This textbook focuses on applications of compressed sensing (CS) and sub-Nyquist sampling techniques to wireless communications such as multi-carrier, IMIMO, UWB, LTE, 5G, Internet of Things, and machine learning. Written for an engineering audience, the book is presented in a strictly mathematical manner, and to keep it self-contained and accessible to engineering students it explains all the mathematical tools used. It also develops a generalization of CS to more structured signal models, which is necessary in order to apply CS to digital communication. The work is based on research material collected by the authors over recent years.

Philipp Walk is a member of IEEE and he received his Dipl.-Phys in mathematical physics in 2006 from the Technical University of Berlin (TUB), Berlin, Germany. He has been with the Department of Mobile Communications at TUB since 2007 and the Department of Theoretical Information Technology at the Technical University of München (TUM), Munich, Germany since 2010. He received his Dr.-rer.nat (Ph.D.) degree in 2014 (on Convolutions with Support Restrictions) from TUM and is currently working under the DFG grant WA 3390/1-1 at the California Institute of Technology, Pasadena, CA, United States, in the field of signal processing and communication theory. His current research interests are in the area of compressed sensing, Fourier analysis, time-frequency analysis and additive combinatorics. He has also been giving lectures on compressed sensing at TUM since 2014.  Peter Jung is a Member of IEEE and VDE/ITG. He received the Dipl.-Phys. in high energy physics in 2000 from Humboldt University, Berlin, Germany, in cooperation with DESY Hamburg. He has been with the Department of Broadband Mobile Communication Networks at Fraunhofer Institute for Telecommunications, Heinrich-Hertz-Institut (HHI) since 2001 and the Fraunhofer German-Sino Lab for Mobile Communications since 2004. He received his Dr.-rer.nat (Ph.D.) degree in 2007 (on Weyl--Heisenberg representations in Communication Theory) from the Technical University of Berlin (TUB), Germany and is currently working under DFG grants JU 2795/1-\&2\&3 at TUB in the field of signal processing and information and communication theory. His current research interests are in the area of compressed sensing, time-frequency analysis, dimension reduction and randomized algorithms. He has also been giving lectures in compressed sensing and estimation theory.

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