A proof of the log-concavity conjecture related to the computation of the ergodic capacity of MIMO channels

Journal Article · Thu Jan 01 00:00:00 EST 2009 · IEEE Transactions on Information Theory

OSTI ID:971648

Gurvitis, Leonid ^[1]

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1. Los Alamos National Laboratory

An upper bound on the ergodic capacity of MIMO channels was introduced recently in [1]. This upper bound amounts to the maximization on the simplex of some multilinear polynomial p({lambda}{sub 1}, ..., {lambda}{sub n}) with non-negative coefficients. In general, such maximizations problems are NP-HARD. But if say, the functional log(p) is concave on the simplex and can be efficiently evaluated, then the maximization can also be done efficiently. Such log-concavity was conjectured in [1]. We give in this paper self-contained proof of the conjecture, based on the theory of H-Stable polynomials.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC52-06NA25396
• OSTI ID: 971648
• Report Number(s): LA-UR-09-06428; LA-UR-09-6428; TRN: US201004%%231
• Journal Information: IEEE Transactions on Information Theory, Journal Name: IEEE Transactions on Information Theory
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
97 MATHEMATICS AND COMPUTING
CAPACITY
FUNCTIONALS
POLYNOMIALS