Predictability Analysis of Spectrum State Evolution: Performance Bounds and Real-World Data Analytics

Predictability in spectrum prediction refers to the degree to which a correct prediction of the radio spectrum state (RSS) can be made quantitatively. It is obvious that the possibility that the future RSS is accurately predicted will be different when using different spectrum prediction algorithms. However, the fundamental limits on the accuracy of various spectrum prediction algorithms should exist and be worthwhile to be paid attention to. In this paper, we define these fundamental limits as the performance bounds of predictability, which can be the important indexes when evaluating the performance of different spectrum prediction algorithms. Real-world spectrum data is involved to present comprehensive and profound analysis of the predictability. We first transform large amount of spectrum data into symbol sequences by sampling and quantization, to calculate the entropy of the symbol sequence, which represents the randomness of the RSS evolution. Then, we derive the upper bound and the lower bound of the predictability mainly from entropies of the symbol sequences. Further, we conduct the detailed analysis on the performance bounds of the predictability of the RSS. Based on real-world data analytics, the key insights among others include: 1) entropies almost have no relationship with selection of sampling intervals in the data preprocessing; 2) the upper and the lower bounds of the predictability will both decrease as the quantization level rises and tend to be stable around a value at last; and 3) two kinds of lower bounds of the predictability are proposed, and one of the lower bounds, the regularity $R$ , can reveal the tidal effect of the evolution of the RSS.