High-SNR Comparison of Linear Precoding and DPC in RIS-Aided MIMO Broadcast Channels

We compare dirty paper coding (DPC) and linear precoding methods in a reconfigurable intelligent surface (RIS)- aided high-signal-to-noise ratio (SNR) scenario, where the channel between the base station (BS) and the RIS is dominated by a line-of-sight (LOS) component. Furthermore, we consider two groups of users where one group can be efficiently served by the BS, whereas the other one has a negligible direct channel and has to be served via the RIS. Within this scenario, we analytically show fundamental differences between DPC and linear methods. In particular, our analysis addresses two essential aspects, i.e., the orthogonality of the BS-RIS channel with the direct channel and a channel mitigation term, depending on the number of RIS elements, that is present only for linear precoding techniques. The mitigation term generally leads to strong limitations for the linear method, especially for random or statistical phase shifts. Moreover, we discuss under which circumstances this mitigation term is negligible and in which scenarios DPC and linear precoding lead to the same performance.