HpGAN: Sequence Search with Generative Adversarial Networks

Sequences play an important role in many engineering applications and systems. Searching sequences with desired properties has long been an interesting but also challenging research topic. This article proposes a novel method, called HpGAN, to search desired sequences algorithmically using generative adversarial networks (GAN). HpGAN is based on the idea of zero-sum game to train a generative model, which can generate sequences with characteristics similar to the training sequences. In HpGAN, we design the Hopfield network as an encoder to avoid the limitations of GAN in generating discrete data. Compared with traditional sequence construction by algebraic tools, HpGAN is particularly suitable for intractable problems with complex objectives which prevent mathematical analysis. We demonstrate the search capabilities of HpGAN in two applications: 1) HpGAN successfully found many different mutually orthogonal complementary code sets (MOCCS) and optimal odd-length Z-complementary pairs (OB-ZCPs) which are not part of the training set. In the literature, both MOCSSs and OB-ZCPs have found wide applications in wireless communications. 2) HpGAN found new sequences which achieve four-times increase of signal-to-interference ratio--benchmarked against the well-known Legendre sequence--of a mismatched filter (MMF) estimator in pulse compression radar systems. These sequences outperform those found by AlphaSeq.Comment: 12 pages, 16 figure

Chaotic Phase-Coded Waveforms with Space-Time Complementary Coding for MIMO Radar Applications

A framework for designing orthogonal chaotic phase-coded waveforms with space-time complementary coding (STCC) is proposed for multiple-input multiple-output (MIMO) radar applications. The phase-coded waveform set to be transmitted is generated with an arbitrary family size and an arbitrary code length by using chaotic sequences. Due to the properties of chaos, this chaotic waveform set has many advantages in performance, such as anti-interference and low probability of intercept. However, it cannot be directly exploited due to the high range sidelobes, mutual interferences, and Doppler intolerance. In order to widely implement it in practice, we optimize the chaotic phase-coded waveform set from two aspects. Firstly, the autocorrelation property of the waveform is improved by transmitting complementary chaotic phase-coded waveforms, and an adaptive clonal selection algorithm is utilized to optimize a pair of complementary chaotic phase-coded pulses. Secondly, the crosscorrelation among different waveforms is eliminated by implementing space-time coding into the complementary pulses. Moreover, to enhance the detection ability for moving targets in MIMO radars, a method of weighting different pulses by a null space vector is utilized at the receiver to compensate the interpulse Doppler phase shift and accumulate different pulses coherently. Simulation results demonstrate the efficiency of our proposed method

Adaptive waveform design for SAR in a crowded spectrum

This thesis concerns the development of an adaptive waveform design scheme for synthetic aperture radar (SAR) to support its operation in the increasingly crowded radio frequency (RF) spectrum, focusing on mitigating the effects of external RF interference. The RF spectrum is a finite resource and the rapid expansion of the telecommunications industry has seen radar users face a significant restriction in the range of available operational frequencies. This crowded spectrum scenario leads to increased likelihood of RF interference either due to energy leakage from neighbouring spectral users or from unlicensed transmitters. SAR is a wide bandwidth radar imaging mode which exploits the motion of the radar platform to form an image using multiple one dimensional profiles of the scene of interest known as the range profile. Due to its wideband nature, SAR is particularly vulnerable to RF interference which causes image impairments and overall reduction in quality. Altering the approach for radar energy transmission across the RF spectrum is now imperative to continue effective operation. Adaptive waveforms have recently become feasible for implementation and offer the much needed flexibility in the choice and control over radar transmission. However, there is a critically small processing time frame between waveform reception and transmission, which necessitates the use of computationally efficient processing algorithms to use adaptivity effectively. This simulation-based study provides a first look at adaptive waveform design for SAR to mitigate the detrimental effects of RF interference on a pulse-to-pulse basis. Standard SAR systems rely on a fixed waveform processing format on reception which restricts its potential to reap the benefits of adaptive waveform design. Firstly, to support waveform design for SAR, system identification techniques are applied to construct an alternative receive processing method which allows flexibility in waveform type. This leads to the main contribution of the thesis which is the formation of an adaptive spectral waveform design scheme. A computationally efficient closed-form expression for the waveform spectrum that minimizes the error in the estimate of the SAR range profile on a pulse to pulse basis is derived. The range profile and the spectrum of the interference are estimated at each pulse. The interference estimate is then used to redesign the proceeding waveform for estimation of the range profile at the next radar platform position. The solution necessitates that the energy is spread across the spectrum such that it competes with the interferer. The scenario where the waveform admits gaps in the spectrum in order to mitigate the effects of the interference is also detailed and is the secondary major thesis contribution. A series of test SAR images demonstrate the efficacy of these techniques and yield reduced interference effects compared to the standard SAR waveform

Methodology of synthesis and signal processing of generalized binary Barker sequences for spread spectrum communications

Дисертація на здобуття наукового ступеня доктора технічних наук за спеціальністю 05.12.02 – «Телекомунікаційні системи та мережі». – Національний авіаційний університет, Київ, 2019. У дисертаційній роботі вирішується актуальна науково-технічна проблема синтезу бінарних дискретно-кодованих послідовностей (ДКП), які є оптимальними за мінімаксним критерієм щодо їх автокореляційної функції (АКФ), у частині синтезу регулярних структур цих ДКП та їх комбінаторних систем в умовах обмежень на максимальний рівень абсолютних значень бічних пелюсток їх АКФ (ДКП Баркера). Вирішенням зазначеної проблеми у дисертації є новий синтезований тип ДКП – узагальнені бінарні послідовності Баркера (УБПБ), які характеризуються регулярними структурами, можуть бути синтезовані регулярними методами синтезу та утворюють нові мультиплікативно комплементарні структури бінарних ДКП. У роботі розроблено методологію синтезу та обробки УБПБ та їх мультиплікативно комплементарних структур, яка у своєму складі містить розроблену параметрично-критеріальну модифікацію EM-алгоритму з видаленням компонент гаусівської змішаної моделі для аналізу кореляційних зв’язків у системах ДКП та доведені теореми про його математичну сингулярність за певних умов такого статистичного аналізу для обґрунтування введених у модифікації алгоритму критеріїв, розроблені метод структуризації ДКП з апріорі невідомими внутрішніми структурами, регулярний метод синтезу УБПБ, метод синтезу та сумісної обробки мультиплікативно комплементарних структур УБПБ, метод декомпозиції структури вихідного сигналу системи обробки мультиплікативно комплементарних УБПБ, метод39 оцінювання енергетичних параметрів ортогональних сигнально-кодових конструкцій та завад при передаванні УБПБ. У дослідженні також обґрунтовано класифікацію УБПБ, виявлено та досліджено системні властивості регулярних структур УБПБ та їх АКФ, синтезовано повну систему математичних моделей для аналітичного опису АКФ УБПБ, розроблено аналітичні моделі оцінювання показників якості передавання повідомлень у телекомунікаційних системах при використанні УБПБ.Диссертация на соискание учёной степени доктора технических наук по специальности 05.12.02 – «Телекоммуникационные системы и сети». – Национальный авиационный университет, Киев, 2019. Диссертационная работа посвящена решению актуальной научно-технической проблемы синтеза бинарных дискретно-кодированных последовательностей (ДКП), оптимальных по минимаксному критерию в отношении их автокорреляционной функции (АКФ), в части синтеза регулярных структур этих ДКП и их комбинаторных систем в условиях ограничений на максимальный уровень абсолютных значений боковых лепестков их АКФ (ДКП Баркера). Решением указанной проблемы в диссертации является новый синтезированный тип ДКП – обобщённые бинарные последовательности Баркера (ОБПБ), которые характеризуются регулярными структурами, могут быть синтезированы регулярными методами синтеза и образовывают новые мультипликативно комплементарные структуры бинарных ДКП. В работе разработана методология синтеза и обработки ОБПБ и их мультипликативно комплементарных структур, которая в своём составе содержит разработанную параметрически-критериальную модификацию EM-алгоритма с удалением компонент гауссовской смешанной модели для анализа корреляционных связей в системах ДКП и доказанные теоремы о его математической сингулярности в определённых условиях такого статистического анализа для обоснования введённых в модификации алгоритма критериев, разработанные метод структуризации ДКП с априори неизвестными внутренними структурами, регулярный метод синтеза ОБПБ, метод синтезу и совместной обработки мультипликативно комплементарных структур ОБПБ, метод декомпозиции структуры сигнала на выходе системы обработки мультипликативно комплементарных ОБПБ, метод оценивания энергетических параметров ортогональных сигнально-кодовых конструкций и помех при передаче ОБПБ. В исследовании также обоснована классификация ОБПБ, выявлены и исследованы системные свойства регулярных структур ОБПБ и их АКФ, синтезирована полная система математических моделей для аналитического описания АКФ ОБПБ, разработаны аналитические модели оценивания показателей качества передачи сообщений в телекоммуникационных системах при использовании ОБПБ.Thesis for a degree of Doctor of Technical Science in specialty 05.12.02 – «Telecommunication Systems and Networks». – National Aviation University. – Kyiv, 2019. The thesis is devoted to solving the actual scientific and engineering problem dealing with a synthesis of binary sequences, which are optimal by the minimax criterion with respect to their autocorrelation function, in terms of a synthesis of regular structures of these binary sequences and their combinatorial systems under additional restrictions on the peak sidelobe level of their autocorrelation function (Barker sequences). The solution of the problem, proposed in the thesis, boils down to a new synthesized kind of binary sequences – generalized binary Barker sequences, which are characterized by regular structures, can be synthesized by means of regular synthesis method and form new multiplicative complementary structures of binary sequences. The methodology of synthesis and signal processing of generalized binary Barker sequences and their multiplicative complementary structures, developed in the thesis, consists of: (a) the modification (parametric and criteria features) of the expectationmaximization (EM) algorithm with removing components of the Gaussian mixture model and additional clustering criteria for a statistical analysis of cross-correlations between sequences in a system for their further structuring, based on proved theorems on mathematical singularities in the log-likelihood function in the mentioned statistical analysis of cross-correlations; (b) the method of structuring binary sequences with a priori unknown structures, which provides selecting groups of binary sequences with interconnected structures and further detecting these interconnected structures in an explicit form; (c) the regular method for synthesis of generalized binary Barker sequences, based on the deterministic generation rules for these sequences; (d) the method for synthesis and joint signal processing of multiplicative complementary structures of generalized binary Barker sequences, based on the multiplication of results of matched filtering of signal components; (e) the method of a structural decomposition of output signal in signal processing system for multiplicative complementary generalized binary Barker sequences (an output signal can be represented by some number of separately taken partial lobes, each of which is characterized by constant mean value and variance of signal), which allows to perform a statistical analysis of output signal for noise immunity analysis, detection and other purposes in telecommunication system; (f) the method of estimation of energetic parameters of orthogonal signal-code constructions and noise on the physical layer of telecommunication system in case of use of generalized binary Barker sequences. The classification by types and subtypes of generalized binary Barker sequences, based on statistical clustering using the EM and k-means algorithms, is also justified in the research. The properties of regular structures of generalized binary Barker sequences and properties of their autocorrelation functions are detected and studied. A complete system of mathematical models for analytical description of the autocorrelation function of generalized binary Barker sequences is synthesized. The analytical models for estimation of quality characteristics on the physical layer of telecommunication system in case of use of generalized binary Barker sequences are developed. Spectral and detection features of generalized binary Barker sequences and their comparison with Golay complementary sequences are also studied in the research. In contrast with Golay complementary sequences, generalized binary Barker sequences provide larger values of the processing gain in sidelobes (by 4.1 dB for a considered case), which provides less noise in sidelobes and a lower number of errors of the first genus in the case of the use of generalized binary Barker sequences. At the same time, the main disadvantage of generalized binary Barker sequences in comparison with Golay complementary sequences is that the processing gain in the main central lobe is lower (by 8.9 dB for a considered case), which causes more noise in the main lobe and a greater number of errors of the second genus in the case of the use of generalized binary Barker sequences. With this, the compared systems of sequences are characterized by almost the same total bandwidth, and the fact that generalized binary Barker sequences also provide a lower pulse width in the main lobe after signal processing (by 1.5 times), which provides a greater maximum data transfer rate and spectral efficiency on the physical layer of spread-spectrum telecommunication system (up to 1.5 times). The research results were implemented in the production and research activities of the UkSATSE Flight Calibration & Rescue Service (Ukrainian State Air Traffic Services Enterprise «UkSATSE») and educational processes at the Faculty of Air Navigation, Electronics and Telecommunications (National Aviation University, Kyiv)