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An upper bound on the ergodic capacity of {\bf MIMO} channels was introducedrecently in arXiv:0903.1952. This upper bound amounts to the maximization onthe simplex of some multilinear polynomial $p(\lambda_1,...,\lambda_n)$ withnon-negative coefficients. Interestingly, the coefficients are subpermanents ofsome non-negative matrix. In general, such maximizations problems are {\bfNP-HARD}. But if say, the functional $\log(p)$ is concave on the simplex andcan be efficiently evaluated, then the maximization can also be doneefficiently. Such log-concavity was conjectured in arXiv:0903.1952. We give inthis paper self-contained proof of the conjecture, based on the theory of {\bfH-Stable} polynomials.

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