A General Framework for Secrecy Performance Analysis via Quantifier Elimination

Abstract

The problems of finding accurate limits of integration in symbolic form are non-trivial when analyzing the secrecy outage probability (SOP) over complicated communication schemes. To identify these limits, we formulate an existential quantifier elimination (QE) problem based on the description of the secrecy outage events. After that, the resulting QE problem can be solved using QE algorithms such as cylindrical algebraic decomposition (CAD) via existing solvers. Since CAD is an exact algorithm, our approach does not require Monte-Carlo simulations to verify the correctness of the SOP integration limits. Finally, two complex SOP analysis scenarios for cognitive radio systems are presented to demonstrate the generality of the proposed method.