A New Model of beyond Diagonal Reconfigurable Intelligent Surfaces (BD-RIS) for the Corresponding Quantization and Optimization

Reconfigurable Intelligent Surfaces (RISs) have been considered as a promising technology for next generation communications. The existing works mainly focused on the single-connected RIS, which is always mathematically characterized as diagonal phase shift matrices, because that each element of traditional RIS separately controls its status and would not like to apply influence to any other elements. Although there exist some research on sub-array RIS, the grouping conception is based on the controlling strategy level but not on the hardware realization level. Fortunately, a new type of beyond diagonal RIS (BD-RIS) is proposed with its mathematical expression is symmetric and not limited to traditional diagonal phase shift matrices. BD-RIS model can fully cover the previous various types of RIS like: reflective RIS, refractive RIS, IOS (Intelligent Omni-Surfaces) or STAR-RIS (Simultaneously Transmitting And Reflecting RIS). In this work, a new model of BD-RIS is proposed to explain its working principle. Then, the quantization strategy for the new model BD-RIS is analyzed. Finally, the optimization algorithms for BD-RIS in single-user multi-input-multi-output (SU-MISO) systems and in multi-user multi-input-multi-output (MU-MISO) systems are proposed. Simulation results verifies the effectiveness of the the algorithms' performance.