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Direct Derivation of the Gradient Method for Network Utility Maximization in Broadcast Channels and Its Application

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4 Author(s)
Heejin Joung ; Dept. of Electr. & Electron. Eng., Yonsei Univ., Seoul, South Korea ; Cheol Mun ; Jae-Yun Ko ; Jong-Gwan Yook

In broadcast channels, network utility maximization formulates a scheduling problem in order to maximize a sum of given utility functions. It is known that the network utility maximization is achieved if a gradient method is used. In this paper, however, we show that the network utility maximization is achieved only if a gradient method is used. That proves the equivalence between a problem formulated by the network utility maximization and a problem with a gradient method. The gradient method simplifies the object function of a scheduling problem by modifying utility functions to a gradient form, so that it makes easy to deal with the problem. We apply the gradient method to a problem with utility functions given by generalized proportional fairness. It is revealed that using the gradient method for the generalized proportional fairness is equivalent to applying a binomial approximation. Simulation results are presented with various scheduling parameters.

Published in:

Vehicular Technology Conference (VTC Spring), 2011 IEEE 73rd

Date of Conference:

15-18 May 2011