Time-Frequency Localization Measures for Packets of Orthogonally Multiplexed Signals

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Volume Title

A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Date

2019-09

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Mcode

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Language

en

Pages

12
6374-6385

Series

IEEE Transactions on Communications, Volume 67, issue 9

Abstract

We consider measures of time-frequency localization (TFL) for stochastic signals. The approach is complementary to the use of TFL in prototype filter design; here, TFL is instead applied to multiplexed waveform packets with the objective to evaluate multi-user interference in a multiple access scenario rather than combat channel dispersion. We show that a generalization of the Heisenberg parameter to N-D stochastic signals directly characterizes the localization of the inter-user interference in the time-frequency phase space. A tight bound is provided, which shows the fundamental tradeoff between the TFL of a packet and the orthogonality among the multiplexed waveforms inside the packet. The Hermite-Gauss waveforms are optimally localized with regard to this measure. We also derive the expressions for the TFL of a Gabor system consisting of N-t time and N-f frequency shifts of a prototype, on the conventional and staggered lattices. In the limit of large N, the particular properties of the prototype yield diminishing returns to the overall localization. Finally, we compare the performance of waveforms in a connectionless and asynchronous random access scenario. At lower access intensities, where the out-of-band emissions are the significant limiting factor, the outage probability for smaller access packets is shown to vary significantly between the modulations. This variability diminishes when N is increased, which is consistent with the presented theory.

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Keywords

Time-frequency localization, Heisenberg parameter, stochastic signals, orthogonal multiplexing, Hermite-Gauss functions, asynchronous random access, WAVE-FORMS, UNCERTAINTY PRINCIPLE, OFDM, DESIGN

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Citation

Boyd, C, Pitaval, R-A, Tirkkonen, O & Wichman, R 2019, ' Time-Frequency Localization Measures for Packets of Orthogonally Multiplexed Signals ', IEEE Transactions on Communications, vol. 67, no. 9, pp. 6374-6385 . https://doi.org/10.1109/TCOMM.2019.2923996