De nos jours, l'utilisation des drones ne cesse d'augmenter et de nombreuses études sont réalisées afin de mettre en place des systèmes de communication dronique destinés à des applications non seulement militaires mais aussi civiles. Pour le moment, les règles d'intégration des drones commerciaux dans l’espace aérien doivent encore être définies et le principal enjeu occupation est d'assurer une communication fiable et sécurisée. Cette thèse s’inscrit dans ce contexte de communication. Motivée par la croissance rapide du nombre des drones et par les nouvelles générations des drones commandés par satellite, la thèse vise à étudier les différents liens possibles qui relient le drone aux autres composants du système de communication. Trois principaux liens sont à mettre en place : le lien de contrôle, le lien de retour et le lien de mission. En raison de la rareté des ressources fréquentielles déjà allouées pour les futurs systèmes droniques, l'efficacité spectrale devient un paramètre crucial pour leur déploiement à grande échelle. Afin de mettre en place un système de communication par drones spectralement efficace, une bonne compréhension des canaux de transmission pour chacune des trois liaisons est indispensable, ainsi qu’un choix judicieux de la forme d’onde. Cette thèse commence par étudier les canaux de propagation pour chaque liaison : canaux de type muti-trajets avec ligne de vue directe, dans un contexte d’utilisation de drones à moyenne altitude et longue endurance (drones MALE). L’objectif de cette thèse est de proposer de nouveaux algorithmes de réception permettant d’estimer et égaliser ces canaux de propagation muti-trajets. Les méthodes proposées dépendent du choix de la forme d’onde. Du fait de la présence d’un lien satellite, les formes d’onde considérées sont de type mono-porteuse (avec un faible facteur de crête) : SC et EW-SCOFDM. L’égalisation est réalisée dans le domaine temporel (SC) ou fréquentiel (EW-SC-OFDM). L'architecture UAV prévoit l'implantation de deux antennes placées aux ailes. Ces deux antennes peuvent être utilisées pour augmenter le gain de diversité (gain de matrice de canal). Afin de réduire la complexité de l'égalisation des canaux, la forme d'onde EW-SC-OFDM est proposée et étudiée dans un contexte muti-antennes, dans le but d'améliorer l'endurance de l'UAV et d'accroître l'efficacité spectrale, une nouvelle technique de modulation est considérée: Modulation spatiale ( SM). Dans SM, les antennes de transmission sont activées en alternance. L'utilisation de la forme d'onde EW-SC-OFDM combinée à la technique SM nous permet de proposer de nouvelles structures modifiées qui exploitent l’étalement spectrale pour mieux protéger des bits de sélection des antennes émettrices et ainsi améliorer les performances du système. / Nowadays, several studies are launched for the design of reliable and safe communications systems that introduce Unmanned Aerial Vehicle (UAV), this paves the way for UAV communication systems to play an important role in a lot of applications for non-segregated military and civil airspaces. Until today, rules for integrating commercial UAVs in airspace still need to be defined, the design of secure, highly reliable and cost effective communications systems still a challenging task. This thesis is part of this communication context. Motivated by the rapid growth of UAV quantities and by the new generations of UAVs controlled by satellite, the thesis aims to study the various possible UAV links which connect UAV/aircraft to other communication system components (satellite, terrestrial networks, etc.). Three main links are considered: the Forward link, the Return link and the Mission link. Due to spectrum scarcity and higher concentration in aircraft density, spectral efficiency becomes a crucial parameter for largescale deployment of UAVs. In order to set up a spectrally efficient UAV communication system, a good understanding of transmission channel for each link is indispensable, as well as a judicious choice of the waveform. This thesis begins to study propagation channels for each link: a mutipath channels through radio Line-of-Sight (LOS) links, in a context of using Meduim Altitude Long drones Endurance (MALE) UAVs. The objective of this thesis is to maximize the solutions and the algorithms used for signal reception such as channel estimation and channel equalization. These algorithms will be used to estimate and to equalize the existing muti-path propagation channels. Furthermore, the proposed methods depend on the choosen waveform. Because of the presence of satellite link, in this thesis, we consider two low-papr linear waveforms: classical Single-Carrier (SC) waveform and Extented Weighted Single-Carrier Orthogonal Frequency-Division Multiplexing (EW-SC-OFDM) waveform. channel estimation and channel equalization are performed in the time-domain (SC) or in the frequency-domain (EW-SC-OFDM). UAV architecture envisages the implantation of two antennas placed at wings. These two antennas can be used to increase diversity gain (channel matrix gain). In order to reduce channel equalization complexity, the EWSC- OFDM waveform is proposed and studied in a muti-antennas context, also for the purpose of enhancing UAV endurance and also increasing spectral efficiency, a new modulation technique is considered: Spatial Modulation (SM). In SM, transmit antennas are activated in an alternating manner. The use of EW-SC-OFDM waveform combined to SM technique allows us to propose new modified structures which exploit exces bandwidth to improve antenna bit protection and thus enhancing system performances.

A necessidade de transmissão de canais modulados a taxas a partir de 400 Gb/s tem motivado a pesquisa e os esforços relativos às tecnologias de camada física habilitadores desta alta capacidade. A atenção se volta, principalmente, aos frontends (transmissores e receptores), aliados aos processadores digitais de sinal (Digital Signal Processors, DSPs), às técnicas de amplificação óptica e a novos tipos de fibra óptica. Em particular a técnica baseada no emprego de filtros de Nyquist combinados à multiplexação de comprimentos de onda (Wavelength Division Multiplexing, DWM), conhecida como Nyquist-WDM, ou N-WDM, tem atraído grande interesse para geração de supercanais ópticos, hoje um dos elementos chave nos sistemas de redes ópticas. O estudo dos fundamentos e casos particulares dos filtros de Nyquist são aprofundados nesta dissertação para o controle de seus parâmetros, em especial o parâmetro conhecido como fator de roll-off, em aplicações que requerem flexibilidade na ocupação espectral e até o reaproveitamento das limitações do filtro para atenuar alguns efeitos lineares e não lineares na fibra. A técnica utiliza um tipo de formatação geométrica de pulso e é limitada pelo ajuste grosso do fator de roll-off, mas como abordagem inicial, permite estabelecer uma série de compromissos na concepção do circuito eletrônico de um transponder sintonizável. Uma investigação teórica foi feita em um sistema PM-16QAM de 21x256 Gb/s, a partir de dados experimentais obtidos com roll-off igual 0,1, para análise do efeito no desempenho sistêmico do ajuste do excesso de largura de banda (em relação à banda de Nyquist) de um filtro formatador de pulso. O fator de roll-off foi ajustado e seu impacto no desempenho do sistema, em termos de alcance, foi verificado. A partir dos resultados, foi observado que, desde que a taxa de erro de bit, BER, esteja dentro do limite do código corretor de erro (forward error corrector, FEC), o valor de roll-off pode ser ajustado para um valor ótimo de acordo com a configuração do sistema e as metas requeridas. Uma vez encontrada a relação entre a BER e o fator de roll-off, foi possível determinar um fator de mérito que relaciona a resolução do filtro de Nyquist, em função do número de taps que ele emprega, o consumo de energia da DSP e, consequentemente, a BER. O compromisso assim estabelecido entre o desempenho sistêmico, o consumo de energia e o fator de roll-off representa a principal contribuição desta dissertação. / The need for transmission of channels modulated at rates greater than 400 Gb/s has motivated the research and efforts related to the physical layer technologies that will enable this high capacity. The attention turns mainly to the frontends (transmitters and receivers), allied to digital signal processors (DSPs), optical amplification techniques and new types of optical fiber. The technique based on the use of Nyquist filters combined withWavelength Division Multiplexing (WDM), known as Nyquist-WDM, or N-WDM, has attracted great interest for the generation of optical super-channels, today one of the key elements in optical network systems. The study of the fundamentals and particular cases of the Nyquist filters are detailed in this dissertation for mastering the control of the parameters, especially the parameter known as roll-off factor, for applications that require flexibility in the spectral occupation and even the reutilization of the limitations of the filter to attenuate some linear and non-linear effects on the fiber. The technique uses a geometric type of pulse-shaping, and is limited by the roll-off factor tunning, but as an initial approach, it allows to establish a series of compensations in the design of the electronic circuit of a tunable transponder. A theoretical investigation was made on a 21x256 Gb/s PM-16QAM system, taken as reference the experimental data obtained with roll-off equal to 0.1, to analyze the effects of adjusting the excess bandwidth (relative to the Nyquist band) of a pulse-shaping filter. The roll-off factor was tunned and its impact on the system performance in terms of range effects was verified. From the results, it was observed that, as long as the bit error ratio, BER, is within the FEC limit, the roll-off parameter can be set to an optimum value according to the system configuration and required targets. Once the relationship between the BER and the roll-off factor was found, it was possible to determine a merit factor that relates the resolution of the Nyquist filter, as a function of the number of taps it uses, the energy consumption of the DSP and, consequently, the BER. The compromise thus established between system performance, energy consumption and roll off represents the main contribution of this work.

La croissance exponentielle du trafic de données sans fils, causée par l'Internet mobile et les smartphones, contraint les futurs systèmes radio à inclure des modulations/formes d'ondes plus avancées offrant un débit plus élevé et une utilisation efficace des ressources spectrales. Les transmissions dites Faster-Than-Nyquist (FTN), introduites en 1975, sont parmi les meilleurs candidates pour répondre à ces besoins. En transmettant les symboles à une cadence plus rapide que celle définie par le critère de Nyquist, FTN peut théoriquement augmenter le débit mais en introduisant des interférences en contrepartie. Dans cette thèse, nous explorons le concept des transmissions FTN à travers un canal AWGN (Additive White Gaussian Noise) dans le contexte des modulations OFDM/OQAM (Orthogonal Frequency Division Multiplexing with Offset Quadrature Amplitude Modulation).L'objectif principal de cette thèse est de présenter un système OFDM/OQAM qui permet de transmettre l'information au-delà de la cadence de Nyquist tout en tenant en compte la complexité globale du système. Tout d'abord, nous proposons une nouvelle implémentation efficace des systèmes OFDM/OQAM appliquant le concept FTN, désignée ici par FTN-OQAM, qui garde la même complexité que les systèmes OFDM/OQAM et qui permet un gain en débit très proche du gain théorique. Vu que la condition de Nyquist n'est plus respectée, le signal transmis est maintenant perturbé par des interférences. Pour remédier à ce problème, nous proposons un récepteur basé sur le principe de l'égalisation linéaire sous le critère minimum erreur quadratique moyenne avec annulation d'interférences appelé MMSE LE-IC. Le but de notre système est d'augmenter le débit de transmission, ce qui signifie que des constellations d'ordres élevés seront ciblées. Dans ce contexte, le MMSE LE-IC, dont la complexité est indépendante de la constellation, représente un bon compromis entre efficacité et complexité. Puisque la modulation OFDM/OQAM utilise différents types de formes d'ondes, nous proposons pour plusieurs d'entre elles un algorithme pour déterminer la valeur minimale du facteur d'accélération, en fonction de l'ordre de constellation, qui apporte un gain en efficacité spectrale tout en gardant les mêmes performances que les systèmes respectant le critère de Nyquist à un SNR fixé. Ensuite, nous étudions l'amélioration du traitement itératif de l'émetteur-récepteur. La méthode proposée consiste à combiner un précodeur avec le système FTN-OQAM afin de réduire les interférences causées par du FTN à l'émission. Nous proposons un modèle de précodage dispersé, car il est difficile de précoder conjointement tous les symboles transmis. Nous présentons trois familles de précodeurs avec les récepteurs correspondants. En outre, nous modifions différents blocs de l'émetteur FTN-OQAM tels que le codage canal, le mappage des bits et le mappage des symboles afin d'améliorer davantage le transmetteur FTN-OQAM. Les résultats présentés révèlent le potentiel important des systèmes proposés. / The exponential growth of wireless data traffic driven by mobile Internet and smart devices constrains the future radio systems to include advanced modulations/waveforms offering higher data rates with more efficient bandwidth usage. One possibility is to violate the well known Nyquist criterion by transmitting faster than the Nyquist rate, i.e., using a technique also known as Faster-Than-Nyquist (FTN) signaling. Nyquist-based systems have the advantage of simple transmitter and receiver architectures at the detriment of bandwidth efficiency. The idea of signaling beyond the Nyquist rate to trade the interference-free transmission for more throughput goes back to 1975. In this dissertation, we investigate the concept of FTN signaling over Additive White Gaussian Noise (AWGN) channel in the context of Orthogonal Frequency Division Multiplexing with Offset Quadrature Amplitude Modulation OFDM/OQAM modulation.The main objective of our work is to present an OFDM/OQAM system signaling faster than the Nyquist one and explore its potential rate improvement while keeping under consideration the overall system complexity. First, we propose a new efficient FTN implementation of OFDM/OQAM systems, denoted by FTN-OQAM, that has the same complexity as OFDM/OQAM systems, while approaching very closely the FTN theoretical rate improvement. As the Nyquist condition is no longer respected, severe interference impacts the transmitted signals. To deal with the introduced interferences, we propose a turbo-like receiver based on Minimum Mean Square Error Linear Equalization and Interference Cancellation, named MMSE LE-IC. The aim of our system is to boost the transmission rate, which means that high constellation orders will be targeted. In this respect, the MMSE LE-IC, whose complexity is independent of the constellation, turns out to be a good candidate. Since OFDM/OQAM modulation can be equipped with different types of pulse shapes, we propose an algorithm to find, for different constellation orders, the minimum achieved FTN packing factor for various pulse shapes. Then, we aim at improving the iterative processing of the introduced transceiver. The proposed method involves combining a precoder with the FTN-OQAM system in order to remove FTN-induced interference at the transmitter. We also present a sparse precoding pattern as it is difficult to jointly precode all the transmitted symbols. We introduce three families of precoders along with the corresponding receivers. Furthermore, we propose several modifications of the FTN-OQAM transmitter concerning different blocks such as channel coding, bits mapping and symbols mapping to further enhance the FTN-OQAM transceiver design. Presented results reveal the significant potential of the proposed methods.

Sustainably realizing applications of the future with high performance demands requires that energy efficiency becomes a central design criterion for the entire system. For example, the power consumption of the analog-to-digital converter (ADC) can become a major factor when transmitting at large bandwidths and carrier frequencies, e.g., for ultra-short range high data rate communication. The consumed energy per conversion step increases with the sampling rate such that high resolution ADCs become unfeasible in the sub-THz regime at the very high sampling rates required. This makes signaling schemes adapted to 1-bit quantizers a promising alternative. We therefore quantify the performance of bandlimited 1-bit quantized wireless communication channels using techniques like oversampling and faster-than-Nyquist (FTN) signaling to compensate for the loss of achievable rate. As a limiting case, we provide bounds on the mutual information rate of the hard bandlimited 1-bit quantized continuous-time – i.e., infinitely oversampled – additive white Gaussian noise channel in the mid-to-high signal-to-noise ratio (SNR) regime. We derive analytic expressions using runlength encoded input signals. For real signals the maximum value of the lower bound on the spectral efficiency in the high-SNR limit was found to be approximately 1.63 bit/s/Hz. Since in practical scenarios the oversampling ratio remains finite, we derive bounds on the achievable rate of the bandlimited oversampled discrete-time channel. These bounds match the results of the continuous-time channel remarkably well. We observe spectral efficiencies up to 1.53 bit/s/Hz in the high-SNR limit given hard bandlimitation. When excess bandwidth is tolerable, spectral efficiencies above 2 bit/s/Hz per domain are achievable w.r.t. the 95 %-power containment bandwidth. Applying the obtained bounds to a bandlimited oversampled 1-bit quantized multiple-input multiple-output channel, we show the benefits when using appropriate power allocation schemes. As a constant envelope modulation scheme, continuous phase modulation is considered in order to relieve linearity requirements on the power amplifier. Noise-free performance limits are investigated for phase shift keying (PSK) and continuous phase frequency shift keying (CPFSK) using higher-order modulation alphabets and intermediate frequencies. Adapted waveforms are designed that can be described as FTN-CPFSK. With the same spectral efficiency in the high-SNR limit as PSK and CPFSK, these waveforms provide a significantly improved bit error rate (BER) performance. The gain in SNR required for achieving a certain BER can be up to 20 dB. / Die nachhaltige Realisierung von zukünftigen Übertragungssystemen mit hohen Leistungsanforderungen erfordert, dass die Energieeffizienz zu einem zentralen Designkriterium für das gesamte System wird. Zum Beispiel kann die Leistungsaufnahme des Analog-Digital-Wandlers (ADC) zu einem wichtigen Faktor bei der Übertragung mit großen Bandbreiten und Trägerfrequenzen werden, z. B. für die Kommunikation mit hohen Datenraten über sehr kurze Entfernungen. Die verbrauchte Energie des ADCs steigt mit der Abtastrate, so dass hochauflösende ADCs im Sub-THz-Bereich bei den erforderlichen sehr hohen Abtastraten schwer einsetzbar sind. Dies macht Signalisierungsschemata, die an 1-Bit-Quantisierer angepasst sind, zu einer vielversprechenden Alternative. Wir quantifizieren daher die Leistungsfähigkeit von bandbegrenzten 1-Bit-quantisierten drahtlosen Kommunikationssystemen, wobei Techniken wie Oversampling und Faster-than-Nyquist (FTN) Signalisierung eingesetzt werden, um den durch Quantisierung verursachten Verlust der erreichbaren Rate auszugleichen. Wir geben Grenzen für die Transinformationsrate des Extremfalls eines strikt bandbegrenzten 1-Bit quantisierten zeitkontinuierlichen – d.h. unendlich überabgetasteten – Kanals mit additivem weißen Gauß’schen Rauschen bei mittlerem bis hohem Signal-Rausch-Verhältnis (SNR) an. Wir leiten analytische Ausdrücke basierend auf lauflängencodierten Eingangssignalen ab. Für reelle Signale ist der maximale Wert der unteren Grenze der spektralen Effizienz im Hoch-SNR-Bereich etwa 1,63 Bit/s/Hz. Da die Überabtastrate in praktischen Szenarien endlich bleibt, geben wir Grenzen für die erreichbare Rate eines bandbegrenzten, überabgetasteten zeitdiskreten Kanals an. Diese Grenzen stimmen mit den Ergebnissen des zeitkontinuierlichen Kanals bemerkenswert gut überein. Im Hoch-SNR-Bereich sind spektrale Effizienzen bis zu 1,53 Bit/s/Hz bei strikter Bandbegrenzung möglich. Wenn Energieanteile außerhalb des Frequenzbandes tolerierbar sind, können spektrale Effizienzen über 2 Bit/s/Hz pro Domäne – bezogen auf die Bandbreite, die 95 % der Energie enthält – erreichbar sein. Durch die Anwendung der erhaltenen Grenzen auf einen bandbegrenzten überabgetasteten 1-Bit quantisierten Multiple-Input Multiple-Output-Kanal zeigen wir Vorteile durch die Verwendung geeigneter Leistungsverteilungsschemata. Als Modulationsverfahren mit konstanter Hüllkurve betrachten wir kontinuierliche Phasenmodulation, um die Anforderungen an die Linearität des Leistungsverstärkers zu verringern. Beschränkungen für die erreichbare Datenrate bei rauschfreier Übertragung auf Zwischenfrequenzen mit Modulationsalphabeten höherer Ordnung werden für Phase-shift keying (PSK) and Continuous-phase frequency-shift keying (CPFSK) untersucht. Weiterhin werden angepasste Signalformen entworfen, die als FTN-CPFSK beschrieben werden können. Mit der gleichen spektralen Effizienz im Hoch-SNR-Bereich wie PSK und CPFSK bieten diese Signalformen eine deutlich verbesserte Bitfehlerrate (BER). Die Verringerung des erforderlichen SNRs zur Erreichung einer bestimmten BER kann bis zu 20 dB betragen.

The objective of the proposed research is to develop a framework for the signal reconstruction algorithm with sub-Nyquist sampling rate and the low-cost hardware design in system level. A further objective of the proposed research is to monitor the device-under-test (DUT) and to adapt its behaviors. The key contribution of this research is that the high-speed signal acquisition is done by direct subsampling. As the signal is directly sampled without any front-end radio-frequency (RF) components such as mixers or filters, the cost of hardware is reduced. Furthermore, the distortion and the nonlinearity from the RF components can be avoided. The first proposed work is wideband signal reconstruction by dual-rate time-interleaved subsampling hardware and Multi-coset signal reconstruction. Using the combination of the dual-rate hardware and the multi-coset algorithm, the number of sampling channel is significantly reduced compared to the conventional multi-coset works. The second proposed work is jitter tracking by accurate period estimation with incoherent subsampling. In this work, the long-term jitter in PRBS is tracked without hardware synchronization and clock-data-recovery (CDR) circuits. The third proposed work is eye-monitoring and time-domain-reflectometry (TDR) by monobit receiver signal reconstruction. Using a monobit receiver based on incoherent subsampling and time-variant threshold signal, high resolution of reconstructed signal in both amplitude and time is achieved. Compared to a multibit-receiver, the scalability of the test-system is significantly increased.

Nowadays, several studies are launched for the design of reliable and safe communications systems that introduce Unmanned Aerial Vehicle (UAV), this paves the way for UAV communication systems to play an important role in a lot of applications for non-segregated military and civil airspaces. Until today, rules for integrating commercial UAVs in airspace still need to be defined, the design of secure, highly reliable and cost effective communications systems still a challenging task. This thesis is part of this communication context. Motivated by the rapid growth of UAV quantities and by the new generations of UAVs controlled by satellite, the thesis aims to study the various possible UAV links which connect UAV/aircraft to other communication system components (satellite, terrestrial networks, etc.). Three main links are considered: the Forward link, the Return link and the Mission link. Due to spectrum scarcity and higher concentration in aircraft density, spectral efficiency becomes a crucial parameter for largescale deployment of UAVs. In order to set up a spectrally efficient UAV communication system, a good understanding of transmission channel for each link is indispensable, as well as a judicious choice of the waveform. This thesis begins to study propagation channels for each link: a mutipath channels through radio Line-of-Sight (LOS) links, in a context of using Meduim Altitude Long drones Endurance (MALE) UAVs. The objective of this thesis is to maximize the solutions and the algorithms used for signal reception such as channel estimation and channel equalization. These algorithms will be used to estimate and to equalize the existing muti-path propagation channels. Furthermore, the proposed methods depend on the choosen waveform. Because of the presence of satellite link, in this thesis, we consider two low-papr linear waveforms: classical Single-Carrier (SC) waveform and Extented Weighted Single-Carrier Orthogonal Frequency-Division Multiplexing (EW-SC-OFDM) waveform. channel estimation and channel equalization are performed in the time-domain (SC) or in the frequency-domain (EW-SC-OFDM). UAV architecture envisages the implantation of two antennas placed at wings. These two antennas can be used to increase diversity gain (channel matrix gain). In order to reduce channel equalization complexity, the EWSC- OFDM waveform is proposed and studied in a muti-antennas context, also for the purpose of enhancing UAV endurance and also increasing spectral efficiency, a new modulation technique is considered: Spatial Modulation (SM). In SM, transmit antennas are activated in an alternating manner. The use of EW-SC-OFDM waveform combined to SM technique allows us to propose new modified structures which exploit exces bandwidth to improve antenna bit protection and thus enhancing system performances.

Sampling theory studies the equivalence between continuous and discrete representations of information. This equivalence is ubiquitously used in communication engineering and signal processing. For example, it allows engineers to store continuous signals as discrete data on digital media. The classical sampling theorem, also known as the theorem of Whittaker-Shannon-Kotel'nikov, enables one to perfectly and stably reconstruct continuous signals with a constant bandwidth from their discrete samples at a constant Nyquist rate. The Nyquist rate depends on the bandwidth of the signals, namely, the frequency upper bound. Intuitively, a signal's `information density' and `effective bandwidth' should vary in time. Adjusting the sampling rate accordingly should improve the sampling efficiency and information storage. While this old idea has been pursued in numerous publications, fundamental problems have remained: How can a reliable concept of time-varying bandwidth been defined? How can samples taken at a time-varying Nyquist rate lead to perfect and stable reconstruction of the continuous signals? This thesis develops a new non-Fourier generalized sampling theory which takes samples only as often as necessary at a time-varying Nyquist rate and maintains the ability to perfectly reconstruct the signals. The resulting Nyquist rate is the critical sampling rate below which there is insufficient information to reconstruct the signal and above which there is redundancy in the stored samples. It is also optimal for the stability of reconstruction. To this end, following work by A. Kempf, the sampling points at a Nyquist rate are identified as the eigenvalues of self-adjoint extensions of a simple symmetric operator with deficiency indices (1,1). The thesis then develops and in a sense completes this theory. In particular, the thesis introduces and studies filtering, and yields key results on the stability and optimality of this new method. While these new results should greatly help in making time-variable sampling methods applicable in practice, the thesis also presents a range of new purely mathematical results. For example, the thesis presents new results that show how to explicitly calculate the eigenvalues of the complete set of self-adjoint extensions of such a symmetric operator in the Hilbert space. This result is of interest in the field of functional analysis where it advances von Neumann's theory of self-adjoint extensions.

Recently, there has been a significant surge of interest towards the design and development of a new global-scale communication network that can overcome the limitations of the current Internet. Among the numerous directions of improvement in networking technology, recent pursuit to do better flow control of network traffic has led to the emergence of several explicit-feedback congestion control methods. As a first step towards understanding these methods, we analyze the stability and transient performance of Rate Control Protocol (RCP).We find that RCP can become unstable in certain topologies and may exhibit very high buffering requirements at routers. To address these limitations, we propose a new controller called Proportional Integral Queue Independent RCP (PIQI-RCP), prove its stability under heterogeneous delay, and use simulations to show that the new method has significantly lower transient queue lengths, better transient dynamics, and tractable stability properties. As a second step in understanding explicit congestion control, we experimentally evaluate proposed methods such as XCP, JetMax, RCP, and PIQI-RCP using their Linux implementation developed by us. Our experiments show that these protocols are scalable with the increase in link capacity and round-trip propagation delay. In steady-state, they have low queuing delay and almost zero packet-loss rate. We confirm that XCP cannot achieve max-min fairness in certain topologies. We find that JetMax significantly drops link utilization in the presence of short flows with long flow and RCP requires large buffer size at bottleneck routers to prevent transient packet losses and is slower in convergence to steady-state as compared to other methods. We observe that PIQI-RCP performs better than RCP in most of the experiments.

The noise in the Langmuir Probe and Plasma Wave Instrument (LP-PWI) on board ESA:s future Jupiter satellite JUICE (Jupiter ICy Moons Explorer) was investigated. Thermal Johnson-Nyquist noise and shot noise, caused by fluctuations in the probe-plasma currents, were combined with the quasi-thermal noise (QTN) due to thermal fluctuations in the electric field in the plasma, using a small signal equivalent circuit model. The contributions and effects of each of the considered noise sources were examined and compared for a number of representative space plasma conditions, including the cold dense plasma of Ganymede's ionosphere and the hot tenuous plasma out in the Jovian magnetosphere. The results showed that in the cold dense plasma of Ganymede's ionosphere, the antenna was long compared to the Debye length and the quasi-thermal noise had a clearly pronounced peak and a steep high-frequency cut-off. For an antenna biased to 1 V with respect to the plasma, the shot noise due to the ambient plasma was the dominant source of noise. For a an antenna at the floating potential the photoelectron shot noise coalesced with the shot and Nyquist noises of the ambient plasma to form almost a single curve. In the hot tenuous plasma out in Jupiter's magnetosphere, the antenna was short compared to the Debye length and the QTN spectrum was much flatter, with little or no peak at the plasma frequency and a very weak high-frequency cut-off. For an antenna biased to 1 V, the shot noise due to photoelectron emission dominated at Callisto's orbital position whereas at Ganymede's and Europa's orbital positions the Nyquist and shot noises of the ambient plasma particles were the dominant noise components. For an antenna at the floating potential, the shot and Nyquist noises of the ambient plasma also dominated the output noise, except at Europa's orbital position, where the quasi-thermal noise was the largest noise component for frequencies at and above the plasma frequency. The numerical calculations were performed using MATLAB. The code was made available in a Git repository at https://github.com/eliasodelstad/irfuproj_JUICE_noise.

Sampling theory studies the equivalence between continuous and discrete representations of information. This equivalence is ubiquitously used in communication engineering and signal processing. For example, it allows engineers to store continuous signals as discrete data on digital media. The classical sampling theorem, also known as the theorem of Whittaker-Shannon-Kotel'nikov, enables one to perfectly and stably reconstruct continuous signals with a constant bandwidth from their discrete samples at a constant Nyquist rate. The Nyquist rate depends on the bandwidth of the signals, namely, the frequency upper bound. Intuitively, a signal's `information density' and `effective bandwidth' should vary in time. Adjusting the sampling rate accordingly should improve the sampling efficiency and information storage. While this old idea has been pursued in numerous publications, fundamental problems have remained: How can a reliable concept of time-varying bandwidth been defined? How can samples taken at a time-varying Nyquist rate lead to perfect and stable reconstruction of the continuous signals? This thesis develops a new non-Fourier generalized sampling theory which takes samples only as often as necessary at a time-varying Nyquist rate and maintains the ability to perfectly reconstruct the signals. The resulting Nyquist rate is the critical sampling rate below which there is insufficient information to reconstruct the signal and above which there is redundancy in the stored samples. It is also optimal for the stability of reconstruction. To this end, following work by A. Kempf, the sampling points at a Nyquist rate are identified as the eigenvalues of self-adjoint extensions of a simple symmetric operator with deficiency indices (1,1). The thesis then develops and in a sense completes this theory. In particular, the thesis introduces and studies filtering, and yields key results on the stability and optimality of this new method. While these new results should greatly help in making time-variable sampling methods applicable in practice, the thesis also presents a range of new purely mathematical results. For example, the thesis presents new results that show how to explicitly calculate the eigenvalues of the complete set of self-adjoint extensions of such a symmetric operator in the Hilbert space. This result is of interest in the field of functional analysis where it advances von Neumann's theory of self-adjoint extensions.