Spectogram Reconstruction from Random Sampling: Application to the GSM Band Sensing

In the context of cognitive radios, we present a method to sense wideband radio spectra from randomly distributed samples with an average sampling rate smaller than the Nyquist sampling rate. The method finds its roots in the compressed sensing paradigm. The Gabor time-frequency is employed as a sparsifying transform to represent the radio signals generated in the framework of TDMA/FDMA based radio access technologies. Indeed, many white spaces are observable in these wideband spectrograms. In addition, noisy measurements are modeled through the Basis Pursuit DeNoise formulation, which enables to reconstruct the time-frequency representation with some errors or information losses. The method is experimented on measured baseband radio signals sampled at 51.2 MHZ and acquired in the GSM 900 downlink band. Finally, results about the effects of the algorithm parameters and about the algorithm complexity are provided and discussed.