Distributed Robust Multicell Coordinated Beamforming With Imperfect CSI: An ADMM Approach

TLDR

Multi‑cell coordinated beamforming mitigates inter‑cell interference, yet most designs assume perfect CSI, which is unrealistic, making the robust problem challenging even centrally. This work seeks to minimize weighted sum transmit power under worst‑case SINR constraints with elliptically bounded CSI errors, aiming for a decentralized solution using only local CSI and minimal backhaul. We first apply semidefinite relaxation to approximate the centralized problem, then develop a distributed ADMM‑based algorithm that iteratively exchanges local messages to obtain the robust beamforming solution, with simulation studies validating its effectiveness. The proposed algorithm converges to the optimal centralized solution and achieves superior backhaul bandwidth efficiency compared to dual‑decomposition methods.

Abstract

Multi-cell coordinated beamforming (MCBF), where multiple base stations (BSs) collaborate with each other in the beamforming design for mitigating the inter-cell interference, has been a subject drawing great attention recently. Most MCBF designs assume perfect channel state information (CSI) of mobile stations (MSs); however CSI errors are inevitable at the BSs in practice. Assuming elliptically bounded CSI errors, this paper studies the robust MCBF design problem that minimizes the weighted sum power of BSs subject to worst-case signal-to-interference-plus-noise ratio (SINR) constraints on the MSs. Our goal is to devise a distributed optimization method that can obtain the worst-case robust beamforming solutions in a decentralized fashion, with only local CSI used at each BS and little backhaul signaling for message exchange between BSs. However, the considered problem is difficult to handle even in the centralized form. We first propose an efficient approximation method in the centralized form, based on the semidefinite relaxation (SDR) technique. To obtain the robust beamforming solution in a decentralized fashion, we further propose a distributed robust MCBF algorithm, using a distributed convex optimization technique known as alternating direction method of multipliers (ADMM). We analytically show the convergence of the proposed distributed robust MCBF algorithm to the optimal centralized solution and its better bandwidth efficiency in backhaul signaling over the existing dual decomposition based algorithms. Simulation results are presented to examine the effectiveness of the proposed SDR method and the distributed robust MCBF algorithm.