Explore the mathematics behind signal design for communication systems in this lecture by Holger Boche from TU München. Delve into the challenges of orthogonal transmission schemes, focusing on their high dynamical behavior and its impact on system performance and efficiency. Discover the connections between this problem and various mathematical fields, including functional analysis, additive combinatorics, and harmonic analysis. Examine the Peak-to-Average power ratio (PAPR) reduction problem and its relationship to Szemerédi's Theorem on arithmetic progressions. Investigate necessary and sufficient conditions for solving the PAPR problem in OFDM and CDMA systems, and learn about asymptotic tightenings and perfect Walsh sums. Gain insights into the interdisciplinary nature of signal processing and its applications in modern communication standards.