Quasi-concavity conjecture for the UPA goodput-to-power ratio

Let $\mathbf{D}$ be the transmit covariance matrix under uniform power allocation, with $\mathbf{D}=\frac{p}{n_t}\mathbf{I}_{n_t}$, where $p$ is the allocated power and $\overline{P}$ is the maximum available power. Let $\Gamma_{\mathrm{UPA}}(p,R)$ denote the resulting goodput-to-power ratio. UPA quasi-concavity conjecture. Assuming

$$\mathbf{D}=\frac{p}{n_t}\mathbf{I}_{n_t},$$

$\Gamma_{\mathrm{UPA}}(p,R)$ is quasi-concave with respect to $p\in[0,\overline{P}]$.

The conjectured property would facilitate analysis of the energy-efficiency maximum and is also useful in distributed power-allocation settings, where quasi-concavity supports equilibrium results. The source presents this as a conjecture, although the supplied parser evidence is inconsistent and does not establish a resolution.