Compressive power spectral density estimation

In this paper, we consider power spectral density estimation of bandlimited, wide-sense stationary signals from sub-Nyquist sampled data. This problem has recently received attention from within the emerging field of cognitive radio for example, and solutions have been proposed that use ideas from compressed sensing and the theory of digital alias-free signal processing. Here we develop a compressed sensing based technique that employs multi-coset sampling and produces multi-resolution power spectral estimates at arbitrarily low average sampling rates. The technique applies to spectrally sparse and nonsparse signals alike, but we show that when the wide-sense stationary signal is spectrally sparse, compressed sensing is able to enhance the estimator. The estimator does not require signal reconstruction and can be directly obtained from a straightforward application of nonnegative least squares.