SAS: Modeling and Analysis of Spectrum Activity Surveillance in Wireless Overlay Networks

Spectrum monitoring, run-time usage acquisition, and regulation enforcement, in general can be referred to as spectrum activity surveillance (SAS). It is essential to dynamic spectrum access with a two-fold impact: it is a primitive mechanism to continuously scan spectrum usage for system optimization purposes; it is also a prime widget to obtain spectrum footprints of legitimate users, and record misuse by unauthorized or malicious users. Seemingly trivial, large-scale SAS in wireless overlay networks is actually an open yet challenging problem. This is because on one hand, such a system is time and energy-sensitive and hence unlikely (or not necessary) to implement in practice, due to constraints of radio spectrum license and system deployment. On the other hand, it is not clear how to characterize the efficacy and performance of spectrum monitoring strategies in surveillance over a large geographical region, and detection of spectrum culprits, that is, unauthorized spectrum occupants. To address such a challenge, we consider SAS in a 3-dimensional space that is composed of spectrum, time, and geographical region, and then formulate monitoring strategies as graph walks by accounting for the locality of spectrum activities. In particular, our approach transforms the SAS problem from a globally collective activity to a set of localized, distributed actions, and strategy objectives from qualitative attributes to quantitative measures. We find that randomized strategies with m monitors can achieve a sweep-coverage over a space of n assignment points in Θ(n/m ln n) time, and detect an oblivious or adversarial spectrum culprit in Θ(n/m) time for SAS systems.