Stability of fair trade-off solution between radar and communication objectives on hostile interference

One of the challenges in jointly designing a system to support both communication and radar is that such a system has multiple objectives to address simultaneously. This challenge becomes more difficult when considering the potential for adversarial interference. A question that arises is what are appropriate design criteria that are stable when facing hostile interference, and from this arrive at realistic solutions to the trade-off between the two objectives. To address this question, we first show that the bargaining tradeoff can be correctly embedded in a uniform manner using the α-fairness tradeoff criteria. To investigate the impact of hostile interference, a zero sum game between the system and a jammer is formulated. It is proved that, within an interval for the fairness coefficient that is bounded by two cooperative solutions (maximizing total performance and minimizing total delay in objectives), the equilibrium exists and is unique. Moreover, the bargaining solution is the median point of this interval, while outside of this interval the existence of the equilibrium, and thus of stability of the system can be quite sensitive to jamming.