Robust MISO Beamforming Under the Deterministic Model in Two-Tier Heterogeneous Networks

Heterogeneous networks are a promising technology in fifth generation (5G) wireless networks, which has been shown to significantly increase the capacity and coverage compared with the conventional wireless networks. In this paper, we consider the robust multiple-input single-output beamforming design in a two-tier heterogeneous network. By considering the worst case deterministic model, our objective is to maximize the worst case signal-to-interference-plus-noise-ratio in a small cell base station while guaranteeing that its interference to a macro cell user equipment is less than a threshold. Although interesting and attractive, such a problem is non-convex and also essentially involves an infinite number of constraints. Nevertheless, we first transform the problem into an equivalent one which is more tractable and then propose an efficient algorithm to obtain a near optimal solution. Furthermore, we also develop two algorithms that provide an upper bound and a lower bound of the original problem, respectively. Simulation results validate the effectiveness of the proposed algorithms.