Beyond Diagonal RIS: Passive Maximum Ratio Transmission and Interference Nulling Enabler

beyond diagonal reconfigurable intelligent surfaces (BD-RIS) generalizes and goes beyond conventional diagonal reconfigurable intelligent surfaces (D-RIS) by interconnecting elements to generate beyond diagonal scattering matrices, which significantly strengthen the wireless channels. In this work, we use BD-RIS for passive multiuser beamforming in multiuser multiple-input-single-output (MU-MISO) systems. Specifically, we design the scattering matrix of BD-RIS to either maximize the sum received signal power at the users following maximum ratio transmission (MRT), or to nullify the interference at the users following zero forcing (ZF). To control the BD-RIS circuit topology complexity, we present the scattering matrix designs for the single/group/fully-connected BD-RIS architectures. Furthermore, we investigate uniform/optimized power allocation and ZF precoding at the base station (BS). Numerical results show that BD-RIS improves the interference nulling capability and sum rate with fewer reflecting elements (REs) compared to D-RIS. In addition, at moderate to high signal to noise ratios (SNRs), passive interference nulling reduces the complexity at the BS by relaxing the need for precoding or water-filling power allocation design. Furthermore, the passive MRT with ZF precoding achieves a tight sum rate performance to the joint design considering MU-MISO scenarios with many REs while maintaining low computational complexity and simplifying the channel estimation.