Analysis and design of COFDM multicarrier modulation techniques in view of transmission stability in time variant channels

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The central goal of this project is the mathematical analysis and optimization of coded orthogonal frequency division multiplexing (COFDM) in view of transmission stability in wireless and other time variant environments. The resulting COFDM design should include an adaptive, channel dependent, choice of COFDM parameters such as code redundancy, symbol duration, guard interval length, and carrier frequencies. For years, OFDM has dominated multicarrier transmission systems in time invariant environments as present in xDSL applications. In such stationary set-ups, the carrier signals are approximate eigenfunctions of the channel operator, a phenomenon that can be enhanced by including a cyclic prefix. Recently, COFDM has been applied to mobile communications where the channel is generally time varying. Its structural optimality in this setting is not fully understood. Within mathematics on the other side, OFDM has been extensively studied under the disguise of Gabor analysis, where stability issues, synthesis and analysis algorithms, and carrier prototype function design are discussed at length. For example, including a cyclic prefix is covered by the more general mathematical concept of replacing an orthogonal synthesis and analysis system with biorthogonal Riesz basic sequences. Further, recent results in Gabor analysis aimed at the time frequency analysis of operators should lead to insights relating to slowly time varying operators as present in wireless systems. The applicability of Gabor analysis for COFDM design becomes even more evident when taking coding into account. The redundancy inherent in the transmitted data leads to a reduction of possible transmission signals. An integrative analysis of coding and modulation might lead to the choice of an a-priori over complete system, i.e., the well-studied Gabor frames might lead to a better utilization of channel capacity.