This thesis examines the problem in initializing communications whereby cognitive radios need to find common spectrum with other cognitive radios, a process known as frequency rendezvous. It examines the rendezvous problem as it exists in a dynamic spectrum access cognitive network. Specifically, it addresses the problem of rendezvous in an infrastructureless environment. A new algorithm, the modular clock algorithm, is developed and analyzed as a solution for the simple rendezvous environment model, coupled with a modified version for environment models with less information. The thesis includes a taxonomy of commonly used environment models, and analysis of previous efforts to solve the rendezvous problem. Mathematical models and solutions used in applied statistics are analyzed for use in cognitive networking. A symmetric rendezvous pursuit-evasion game is developed and analyzed. Analysis and simulation results show that the modular clock algorithm performs better than random under a simple rendezvous environment model, while a modified version of the modular clock algorithm performs better than random in more difficult environment models
