Compressive and Noncompressive Power Spectral Density Estimation from Periodic Nonuniform Samples

This paper presents a novel power spectral density estimation technique for bandlimited, wide-sense stationary signals from sub-Nyquist sampled data. The technique employs multi-coset sampling and applies to spectrally sparse and nonsparse power spectra alike. For sparse density functions, we apply compressed sensing theory and the resulting compressive estimates exhibit better tradeoffs among the estimator’s resolution, system complexity, and average sampling rate compared to their noncompressive counterparts. Both compressive and noncompressive estimates, however, can be computed at arbitrarily low sampling rates. The estimator does not require signal reconstruction and can be directly obtained from solving either a least squares or a nonnegative least squares problem. The estimates are piecewise constant approximations whose resolutions (width of the piecewise constant segments) are controlled by the periodicity of the multi-coset sampling. The estimates are also statistically consistent. This method is widely applicable, but it is targeted to situations where one wants to sense a wideband spectrum at low sampling rates.