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36
The finite HeisenbergWeyl group in radar and communications
 EURASIP Journal of Applied Signal Processing
"... We investigate the theory of the finite HeisenbergWeyl group in relation to the development of adaptive radar and to the construction of spreading sequences and errorcorrecting codes in communications. We contend that this group can form the basis for the representation of the radar environment i ..."
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Cited by 31 (3 self)
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We investigate the theory of the finite HeisenbergWeyl group in relation to the development of adaptive radar and to the construction of spreading sequences and errorcorrecting codes in communications. We contend that this group can form the basis for the representation of the radar environment in terms of operators on the space of waveforms. We also demonstrate, following recent developments in the theory of errorcorrecting codes, that the finite HeisenbergWeyl groups provide a unified basis for the construction of useful waveforms/sequences for radar, communications, and the theory of errorcorrecting codes. Copyright © 2006 S. D. Howard et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1.
Axel Thue's work on repetitions in words
 Invited Lecture at the 4th Conference on Formal Power Series and Algebraic Combinatorics
, 1992
"... The purpose of this survey is to present, in contemporary terminology, the fundamental contributions of Axel Thue to the study of combinatorial properties of sequences of symbols, insofar as repetitions are concerned. The present state of the art is also sketched. ..."
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Cited by 25 (3 self)
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The purpose of this survey is to present, in contemporary terminology, the fundamental contributions of Axel Thue to the study of combinatorial properties of sequences of symbols, insofar as repetitions are concerned. The present state of the art is also sketched.
On Cosets of the Generalized FirstOrder Reed–Muller Code with Low PMEPR
, 2006
"... Golay sequences are well suited for use as codewords in orthogonal frequencydivision multiplexing (OFDM) since their peaktomean envelope power ratio (PMEPR) in qary phaseshift keying (PSK) modulation is at most 2. It is known that a family of polyphase Golay sequences of length 2m organizes in ..."
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Cited by 21 (3 self)
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Golay sequences are well suited for use as codewords in orthogonal frequencydivision multiplexing (OFDM) since their peaktomean envelope power ratio (PMEPR) in qary phaseshift keying (PSK) modulation is at most 2. It is known that a family of polyphase Golay sequences of length 2m organizes in m!/2 cosets of a qary generalization of the firstorder Reed–Muller code, RMq(1, m). In this paper a more general construction technique for cosets of RMq(1, m) with low PMEPR is established. These cosets contain socalled nearcomplementary sequences. The application of this theory is then illustrated by providing some construction examples. First, it is shown that the m!/2 cosets of RMq(1, m) comprised of Golay sequences just arise as a special case. Second, further families of cosets of RMq(1, m) with maximum PMEPR between 2 and 4 are presented, showing that some previously unexplained phenomena can now be understood within a unified framework. A lower bound on the PMEPR of cosets of RMq(1, m) is proved as well, and it is demonstrated that the upper bound on the PMEPR is tight in many cases. Finally it is shown that all upper bounds on the PMEPR of cosets of RMq(1, m) also hold for the peaktoaverage power ratio (PAPR) under the Walsh–Hadamard transform.
A survey of the merit factor problem for binary sequences, Sequences and Their
 Applications, Proceedings of SETA 2004, Lecture Notes in Computer Science 3486, 30–55
, 2005
"... A classical problem of digital sequence design, first studied in the 1950s but still not well understood, is to determine those binary sequences whose aperiodic autocorrelations are collectively small according to some suitable measure. The merit factor is an important such measure, and the problem ..."
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Cited by 13 (7 self)
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A classical problem of digital sequence design, first studied in the 1950s but still not well understood, is to determine those binary sequences whose aperiodic autocorrelations are collectively small according to some suitable measure. The merit factor is an important such measure, and the problem of determining the best value of the merit factor of long binary sequences has resisted decades of attack by mathematicians and communications engineers. In equivalent guise, the determination of the best asymptotic merit factor is an unsolved problem in complex analysis proposed by Littlewood in the 1960s that until recently was studied along largely independent lines. The same problem is also studied in theoretical physics and theoretical chemistry as a notoriously difficult combinatorial optimisation problem. The best known value for the asymptotic merit factor has remained unchanged since 1988. However recent experimental and theoretical results strongly suggest a possible improvement. This survey describes the development of our understanding of the merit factor problem by bringing together results from several disciplines, and places the recent results within their historical and scientific framework. 1
Golay complementary array pairs
 Designs, Codes and Cryptography
"... Constructions and nonexistence conditions for multidimensional Golay complementary array pairs are reviewed. A construction for a ddimensional Golay array pair from a (d + 1)dimensional Golay array pair is given. This is used to explain and expand previously known constructive and nonexistence re ..."
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Cited by 7 (4 self)
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Constructions and nonexistence conditions for multidimensional Golay complementary array pairs are reviewed. A construction for a ddimensional Golay array pair from a (d + 1)dimensional Golay array pair is given. This is used to explain and expand previously known constructive and nonexistence results in the binary case.
AMBIGUITY FUNCTION AND FRAME THEORETIC PROPERTIES OF PERIODIC ZERO AUTOCORRELATION WAVEFORMS
"... Constant Amplitude Zero Autocorrelation (CAZAC) waveforms u are analyzed in terms of the ambiguity function Au. Elementary number theoretic considerations illustrate that peaks in Au are not stable under small pertubations in its domain. Further, it is proved that the analysis of vectorvalued CAZA ..."
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Cited by 7 (2 self)
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Constant Amplitude Zero Autocorrelation (CAZAC) waveforms u are analyzed in terms of the ambiguity function Au. Elementary number theoretic considerations illustrate that peaks in Au are not stable under small pertubations in its domain. Further, it is proved that the analysis of vectorvalued CAZAC waveforms depends on methods from the theory of frames. Finally, techniques are introduced to characterize the structure of Au, to compute u in terms of Au, and to evaluate MSE for CAZAC waveforms.
Peaktoaverage power ratio reduction of OFDM systems using cross entropy method
 in 17th Int. Conf. on Wireless Commun
, 2005
"... copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. The author reserves all other publication and other rights in association with the copyright in the thesis, and except as herein before provided, neither the thesis nor any substantial ..."
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Cited by 5 (4 self)
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copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. The author reserves all other publication and other rights in association with the copyright in the thesis, and except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatever without the author’s prior written permission.
Generalised complementary arrays
 Lecture Notes in Computer Science, LNCS 7089
, 2011
"... Abstract. We present a generalised setting for the construction of complementary array pairs and its proof, using a unitary matrix notation. When the unitaries comprise multivariate polynomials in complex space, we show that four definitions of conjugation imply four types of complementary pair typ ..."
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Abstract. We present a generalised setting for the construction of complementary array pairs and its proof, using a unitary matrix notation. When the unitaries comprise multivariate polynomials in complex space, we show that four definitions of conjugation imply four types of complementary pair types I, II, III, and IV. We provide a construction for complementary pairs of types I, II, and III over {1, −1}, and further specialize to a construction for all known 2 × 2 ×... × 2 complementary array pairs of types I, II, and III over {1, −1}. We present a construction for typeIV complementary array pairs, and call them Rayleigh quotient pairs. We then generalise to complementary array sets, provide a construction for complementary sets of types I, II, and III over {1, −1}, further specialize to a construction for all known 2 × 2 ×... × 2 complementary array sets of types I, II, and III over {1, −1}, and derive closedform Boolean formulas for these cases.