Upper and Lower Bound Sum Rate Approximation for RIS Aided MIMO Interference Network

Reconfigurable intelligent surface (RIS) has emerged as a prospective technology, capable of shaping radio wave propagation and enhancing performance gains. The RIS aided multiple input multiple output interference channel is considered. We aim to maximize the sum rate by jointly optimizing the precoding matrices and RIS parameters, subject to the transmit power constraints. Both upper and lower bound sum rate approximation schemes are designed for this nonconvex problem. First, for the upper bound approximation, the minimax problem is formulated through the approximated Lagrangian function, where the precoding matrices are determined by the RIS matrix and the Lagrange multiplier, and are eliminated in the problem. A single loop primal dual algorithm is proposed. In each iteration, the RIS parameter and the Lagrange multiplier are updated by one projected gradient step and quadratic interpolation, respectively. Its complexity only grows linearly in the number of RIS elements. In addition, the total signal to total interference plus noise ratio is introduced for the sum rate lower bound approximation. The fractional objective function is reformulated via the Dinkelbach’s technique, and the variables are updated with closed form through alternating optimization and projected gradient method. The proposed two approximation schemes and methods are also extended to the general multi-RIS multi-cell network with multiple users. Simulations show that the upper bound approach performs well with only 10% computational time of the compared methods, and shows high efficiency in one-iteration test; the lower bound approach achieves almost the highest sum rate using little computational cost.