We introduce a general framework for OFDM pulse shape design and demonstrate how to obtain a pulse optimally matched to given channel properties. Furthermore, standard OFDM systems are associated with a rectangular grid in the time-frequency plane, which is not optimal for pulse-shaping OFDM systems for doubly dispersive channels. We introduce Lattice OFDM systems which are OFDM systems using general lattices in the time-frequency plane.

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