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In cognitive radio (CR) networks, multi-CR cooperation is required during spectrum sensing in order to cope with wireless fading effects and the hidden terminal problem. User cooperation offers not only channel diversity gain against fading, but also complexity gain in terms of reduced sampling costs per CR. The latter is particularly useful when the monitored spectrum has very wide bandwidth and yet individual CRs only have limited hardware capability. To jointly collect both diversity gain and complexity gain, this paper develops a novel cooperative spectrum sensing technique based on matrix rank minimization. Subject to sampling-rate limitations, CRs individually collect digital measurements from a segment of the wide spectrum via coordinated selective filtering, with optional compressive sampling to further reduce the sampling rates. The solutions representing the measurements of all users are modeled to possess a low-rank property, and the rank order is the same as the size of the nonzero support of the monitored wide spectrum. Accordingly, a nuclear norm minimization problem is formulated to jointly identify the nonzero support and hence the overall wideband spectrum occupancy. Both tradeoff evaluation and simulation results corroborate that the proposed cooperative sensing technique outperforms traditional averaging-based cooperative schemes given the same sampling costs, because the low-rank property enables efficient utilization and tradeoff of the user diversity in the absence of any channel knowledge.