Multiple-input multiple-output (MIMO) channels provide an abstract and unified representation of different physical communication systems, ranging from multi-antenna wireless channels to wireless digital subscriber line systems. They have the key property that several data streams can be simultaneously established.
  In general, the design of communication systems for MIMO channels is quite involved. The first difficulty lies on how to measure the global performance of such systems given the tradeoff on the performance among the different data streams. Once the problem formulation is defined, the resulting mathematical problem is typically too complicated to be optimally solved as it is a matrix-valued nonconvex optimization problem. This design problem has been studied for the past three decades.
  In this talk, we will overview the state-of-the-art unified mathematical framework for the design of point-to-point MIMO transceivers with channel state information at both sides of the link according to an arbitrary cost function as a measure of the system performance. First, we will consider the case of linear MIMO transceivers. Then, we will cover the more general case of nonlinear decision-feedback (DF) MIMO transceivers.
  Majorization theory is the underlying mathematical theory on which the framework hinges. It allows the transformation of the originally complicated matrix-valued nonconvex problem into a simple scalar convex problem. We will see how the additive majorization relation plays a key role in the linear case, whereas the multiplicative majorization relation arises in the nonlinear DF case.