2,765 research outputs found
New Constructions of Zero-Correlation Zone Sequences
In this paper, we propose three classes of systematic approaches for
constructing zero correlation zone (ZCZ) sequence families. In most cases,
these approaches are capable of generating sequence families that achieve the
upper bounds on the family size () and the ZCZ width () for a given
sequence period ().
Our approaches can produce various binary and polyphase ZCZ families with
desired parameters and alphabet size. They also provide additional
tradeoffs amongst the above four system parameters and are less constrained by
the alphabet size. Furthermore, the constructed families have nested-like
property that can be either decomposed or combined to constitute smaller or
larger ZCZ sequence sets. We make detailed comparisons with related works and
present some extended properties. For each approach, we provide examples to
numerically illustrate the proposed construction procedure.Comment: 37 pages, submitted to IEEE Transactions on Information Theor
Design and Analysis of Ternary m-sequences with Interleaved Structure by d-Transform
Multilevel sequences find more and more applications in modern modulation schemes [4QPSK, 8QPSK,16QAM..] for the 3G ,4G system air interface [1,2].Furthermore, in modern cryptography they are also widerly used. It is also interesting to point out that the length L of these sequences are composite numbers( L=NS),that means the sequence can be easily implemented by interleaving S subsequences, each of length S.Therefore, the methods to develop multilevel sequence with interleaved structure draw a lot of attentions [3, 4]. In this contribution, a method for design and analysis of ternary m-sequences with interleaved structure is presented, based on the d-transform, Which turns out to be a very effective and versal tool for this purpose. Simulations have been made to verify the theory. We first introduce d-transform and its properties and then work out the procedure to design an interleaving sequence in d-transform. Keywords: d-transform,q-ary sequences, interleaved sequence
Permutation Polynomial Interleaved Zadoff-Chu Sequences
Constant amplitude zero autocorrelation (CAZAC) sequences have modulus one
and ideal periodic autocorrelation function. Such sequences have been used in
communications systems, e.g., for reference signals, synchronization signals
and random access preambles. We propose a new family CAZAC sequences, which is
constructed by interleaving a Zadoff-Chu sequence by a quadratic permutation
polynomial (QPP), or by a permutation polynomial whose inverse is a QPP. It is
demonstrated that a set of orthogonal interleaved Zadoff-Chu sequences can be
constructed by proper choice of QPPs.Comment: Submitted to IEEE Transactions on Information Theor
Design of sequences with good correlation properties
This thesis is dedicated to exploring sequences with good correlation properties. Periodic sequences with desirable correlation properties have numerous applications in communications. Ideally, one would like to have a set of sequences whose out-of-phase auto-correlation magnitudes and cross-correlation magnitudes are very small, preferably zero. However, theoretical bounds show that the maximum magnitudes of auto-correlation and cross-correlation of a sequence set are mutually constrained, i.e., if a set of sequences possesses good auto-correlation properties, then the cross-correlation properties are not good and vice versa. The design of sequence sets that achieve those theoretical bounds is therefore of great interest. In addition, instead of pursuing the least possible correlation values within an entire period, it is also interesting to investigate families of sequences with ideal correlation in a smaller zone around the origin. Such sequences are referred to as sequences with zero correlation zone or ZCZ sequences, which have been extensively studied due to their applications in 4G LTE and 5G NR systems, as well as quasi-synchronous code-division multiple-access communication systems.
Paper I and a part of Paper II aim to construct sequence sets with low correlation within a whole period. Paper I presents a construction of sequence sets that meets the Sarwate bound. The construction builds a connection between generalised Frank sequences and combinatorial objects, circular Florentine arrays. The size of the sequence sets is determined by the existence of circular Florentine arrays of some order. Paper II further connects circular Florentine arrays to a unified construction of perfect polyphase sequences, which include generalised Frank sequences as a special case. The size of a sequence set that meets the Sarwate bound, depends on a divisor of the period of the employed sequences, as well as the existence of circular Florentine arrays.
Paper III-VI and a part of Paper II are devoted to ZCZ sequences.
Papers II and III propose infinite families of optimal ZCZ sequence sets with respect to some bound, which are used to eliminate interference within a single cell in a cellular network. Papers V, VI and a part of Paper II focus on constructions of multiple optimal ZCZ sequence sets with favorable inter-set cross-correlation, which can be used in multi-user communication environments to minimize inter-cell interference. In particular, Paper~II employs circular Florentine arrays and improves the number of the optimal ZCZ sequence sets with optimal inter-set cross-correlation property in some cases.Doktorgradsavhandlin
Improving Interferometric Null Depth Measurements using Statistical Distributions: Theory and First Results with the Palomar Fiber Nuller
A new "self-calibrated" statistical analysis method has been developed for
the reduction of nulling interferometry data. The idea is to use the
statistical distributions of the fluctuating null depth and beam intensities to
retrieve the astrophysical null depth (or equivalently the object's visibility)
in the presence of fast atmospheric fluctuations. The approach yields an
accuracy much better (about an order of magnitude) than is presently possible
with standard data reduction methods, because the astrophysical null depth
accuracy is no longer limited by the magnitude of the instrumental phase and
intensity errors but by uncertainties on their probability distributions. This
approach was tested on the sky with the two-aperture fiber nulling instrument
mounted on the Palomar Hale telescope. Using our new data analysis approach
alone-and no observations of calibrators-we find that error bars on the
astrophysical null depth as low as a few 10-4 can be obtained in the
near-infrared, which means that null depths lower than 10-3 can be reliably
measured. This statistical analysis is not specific to our instrument and may
be applicable to other interferometers
Design of One-Coincidence Frequency Hopping Sequence Sets for FHMA Systems
Department of Electrical EngineeringIn the thesis, we discuss frequency hopping multiple access (FHMA) systems and construction of optimal frequency hopping sequence and applications. Moreover, FHMA is widely used in modern communication systems such as Bluetooth, ultrawideband (UWB), military, etc. For these systems, it is desirable to employ frequency-hopping sequences (FHSs) having low Hamming correlation in order to reduce the multiple-access interference.
In general, optimal FHSs with respect to the Lempel-Greenberger bound do not always exist for all lengths and frequency set sizes. Therefore, it is an important problem to verify whether an optimal FHS with respect to the Lempel-Greenberger bound exists or not for a given length and a given frequency set size.
I constructed FHS satisfying optimal with respect to the Lempel-Greenberger bound and Peng-Fan bound for efficiency of available frequency. Parameters of a new OC-FHS set are length p^2-p over Z_(p^2 ) by using a primitive element of Z_p. The new OC-FHS set with H_a (X)=0 and H_c (X)=1 can be applied to several recent applications using ISM band (e.g. IoT) based on BLE and Zigbee.
In the construction and theorem, I used these mathematical back grounds in preliminaries (i.e., finite field, primitive element, primitive polynomial, frequency hopping sequence, multiple frequency shift keying, DS/CDMA) in order to prove mathematically.
The outline of thesis is as follows. In preliminaries, we explain algorithm for minimal polynomial for sequence, linear complexities, Hamming correlation and bounds for FHSs and some applications are presented. In section ???, algorithm for complexity, correlation and bound for FHSs and some applications are presented. In section ???, using information in section ??? and ???, a new construction of OC-FHS is presented. In order to prove the optimality of FHSs, all cases of Hamming autocorrelation and Hamming cross-correlation are mathematically calculated.
Moreover, in order to raise data rate or the number of users, a new method is presented. Using this method, sequences are divided into two times of length and satisfies Lempel-Greenberger bound and Peng-Fan bound.clos
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