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 will derive 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 will develop a qualitative and quantitative theory for the approximate diagonalization of operators associated with time-varying systems. These theoretical results will form a key stone in the construction of fast and reliable numerical equalization methods which will be based Krylov subspace techniques. The investigator will also study the use of frame theory in wireless communications. Using concepts from sphere packings and group theory he will analyze theoretical properties of special frames such as Grassmannian frames. Furthermore he will develop 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 research activity will enable further advances and breakthroughs in wireless communications. At the same time it will stimulate new research areas in applied mathematics and pave 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 will combine 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, since it provides the theoretical basis as well as the means for efficient numerical implementations. By improving radio link reliability and increasing data rates this research activity will be instrumental in fulfilling the increasing requirements on future wireless communications systems. The project will produce conceptual deliverables in the form of new mathematical methods to analyze and construct wireless transmission systems. The project will also produce concrete deliverables in the form of numerical algorithms for use in the scientific and industrial sector.
