Applications of game theory in cognitive radar

In this chapter, the game theory is applied to deal with the problem of spectrum sharing between cognitive multistatic radar and a communication system. To be specific, the non-cooperative game theory-based power allocation (NCGT-PA) problem for cognitive multistatic radar systems is studied, which coexists with a communications system in the same frequency band. The key mechanism of the cognitive radar system is to reduce the transmit power of each radar node while satisfying a certain target detection criterion and a maximum tolerable interference constraint for the communication system. Considering the rationality and selfishness of each radar, we adopt the non-cooperative game model to capture the interactions among multiple radars. The utility function of each radar is defined and serves as the optimization criterion for designing the sub-optimal power allocation strategy, taking into account the target detection requirement and the total interference to the communications system. Furthermore, the analytical expression for the Nash equilibrium of the established game model is derived, and the existence and uniqueness of the Nash equilibrium are strictly proved. An efficient iterative power allocation approach that determines the transmit power of each radar is put forward. Finally, several simulation results are provided to demonstrate the theoretical analysis of the Nash equilibrium and the effectiveness of the proposed strategy.