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Correlation and set size bounds of complementary sequences with low correlation zones
 IEEE Trans. Commun
, 2011
"... The correlation lower bounds, as well as the set size upper bounds, of lowcorrelationzone complementary sequences are presented in this paper. They can be treated as an extension of TangFanMatsufuji bounds in [2] and [3], which considered only the conventional (noncomplementary) lowcorrelation ..."
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Cited by 8 (7 self)
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The correlation lower bounds, as well as the set size upper bounds, of lowcorrelationzone complementary sequences are presented in this paper. They can be treated as an extension of TangFanMatsufuji bounds in [2] and [3], which considered only the conventional (noncomplementary) lowcorrelationzone sequence sets.
Equivalence Between Certain Complementary Pairs of Types I and III
"... Building on a recent paper which defined complementary array pairs of types I, II, and III, this paper further characterises a class of typeI pairs defined over the alphabet {−1, 0, 1} and shows that a subset of these pairs are localunitaryequivalent to a subset of the typeIII pairs defined over ..."
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Cited by 6 (5 self)
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Building on a recent paper which defined complementary array pairs of types I, II, and III, this paper further characterises a class of typeI pairs defined over the alphabet {−1, 0, 1} and shows that a subset of these pairs are localunitaryequivalent to a subset of the typeIII pairs defined over a bipolar ({1, −1}) alphabet. Enumerations of the distinct structures in this class and its subset are given.
A Tighter Correlation Lower Bound for QuasiComplementary Sequence Sets
"... Levenshtein improved the famous Welch bound on aperiodic correlation for binary sequences by utilizing some properties of the weighted mean square aperiodic correlation. Following Levenshtein’s idea, a new correlation lower bound for quasicomplementary sequence sets (QCSSs) over the complex roots o ..."
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Cited by 5 (5 self)
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Levenshtein improved the famous Welch bound on aperiodic correlation for binary sequences by utilizing some properties of the weighted mean square aperiodic correlation. Following Levenshtein’s idea, a new correlation lower bound for quasicomplementary sequence sets (QCSSs) over the complex roots of unity is proposed in this paper. The derived lower bound is shown to be tighter than the Welch bound for QCSSs when the set size is greater than some value. The conditions for meeting the new bound with equality are also investigated.
Optimal Polarized Beampattern Synthesis Using a Vector Antenna Array
"... Abstract—Using polarized waveforms increases the capacity of communication systems and improves the performance of active sensing systems such as radar. We consider the optimal synthesis of a directional beam with full polarization control using an array of electromagnetic vector antennas (EMVA). In ..."
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Abstract—Using polarized waveforms increases the capacity of communication systems and improves the performance of active sensing systems such as radar. We consider the optimal synthesis of a directional beam with full polarization control using an array of electromagnetic vector antennas (EMVA). In such an array, each antenna consists of p 2 orthogonal electric or magnetic dipole elements. The control of polarization and spatial power patterns is achieved through carefully designing the amplitudes and phases of the weights of these dipole antennas. We formulate the problem in a convex form, which is thus efficiently solvable by existing solvers such as the interior point method. Our results indicate that vector antenna arrays not only enable full polarization control of the beampattern, but also improve the power gain of the main beam (over the sidelobes), where the gain is shown numerically to be linearly proportional to vector antenna dimensionality p. This implies that EMVA not only offers the freedom to control the beampattern polarization, but also virtually increases the array size by exploiting the full electromagnetic (EM) field components. We also study the effect of polarization on the spatial power pattern. Our analysis shows that for arrays consisting of pairs of electrical and magnetic dipoles, the spatial power pattern is independent of the mainbeam polarization constraint. Index Terms—Beampattern synthesis, convex optimization, vector antenna, waveform polarization. I.
Generating Pictures from Waves: Aspects of Image Formation
 Doctoral thesis, MIT
, 2010
"... The research communities, technologies, and tools for image formation are diverse. On the one hand, computer vision and graphics researchers analyze incoherent light using coarse geometric approximations from optics. On the other hand, array signal processing and acoustics researchers analyze cohere ..."
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The research communities, technologies, and tools for image formation are diverse. On the one hand, computer vision and graphics researchers analyze incoherent light using coarse geometric approximations from optics. On the other hand, array signal processing and acoustics researchers analyze coherent sound waves using stochastic estimation theory and diffraction formulas from physics. The ability to inexpensively fabricate analog circuitry and digital logic for millimeterwave radar and ultrasound creates opportunities in comparing diverse perspectives on image formation, and presents challenges in implementing imaging systems that scale in size. We present algorithms, architectures, and abstractions for image formation that relate the different communities, technologies, and tools. We address practical technical challenges in operating millimeterwave radar and ultrasound systems in the presence of phase noise and scattering.
A mixing of ProuhetThueMorse sequences and Rademacher functions,” preprint
, 2014
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By Entitled
, 2013
"... Is approved by the final examining committee: Chair To the best of my knowledge and as understood by the student in the Research Integrity and Copyright Disclaimer (Graduate School Form 20), this thesis/dissertation adheres to the provisions of Purdue University’s “Policy on Integrity in Research ” ..."
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Is approved by the final examining committee: Chair To the best of my knowledge and as understood by the student in the Research Integrity and Copyright Disclaimer (Graduate School Form 20), this thesis/dissertation adheres to the provisions of Purdue University’s “Policy on Integrity in Research ” and the use of copyrighted material.
EQUATIONS OF THE FORM t(x + a) = t(x) AND t(x + a) = 1 − t(x) FOR THUEMORSE SEQUENCE
, 907
"... Abstract. For every a ≥ 1 we give a recursion algorithm of building of set of solutions of equations of the form t(x+a) = t(x) and t(x+a) = 1 − t(x), where {t(n)} is ThueMorse sequence. In particular, we prove that for every nonnegative integer n there exists x = 1, 2 or 3 such that t(n + x) = t( ..."
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Abstract. For every a ≥ 1 we give a recursion algorithm of building of set of solutions of equations of the form t(x+a) = t(x) and t(x+a) = 1 − t(x), where {t(n)} is ThueMorse sequence. In particular, we prove that for every nonnegative integer n there exists x = 1, 2 or 3 such that t(n + x) = t(n), and pose an open problem and a conjecture. 1. Introduction and
1 Coordinating Complementary Waveforms for Sidelobe Suppression
"... Abstract—We present a general method for constructing radar transmit pulse trains and receive filters for which the radar pointspread function in delay and Doppler, given by the crossambiguity function of the transmit pulse train and the pulse train used in the receive filter, is essentially free ..."
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Abstract—We present a general method for constructing radar transmit pulse trains and receive filters for which the radar pointspread function in delay and Doppler, given by the crossambiguity function of the transmit pulse train and the pulse train used in the receive filter, is essentially free of range sidelobes inside a Doppler interval around the zeroDoppler axis. The transmit pulse train is constructed by coordinating the transmission of a pair of Golay complementary waveforms across time according to zeros and ones in a binary sequence P. The pulse train used to filter the received signal is constructed in a similar way, in terms of sequencing the Golay waveforms, but each waveform in the pulse train is weighted by an element from another sequence Q. We show that a spectrum jointly determined by P and Q sequences controls the size of the range sidelobes of the crossambiguity function and by properly choosing P and Q we can clear out the range sidelobes inside a Doppler interval around the zeroDoppler axis. The joint design of P and Q enables a tradeoff between the order of the spectral null for range sidelobe suppression and the signaltonoise ratio at the receiver output. We establish this tradeoff and derive a necessary and sufficient condition for the construction of P and Q sequences that produce a null of a desired order. I.