Secrecy Outage Probability: Revisited

This paper technically explores the secrecy outage probability (SOP) $\Lambda$ and a minimisation problem over it as $\mathop{{\rm \mathbb{M}in}}\limits_{(\cdot) } {\rm \; } \mathbb{P}\mathscr{r} \big( \Lambda \ge \lambda \big) $. We consider a Riemannian manifold for it and we mathematically define a volume for it as $\mathbb{V}\mathscr{ol}\big \lbrace \Lambda \big \rbrace$. Through achieving a new upper-bound for the Riemannian manifold and its volume, we subsequently relate it to the number of eigenvalues existing in the relative probabilistic closure. We prove in-between some novel lemmas with the aid of some useful inequalities such as the Finsler's lemma, the generalised Young's inequality, the generalised Brunn-Minkowski inequality, the Talagrand's concentration inequality.