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A cooperative hybrid cognitive radio (CR) network is proposed to simultaneously operate on a dedicated licensed band and a secondary band. The licensed band is used for communications between a base station (BS) and mobile CR users, whereas the secondary band is used to facilitate the licensed band communication by coordinating multiple CR users to form distributed virtual antenna arrays (VAAs). The capacity of the proposed CR network is studied at both the link and system levels. At the link level (single VAA case), we present an amplify-and-forward-based cooperative signaling scheme that employs power control to prevent harmful noise propagation. The resulting virtual multiple-input-multiple-output (MIMO) link capacity is derived and compared with the real MIMO system. At the system level (multiple VAAs case), the system capacity is derived as a function of multiple parameters, including the primary user density, CR user density, primary exclusion region radius, and VAA radius. Under an average interference power constraint, the maximum system capacity is further calculated by solving an optimization problem with adjustable system parameters. Numerical studies reveal that the proposed cooperative hybrid CR network has a fundamental advantage over a pure CR network by being insensitive to the characteristics of the coexisting primary network. This merit, however, relies on a high CR user density and a wide bandwidth of the secondary band.