UWB Orthogonal Pulse Design using Sturm-Liouville Boundary Value Problem

Journal article


Amini, A, Mohajerin Esfahani, P, Ghavami, M and Marvasti, F (2019). UWB Orthogonal Pulse Design using Sturm-Liouville Boundary Value Problem. Signal Processing. 159 (2019), pp. 147-158. https://doi.org/10.1016/j.sigpro.2019.02.008
AuthorsAmini, A, Mohajerin Esfahani, P, Ghavami, M and Marvasti, F
Abstract

The problem of designing UWB pulses which meet specific spectrum requirements is usually treated by filtering common pulses such as Gaussian doublets, modified Hermite polynomials and wavelets. When there is the need to have a number of orthogonal pulses (e.g., in a multiuser scenario), a naive approach is to filter all the members of an orthogonal set, which is likely to destroy their orthogonality property. In this paper, we study the design of a set of pulses that simultaneously satisfy the orthogonality property and spectrum requirements. Our design is based on the eigenfunctions of Sturm-Liouville boundary value problems. Indeed, we introduce Sturm-Liouville differential equations for which the eigenfunctions meet the FCC mask constraints. Computer simulation results show that all such waveforms occupy almost 55% of the allowed spectrum (utilization efficiency). A comparison of the proposed method with some conventional techniques of orthogonal UWB pulse generation will demonstrate the advantages of the new proposal.

KeywordsOrthogonal UWB pulses; Sturm-Liouville theory; spectral mask
Year2019
JournalSignal Processing
Journal citation159 (2019), pp. 147-158
PublisherElsevier
ISSN0165-1684
Digital Object Identifier (DOI)https://doi.org/10.1016/j.sigpro.2019.02.008
Web address (URL)https://www.sciencedirect.com/science/article/pii/S016516841930057X?via%3Dihub
Publication dates
Print08 Feb 2019
Publication process dates
Deposited07 Feb 2019
Accepted06 Feb 2019
Accepted author manuscript
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Open
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