A method for optimizing matrix valued functions and its applications to capacity of MIMO systems

Abstract

We present a method, that is based on differential matrix calculus, for optimizing matrix valued functions. This method can be applied to MIMO capacity optimization problems where a transmit covariance matrix has to be chosen optimally. We first state the necessary mathematical preliminaries regarding matrix differential calculus. Then, we apply the method to some of the already solved MIMO systems. This gives an insight on how the method works. Finally, we apply the method to some unsolved MIMO systems and find their optimum solutions. © 2011 IEEE. © 2012 Elsevier B.V., All rights reserved.