Orthogonal frequency division multiplexing (OFDM) has gained considerable interest as an efficient technology for high-date-data transmission over wireless channels. The design of pulseshapes that are well-localized in the time-frequency plane is of great importance in order to combat intersymbol interference and interchannel interference caused by the mobile radio channel. Recently proposed methods to construct such well-localized (orthogonal) functions are utilizing the link between OFDM and Gabor systems. We derive a theoretical framework that shows why and under which conditions these methods will yield well-localized pulse shapes. In our analysis we exploit the connection between Gabor systems, Laurent operators and the classical work of Gelfand, Raikov, and Shilov on commutative Banach algebras. In the language of Gabor analysis we derive a general condition under which the dual window and the canonical tight window inherit the decay properties of the analysis window.
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