RIS Assisted Multiple User Interference Mitigation via an Accelerated Coordinate Descent Method

Reconfigurable intelligent surfaces (RIS) aided multiple user interference mitigation with constant modulus constraint (CMC) is the key issue in the multiple-input-multiple-output (MIMO) communication systems. Usually, the existing methods solve this problem by relaxation (relaxing CMC or cost function) or with designing phase, which either degrade the performance or need huge computational cost. To address this issue, a low-complexity Accelerated Coordinate Descent (ACD) method is proposed to design the phase. First, the problem is reformulated as a penalty quadratic function with CMC. Then, a Coordinate Descent (CD) algorithm is derived to obtain the solution, by transforming the problem into a decomposable problem with multiple one-dimensional subproblems. Finally, the ACD algorithm is derived by using the square iterative technique. Particularly, RIS discrete phase design is also considered due to practical hardware constraints. Compared with the existing methods, the proposed method has the following advantages: (1) The achievable rate per user is 0.64 bits/s/Hz higher than Pan et al. (2020) and ElMossallamy et al. (2021). (2) The computational cost is an order of magnitude lower than Pan et al. (2020) and ElMossallamy et al. (2021).