Computing Important Points via Monotonic Optimization Sample Clauses

Computing Important Points via Monotonic Optimization. An explicit parameterization of the Pareto boundary for the K-user Gaussian MISO IC, for the case when all multiuser interference is treated as additive Gaussian noise at the receivers, was presented in the previous section. Also, it was shown that for the special case of two users, any point in the rate region can be achieved by choosing beamforming vectors that are linear combinations of the ZF and the MRT beamformers. Hence, all important (i.e., Pareto-efficient) operating points can be expressed by two real-valued parameters between zero and one 0 ≤ λ = [λ1, λ2] ≤ 1. In this section, we build on this parameterization and focus on the maximum sum- rate operating point, the proportional-fair operating point and the max-min rate point. The corresponding optimization problems are non-convex problems which are difficult to solve directly. In particular, the max-min problem is non-smooth and therefore derivative-based (gradient) optimization approaches cannot be applied. A suboptimal iterative algorithm based on alternating projection was proposed in [11]. In general, this algorithm converges to a local optimum. Therefore, we are interested in formulating a unified non-convex optimization framework which takes as much as possible of the problem structure into account, and which is able to find the global optimum of the problems. The main contribution of this work is the development of a systematic approach to solve the non-convex optimization problem. In contrast to exhaustive search methods, such as a grid search, the proposed approach has the advantage that it can achieve a given accuracy. The details of the following derivations including proofs and further discussions can be found in [3].