A compressive sampling based method for power measurement of band-pass signals

The paper deals with the problem of measuring the power of band-pass signals; to this aim, a new method, taking advantage of the interesting features of compressive sampling, is presented. The method proves to be particularly tailored for band-pass signals characterizing wireless communications system, whose parameters of interest are typically evaluated in frequency domain and require spectrum estimation with high frequency resolution. The use of compressive sampling, in fact, allows to preserve elevated sampling rate (needed to assure alias-free sampling of the signal of interest) and, simultaneously, avoid to acquire very long record (necessary to assure the desired frequency resolution). Moreover, the authors suggest a strategy for appropriately choosing the random sampling sequence of the input signal to overcome some known limitations of compressive sampling in terms of computational burden. Preliminary tests conducted by means of numerical simulations show promising results; differences, expressed in relative percentage terms, between estimated and nominal power never greater than 2% have been encountered, if the proper number of samples is chosen.