Journal
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
Volume 32, Issue 3, Pages 1030-1055Publisher
SIAM PUBLICATIONS
DOI: 10.1137/090757137
Keywords
nonconvex optimization; convex relaxation; maximization of convex functions; nonnegative matrix theory; spectral radii of irreducible nonnegative matrices; wireless networks
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Funding
- ARO MURI [W911NF-08-1-0233]
- NSF NetSE [CNS-0911041]
- City University Hong Kong [7200183, 7008087]
- American Institute of Mathematics
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Maximizing the sum rates in a multiuser Gaussian channel by power control is a nonconvex NP-hard problem that finds engineering application in code division multiple access (CDMA) wireless communication network. In this paper, we extend and apply several fundamental nonnegative matrix inequalities initiated by Friedland and Karlin in a 1975 paper to solve this nonconvex power control optimization problem. Leveraging tools such as the Perron-Frobenius theorem in nonnegative matrix theory, we (1) show that this problem in the power domain can be reformulated as an equivalent convex maximization problem over a closed unbounded convex set in the logarithmic signal-to-interference-noise ratio domain, (2) propose two relaxation techniques that utilize the reformulation problem structure and convexification by Lagrange dual relaxation to compute progressively tight bounds, and (3) propose a global optimization algorithm with epsilon-suboptimality to compute the optimal power control allocation. A byproduct of our analysis is the application of Friedland-Karlin inequalities to inverse problems in nonnegative matrix theory.
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