Orthogonal frequency division multiplexing (OFDM) has gained considerable interest as an efficient technology for high-date-data transmission over wireless channels. Standard OFDM systems are associated with a rectangular grid in the time-frequency plane. However such a setup is in general not optimum for pulse shaping OFDM systems for doubly dispersive channels. We introduce lattice-OFDM systems (LOFDM), which are OFDM systems constructed with respect to general lattices in the time-frequency plane. We show how to design optimum pulse shaping LOFDM system. Our analysis is based on results from Heisenberg groups, Gabor frames, and sphere coverings. Numerical simulations confirm that LOFDM systems outperform ordinary OFDM systems with regard to robustness against intersymbol interference and interchannel interference.
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