  It has been shown recently that the dirty-paper coding is the optimal
strategy for maximizing the sum rate of 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 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.
