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On schur-convexity of expectation of weighted sum of random variables with applications

: Boche, H.; Jorswieck, Eduard A.

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Journal of inequalities in pure and applied mathematics : JIPAM 5 (2004), No.2, Art. 46, 14 pp.
ISSN: 1443-5756
Journal Article, Electronic Publication
Fraunhofer HHI ()

We show that the expectation of a class of functions of the sum of weighted identically independent distributed positive random variables is Schur-concave with respect to the weights. Furthermore, we optimise the expectation by choosing extra-weights with a sum constraint. We show that under this optimisation the expectation becomes Schur-convex with respect to the weights. Finally, we explain the connection to the ergodic capacity of some multiple-antenna wireless communication systems with and without adaptive power allocation.