A multi-user cognitive (secondary) radio system is considered, where thespatial multiplexing mode of operation is implemented amongst the nodes, underthe presence of multiple primary transmissions. The secondary receiver carriesout minimum mean-squared error (MMSE) detection to effectively decode thesecondary data streams, while it performs spectrum sensing at the remainingsignal to capture the presence of primary activity or not. New analyticalclosed-form expressions regarding some important system measures are obtained,namely, the outage and detection probabilities; the transmission power of thesecondary nodes; the probability of unexpected interference at the primarynodes; {\color{blue}and the detection efficiency with the aid of the area underthe receive operating characteristics curve}. The realistic scenarios ofchannel fading time variation and channel estimation errors are encountered forthe derived results. Finally, the enclosed numerical results verify theaccuracy of the proposed framework, while some useful engineering insights arealso revealed, such as the key role of the detection accuracy to the overallperformance and the impact of transmission power from the secondary nodes tothe primary system.
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