, is asymptotically normally distributed as $$\begin{gathered} \label{eq:asyc0_MAI_MP_lemma} a\sim\mathcal{N}\left(0\,,\,\frac{E}{N_c}\textrm{E}\{\sigma^0_{MAI,k}(\epsilon_k)\}\right),\end{gathered}$$ where $$\begin{aligned} \label{eq: