Concavity conjecture for the logarithm of a matrix permanent

Let ${\bf A}$ be an $M\times N$ matrix with non-negative elements. For $\boldsymbol\lambda=(\lambda_1,\ldots,\lambda_N)$, let

$$f(\boldsymbol\lambda)=\log \operatorname{Per}({\bf A}\operatorname{diag}(\boldsymbol\lambda)).$$

Define

$$\mathcal{D}^{N}=\{\boldsymbol\lambda\mid \operatorname{Per}({\bf A}\operatorname{diag}(\boldsymbol\lambda))>0,\ \lambda_i\geq 0,\ 1\leq i\leq N\}.$$

Concavity conjecture. The function $f(\boldsymbol\lambda)$ is concave on $\mathcal{D}^{N}$.

This conjecture concerns the concavity of the logarithm of a permanent under non-negative diagonal scaling and is intended for the optimal power allocation problem in jointly correlated MIMO channels. The supplied text does not indicate whether the conjecture has been resolved.