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
Authors | Amini, A., Mohajerin Esfahani, P., Ghavami, M. and Marvasti, F. |
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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. |
Keywords | Orthogonal UWB pulses; Sturm-Liouville theory; spectral mask |
Year | 2019 |
Journal | Signal Processing |
Journal citation | 159 (2019), pp. 147-158 |
Publisher | Elsevier |
ISSN | 0165-1684 |
Digital Object Identifier (DOI) | https://doi.org/10.1016/j.sigpro.2019.02.008 |
Web address (URL) | http://www.scopus.com/inward/record.url?eid=2-s2.0-85061329235&partnerID=MN8TOARS |
Publication dates | |
08 Feb 2019 | |
2019 | |
Publication process dates | |
Deposited | 07 Feb 2019 |
Accepted | 06 Feb 2019 |
Accepted author manuscript | License File Access Level Open |
ISBN | 01651684 |
https://openresearch.lsbu.ac.uk/item/867v1
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