A Bandwidth Scanning Game with a Sophisticated Adversary

Scanning a large bandwidth of radio spectrum for anomalous signals is a fundamental challenge that must be addressed in building a secure spectrum sharing system. When designing a bandwidth scanning algorithm, the system engineer faces a problem of which band to scan and how long to scan each band. Traditionally, in such a problem, the adversary is considered as one who wants to achieve a malicious goal, e.g., to sneak usage of a particular band while being undetected. In this paper, we deal with a new type of adversary, called a sophisticated adversary, who, besides the basic goal of being malicious and undetected, also has a secondary goal to achieve the basic goal in the most unpredictable way. As a metric for such unpredictability we consider the entropy associated with the adversary’s strategy. The problem is modeled by a two-player game between an Intrusion Detection System (IDS) and the adversary. The equilibrium is found in closed form. Finally, weighting coefficients for the basic and secondary goals of the adversary are optimized via proportional fairness criteria.