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Compressive sampling is a well-known approach to reconstruct sparse signals based on a limited number of measurements. In spectrum sensing applications for cognitive radio though, only reconstruction of the power spectrum of the signal is required, instead of the signal itself. In this paper, the authors present a new method for power spectrum reconstruction based on samples produced by a sub-Nyquist rate sampling device. The stationary assumption on the received analog signal causes the measurements at the output of the compressive sampling block to be cyclo-stationary, or the measurement vectors to be stationary. They investigate the relationship between the autocorrelation matrix of the measurement vectors and that of the received analog signal, which they represent by its Nyquist rate sampled version.
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