Pareto Region Characterization for Rate Control in MIMO Interference Systems and Nash Bargaining

In this note, the problem of rate control in multiuser 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 by giving a sufficient condition for the convexity of the Pareto rate region. Second, various rate region convexification approaches including a multistage interference cancellation and a full projection (FP)-based interference avoidance scheme are analyzed. An achievable rate region based on FP is also given for MIMO interference systems. Third, 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 and optimality of different type NB solutions are investigated. A method to determine the optimality of FP- and time-division multiplexing-based NB solutions is presented as well. Finally, the convexity of the rate region and the existence of the FP-based NB solution for MIMO interference systems are examined numerically.