Mathematical optimization techniques for resource allocation in cognitive radio networks RahulamathavanYogachandran 2011 Introduction of data intensive multimedia and interactive services together with exponential growth of wireless applications have created a spectrum crisis. Many spectrum occupancy measurements, however, have shown that most of the allocated spectrum are used inefficiently indicating that radically new approaches are required for better utilization of spectrum. This motivates the concept of opportunistic spectrum sharing or the so-called cognitive radio technology that has great potential to improve spectrum utilization. This technology allows the secondary users to access the spectrum which is allocated to the licensed users in order to transmit their own signal without harmfully affecting the licensed users' communications. In this thesis, an optimal radio resource allocation algorithm is proposed for an OFDM based underlay cognitive radio networks. The proposed algorithm optimally allocates transmission power and OFDM subchannels to the users at the basestation in order to satisfy the quality of services and interference leakage constraints based on integer linear programming. To reduce the computational complexity, a novel recursive suboptimal algorithm is proposed based on a linear optimization framework. To exploit the spatial diversity, the proposed algorithms are extended to a MIMO-OFDM based cognitive radio network. Finally, a novel spatial multiplexing technique is developed to allocate resources in a cognitive radio network which consists of both the real time and the non-real users. Conditions required for convergence of the proposed algorithm are analytically derived. The performance of all these new algorithms are verified using MATLAB simulation results.