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. The authors study the non-convex 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 non-negative matrices, they derive necessary and sufficient optimality conditions and propose a global optimization algorithm based on the outer approximation method.