In this paper, we consider the robust beamforming design in a reconfigurable intelligent surface (RIS)-aided cell-free (CF) system considering the channel state information (CSI) uncertainties of both the direct channels and cascaded channels at the transmitter with capacity-limited backhaul. We jointly optimize the precoding at the access points (APs) and the phase shifts at multiple RISs to maximize the worst-case sum rate of the CF system subject to the constraints of maximum transmit power of APs, unit-modulus phase shifts, limited backhaul capacity, and bounded CSI errors. By applying a series of transformations, the non-smoothness and semi-infinite constraints are tackled in a low-complexity manner that facilitates the design of an alternating optimization (AO)-based iterative algorithm. The proposed algorithm divides the considered problem into two subproblems. For the RIS phase shifts optimization subproblem, we exploit the penalty convex-concave procedure (P-CCP) to obtain a stationary solution and achieve effective initialization. For precoding optimization subproblem, successive convex approximation (SCA) is adopted with a convergence guarantee to a Karush-Kuhn-Tucker (KKT) solution. Numerical results demonstrate the effectiveness of the proposed robust beamforming design, which achieves superior performance with low complexity. Moreover, the importance of RIS phase shift optimization for robustness and the advantages of distributed RISs in the CF system are further highlighted.

翻译：本文研究了在可重构智能表面（RIS）辅助的无蜂窝（CF）系统中，考虑发射端直连信道和级联信道的信道状态信息（CSI）不确定性以及容量受限回程链路下的鲁棒波束赋形设计。我们联合优化接入点（AP）的预编码和多个RIS的相移，在满足AP最大发射功率、单位模值相移、有限回程容量和有界CSI误差约束的条件下，最大化CF系统最差情况下的和速率。通过一系列变换，我们以低复杂度方式处理了非光滑性和半无限约束，基于此设计了一种交替优化（AO）迭代算法。所提算法将原问题分解为两个子问题。针对RIS相移优化子问题，采用惩罚凸凹过程（P-CCP）获取稳定解并实现有效初始化；针对预编码优化子问题，采用逐次凸近似（SCA）方法，确保收敛到Karush-Kuhn-Tucker（KKT）解。数值结果验证了所提鲁棒波束赋形设计的有效性，该设计在低复杂度下实现了优越性能，并进一步突出了RIS相移优化对鲁棒性的重要性以及分布式RIS在CF系统中的优势。