On the autocorrelation properties of truncated maximum-length sequences and their effect on the power spectrum

Marco Baldi; Franco Chiaraluce; Noureddine Boujnah; Roberto Garello

doi:10.1109/TSP.2010.2070500

On the autocorrelation properties of truncated maximum-length sequences and their effect on the power spectrum

Marco Baldi, Franco Chiaraluce, Noureddine Boujnah, Roberto Garello

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

Truncated maximum-length binary sequences are studied in this paper. The impact of truncation on their autocorrelation properties and power spectral density is investigated. Several new analytical results are given and validated through simulation. The first- and second-order statistics of the periodic autocorrelation function and the spectral peak amplitudes over the ensemble of all possible starting seeds are analyzed. Explicit bounds are found for the mean square of the periodic autocorrelation function. An analytical technique for evaluating the maximum spectral peak values is derived. As a case study, high data rate space links using LFSR randomizers are considered. Truncation may induce high peaks in the spectrum, requiring suitable margins to comply with power flux density constraints. The new results allow to analytically estimate the margin, providing useful information for the link design.

Original language	English
Article number	5557829
Pages (from-to)	6284-6297
Number of pages	14
Journal	IEEE Transactions on Signal Processing
Volume	58
Issue number	12
DOIs	https://doi.org/10.1109/TSP.2010.2070500
Publication status	Published - Dec 2010
Externally published	Yes

Keywords

Linear feedback shift registers
maximum-length sequences
periodic autocorrelation function
truncation noise

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10.1109/TSP.2010.2070500

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title = "On the autocorrelation properties of truncated maximum-length sequences and their effect on the power spectrum",

abstract = "Truncated maximum-length binary sequences are studied in this paper. The impact of truncation on their autocorrelation properties and power spectral density is investigated. Several new analytical results are given and validated through simulation. The first- and second-order statistics of the periodic autocorrelation function and the spectral peak amplitudes over the ensemble of all possible starting seeds are analyzed. Explicit bounds are found for the mean square of the periodic autocorrelation function. An analytical technique for evaluating the maximum spectral peak values is derived. As a case study, high data rate space links using LFSR randomizers are considered. Truncation may induce high peaks in the spectrum, requiring suitable margins to comply with power flux density constraints. The new results allow to analytically estimate the margin, providing useful information for the link design.",

keywords = "Linear feedback shift registers, maximum-length sequences, periodic autocorrelation function, truncation noise",

author = "Marco Baldi and Franco Chiaraluce and Noureddine Boujnah and Roberto Garello",

note = "Funding Information: Manuscript received February 26, 2010; accepted August 05, 2010. Date of publication August 26, 2010; date of current version November 17, 2010. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Maja Bystrom. This work has been sponsored in part by the European Space Agency, under the ESOC Contract 20959/07/D/MRP.",

year = "2010",

month = dec,

doi = "10.1109/TSP.2010.2070500",

language = "English",

volume = "58",

pages = "6284--6297",

journal = "IEEE Transactions on Signal Processing",

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AU - Baldi, Marco

AU - Chiaraluce, Franco

AU - Boujnah, Noureddine

AU - Garello, Roberto

N1 - Funding Information: Manuscript received February 26, 2010; accepted August 05, 2010. Date of publication August 26, 2010; date of current version November 17, 2010. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Maja Bystrom. This work has been sponsored in part by the European Space Agency, under the ESOC Contract 20959/07/D/MRP.

PY - 2010/12

Y1 - 2010/12

N2 - Truncated maximum-length binary sequences are studied in this paper. The impact of truncation on their autocorrelation properties and power spectral density is investigated. Several new analytical results are given and validated through simulation. The first- and second-order statistics of the periodic autocorrelation function and the spectral peak amplitudes over the ensemble of all possible starting seeds are analyzed. Explicit bounds are found for the mean square of the periodic autocorrelation function. An analytical technique for evaluating the maximum spectral peak values is derived. As a case study, high data rate space links using LFSR randomizers are considered. Truncation may induce high peaks in the spectrum, requiring suitable margins to comply with power flux density constraints. The new results allow to analytically estimate the margin, providing useful information for the link design.

AB - Truncated maximum-length binary sequences are studied in this paper. The impact of truncation on their autocorrelation properties and power spectral density is investigated. Several new analytical results are given and validated through simulation. The first- and second-order statistics of the periodic autocorrelation function and the spectral peak amplitudes over the ensemble of all possible starting seeds are analyzed. Explicit bounds are found for the mean square of the periodic autocorrelation function. An analytical technique for evaluating the maximum spectral peak values is derived. As a case study, high data rate space links using LFSR randomizers are considered. Truncation may induce high peaks in the spectrum, requiring suitable margins to comply with power flux density constraints. The new results allow to analytically estimate the margin, providing useful information for the link design.

KW - Linear feedback shift registers

KW - maximum-length sequences

KW - periodic autocorrelation function

KW - truncation noise

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DO - 10.1109/TSP.2010.2070500

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JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

SN - 1053-587X

IS - 12

M1 - 5557829

ER -

On the autocorrelation properties of truncated maximum-length sequences and their effect on the power spectrum

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Keywords

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