  An upper bound on the ergodic capacity of {\bf MIMO} channels was introduced
recently in arXiv:0903.1952. This upper bound amounts to the maximization on
the simplex of some multilinear polynomial $p(\lambda_1,...,\lambda_n)$ with
non-negative coefficients. Interestingly, the coefficients are subpermanents of
some non-negative matrix. In general, such maximizations problems are {\bf
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 arXiv:0903.1952. We give in
this paper self-contained proof of the conjecture, based on the theory of {\bf
H-Stable} polynomials.
