ADMM-Based Robust Beamforming Design for Downlink Cloud Radio Access Networks

The cloud radio access network (C-RAN) has been considered as a promising network architecture to improve both spectrum efficiency and energy efficiency of current wireless networks. In this paper, we aim to address the channel uncertainty issue in the multi-input single-output C-RAN by studying the robust beamforming. We formulate the robust beamforming design problem with an aim to minimize the overall network power and backhaul cost while satisfying the each radio remote head power constraint and guaranteeing individual signal-to-interference-plus-noise ratio (SINR) requirements. The channel state information is assumed to be imperfect, and the additive channel state information error is modeled as Gaussian distributed variables. Formulated problem is hard to solve due to the non-convex
$\ell _{0}$
-norm functions and channel uncertainty in the constraints. Two statistical approaches, named average approach and probability approach, are proposed to deal with SINR requirements when including the channel uncertainty.
$\ell _{0}$
-norm approximation and a majorization-minimization algorithm are utilized to transform
$\ell _{0}$
-norm problem into a series of semidefinite programing (SDP) problems. After that, we propose an alternating direction method of multipliers (ADMM)-based algorithm to solve each SDP problem. We introduce two auxiliary variables to reformulate the SDP problems in an ADMM form, which further ensure that solving the SDP problem can be decomposed to solve three convex subproblems. A subgradient algorithm, Karush–Kuhn–Tucker conditions, and a projected gradient method are applied to solve them, respectively. Simulation results verify that the proposed robust algorithm can significantly enhance the performance compared the non-robust case.