Maximum Weighted Sum Rate of Multi-Antenna Broadcast Channels

Recently, researchers showed that dirty paper coding (DPC) is the optimal transmission strategy for multiple-input multiple-output broadcast channels (MIMO-BC). In this paper, we study how to determine the maximum weighted sum of DPC rates through solving the maximum weighted sum rate problem of the dual MIMO multiple access channel (MIMO-MAC) with a sum power constraint. We first simplify the maximum weighted sum rate problem such that enumerating all possible decoding orders in the dual MIMO-MAC is unnecessary. We then design an efficient algorithm based on conjugate gradient projection (CGP) to solve the maximum weighted sum rate problem. Our proposed CGP method utilizes the powerful concept of Hessian conjugacy. We also develop a rigorous algorithm to solve the projection problem. We show that CGP enjoys provable convergence, nice scalability, and great efficiency for large MIMO-BC systems.