On the Limits of Predictability in Real-World Radio Spectrum State Dynamics: From Entropy Theory to 5G Spectrum Sharing

A range of applications in cognitive radio networks, from adaptive spectrum sensing to predictive spectrum mobility and dynamic spectrum access, depend on our ability to foresee the state evolution of radio spectrum, raising a fundamental question: To what degree is radio spectrum state (RSS) predictable? In this paper, we explore the fundamental limits of predictability in RSS dynamics by studying the RSS evolution patterns in spectrum bands of several popular services, including TV bands, ISM bands, and Cellular bands, etc. From an information theory perspective, we introduce a methodology of using statistical entropy measures and Fano inequality to quantify the degree of predictability underlying real-world spectrum measurements. Despite the apparent randomness, we find a remarkable predictability, as large as 90%, in the real-world RSS dynamics over a number of spectrum bands for all popular services. Furthermore, we discuss the potential applications of prediction-based spectrum sharing in 5G wireless communications.