Abstract
This paper considers multiuser interference channels in which the transmitters have imperfect channel state information (CSI) where CSI perturbations are modeled stochastically. Transmitters are assumed to be equipped with multiple antennas serving single-antenna receivers. Transmitters use pre-designed discrete codebooks for beamforming directions and dynamically (based on the available CSI) select the best set of beamformers from the given codebook. The objective is to perform optimal power allocation to different users while certain quality of service (QoS) guarantees are ensured for the users. Imposed by stochastic CSI uncertainties, guarantees provided for the QoS measures have a stochastic nature too. The primary focus is placed on the interference channels for which two power allocation problems are considered. The first problem minimizes power consumption subject to serving users at certain data rates and the second problem considers max-min rate allocation subject to given power budgets for the transmitters. The core step in formalizing these problems in mathematically tractable forms relies on using Bernstein approximation, which approximates and convexifies the non-convex stochastic guarantees by conservative convex and deterministic counterparts. For solving this resulting convex and deterministic optimization problem, a specialized version of the long-step logarithmic barrier cutting plane (LLBCP) algorithm is used. Effectiveness of the proposed solutions and comparisons with other existing methods are assessed via extensive simulation results.