Double-layer dynamics of cognitive radio networks

There are two worlds of wireless communications: the legacy wireless world and the cognitive wireless world. Spectrum holes are the medium through which the two worlds interact. Releasing subbands by primary users allows the cognitive radio users to perform their normal tasks and, therefore, to survive. In other words, the old world affects the new world through appearance and disappearance of the spectrum holes and there is a master-slave relationship between them. Hence, the two worlds of wireless communications are going on side by side. This makes a cognitive radio network a multiple-time-scale dynamic system: a large-scale time in which the activities of primary users change and a small-scale time in which the activities of secondary users change accordingly. Such systems are called double-layer dynamic systems. A model is built that can be used as a testing tool for policy forecast and incorporates time evolution as the life span (control horizon) of a given policy. Two types of time dependency are studied: time-dependent equilibria and time-dependent behaviour away from the predicted curve of equilibria. Theories of evolutionary variational inequalities and projected dynamic systems on Hilbert spaces are used to study these two types of time dependency, respectively.