Fast Algorithms for Sum-Rate Maximization in Rate-Splitting Multiple Access With Perfect and Imperfect CSIT

Rate Splitting (RS) is a versatile and powerful technique for multi-antenna transmission. In this paper, we study the precoding optimization for RS, which is critically important for improving the system performance but often challenging to address. We first investigate the non-convex sum rate maximization problem under perfect Channel State Information at the Transmitter (CSIT). By constructing a separable structure for the sum-of-functions-of-ratios problem and jointly leveraging the Convex Concave Procedure (CCP) and the Alternating Direction Method of Multipliers (ADMM), we obtain a fast algorithm that substantially reduces the overall computational time through the parallel computation and explicit closed-form solutions. We then investigate the average sum rate maximization problem under imperfect CSIT, which is known as a more challenging non-convex stochastic problem. To obtain a fast algorithm for practical use, we carefully approximate the non-convex stochastic problem to a non-convex deterministic one with acceptable performance loss and tailor the fast algorithm derived from perfect CSIT for imperfect CSIT with modest changes. Numerical results show that compared to the state-of-the-art algorithms, the proposed algorithms achieve comparable sum rates or average sum rates but short computation times for large problem sizes, owing to the unique parallel computation structures and few matrix inverse operations.