Spectrum Management in Multiuser Cognitive Wireless Networks: Optimality and Algorithm
Spectrum management is used to improve performance in multiuser communication system, e.g., cognitive radio or femtocell networks, where multiuser interference can lead to data rate degradation. We study the nonconvex NP-hard problem of maximizing a weighted sum rate in a multiuser Gaussian interference channel by power control subject to affine power constraints. By exploiting the fact that this problem can be restated as an optimization problem with constraints that are spectral radii of specially crafted nonnegative matrices, we derive necessary and sufficient optimality conditions and propose a global optimization algorithm based on the outer approximation method. Central to our techniques is the use of nonnegative matrix theory, e.g., nonnegative matrix inequalities and the Perron-Frobenius theorem. We also study an inner approximation method and a relaxation method that give insights to special cases. Our techniques and algorithm can be extended to a multiple carrier system model, e.g., OFDM system or receivers with interference suppression capability.
© 2011 IEEE. Manuscript received 1 December 2009; revised 28 April 2010. This research has been supported in part by ARO MURI Award W911NF-08-1-0233, NSF NetSE grant CNS-0911041, CityU HK project grant 7200183, and a grant from the American Institute of Mathematics.