Compressive sensing (CS) is a novel digital signal processing technique that has found great interest inudmany applications including communication theory and wireless communications. In wireless communications, CSudis particularly suitable for its application in the area of spectrum sensing for cognitive radios, where the completeudspectrum under observation, with many spectral holes, can be modeled as a sparse wide-band signal in the frequencyuddomain. Considering the initial works performed to exploit the benefits of Bayesian CS in spectrum sensing, the fadingudcharacteristic of wireless communications has not been considered yet to a great extent, although it is an inherent featureudfor all sorts of wireless communications and it must be considered for the design of any practically viable wireless system.udIn this paper, we extend the Bayesian CS framework for the recovery of a sparse signal, whose nonzero coefficients followuda Rayleigh distribution. It is then demonstrated via simulations that mean square error significantly improves whenudappropriate prior distribution is used for the faded signal coefficients and thus, in turns, the spectrum reconstructionudimproves. Different parameters of the system model, e.g., sparsity level and number of measurements, are then variedudto show the consistency of the results for different cases.
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