| Cognitive radio is considered as an efficient technology to alleviate the scarcity of spectrum resources. Developed from Cognitive radio, Cognitive Network is a new kind of wireless network, which is a new focus of study in recent years.In this thesis, the joint relay selection and channel allocation problem in cognitive networks was studied. Firstly, the problem was modeled as a three-dimensional assignment problem. We solved this problem by Lagrangian relaxation in conjunction with the sub-gradient method. By jointly considered the Qos requirement of each cognitive node, we adjusted the solution and got an algorithm for the joint relay selection and channel allocation problem, i.e., the JRSCA(Joint Relay Selection and Channel Allocation, JRSCA) algorithm. Secondly, we considered the joint relay selection and channel allocation problem in a cognitive network whose number of channels is less than that of the sources. In order to take the fairness of the network into account, we developed an algorithm to solve a class of two-dimensional assignment problem whose weights is a function of its assignment. By replacing the Kuhn-Munkres algorithms used in the JRSCA algorithm by this algorithm, we got the FJRSCA(Fair Joint Relay Selection and Channel Allocation, FJRSCA) algorithm, which can efficiently improve the fairness of the network. Thirdly, we considered the power allocation along with relay selection and channel allocation in the cognitive network with single source-destination node and got the SJRCP(Single source Joint Relay, Channel and Power allocation, SJRCP) algorithm. Besides, to simplify the power allocation, an algorithm for a class of convex optimization problem was introduced. This algorithm is very useful for the power allocation and other allocation problems in multi-carrier systems. Simulation results shows that this algorithm is more efficient than the interior point algorithm for this kind of problems because the scale of the problem does not affect both the running time and the number of iterations of the algorithm.Simulation results show that all of the three algorithms have very good performance. In multi-source node cognitive radio networks, JRSCA algorithm can increase the throughput about 10% than GRC algorithm does. When the number of channels in the cognitive networks is less than that of source nodes, FJRSCA algorithm can not only bring about 5% more throughput, but also can be fairer than GRC algorithm. What’s more, in a cognitive radio network which has only one source nodes, our proposed algorithm SJRCP can bring about 10% throughput than similar algorithms. |