Nested code sequences of Barker — Mersenne — Raghavarao
21 Jun 2019-Iss: 3, pp 71-81
TL;DR: Nested code sequences derived from the rows of quasi-orthogonal cyclic matrices of Mersenne, Raghavarao and Hadamard are studied, providing estimates for the characteristics of the autocorrelation function of nested Barker, MERSenne and Raghavao codes, and their combinations.
Abstract: Introduction: The problem of noise-free encoding for an open radio channel is of great importance for data transfer. The results presented in this paper are aimed at stimulating scientific interest in new codes and bases derived from quasi-orthogonal matrices, as a basis for the revision of signal processing algorithms.Purpose: Search for new code sequences as combinations of codes formed from the rows of Mersenne and Raghavarao quasi-orthogonal matrices, as well as complex and more efficient Barker — Mersenne — Raghavarao codes.Results: We studied nested code sequences derived from the rows of quasi-orthogonal cyclic matrices of Mersenne, Raghavarao and Hadamard, providing estimates for the characteristics of the autocorrelation function of nested Barker, Mersenne and Raghavarao codes, and their combinations: in particular, the ratio between the main peak and the maximum positive and negative “side lobes”. We have synthesized new codes, including nested ones, formed on the basis of quasi-orthogonal matrices with better characteristics than the known Barker codes and their nested constructions. The results are significant, as this research influences the establishment and development of methods for isolation, detection and processing of useful information. The results of the work have a long aftermath because new original code synthesis methods need to be studied, modified, generalized and expanded for new application fields.Practical relevance: The practical application of the obtained results guarantees an increase in accuracy of location systems, and detection of a useful signal in noisy background. In particular, these results can be used in radar systems with high distance resolution, when detecting physical objects, including hidden ones.
Citations
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17 Jun 2020
TL;DR: Methods for assessing the symmetries of Hadamard matrices and special quasi-orthogonal matrices ofcirculant and two circulant structures used as the basis for searching for noise-resistant codes are discussed.
Abstract: The paper discusses methods for assessing the symmetries of Hadamard matrices and special quasi-orthogonal matrices of circulant and two circulant structures used as the basis for searching for noise-resistant codes. Such codes, obtained from matrix rows intended for use in open communications, expand the basic and general theory of signal coding and ensure that the requirements for contemporary telecommunication systems are met. Definitions of the indices of symmetry, asymmetry, and symmetry defect of special matrices are given. The connection of symmetric and antisymmetric circulant matrices with primes, compound numbers, and powers of a prime number is shown. Examples of two circulant matrices that are optimal by their determinant, as well as special circulant matrices, are given. The maximum orders of the considered matrices of symmetric structures are determined.
3 citations
01 Jan 2021
TL;DR: The origin of the names of quasi-orthogonal matrix families and the connection of their orders with known numerical sequences are described and examples of the applicability of the matrices for various tasks of information transformation and processing are given.
Abstract: The evolution of knowledge about quasi-orthogonal matrices as a generalization of Hadamard matrices is briefly considered in the paper. We describe the origin of the names of quasi-orthogonal matrix families and the connection of their orders with known numerical sequences. The structured matrices, searching for which is of the greatest practical interest, are distinguished: symmetric, persymmetric, cyclic, structured according to Walsh. There are also features and characteristics of such matrices highlighted in the paper. Examples of the applicability of the matrices for various tasks of information transformation and processing are given: noise immune coding, masking, compression, signal coding.
3 citations
18 Apr 2021
TL;DR: It is shown that combining information in an optical location system allows detecting, classifying and determining the parameters of motion of objects, including people and animals.
Abstract: The article discusses the possibility of using a two-position onboard optical-location system for detecting, classifying and determining the coordinates of the trajectory of objects in the video stream installed on the small aircraft. Every year the requirements for new monitoring systems are becoming more stringent. The data obtained from a single, albeit highquality, optical sensor can no longer meet the assigned tasks, such as performing search and rescue operations in remote areas, as well as solving problems of finding people in disaster zones. and environmental disasters in a complex noise environment. The system considered in the article includes optical-location sensors, each of which is capable of forming a high-resolution image and classifying the observed objects, as well as, when used together using stereo vision methods, to obtain estimates of the coordinates of the object's trajectory. observed objects. It is shown that combining information in an optical location system allows detecting, classifying and determining the parameters of motion of objects, including people and animals. The article presents the operating modes of the system, and the corresponding restrictions on the conditions for its effective operation.
2 citations
20 Sep 2020
TL;DR: The results show the possibility for their use in distributed location systems, not only in the case of remote sensing of the earth, but also in the field of application of the transmission of generated signals to points of joint information processing.
Abstract: The article provides an analysis of new code structures of maximum length obtained from rows of quasi-orthogonal matrices. Codes of maximum length (m-sequences, codes constructed on the basis of Legendre symbols or quadratic residues, codes generated on the basis of Jacobi symbols and others) have the potential to be widely used both in remote sensing radar systems and in noise-immune and noise-proof systems high-speed communications as a replacement for widely used Barker codes. The questions of searching and researching new noise-resistant codes constructed on the basis of persymmetric circulants are considered. Comparison of performance ratings obtained with the new code sequences is given. The advantages of the codes obtained in the work are discussed in the aspects of increasing the correlation characteristics, their detection, and noise immunity in the radio channels of distributed systems. Since these codes have potential applications in radar, not only the correlation properties (autocorrelation and periodic correlation function) are considered, as for communication systems, but also the ambiguity function, which takes into account not only the correlation of signals in time, but also in frequency. The results show the possibility for their use in distributed location systems, not only in the case of remote sensing of the earth, but also in the field of application of the transmission of generated signals to points of joint information processing.
1 citations
26 Dec 2020
TL;DR: Simulation modeling confirmed the possibility of using new composite Barker codes as synchronization signals in the BCS and showed a greater noise immunity of new composite codes to the influence of various modulating sequences of an information signal in comparison with known composite codes.
Abstract: Background. At present, the demand for broadband signals (BВS) is determined by the qualities inherent in these signals, which make it possible to ensure high noise immunity of broadband communication systems (BСS) when transmitting confidential information in an open radio channel, especially in emergency situations. Although the foundations of the BВS theory are well known, the development of wireless communication networks requires constant refinements of theoretical provisions in accordance with new data on methods for constructing Barker code sequences used in wireless communicationsystems with direct sequence spread spectrum technology.Objective. The aim of the paper is to study new composite Barker codes as synchronization signals and compare them with known composite codes using simulation.Methods. Analytical methods of calculation are used, as well as simulation modeling in the MatLab software package.Results. Simulation modeling was carried out, which confirmed the possibility of using new composite Barker codes as synchronization signals in the BCS.Conclusions. Modeling in the MatLab software package showed a greater noise immunity of new composite codes to the influence of various modulating sequences of an information signal in comparison with known composite codes.
1 citations
Cites background from "Nested code sequences of Barker — M..."
...11 family of wireless communication systems with Direct Sequence Spread Spectrum (DSSS) [2], in modern radar systems [3]....
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References
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01 Oct 2017
31 citations
23 Sep 2018
TL;DR: It has been found out that the characteristics of autocorrelation functions for Mersenne codes 3, 7 and 11 exceed those for Barker codes, which is a basis for ensuring greater noise immunity of probing signals in radar channels and for increasing the probability of their correct detection.
Abstract: Introduction: Barker codes representing binary sequences (codes) of finite lengths 2, 3, 4, 5, 7, 11 and 13 are widely used in solving the problem of increasing the noise immunity of radar channels. However, the code sequences for n > 13 are unknown. Sequences derived from quasi-orthogonal Mersenne matrices also have not been used for these purposes.Purpose: Studying the ways to compress a complex modulated signal by Mersenne sequences obtained from the first rows of a monocyclic quasi-orthogonal Mersenne matrix, as an alternative to Barker codes.Results:It has been found out that the characteristics of autocorrelation functions for Mersenne codes 3, 7 and 11 exceed those for Barker codes. This is a basis for ensuring greater noise immunity of probing signals in radar channels, as well as for increasing the probability of their correct detection, proving the expediency of their application for amplitude and phase modulation of radio signals.Practical relevance:The obtained results allow you to increase the compression characteristics in radar systems when solving the problem of detecting targets under noise and interference. The wide application of Barker codes of length 3, 7 and 11 in digital data transmission systems provides a special interest in similar Mersenne codes when implementing noise-resistant data transmission in radio channels in a complex electromagnetic environment. Discussion: An unresolved problem is the non-symmetry of elements in a coding Mersenne sequence. This problem can be solved either by special synthesis of a phase-modulated signal or by finding new approaches to their compression.
14 citations
01 Jan 2018
TL;DR: This book maximizes reader insights into the field of mathematical models and methods for the processing of two-dimensional remote sensing images by presenting a broad analysis of the field, encompassing passive and active sensors, hyperspectral images, synthetic aperture radar, interferometric SAR, and polarimetric SAR data.
Abstract: This book maximizes reader insights into the field of mathematical models and methods for the processing of two-dimensional remote sensing images. It presents a broad analysis of the field, encompassing passive and active sensors, hyperspectral images, synthetic aperture radar (SAR), interferometric SAR, and polarimetric SAR data. At the same time, it addresses highly topical subjects involving remote sensing data types (e.g., very high-resolution images, multiangular or multiresolution data, and satellite image time series) and analysis methodologies (e.g., probabilistic graphical models, hierarchical image representations, kernel machines, data fusion, and compressive sensing) that currently have primary importance in the field of mathematical modelling for remote sensing and image processing. Each chapter focuses on a particular type of remote sensing data and/or on a specific methodological area, presenting both a thorough analysis of the previous literature and a methodological and experimental discussion of at least two advanced mathematical methods for information extraction from remote sensing data. This organization ensures that both tutorial information and advanced subjects are covered. With each chapter being written by research scientists from (at least) two different institutions, it offers multiple professional experiences and perspectives on each subject. The book also provides expert analysis and commentary from leading remote sensing and image processing researchers, many of whom serve on the editorial boards of prestigious international journals in these fields, and are actively involved in international scientific societies. Providing the reader with a comprehensive picture of the overall advances and the current cutting-edge developments in the field of mathematical models for remote sensing image analysis, this book is ideal as both a reference resource and a textbook for graduate and doctoral students as well as for remote sensing scientists and practitioners.
13 citations
12 citations
01 Nov 2018
TL;DR: Three practical schemes for digital detectors of bursts of ultra-wideband signals are presented and analytical expressions for calculating their performance are provided.
Abstract: Ultra-wideband (further UWB) signals are increasingly being used in communication systems. The paper presents three practical schemes for digital detectors of bursts of ultra-wideband signals and provides analytical expressions for calculating their performance.
9 citations