Optimal OFDM design for time-frequency dispersive channels

Thomas Strohmer and Scott Beaver

Transmission over wireless channels is subject to time dispersion due to multipath propagation as well as frequency dispersion due to the Doppler effect. Standard OFDM systems using a guard time interval or cyclic prefix combat intersymbol interference but provide no protection against intersymbol interference. This drawback has lead to the introduction of pulse-shaping OFDM systems. In the first part of the paper we 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. In the second part of the paper we 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 optimally design LOFDM systems (the lattice and the pulse shape) for time- and 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.

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