Pareto Region Characterization for Rate Control in Multi-User Systems and Nash Bargaining

In this paper, the problem of rate control in multi-user multiple-input multiple-output (MIMO) interference systems is formulated as a multicriteria optimization (MCO) problem. The Pareto rate region of the MCO problem is first characterized. It is shown that for the convexity of the Pareto rate region it is sufficient that the interference-plus-noise covariance matrices of multiple users with conflicting objectives approach identity matrix. The latter can be achieved by using either orthogonal signaling, tame-sharing, or interference cancellation strategies. It is argued that, in the case of high interference, the interference cancellation is preferable in order to increase the Pareto boundary and guarantee the convexity of the Pareto rate region. Secondly, the Nash bargaining (NB) is applied to transform the MCO problem into a single-objective problem. The characteristics of the NB over MIMO interference systems such as the uniqueness, the existence of the NB solution and the feasibility of the NB set are investigated. It is found that when the NB solution exists, the sufficient condition for the corresponding single-objective problem to have a unique solution is also that the interference-plus-noise covariance matrices of multiple users approach identity matrix. A simple multi-stage interference cancellation scheme, which leads to a larger convex Pareto rate region and, correspondingly, a unique NB solution with larger user rates compared to the orthogonal and time-sharing signaling schemes, is proposed. The convexity of the rate region, the effectiveness of the proposed interference cancellation technique, and the existence of the NB solution for MIMO interference systems are examined by means of numerical studies. The fairness of the NB solution is also demonstrated. Finally, the special cases of multi-input single-output (MISO) and single-input single-output (SISO) interference systems are also considered. Index Terms Multicriteria optimization, Pareto region, Nash bargaining, game theory, MIMO interference channel. IEEE TRANSACTION ON AUTOMATIC CONTROL, VOL. XX, NO. Y, MONTH 2009 2