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27038 Spectrum efficient, localized, orthogonal waveforms: closing the gap with the Balian-low theorem
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Korevaar, C.W. and Kokkeler, A.B.J. and de Boer, P.T. and Smit, G.J.M. (2016) Spectrum efficient, localized, orthogonal waveforms: closing the gap with the Balian-low theorem. IEEE transactions on communications, 64 (5). pp. 2155-2165. ISSN 0090-6778 *** ISI Impact 2,298 ***

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Official URL: http://dx.doi.org/10.1109/TCOMM.2016.2535333

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Abstract

The Balian-Low theorem (BLT) states the fundamental impossibility to design waveforms for L2(ℝ), which 1) form an orthogonal set, 2) are time-frequency localized, and 3) attain a critical waveform density such that they form an orthogonal basis. This article closes the gap between existing waveform designs and the BLT. The main contribution is the design of orthogonal, time-frequency localized, spectrum efficient waveforms for hexagonal lattices. The waveform design is adaptive by a single design parameter, which trades off time-frequency localization with the waveform density. As the orthogonalization procedure is based on employing the minimum number of most time-frequency localized waveforms (Hermite functions) it is argued that the results may be optimal in terms of combined spectrum efficiency and time-frequency localization. An example is provided for waveforms for a hexagonal lattice, which are quasi-orthogonal, time-frequency localized, and up to 99% of the critical waveform density. Although the designed waveforms are not strictly orthogonal, their cross-correlation can be made arbitrarily small. The robustness in doubly dispersive channels and the efficiency for multiuser scenarios are discussed and compared to conventional orthogonal frequency division multiplexing (OFDM).

Item Type:Article
Research Group:EWI-CAES: Computer Architecture for Embedded Systems, EWI-DACS: Design and Analysis of Communication Systems
Research Program:CTIT-General
Research Project:TSP: Tracking, tracing, Sensoring Platform
Uncontrolled Keywords:Balian-low theorem
Hermite functions
Pulse shaping
hexagonal lattice communications
orthogonal frequency division multiplexing (OFDM)
ID Code:27038
Status:Published
Deposited On:16 June 2016
Refereed:Yes
International:Yes
ISI Impact Factor:2,298
More Information:statisticsmetis

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