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Spectrum sensing is an essential functionality that enables cognitive radios to detect spectral holes and to opportunistically use under-utilized frequency bands without causing harmful interference to legacy (primary) networks. In this paper, a novel wideband spectrum sensing technique referred to as multiband joint detection is introduced, which jointly detects the primary signals over multiple frequency bands rather than over one band at a time. Specifically, the spectrum sensing problem is formulated as a class of optimization problems, which maximize the aggregated opportunistic throughput of a cognitive radio system under some constraints on the interference to the primary users. By exploiting the hidden convexity in the seemingly nonconvex problems, optimal solutions can be obtained for multiband joint detection under practical conditions. The situation in which individual cognitive radios might not be able …