Mathematics of Signal Design for Communication Systems and Szemerédi’s and Green-Tao’s Theorems
Hausdorff Center for Mathematics via YouTube
Overview
Syllabus
Intro
Motivation - Orthogonal Transmission Scheme
Orthogonal Transmission Scheme - Sketch
Motivation - Dynamics of Orthogonal Transmission Scheme
Drawback of OFDM - The Effect of Clipping
Motivation - High Dynamics of Orthogonal Transmission Scheme
Motivation - Tone Reservation method
PAPR Reduction Problem - Remarks
Necessary and Sufficient Conditions - Essential Subspaces
Necessary Condition - Sketch of Proof
Outline
Solvability of PAPR Problem - OFDM
Szemerédi Theorem on Arithmetic Progressions
Szemerédi Theorem - Historical Remarks
Szemerédi Theorem - Asymptotic Case and Probabilistic Case
Solvability of PAPR reduction problem & Arithmetic Progressions
Asymptotic Tightenings of Thm. 3.7
Walsh functions
Perfect Walsh Sum
PAPR reduction problem for CDMA Case - PWS
Asymptotic results for PWS
Summary and Conclusions
PAPR Reduction Problem - Formulation
Taught by
Hausdorff Center for Mathematics