A New Linear Precoding Strategy for MIMO BC

The problem of maximizing sum rate of a multiple-antenna Gaussian broadcast channel (BC) with dirty-paper coding (DPC) is well known to be efficiently solved via duality, which transforms this nonconvex problem into a well-structured convex multiple-access channel (MAC) problem. To date, however, finding an optimal transmission strategy when employing linear precoding is still open, since it could not be transformed to a convex problem. In this paper, we introduce some restrictive condition and establish a duality between sum rates of MIMO BC and MIMO MAC with linear precoding under that condition, which converts the nonconvex and untractable problem at hand to a well-structured one like the DPC strategy. By doing so, we can anticipate a computationally efficient optimization algorithm which converges to the global optimum.