Unicast Beamforming in the Presence of a Smart Reactive Jammer: A Stackelberg Game Approach

The malicious jamming attacks will disrupt legitimate public wireless communication systems, which has become a critical issue that must be considered in modern communication system design. This paper considers an anti-jamming unicast transmit beamforming problem with a smart reactive jammer. We model this problem as a Stackelberg game and formulate a bilevel optimization problem, in which the base station maximizes the minimum signal-to-interference-jamming-noise ratio (SIJNR) of legitimate users and the jammer minimizes the maximum SIJNR. This problem is quite challenging due to its hierarchical structure and nonconvexity. A penalty method is developed to solve this problem, which transforms it into a mathematical program with equilibrium constraint (MPEC) problem after implementing a tight semi-definite relaxation (SDR) method. The numerical results demonstrate its superior performance.