Majorization Theory with Applications in Signal Processing and Communication Systems
Jiaheng Wang, Daniel P. Palomar · Rare & Special e-Zone (The Hong Kong University of Science and Technology) · 2011
In this chapter we introduce a useful mathematical tool, namely Majorization Theory, and illustrate its applications in a variety of scenarios in signal processing and communication systems. Majorization is a partial ordering and precisely defines the vague notion that the components of a vector are “less spread out” or “more nearly equal” than the components of another vector. Functions that preserve the ordering of majorization are said to be Schur-convex or Schur-concave. Many problems arising in signal processing and communications involve comparing vector-valued strategies or solving optimization problems with vector- or matrix-valued variables. Majorization theory is a key tool that allows us to solve or simplify these problems. © 2011 by Taylor & Francis Group, LLC.