In Cognitive Radio Networks (CRNs), unlicensed users are allowed to access the licensed spectrum when it is not currently being used by primary users (PUs). {To guarantee a high system throughput in CRNs, the channel state of PUs needs to be accurately detected to reduce conflict. To this end, cooperative spectrum sensing has been proposed to improve sensing accuracy by exploiting the spatial diversity of secondary users (SUs). However, existing works either focus on a single-channel setting, or make certain restrictive assumptions for multi-channel scenarios. In particular, most works on multi-channel CRNs place no limit on the number of channels that an SU can sense, which is impractical due to hardware and sensing duration constraints. In this paper, we study the throughput maximization problem for a multi-channel CRN where each SU can only sense a limited number of channels}. We show that this problem is strongly NP-hard, and propose an approximation algorithm with a factor of frac{1}{2}(1+frac{1}{2sqrt{sum_{i=1}^N l_i}}), where l_i is the number of channels that SU i can sense and N is the total number of SUs. This performance guarantee is achieved by exploiting a nice structural property, the subadditivity, of the objective function. We further observe that the throughput function is approximately submodular, and propose a greedy heuristic, which has superior performance for large l_{max}. Our numerical results demonstrate the advantage of our algorithm compared with both a random and a greedy sensing assignment algorithms.
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