A stochastic differential equation model for spectrum utilization

Li Yang, Shang-Pin Sheng, Romesh Saigal, Mingyan Liu, Dawei Chen, Qiang Zhang

Abstract: 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.