RIS-Aided Multiple-Input Multiple-Output Broadcast Channel Capacity

Scalable algorithms are conceived for obtaining the sum-rate capacity of the reconfigurable intelligent surface (RIS)-Aided multiuser (MU) multiple-input multiple-output (MIMO) broadcast channel (BC), where a multi-Antenna base station (BS) transmits signals to multi-Antenna users with the help of an RIS equipped with a massive number of finite-resolution programmable reflecting elements (PREs). As a byproduct, scalable path-following algorithms emerge for determining the sum-rate capacity of the conventional MIMO BCs, closing a long-standing open problem of information theory. The paper also develops scalable algorithms for maximizing the minimum rate (max-min rate optimization) of the users achieved by the joint design of RIS's PRE and transmit beamforming for such an RIS-Aided BC. The simulations provided confirm the high performance achieved by the algorithms developed, despite their low computational complexity.