Maximizing Signal to Interference Noise Ratio for Massive MIMO: A Mathematical Programming Approach

In this paper, we consider the problem of maximizing the worst user signal to interference noise ratio (SINR) for Massive Multiple Input Multiple Output (MaMIMO) systems subject to antenna assignment and multiuser interference constraints. In particular, we aim to choose a subset of antennas from a larger set while imposing a maximum interference value allowed in the system. Notice that MaMIMO technology has recently been considered as a strong candidate for 5G wireless communications by the research community as it provides better performance in terms of data rate. It also allows to transmit in higher frequency bands with strong signal performance and reliability. In order to propose new optimization models for this problem, we model SINR by using Manhattan, Euclidean and Infinity distance norms. Thus, we obtain integer quadratic and linear programming models that allow to obtain optimal solutions for the problem. As such, the proposed models can be used as a source of comparison for any exact or approximation method to be developed as part of future research. Finally, we propose a local search algorithm that allows to obtain feasible solutions in short CPU time. Our preliminary numerical results indicate that the linear models are preferable and that the local search approach obtains better solutions than the quadratic model for some of the tested instances in significantly less CPU time.