Power Spectrum Blind Sampling

Power spectrum blind sampling (PSBS) consists of a sampling procedure and a reconstruction method that is capable of perfectly reconstructing the unknown power spectrum of a signal from the obtained samples. In this letter, we propose a solution to the PSBS problem based on a periodic sampling procedure and a simple least squares (LS) reconstruction method. For this PSBS technique, we derive the lowest possible average sampling rate, which is much lower than the Nyquist rate of the signal. Note the difference with spectrum blind sampling (SBS) where the goal is to perfectly reconstruct the spectrum and not the power spectrum of the signal, in which case sub-Nyquist rate sampling is only possible if the spectrum is sparse. In the current work, we can perform sub-Nyquist rate sampling without making any constraints on the power spectrum, because we try to reconstruct the power spectrum and not the spectrum. In many applications, such as spectrum sensing for cognitive radio, the power spectrum is of interest and estimating the spectrum is basically overkill.