Uniqueness of the local maximum of the aerial-base-station coverage function

Let $\gamma$ be a QoS requirement and let $f_c$ be an operating frequency. For the propagation environments whose parameters are listed in Table 1, define

$$\Gamma(\alpha) = \frac{10^{\frac{\gamma-(A P(\alpha)+B)}{10}}}{1+\alpha^2},$$

where $\alpha\in[0,\infty]$ and $P(\alpha)$ is the propagation-model function. Uniqueness conjecture. For any $\gamma$ and $f_c$, if a local maximum exists for $\Gamma(\alpha)$, then it is the only local maximum of $\Gamma(\alpha)$ on $[0,\infty]$ for each of the listed propagation environments. The uniqueness of this maximum would justify selecting the optimal elevation-to-coverage-radius ratio by one-dimensional maximization of $\Gamma(\alpha)$, although the statement is presented without a proof in the source.