Typical Peak Sidelobe Level of Binary Sequences
For a binary sequence Sn = {si: i=1,2,...,n} E [epsilon] {±1}n [superscript n] , n > 1, the peak sidelobe level (PSL) is defined as M(Sn [subscript n])= max [subscript k=1,2,...,n-1| [divided by] E [epsilon superscript n-k subscript i=1 s [subscript 1] S [subscript 1 = k]. It is shown that the di...
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| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers
2011
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| Online Access: | http://hdl.handle.net/1721.1/62543 |
| _version_ | 1811087808873365504 |
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| author | Alon, Noga Litsyn, Simon Shpunt, Alexander Anatoly |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Alon, Noga Litsyn, Simon Shpunt, Alexander Anatoly |
| author_sort | Alon, Noga |
| collection | MIT |
| description | For a binary sequence Sn = {si: i=1,2,...,n} E [epsilon] {±1}n [superscript n] , n > 1, the peak sidelobe level (PSL) is defined as M(Sn [subscript n])= max [subscript k=1,2,...,n-1| [divided by] E [epsilon superscript n-k subscript i=1 s [subscript 1] S [subscript 1 = k]. It is shown that the distribution of M(Sn) is strongly concentrated, and asymptotically almost surely y [gamma] {S [subscript n])=M(Sn [subscript n] [divided by] [square root of] n 1n n E [epsilon] [1-o(1), [square root of] 2]. Explicit bounds for the number of sequences outside this range are provided. This improves on the best earlier known result due to Moon and Moser that the typical Y [gamma] (Sn {subscript n]) E [epsilon] [o(1 [divided by] [square root of] 1n n).2], and settles to the affirmative the conjecture of Dmitriev and Jedwab on the growth rate of the typical peak sidelobe. Finally, it is shown that modulo some natural conjecture, the typical Y [gamma](Sn [subscript n]) equals [square root of] 2 . |
| first_indexed | 2024-09-23T13:52:17Z |
| format | Article |
| id | mit-1721.1/62543 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:52:17Z |
| publishDate | 2011 |
| publisher | Institute of Electrical and Electronics Engineers |
| record_format | dspace |
| spelling | mit-1721.1/625432022-09-28T16:45:02Z Typical Peak Sidelobe Level of Binary Sequences Alon, Noga Litsyn, Simon Shpunt, Alexander Anatoly Massachusetts Institute of Technology. Department of Physics Shpunt, Alexander Anatoly Shpunt, Alexander Anatoly For a binary sequence Sn = {si: i=1,2,...,n} E [epsilon] {±1}n [superscript n] , n > 1, the peak sidelobe level (PSL) is defined as M(Sn [subscript n])= max [subscript k=1,2,...,n-1| [divided by] E [epsilon superscript n-k subscript i=1 s [subscript 1] S [subscript 1 = k]. It is shown that the distribution of M(Sn) is strongly concentrated, and asymptotically almost surely y [gamma] {S [subscript n])=M(Sn [subscript n] [divided by] [square root of] n 1n n E [epsilon] [1-o(1), [square root of] 2]. Explicit bounds for the number of sequences outside this range are provided. This improves on the best earlier known result due to Moon and Moser that the typical Y [gamma] (Sn {subscript n]) E [epsilon] [o(1 [divided by] [square root of] 1n n).2], and settles to the affirmative the conjecture of Dmitriev and Jedwab on the growth rate of the typical peak sidelobe. Finally, it is shown that modulo some natural conjecture, the typical Y [gamma](Sn [subscript n]) equals [square root of] 2 . United States-Israel Binational Science Foundation European Research Council Israel Science Foundation (Grant 1177/06) Massachusetts Institute of Technology. Di Capua Graduate Fellowship 2011-04-25T20:51:29Z 2011-04-25T20:51:29Z 2009-12 2009-02 Article http://purl.org/eprint/type/JournalArticle 0018-9448 http://hdl.handle.net/1721.1/62543 Alon, N., S. Litsyn, and A. Shpunt. “Typical Peak Sidelobe Level of Binary Sequences.” Information Theory, IEEE Transactions On 56.1 (2010) : 545-554. Copyright © 2010, IEEE en_US http://dx.doi.org/10.1109/tit.2009.2034803 IEEE transactions on information theory Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Institute of Electrical and Electronics Engineers IEEE |
| spellingShingle | Alon, Noga Litsyn, Simon Shpunt, Alexander Anatoly Typical Peak Sidelobe Level of Binary Sequences |
| title | Typical Peak Sidelobe Level of Binary Sequences |
| title_full | Typical Peak Sidelobe Level of Binary Sequences |
| title_fullStr | Typical Peak Sidelobe Level of Binary Sequences |
| title_full_unstemmed | Typical Peak Sidelobe Level of Binary Sequences |
| title_short | Typical Peak Sidelobe Level of Binary Sequences |
| title_sort | typical peak sidelobe level of binary sequences |
| url | http://hdl.handle.net/1721.1/62543 |
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