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Modern Harmonic Analysis (HA) is a highly active mathematical discipline that employs powerful methods from several different mathematical areas, and whose techniques and results are potentially relevant to Signal Processing and Telecommunications. The proposed project is a joint interdisciplinary effort of two research groups in HA and signal processing/wireless communications

Recently, fundamental results in the HA areas of Gabor transforms (GT) and pseudodifferential operators have been obtained by members of our groups. These results create promising opportunities and orientations for future mathematical work. Moreover, joint discussions have suggested a strong potential of these recent results and of future HA research for successful application in wireless communications. This potential is primarily based on the correspondences existing between the GT and multicarrier modulation techniques, and between so-called Gabor multiplier operators and time-varying wireless channels.

The general objective of the project is to capitalize on these opportunities and potentials and put HA results to practical use in wireless communications. The purpose of this project is

• to perform advanced mathematical research in HA, continuing the successful directions mentioned above with a specific orientation towards topics relevant to wireless communications,
• and to develop improved techniques for wireless communications based on existing and future results of HA.

The application of advanced HA methods and results in wireless communications research is expected to yield important benefits. Future wireless communication systems (e.g., the next generation of mobile radio systems, often referred to as ''4G'' or ''Beyond 3G'' ) are supposed to offer higher data rates, reliability, and energy efficiency. Achieving these goals will require substantially improved transmitter and receiver (transceiver) techniques for modulation, demodulation, equalization, detection, synchronization, and channel estimation. These techniques must be suited to the time-varying wireless channels encountered in mobility-dominated scenarios. The results of this project will be an important contribution to the design of wireless communication systems meeting these future demands, and thus the project is expected to have significant industrial impact.

The transfer of existing and future HA results into wireless communications research will be based on

• the development of pertinent mathematical formulations and refined mathematical models of wireless communications, and identification of problems in wireless communications that will stimulate practically relevant HA research;
• the derivation of new results in HA and their application to the development of improved wireless communication techniques.

The resulting cross-fertilization of HA and wireless communications will provide important new impulses to both fields. The mathematics developed is likely to be useful also for other areas, such as underwater acoustics as well as geophysical or astronomical signal processing.