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Volume 5, Issue 2, Article 46 |
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On Schur-Convexity of Expectation of Weighted Sum of Random Variables with Applications
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Authors: |
Holger Boche, Eduard A. Jorswieck, |
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Keywords:
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Schur-convex function, Optimisation, Sum of weighted random variables. |
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Date Received:
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19/11/2003 |
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Date Accepted:
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17/04/2004 |
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Subject Codes: |
Primary 60E15, 60G50; Secondary 94A05.
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Editors: |
Peter S. Bullen, |
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Abstract: |
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.
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