetric zero-mean
stationary Gaussian process from a window of observations consisting of
finitely many samples. This is a prevalent problem in a wide range of
applications in communication theory and signal processing. Due to
stationarity, when the autocorrelation function or equivalently the power
spectral density (PSD) of the process is available, the Minimum Mean Squared
Error (MMSE) predictor is readily obtained. In particular, it is given by a
linear operator that depends on autocorrelation of the process as well as the
noise power in the observed samples. The prediction becomes, however, quite
challenging when the PSD of the process is unknown. In this paper, we propose a
blind predictor that does not require the a priori knowledge of the PSD of the
process and compare its performance with that of an MMSE predictor that has a
full knowledge of the PSD. To design such a blind predictor, we use the random
spectral representation of a stationary Gaussian process. We apply the
well-known atomic-norm minimization technique to the observed samples to obtain
a discrete quantization of the underlying random spectrum, which we use to
predict the process. Our simulation results show that this estimator has a good
performance comparable with that of the MMSE estimator.
