Proportional Fairness in MC-CDMA Networks in the Presence of Jammers: A Game Theoretic Approach

Proportional fairness in the downlink of a single-cell multi-carrier code-division-multiple-access (MC-CDMA) network in the presence of a jammer is considered in this paper. We assume the jammer can find the spreading sequences of the base station (BS) and use them in causing interference on all available channels to reduce the sum rate of the BS to users to the extent possible. Besides, we require the BS to apply proportional fairness in its transmissions to users in the presence of the jammer. Interactions between the BS and the jammer are modeled by a non-cooperative zero-sum generalized game. The game is solved via quasi-variational inequality (QVI), and optimal strategies (transmit power levels) are obtained in closed forms, which are not in the form of water-filling formula. Moreover, we propose a new gradient-based algorithm to solve the QVI, prove its convergence, and obtain the optimal strategies.