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Conjugate Gradient Projection Approach for MIMO Gaussian Broadcast Channels

Researchers have recently shown that the dirty-paper coding (DPC) is the optimal transmission strategy for multiple-input multiple-output Gaussian broadcast channels (MIMO BC). Moreover, by the channel duality, the nonconvex MIMO BC sum rate problem can be transformed to the convex dual MIMO multiple-access channel (MIMO MAC) problem with a sum power constraint. In this paper, we design an efficient algorithm based on conjugate gradient projection (CGP) to solve the MIMO BC maximum sum rate problem. Our proposed CGP algorithm solves the dual sum power MAC problem by utilizing the powerful concept of Hessian conjugate. We also develop a rigorous algorithm to solve the projection problem. We show that CGP enjoys provable convergence, scalability, and efficiency for large MIMO BC systems.