Nowadays, Cognitive Radio (CR) is projected as the technology that will maximize the utilization of the spectrum resources in next generation wireless systems. Therefore, the Spectrum Sensing (SS) is the key function, which allows CR to know the available spectrum resources of an interest band. Nevertheless, one of the major problems in the SS is the big amount of samples that are processed in the multiband signal sampling by Nyquist equal or higher rates, which generates big time detection, high energy consumption and the necessity of high processing capacity in Cognitive Radio Devices (CDR). Taking advantage of the spatial diversity provided by multi-antenna Cognitive Radio Devices (CRD), in order to improve the development of the WideBand Spectrum Sensing (WBSS), in this paper is proposed a compressive local wideband spectrum sensing algorithm for multiantenna cognitive radios. Likewise, it is proposed an uniform sampling matrix for the multiband signal in the sparse domain, and in this wideband cooperative scenario there are obtained close expressions for detection probability, miss detection probability and false alarm probability. Simulation results have shown that the proposed algorithm allows efficient spectrum sensing, it also improves performance of the spectrum sensing, according to the probability of detection and the operational characteristics of the receiver in regard (in comparison) to other narrow/wideband spectrum sensing algorithms Sub-Nyquist - Nyquist based.