Binary and quadriphase sequences with optimal autocorrelation properties: a survey

Lüke, Hans Dieter; Schotten, Hans D.; Hadinejad-Mahram, H.

doi:10.1109/tit.2003.820035

Cited by 127 publications

(46 citation statements)

References 36 publications

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“…An example of quadriphase sequences with ǫ = 1 is the complementary-based sequence. Sequences with other values of ǫ such as 2, 3, and 4, can be found in [28]. The following Lemma shows that for a nearly perfect sequence, µ(A) is bounded by √ 1 + ǫ. Lemma 1 (Bound on the coherence parameter): Let the complex-valued matrix A be defined by (11) where σ = s. If s is a unimodular perfect sequence, then µ(A) = 1.…”

Section: B Main Resultsmentioning

confidence: 99%

Convolutional Compressed Sensing Using Deterministic Sequences

Liu

Ling

2013

IEEE Trans. Signal Process.

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Abstract-In this paper, a new class of circulant matrices built from deterministic sequences is proposed for convolutionbased compressed sensing (CS). In contrast to random convolution, the coefficients of the underlying filter are given by the discrete Fourier transform of a deterministic sequence with good autocorrelation. Both uniform recovery and non-uniform recovery of sparse signals are investigated, based on the coherence parameter of the proposed sensing matrices. Many examples of the sequences are investigated, particularly the Frank-ZadoffChu (FZC) sequence, the m-sequence and the Golay sequence. A salient feature of the proposed sensing matrices is that they can not only handle sparse signals in the time domain, but also those in the frequency and/or or discrete-cosine transform (DCT) domain.

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Section: B Main Resultsmentioning

confidence: 99%

Convolutional Compressed Sensing Using Deterministic Sequences

Liu

Ling

2013

IEEE Trans. Signal Process.

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“…In work on binary sequences, 23 it has been shown that relaxing the requirement for ideal autocovariance enables more different length sequences to be formed. This should also be possible for the ternary sequence case.…”

Section: Array Discussionmentioning

confidence: 99%

Ternary and quadriphase sequence diffusers

Cox

Angus

D’Antonio³

2006

The Journal of the Acoustical Society of America

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A room acoustic diffuser breaks up reflected wavefronts, and this can be achieved by presenting a spatially varying surface impedance. In hybrid surfaces, varying impedance is achieved by patches of absorption and reflection, giving reflection coefficients nominally of 0 and 1. These surfaces are hybrids, absorbing some of the incident sound while diffusing any reflected energy. A problem with planar hybrid surfaces is that specular energy is only removed by absorption. By exploiting interference, by reflecting waves out-of-phase with the specular energy, it is possible to diminish the specular energy further. This can be achieved by using a diffuser based on a ternary sequence that nominally has reflection coefficients of 0, −1, and +1. Ternary sequences are therefore a way of forming hybrid absorber-diffusers that achieve better scattering performance without additional absorption. This paper discusses methods for making ternary sequence diffusers, including giving sequence generation methods. It presents prediction results based on Fourier and boundary element method models to examine the performance. While ternary diffusers have better performance than unipolar binary diffusers at most frequencies, there are frequencies at which the performances are the same. This can be overcome by forming diffusers from four-level, quadriphase sequences.

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“…From a finite field approach, furthermore, binary sequences of period AE Ô Ñ ½ for odd prime Ô corresponding to cases 3) and 4) are also described in [16] and [23], respectively. For a survey of binary and quadriphase sequences with optimal autocorrelation, see [19].…”

Section: Preliminariesmentioning

confidence: 99%

New Binary Sequences With Optimal Autocorrelation Magnitude

Gong

2008

IEEE Trans. Inform. Theory

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New binary sequences of period AE 3 Ñ ½µ for even Ñ are found. These sequences can be described by a ¢´¾ Ñ ½µ interleaved structure. The new sequences are almost balanced and have four-valued autocorrelation, i.e., AE ¼ ¦ , which is optimal with respect to autocorrelation magnitude.Complete autocorrelation distribution and exact linear complexity of the sequences are mathematically derived. From the simple implementation with a small number of shift registers and a connector, the sequences have a benefit of obtaining large linear complexity.

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Binary and quadriphase sequences with optimal autocorrelation properties: a survey

Cited by 127 publications

References 36 publications

Convolutional Compressed Sensing Using Deterministic Sequences

Convolutional Compressed Sensing Using Deterministic Sequences

Ternary and quadriphase sequence diffusers

New Binary Sequences With Optimal Autocorrelation Magnitude

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