ECE 804 Lecture 004 Dr Vahid Tarokh The Theorem of Fisher–Tippett–Gnedenko скачать в хорошем качестве

ECE 804 Lecture 004 Dr Vahid Tarokh The Theorem of Fisher–Tippett–Gnedenko

One of the most profound results in Extreme Value Theory is the Theorem of Fisher-Tippett and Gnedenko. In spite of the fact that it is extremely powerful, it remains (in my opinion) highly under-appreciated (at least) in engineering. I will briefly review this theorem in an elementary manner. Then I will show some applications: a) It is well-known that Claude Shannon has computed the ultimate limit of transmission (capacity) for certain channels. However, the "ultimate throughput" of schedulers are not known. I will use the Theorem of Fisher-Tippett and Gnedenko, and derive the capacity of certain schedulers. b) Using the same theorem, I will discuss the ultimate gain of multiuser antenna selection diversity schemes. c) For a distributed random array (e.g. in radar or astronomy) scenario, I will indicate the distributions of the side-lobes using the same theorem. I note that there exist "Free Extreme Values" generalizations [Ben Arous and Voiculescu] of Fisher-Tippett-Gnedenko Theorem. I may also touch on this (non-elementary) topic.