This paper studies RIS-aided cell-free massive MIMO systems, where multiple RISs are deployed to assist the communication between multiple access points (APs) and multiple users, with either continuous or discrete phase shifts at the RISs. We formulate the max-min fairness problem that maximizes the minimum achievable rate among all users by jointly optimizing the transmit beamforming at active APs and the phase shifts at passive RISs, subject to power constraints at the APs. To address such a challenging problem, we first study the special single-user scenario and propose an algorithm that can transform the optimization problem into semidefinite program (SDP) or integer linear program (ILP) for the cases of continuous and discrete phase shifts, respectively. By solving the resulting SDP and ILP, we first obtain the optimal phase shifts, and then design the optimal transmit beamforming accordingly. To solve the optimization problem for the multi-user scenario and continuous phase shifts at RISs, we extend the single-user algorithm and propose an alternating optimization algorithm, which can first decompose the max-min fairness problem into two subproblems related to transmit beamforming and phase shifts, and then transform the two subproblems into second-order-cone program and SDP, respectively. For the multi-user scenario and discrete phase shifts, the max-min fairness problem is shown to be a mixed-integer non-linear program (MINLP). To tackle it, we design a ZF-based successive refinement algorithm, which can find a suboptimal transmit beamforming and phase shifts by means of alternating optimization. Numerical results show that compared with benchmark schemes of random phase shifts and without using RISs, the proposed algorithms can significantly increase the minimum achievable rate among all users, especially when the number of reflecting elements at each RIS is large.


翻译:本文研究RIS 辅助无细胞大规模IMIM 系统。 在这种系统中,部署多个TRIS来协助多个接入点(APs)和多个用户之间的沟通,在RIS 中进行连续或离散的阶段转移。 我们制定最大最小公平问题,通过在活动APs上优化传输光束,在被动的RISS进行阶段转移,但受APs的电力限制。 为了解决这样一个具有挑战性的问题,我们首先研究特殊单一用户假设方案,并提议一种算法,可以将优化问题转化为半确定程序(SDP)或整型线性程序(ILP),用于连续和离散的阶段转移。我们通过解决由此产生的SDP和ILP,我们首先获得最佳的阶段变化,然后设计最佳的传输光度。为了解决多用户情景的优化问题和在RIS 中的持续阶段的变化,我们扩展了所有用户的算法,并提议一种交替的优化算法,它可以首先将最接近的公平问题化程序(SDP)变成两个分流阶段, 将最低的流流流化程序(Sloverial lial lial) imal livaldal livaldal) 和多级程序分别显示Slivaldal-modal-mod smod smod smod smod smod slipal lipal liction) lipal lipal lipal liction) 。 lipal lipal 。在Slimamod smod smaldalmadalmadaldal 阶段显示一个小程序 和两个小程序, 阶段(我们分别显示一个小阶段, liftal-likedal) 。

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