Exhaustive Search for Optimal Minimum Peak Sidelobe Binary Sequences up to Length 80

Leukhin, Anatolii N.; Potekhin, Egor N.

doi:10.1007/978-3-319-12325-7_14

Cited by 10 publications

(6 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We are in particular interested in constructive existence results. The value of m(n) has been determined via exhaustive search for all n ≤ 80 (see [63] for the latest results). Many authors have put considerable computational effort in finding binary sequences with small peak sidelobe level (see Nunn and Coxson [87] Turyn conjectured [108], [112, p. 198] that the infimum limit of m(n) is infinite.…”

Section: The Peak Sidelobe Level Of Binary Sequencesmentioning

confidence: 99%

Sequences with small correlation

Schmidt

2015

Des. Codes Cryptogr.

View full text Add to dashboard Cite

The extent to which a sequence of finite length differs from a shifted version of itself is measured by its aperiodic autocorrelations. Of particular interest are sequences whose entries are 1 or −1, called binary sequences, and sequences whose entries are complex numbers of unit magnitude, called unimodular sequences. Since the 1950s, there is sustained interest in sequences with small aperiodic autocorrelations relative to the sequence length. One of the main motivations is that a sequence with small aperiodic autocorrelations is intrinsically suited for the separation of signals from noise, and therefore has natural applications in digital communications. This survey reviews the state of knowledge concerning the two central problems in this area: How small can the aperiodic autocorrelations of a binary or a unimodular sequence collectively be and how can we efficiently find the best such sequences? Since the analysis and construction of sequences with small aperiodic autocorrelations is closely tied to the (often much easier) analysis of periodic autocorrelation properties, several fundamental results on corresponding problems in the periodic setting are also reviewed.

show abstract

Section: The Peak Sidelobe Level Of Binary Sequencesmentioning

confidence: 99%

Sequences with small correlation

Schmidt

2015

Des. Codes Cryptogr.

View full text Add to dashboard Cite

show abstract

“…Thus, currently, initiating an exhaustive search is the only way to reveal an optimal PSL value for binary sequences of some fixed length. Given a binary sequence with length n, the PSL-optimal values for n ≤ 40 [9], n ≤ 48 [10], n = 64 [11], n ≤ 68 [12], n ≤ 74 [13], n ≤ 80 [14], n ≤ 82 [15] and n ≤ 84 [16] are obtained. However, the PSL-optimal values of binary sequences with lengths n greater than 84 are still unknown.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Constructions of Binary Sequences with Low Autocorrelation Sidelobes

Dimitrov¹,

Baitcheva²,

Nikolov³

2021

Preprint

View full text Add to dashboard Cite

In this work, a classical problem of the digital sequence design, or more precisely, finding binary sequences with optimal peak sidelobe level (PSL), is revisited. By combining some of our previous works, together with some mathematical insights, few hybrid heuristic algorithms were created. During our experiments, and by using the aforementioned algorithms, we were able to find PSL-optimal binary sequences for all those lengths, which were previously found during exhaustive searches by various papers throughout the literature. Then, by using a general-purpose computer, we further demonstrate the effectiveness of the proposed algorithms by revealing binary sequences with lengths between 106 and 300, the majority of which possess record-breaking PSL values. Then, by using some well known algebraic constructions, we outline few strategies of finding highly-competitive binary sequences, which could be efficiently optimized, in terms of PSL, by the proposed algorithms.

show abstract

“…Thus, currently, initiating an exhaustive search is the only way to reveal an optimal PSL value for binary sequences of some fixed length. Given a binary sequence with length n, the PSL-optimal values for n 8 40 [9], n 8 48 [10], n 64 [11], n 8 68 [12], n 8 74 [13], n 8 80 [14], n 8 82 [15] and n 8 84 [16] are obtained. However, the PSL-optimal values of binary sequences with lengths n greater than 84 are still unknown.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Constructions of Binary Sequences With Low Autocorrelation Sideobes

Dimitrov

Baicheva

Nikolov³

2021

IEEE Access

View full text Add to dashboard Cite

In this work, a classical problem of the digital sequence design, or more precisely, finding binary sequences with optimal peak sidelobe level (PSL), is revisited. By combining some of our previous works, together with some mathematical insights, few hybrid heuristic algorithms were created. During our experiments, and by using the aforementioned algorithms, we were able to find PSL-optimal binary sequences for all those lengths, which were previously found during exhaustive searches by various papers throughout the literature. Then, by using a general-purpose computer, we further demonstrate the effectiveness of the proposed algorithms by revealing binary sequences with lengths between 106 and 300, the majority of which possess record-breaking PSL values. Then, by using some well-known algebraic constructions, we outline few strategies for finding highly competitive binary sequences, which could be efficiently optimized, in terms of PSL, by the proposed algorithms.

show abstract

Exhaustive Search for Optimal Minimum Peak Sidelobe Binary Sequences up to Length 80

Cited by 10 publications

References 24 publications

Sequences with small correlation

Sequences with small correlation

Hybrid Constructions of Binary Sequences with Low Autocorrelation Sidelobes

Hybrid Constructions of Binary Sequences With Low Autocorrelation Sideobes

Contact Info

Product

Resources

About