A stochastic differential equation model for spectrum utilization

Dynamic spectrum access has been a subject of extensive study in recent years. The increasing volume of literature calls for better understanding of the characteristics of current spectrum utilization as well as better tools for analysis. A number of measurement studies have been conducted recently, revealing previously unknown features. On the other hand, analytical studies largely continues to rely on standard models like the two-state Markov (Gilbert-Elliot) model. In this paper we present an alternative, stochastic differential equation (SDE) based spectrum utilization model that captures dynamic changes in channel conditions induced by primary users´ activities. It is in closed form and verified using real spectrum measurement data. We also present a straightforward procedure to generate synthetic spectrum data that can be used for realistic simulation. We then compare this model (in its time-discretized and value-quantized form) with the standard Gilbert-Elliot model, and in particularly examine their performance when the same channel access policy is applied. Finally we introduce a 3-state Markov model that captures certain key features of the SDE model.