Matrix-based gradient-projection algorithm

Abstract

Having established the duality relationship between the MIMO BC and the MIMO MAC in Chaps. 3 and 4, we can handle optimizations originally arising in the BC in its dual MIMO MAC where they have more favorable properties like being convex, for example, as in the weighted sum rate maximization problem. Due to the limited resource power, we have to deal with constrained optimizations. In particular, an upper bound on the dissipated sum power is imposed for the transceiver design in the following two chapters. An attractive iterative scheme that is targeted at solving constrained optimization problems is the gradient-projection algorithm which can be regarded as an extension of the steepest ascent method derived by Cauchy to the case of a constrained optimization.