Abstract: The radio spectrum resource shortage has become the bottleneck of the sustainable development of wireless communications and has limited the application of wireless services. As a new technology, cognitive radio(CR) has changed the traditional paradigm of spectrum utilization by allowing the CR user to access the licensed spectrum authorized by the government, targeting the spectrum efficiency and energy efficiency. Hence, CR is a new method to alleviate the looming spectrum shortage crisis to some degree. Orthogonal frequency division multiplexing(OFDM) is widely accepted as the most popular air interface in cognitive radio systems owing to its inherent advantages, such as adaptive parameter adjustment and dynamic resource allocation. In this thesis, we mainly focus on the dynamic resource allocation in OFDM-based CR systems. We gave the basic optimization model in OFDM-based CR systems, based on which we introduced the spectrum efficient and energy efficient resource allocation problems. For the spectrum efficient resource allocation problem, we try to maximize the sum capacity of the non-real-time (NRT) users and maintain the minimal rate requirements of the real-time (RT) users simultaneously. Additionally, the interference introduced to primary users, which is generated by the access of the SUs, should be kept below a predefined threshold, which makes the optimization task more complex. We show that the formulated optimization problem has a special structure which can be exploited to implement a fast barrier method to obtain the optimal solution with a reasonable complexity. Besides, we propose an effective measurement criterion to normalize OFDM subchannels’ achievable rates, based on which we develop simple but efficient heuristic algorithm for subchannel assignment and power distribution. For the energy efficient resource allocation problem, we aim to maximize the energy efficiency of the considered CR system with practical constraints, such as the power budget of the CR system, the interference thresholds of the primary users, the minimal throughput requirements and the proportional fairness of the CR users. We relax the original mixed integer programming problem and convert it into a quasiconvex one. A bisection-based algorithm is employed to work out the optimal solution in an iterative manner. In each iteration, the convex optimization can also be solved by the fast barrier method. Simulation results show the effectiveness and efficiency of our proposed algorithms.