A resource allocation framework is presented for spectrum underlay in cognitive radio networks. Novel scheduling schemes aiming at reuse of radio resources by secondary users while considering interference limitations to primary users are proposed. The focus of this work is on investigating how cognitive radio networks can benefit from spectrum sharing while maximizing the multi-user and frequency selective diversity gains, assuming single information stream in both primary and secondary links. Opportunistic interference management is used in conjunction with utility-based scheduling for the radio resource assignment in the downlink channel. Furthermore in one of the proposed schemes, network cooperation between the primary and the secondary network is considered as a means to maximize spectral efficiency.