F. Hlawatsch, G. Tauböck, G. Matz:

"Pulse-shaping multicarrier transmission over underspread fading channels: A time-frequency perspective";

Talk: Joint Workshop on Coding and Communications (JWCC), Dürnstein (invited); 10-14-2007 - 10-16-2007.

Although hardly used in practical systems so far, pulse-shaping multicarrier (MC) modulation has a number of advantages over conventional cyclic-preﬁx OFDM modulation. In this tutorial presentation, we discuss the transmission of pulse-shaping MC signals over underspread doubly-dispersive fading channels satisfying the wide-sense stationary uncorrelated scattering (WSSUS) assumption. We emphasize aspects related to time-frequency and frame theory, Gabor transforms and Gabor multipliers, operator symbols, and operator diagonalization. Pulse-shaping MC transmission over underspread channels can be motivated by the fact that the components of the MC signal (the "logons" or Weyl-Heisenberg basis functions) are approximate eigenfunctions of underspread linear time-varying (LTV) systems. This issue is related to the approximation of underspread LTV systems by a simple special type of LTV systems known as a Gabor multiplier, and corresponds to a time-frequency sampling of the system´s time-varying transfer function (or operator symbol). The channel is approximately diagonalized by the Weyl-Heisenberg basis underlying the MC signal, and this fact radically simpliﬁes both the analysis and the equalization of channel effects. We investigate the quality of this diagonalization approximation via expressions of and bounds on the diagonalization error, i.e., the intersymbol interference (ISI) and intercarrier interference (ICI). The importance of good time-frequency localization of the transmit and receive pulses is demonstrated, and recent frame-theoretic results regarding time-frequency localization are discussed. We furthermore review some recent information-theoretic results on the capacity of underspread WSSUS channels, which are again based on the diagonalization approximation. Finally, the case of rapidly varying channels where ICI can no longer be neglected and needs to be equalized is brieﬂy addressed. We discuss a band model for the ICI and present an equalization algorithm that exploits the band structure for a reduction of complexity.

pulse-shaping multicarrier modulation, OFDM, underspread channels, doubly-selective channels, frame theory, Gabor transform, time-varying channels, intercarrier interference, equalization

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