Towards a characterization of localization performance in networks with random geometries

A Statistical Characterization of Localization Performance in Wireless Networks

“…In this work, the authors modeled a cellular network with a homogeneous Poisson point process (PPP), which consequently allowed them to derive bounds on L-localizability, i.e., the probability that a mobile device can hear at least L base stations for participation in a localization procedure. 1 Further, by employing a "dominant interferer analysis," they were able to derive an accurate expression for the probability of L-localizability, which can easily be extended to give the probability of hearing a given number of anchor nodes for participation in a localization procedure. 1 The term hearability (or hearable) is used to describe anchor nodes that are able to participate in a localization procedure, i.e., their received SINR at the target is above some threshold.…”

“…1 Further, by employing a "dominant interferer analysis," they were able to derive an accurate expression for the probability of L-localizability, which can easily be extended to give the probability of hearing a given number of anchor nodes for participation in a localization procedure. 1 The term hearability (or hearable) is used to describe anchor nodes that are able to participate in a localization procedure, i.e., their received SINR at the target is above some threshold.…”

“…k = sin 2 2π − (Θ (L) − Θ(1) ) = sin 2 ∠ L ,(17)where the last two equalities follow from Definition 3. Hence, complete the proof by noting that the first sum may be equivalently expressed by replacing the internodal angles with their order statistics.APPENDIX B PROOF OF COROLLARY 2.1Using Lemma 2 and our assumption of a finite L, the pdf of ∠ (L−1) conditioned on L isf ∠ (L−1) (ϕ|L) = d dϕ F ∠ (L−1) (ϕ|L) = X n=0(−1) n L n n(n − 1)(L − 1) 2π 1 − nϕ 2π L−2…”