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In this paper is proposed a novel cooperative Primary User (PU) detection algorithm in multiband environments (Wideband Spectrum Sensing -WBSS) based on Sub-Nyquist Sampling and Matrix Completion. In this way, addressing the problem of large number of samples to be processed when multiband signals are sampled at Nyquist rate or higher rates, seeking to improve the performance of wideband spectrum sensing in terms of detection probability. The simulation results show that the presented algorithm allows the improvement of the WBSS performance in terms of detection probability and the receiver’s operational characteristics compared to other cooperative WBSS algorithms based on Sub-Nyquist sampling.