Applied Harmonic Analysis and Wireless Communications

University Of California-Davis, Davis CA

Investigators

Abstract

The increasing requirements on data rate and quality of service for wireless communications systems call for new techniques to improve radio link reliability and to increase spectral efficiency. The three key technologies to achieve these goals are equalization, diversity, and channel coding. Mathematics is of fundamental importance to these technologies, providing the theoretical basis as well as the means for efficient numerical implementations. The investigator derives a theoretical and numerical framework for designing equalization techniques for time-varying channels. Using methods from pseudo-differential operator theory and time-frequency analysis, he develops a qualitative and quantitative theory for the approximate diagonalization of operators associated with time-varying systems. These theoretical results form a keystone in the construction of fast and reliable numerical equalization methods that are based on Krylov subspace techniques. The investigator also studies the use of frame theory in wireless communications. Using concepts from sphere packings and group theory, he analyzes theoretical properties of special frames such as Grassmannian frames. Furthermore, he develops theoretical and numerical schemes in connection with multi-carrier communication systems such as OFDM. This includes the design of transmission signals with specific properties using a generalization of the concept of prolate spheroidal wave functions. By taking recent tools from harmonic analysis into the wireless communications community, this project enables further advances and breakthroughs in wireless communications. At the same time it stimulates new research areas in applied mathematics and paves the road for further interactions between applied mathematicians and communication engineers. The goal of this project is to develop mathematical concepts and computational methods for wireless communications technology. The investigator combines modern tools from mathematics with methods from information theory and signal processing to develop new concepts and algorithms for key technologies in wireless communications, such as coding, transmission, and equalization. Mathematics is of fundamental importance to these technologies, because it provides the theoretical basis as well as the means for efficient numerical implementations. By providing tools to improve radio link reliability and increase data rates, this project is instrumental in meeting the increasing requirements on future wireless communications systems. The project produces conceptual deliverables in the form of new mathematical methods to analyze and construct wireless transmission systems. The project also produces concrete deliverables in the form of numerical algorithms for use in the scientific and industrial sector.