The Status of Costas Array Construction

Golomb, Solomon W.

doi:10.1109/ciss.2006.286525

Cited by 3 publications

(4 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Grating lobes are caused by maxima of R 2 (τ ) that appear at τ (k) = k tp∆f t p where k = 0, ±1, ±2 • • • ± floor(t p ∆f ). In the case of rectangular pulses, R 1 ( τ tp ) has a triangular shape and R( τ tp ) shows equally spaced, linearly decreasing grating lobes, as shown in Fig 3, for the Costas code [2,6,3,8,7,5,1,4] and ∆f = 5 tp . Based on the above considerations, a change in Costas pulse waveforms must be operated in order to shape pulse ACF R 1 ( τ tp ) in such a way that, when combined with R 2 ( τ tp ), grating lobes are lowered.…”

Section: Costas Signal Modification 21 Orthogonality Constraint and mentioning

confidence: 91%

“…Ideally, it should be a 2D dirac of maximized energy in (τ, ν) = (0, 0) and zero elsewhere. The properties of Costas codes allow better approximation of the ideal ambiguity function AF, as shown in Fig 2, where the AF of the Costas code [2,6,3,8,7,5,1,4] is plotted. The thumbtack behavior can be clearly seen and all sidelobes have amplitude 1/M , except a few close to the origin, which are a little bit higher.…”

Section: Introductionmentioning

confidence: 99%

“…The thumbtack behavior can be clearly seen and all sidelobes have amplitude 1/M , except a few close to the origin, which are a little bit higher. The literature proposes algorithms for building such codes [4], [5], [6]. A more general approach consists in searching among all possible sequences of length M (all M!…”

Section: Introductionmentioning

confidence: 99%

“…The literature proposes algorithms for building such codes [4–6]. A more general approach consists in searching among all possible sequences of length M (all M !…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Design and performances evaluation of new Costas‐based radar waveforms with pulse coding diversity

Touati

Tatkeu

Chonavel³

et al. 2016

IET Radar, Sonar & Navigation

View full text Add to dashboard Cite

Costas codes are a variant of pulse compression waveforms, largely studied for their attractive time-frequency properties. Their 'thumbtack-like' ambiguity function (AF) makes them highly suitable for delay and Doppler estimation, in radar and sonar applications. However, this behaviour depends heavily on the length of the code: the improvement in delay-Doppler resolutions and AF sidelobes level needs an increase in the size of the code. In this study, designs that allow good performance without increasing the size of the code are proposed. They are based on a modification of Costas codes by widening frequency separation between hops and replacing rectangular pulses by other waveforms. This will lead to a removal of autocorrelation function grating lobes that normally appear when frequency separation is increased. The originality of the work lies in the proposal of diversified pulse waveforms, such as phase codes, Slepian sequences, and other Costas codes, to encode main Costas pulses. A performance comparison of the proposed approaches is supplied. Such waveforms could also be of interest for applications where waveform diversity is desired

show abstract

Section: Costas Signal Modification 21 Orthogonality Constraint and mentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The literature proposes algorithms for building such codes [4–6]. A more general approach consists in searching among all possible sequences of length M (all M !…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Design and performances evaluation of new Costas‐based radar waveforms with pulse coding diversity

Touati

Tatkeu

Chonavel³

et al. 2016

IET Radar, Sonar & Navigation

View full text Add to dashboard Cite

show abstract

Study of construction of Golomb Costas arrays with ideal autocorrelation properties based on extension field

Yao,

Liu,

Wang

2024

IET Communications

View full text Add to dashboard Cite

This paper proposes a specific algebraic structure and demonstrates its nature as an extension field, enabling the construction of Golomb Costas (GC) arrays. It provides detailed instructions and examples for constructing GC arrays using this extension field, along with a corresponding flowchart. Additionally, the paper conducts a thorough analysis, incorporating calculations and comparisons, to evaluate the autocorrelation of a GC array derived from the extension field compared to that of a diagonal frequency hopping array. The analysis reveals the superior autocorrelation properties of GC arrays based on the extension field. Furthermore, the paper establishes a mathematical model for the signal coded by the frequency hopping array and subsequently simulates and compares the ambiguity function of the signal coded by a GC array with that of a signal coded by a diagonal frequency hopping array. This comparison underscores the thumbtack ambiguity function of frequency hopping signal coded by a GC array. Moreover, the paper thoroughly investigates the relationship between the correlation function of GC arrays and the roots of an algebraic equation in a finite field, and strictly proves the ideal autocorrelation properties of Golomb Costas arrays.

show abstract

The Status of Costas Arrays

Golomb

Gong

2007

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

The Status of Costas Array Construction

Abstract: To date, two approaches have been followed to identify Costas arrays. One has been exhaustive search,

Cited by 3 publications

References 11 publications

Design and performances evaluation of new Costas‐based radar waveforms with pulse coding diversity

Design and performances evaluation of new Costas‐based radar waveforms with pulse coding diversity

Study of construction of Golomb Costas arrays with ideal autocorrelation properties based on extension field

The Status of Costas Arrays

Contact Info

Product

Resources

About