Low Complexity Joint User Association, Beamforming and RIS Reflection Optimization for Load Balancing in a Multi-RIS Assisted Network

We study the joint optimization of beamforming, RIS phase shift, and association for the links of BS-user and RIS-user communications in a multi-cell wireless network aided by multiple RISs. Consider a network setting with many RISs, we can optimize the reflection of each RIS for a single associated user, even though the RIS will reflect the signals of all users. We first design the optimal BS transmit beamforming together with the phase shift of RIS in a closed form to maximize the effective channel gain (ECG). Then, we design two different BS-RIS-user association algorithms satisfying the load balancing constraint. The first algorithm uses worst connection swapping on both the BS-user and RIS-user links, whereas the second algorithm uses a simpler max-ECG rule for the RIS-user link because of no load balancing at the RIS. A joint algorithm alternates between BS-RIS-user association and beamforming/reflection design until convergence. The proposed algorithms not only have substantially lower complexity than existing algorithms, but also outperforms the conventional max SINR association and effectively exploits multiple RISs to boost the network sum rate.