Optimal OFDM design for time-frequency dispersive channels

Transmission over wireless channels is subject to time dispersion due to multipath propagation and to frequency dispersion due to the Doppler effect. Standard orthogonal frequency-division multiplexing (OFDM) systems, using a guard-time interval or cyclic prefix, combat intersymbol interference (ISI), but provide no protection against interchannel interference (ICI). This drawback has led to the introduction of pulse-shaping OFDM systems. We first present a general framework for pulse shape design. Our analysis shows that certain pulse shapes proposed in the literature are, in fact, optimal in a well-defined sense. Furthermore, our approach provides a simple way to adapt the pulse shape to varying channel conditions. We then show that (pulse-shaping) OFDM systems based on rectangular time-frequency lattices are not optimal for time- and frequency-dispersive wireless channels. This motivates the introduction of lattice-OFDM (LOFDM) systems which are based on general time-frequency lattices. Using results from sphere packing theory, we show how to design LOFDM systems (lattice and pulse shape) optimally for timeand frequency-dispersive channels in order to minimize the joint ISI/ICI. Our theoretical analysis is confirmed by numerical simulations, showing that LOFDM systems outperform traditional pulse-shaping OFDM systems with respect to robustness against ISI/ICI.