ii ACKNOWLEDGMENTS I would like to thank my Ph.D. advisor Dr. Hongxiang Li for his constant guidance, understanding and encouragement in both work and life. Dr. Li supported me in all ways an advisor can do for a student: he provided me insightful comments and guidance on topic selection; he gave me sufficient freedom to work on the problems that are interesting to me; he provided me great chances to collaborate with many people in both academia and industry; he demonstrated how to write papers and grant proposals, as well as how to give nice presentations; he also provided me generous support in choosing a career path, and etc. I cherish our student-teacher relationship developed during these years. For coexisting networks operating in interweave cognitive radio mode, most existing works focus on the secondary network's spectrum sensing and accessing schemes.However, the primary network can be selfish and tends to use up all the frequency resource. In this dissertation, a novel optimization scheme is proposed to let primary network maximally release unnecessary frequency resource for secondary networks.The optimization problems are formulated for both uplink and downlink orthogonal frequency-division multiple access (OFDMA)-based primary networks, and near optimal algorithms are proposed as well.For coexisting networks in the underlay cognitive radio mode, this work focuses on the resource allocation in distributed secondary networks as long as the primary network's rate constraint can be met. Global optimal multicarrier discrete distritbuted v (MCDD) algorithm and suboptimal Gibbs sampler based Lagrangian algorithm (GSLA) are proposed to solve the problem distributively.Regarding to the dirty paper coding (DPC)-based system where multiple networks share the common transmitter, this dissertation focuses on its fundamental performance analysis from information theoretic point of view. Time division multiple access (TDMA) as an orthogonal frequency sharing scheme is also investigated for comparison purpose. Specifically, the delay sensitive quality of service (QoS) requirements are incorporated by considering effective capacity in fast fading and outage capacity in slow fading. The performance metrics in low signal to noise ratio (SNR) regime and high SNR regime are obtained in closed forms followed by the detailed performance analysis.