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.