Wavelet Modulation (WM)---also referred to as fractal modulation---simultaneously sends data at multiple rates through an unknown channel. This novel multirate diversity strategy offers improved message recovery over conventional modulation techniques: if the message is not received at one rate due to the channel disturbances, it can be received at another rate where the channel is clear. Previous research has demonstrated the performance of wavelet modulation in Gaussian channels. This paper extends the investigation to the performance of wavelet modulation in time varying channels. We show that bit error rate (BER) wavelet demodulation performance in the additive, white, Gaussian noise (AWGN) channel is comparable to theoretical binary phase shift keying. Our results depict the improvement in performance that can be realized for time varying channels by utilizing the various rates of wavelet modulation; BER versus SNR curves for each fading channel show how the message at one rate can be more accurately recovered than at another rate. Furthermore, we also present results indicating the dramatic improvement in wavelet demodulation performance when multiple rates are available and utilized for demodulation. This improvement in performance is highly visible in BER performance for the AWGN and flat fading channels. Finally, a comparison of binary phase shift keying (BPSK) and WM in a frequency selective channel is performed. The BER improvement of WM is shown when demodulation is done at rates which are least corrupted by ISI. We illustrate our new algorithm that: identifies the channel characteristics; determines which rates are maximally corrupted by ISI; and, utilizes only those uncorrupted copies in demodulation. / Master of Science

On étudie le problème de la transmission de l'information à travers le canal AWGN en utilisant des réseaux. On commence par considérer des constellations infinies. Une nouvelle famille de réseaux obtenus par Construction A à partir de codes linéaires non binaires est proposée. Ces réseaux sont appelés LDA ("Low-Density Construction A") et sont caractérisés par des matrices de parité p-aires creuses, qui les mettent en relation directe avec les codes LPDC. Deux résultats sur leur possibilité d'atteindre la capacité de Poltyrev sont provés ; cela est d'abord démontré pour des poids des lignes logarithmiques des matrices de parité associées, puis pour des poids constants. Le deuxième résultat est basé sur certaines propriétés d'expansion des graphes de Tanner correspondants à ces matrices. Un autre sujet de ce travail concerne les constellations finies de réseaux. une nouvelle preuve est donnée du fait que des réseaux aléatoires obtenus par Construction A generale atteignent la capacité avec décodage de type "lattice decoding". Cela prolonge et améliore le travail de Erez et Zamir (2004), Ordentlich et Edrez (2012) Ling et Belfiore (2013). Cette preuve est basée sur les constellations de Coronoï et la multiplication par le coefficient de Wiener ("MMSE scaling") du siganl en sortie du canal. Finalement, ce résultat est adapté au cas des réseaux LDA, qui eux aussi atteignent la capacité avec le même procédé de transmission. Encore une fois, il est nécessaire d'exploiter les propriétés d'expansion des graphes de Tanner. A la fin de la dissertation, on présente un algorithme de décodage itératif et de type "message-passing" approprié au décodage des LDA en grandes dimensions. / The probleme of transmission of information over the AWGN channel using lattices is addressed. Firstly, infinite constellations are considered. A nex family of integer lattices built by means of construction A with non-binary linear condes is introduced. These lattices are called LPA (Low-Density Construction A) and are characterised by sparse p-ary parity-chedk matrices, that put them in direct relation with LPDC codes. Two results about the Poltyrev-capacity-archieving qualities of this family are proved, respectively for logarithmic row degree and constant row degree of the associated parity-check matrices. The second result is based on some expansion poperties of the Tanner graphs related to these matrices. Another topic of this work concerns finite lattice constellations. A new proff that heneral random Construction A lattices achieve capacity under lattice deconding is provided, continuing and pimproving the work of Erez and Zamir (2004), Ordentlich an Erez (2012), and Ling and Belfiore (2013). This proof is based on Voronoi lattice constellations and MMSE scaling of the channel output. Finally, this approach is adapted to the LDA case abd ut us scgiwn tgat LDA lattices achive capacity with the ame transmission scheme, too. Once again, it is necessary to exploit the expansion properties of the Tanner graphs. At he end of the dissertation, an iterative message-passing algorithm suitable for decoding LDA lattices in high dimensions is presented.

Communications receivers that rely on 1-bit analogto-digital conversion are advantageous in terms of hardware complexity and power dissipation. Performance limitations due to the 1-bit quantization can be tackled with oversampling. This paper considers the oversampling gain from an information-theoretic perspective by analyzing the channel capacity with 1-bit quantization and oversampling at the receiver for the particular case of AWGN channels. This includes a numerical computation of the capacity and optimal transmit symbol constellations, as well as the derivation of closed-form expressions for large oversampling ratios and for high signal-to-noise ratios of the channel.

La performance de démodulation des signaux GNSS existants, GPS L1 C/A, L2C ou L5, est satisfaisante en environnements ouverts où le C/N0 disponible est assez élevé. Cependant, en milieu urbain, le niveau de C/N0 du signal reçu est souvent très bas et est affecté de variations rapides qui peuvent nuire la démodulation des messages GNSS. Donc, car les applications du marché de masse sont appelées à être déployées dans ces environnements, il est nécessaire d'étudier et de chercher des méthodes de démodulation/décodage qui améliorent la performance de démodulation des messages GNSS dans ces environnements. Il est aussi nécessaire de considérer les nouveaux signaux GPS L1C et GALILEO E1. Ces signaux doivent fournir un service de positionnement par satellite dans tout type d'environnement, et spécifiquement en milieu urbain. Ainsi, cette thèse analyse aussi les performances de démodulation des nouveaux signaux GNSS tels que définis dans les documents publics actuels. De plus, de nouvelles structures de message GALILEO E1 sont proposées et analysées afin d'optimiser la performance de démodulation ainsi que la quantité d'information diffusée. En conséquence, le but principal de cette thèse est d'analyser et améliorer la performance de démodulation des signaux GNSS ouverts au public, spécifiquement en milieu urbain, et de proposer de nouvelles structures de messages de navigation pour GALILEO E1. La structure détaillée des chapitres de cette thèse est donnée ci-après. En premier lieu, le sujet de cette thèse est introduit, ses contributions originales sont mises en avant, et le plan du rapport est présenté. Dans le 2ième chapitre, la thèse décrit la structure actuelle des signaux GNSS analysés, en se concentrant sur la structure du message de navigation, les codages canal implantés et leurs techniques de décodage. Dans le 3ième chapitre, deux types de modèles de canal de propagation sont présentés pour deux différents types de scénarios. D'un côté, un canal AWGN est choisi pour modéliser les environnements ouverts. De l'autre côté, le modèle mathématique de Perez-Fontan d'un canal mobile est choisi pour représenter les environnements urbains et indoor. Dans le 4ième chapitre, une tentative pour effectuer une prédiction binaire d'une partie du message de navigation GPS L1 C/A est présentée. La prédiction est essayée en utilisant les almanachs GPS L1 C/A, grâce à un programme de prédiction à long terme fourni par TAS-F, et des méthodes de traitement du signal: estimation spectrale, méthode de PRONY et réseau de neurones. Dans le 5ème chapitre, des améliorations à la performance de démodulation du message de GPS L2C et L5 sont apportées en utilisant leur codage canal de manière non traditionnelle. Deux méthodes sont analysées. La première méthode consiste à combiner les codages canal internes et externes du message afin de corriger davantage de mots reçus. La deuxième méthode consiste à utiliser les probabilités des données d'éphémérides afin d'améliorer le décodage traditionnel de Viterbi. Dans le 6ième chapitre, la performance de démodulation des messages de GPS L1C et du Open Service GALILEO E1 est analysée dans différents environnements. D'abord, une étude de la structure de ces deux signaux est présentée pour déterminer le C/N0 du signal utile reçu dans un canal AWGN. Puis, la performance de démodulation de ces signaux est analysée grâce à des simulations dans différents environnements, avec un récepteur se déplaçant à différentes vitesses et avec différentes techniques d'estimation de la phase porteuse du signal. / The demodulation performance achieved by any of the existing GPS signals, L1 C/A, L2C or L5, is satisfactory in open environments where the available C/N0 is quite high. However, in indoor/urban environments, the C/N0 level of the received signal is often very low and suffers fast variations which can further affect the GNSS messages demodulation. Therefore, since the mass-market applications being designed nowadays are aimed at these environments, it is necessary to study and to search alternative demodulation/decoding methods which improve the GNSS messages demodulation performance in these environments. Moreover, new GNSS signals recently developed, such as GPS L1C and GALILEO E1, must also be considered. These signals aim at providing satellite navigation positioning service in any kind of environment, giving special attention to indoor and urban environments. Therefore, the demodulation performances of the new GNSS signals as they are defined in the current public documents is also analysed. Moreover, new GALILEO E1 message structures are proposed and analysed in order to optimize the demodulation performance as well as the quantity of broadcasted information. Therefore, the main goal of this dissertation is to analyse and to improve the demodulation performance of the current open GNSS signals, specifically in indoor and urban environments, and to propose new navigation message structures for GALILEO E1. A detailed structure of this dissertation sections is given next. First, the subject of this thesis is introduced, original contributions are highlighted, and the outline of the report is presented. Second, this dissertation begins by a description of the current structure of the different analysed GNSS signals, paying special attention to the navigation message structure, implemented channel code and their decoding techniques. In the third section, two types of transmission channel models are presented for two different types of environments. On one hand, an AWGN channel is used to model the signal transmission in an open environments. On the other hand, the choice of a specific mobile channel, the Perez-Fontan channel model, is chosen to model the signal transmission in an urban environment. In the fourth section, a tentative to make a binary prediction of the broadcasted satellite ephemeris of the GPS L1 C/A navigation message is presented. The prediction is attempted using the GPS L1 C/A almanacs data, a long term orbital prediction program provided by TAS-F, and some signal processing methods: spectral estimation, the PRONY method, and a neural network. In the fifth section, improvements to the GPS L2C and GPS L5 navigation message demodulation performance are brought by using their channel codes in a non-traditional way. Two methods are inspected. The first method consists in sharing information between the message inner and outer channel codes in order to correct more received words. The second method consists in using the ephemeris data probabilities in order to improve the traditional Viterbi decoding. In the sixth section, the GPS L1C and GALILEO E1 Open Service demodulation performance is analysed in different environments. First, a brief study of the structure of both signals to determine the received C/N0 in an AWGN channel is presented. Second, their demodulation performance is analysed through simulations in different environments, with different receiver speeds and signal carrier phase estimation techniques.

International Telemetering Conference Proceedings / October 20-23, 2003 / Riviera Hotel and Convention Center, Las Vegas, Nevada / An implementation of a Pseudo Error Detection (PSED) system is presented and its performance in conjunction with smart antenna and smart diversity systems tested and evaluated. Non redundancy, instant response and relative simplicity make the Pseudo Error Detectors excellent real time error monitoring systems in smart antenna and smart diversity systems. Because of the Non-redundant Error Detection mechanism in Pseudo Error Detectors, we can monitor the error quality without any coding or overhead. The output of the pseudo error detector in AWGN, selective fading Doppler shift and other interference environments is directly correlated to the BER and BLER. This direct correlation makes it a great tool for online error monitoring of a system and can have numerous applications In a PSED the Eye diagram from the demodulator is sampled once per symbol. By monitoring and comparison of the eye at sampled intervals at different thresholds, we would know if an error has occurred. By integrating this result over a period of time we can get the averaged error level. The results provided in this paper were obtained and verified by both MatLab simulations using dynamic simulation techniques and hardware measurements over dynamic channels.

International Telemetering Conference Proceedings / October 20-23, 2003 / Riviera Hotel and Convention Center, Las Vegas, Nevada / An improved performance smart diversity was invented to improve the signal performance in a combined selective fading, Additive White Gaussian Noise (AWGN), Co-channel interference (CCI) and Doppler shift environment such as the LEO satellite channel. This system is also applicable to aeronautical and telemetry channels. Smart diversity is defined here as a mechanism that selects at each moment the best branch in a n-branch diversity system based on the error quality with no default branch and no prioritization. The predominant novelty of this discovery is the introduction of multi level analog based Pseudo Error Detectors (PSED) in every branch. One of the advantages of PSED is that it is a non redundant error detection system, with no requirement for overhead and no need for additional valuable spectrum. This research was motivated by problems in LEO satellite systems due to low orbit and high relative speed with respect to the ground stations. The system is independent of the modulation techniques and is applicable to both coherent and non-coherent detections. The results from simulations using dynamic simulation techniques and hardware measurements over dynamic channels show significant improvement of both the Bit Error Rate (BER) and the Block Error Rate (BLER).

Dans cette thèse, le compromis entre la consommation d'énergie et le délai dans les réseaux de capteurs sans fil est étudié en exploitant efficacement les liens non fiables. Nous proposons une métrique de l'efficacité énergétique et une métrique de délai moyenne qui sont combinés avec le modèle de lien radio à erreur. En utilisant ces deux métriques et un modèle réaliste de lien radio, nous déduisons la limite inférieure et le front de Pareto du compromis Energie-Délai sont calculés pour trois types de systèmes de communication: la communication multi-saut traditionnelle, la communication opportuniste et la communication coopérative MIMO (CMIMO) dans trois différents canaux: le canal a bruit additif blanc Gaussien, le canal a évanouissements rapides de Rayleigh et le canal a évanouissement de Rayleigh par blocs. Les expressions de ces limites faibles sont obtenues et vérifiées par des simulations bidimensionnelles de réseaux de capteurs distribués aléatoirement. Sur la base de l'expression de la borne inférieure du compromis Energie-Délai, un cadre multi-couche est fourni pour optimiser les paramètres des couches physique, MAC et routage sous contrainte de délai. Les résultats obtenus montrent que pour parvenir à une meilleure performance Energie-Délai, les mécanismes de communication suivants devraient être adoptés selon le type de canal : les communications multi-saut traditionnelles sont les plus performantes pour le canal à bruit additif blanc Gaussien, alors que les communications opportunistes le sont pour les canaux à évanouissements de Rayleigh par blocs et enfin le CMIMO pour les canaux à évanouissements rapides de Rayleigh.

We introduced nested search methods to design (n, k) block codes for arbitrary channels by optimizing an appropriate metric spectrum in each iteration. For a given k, the methods start with a good high rate code, say k/(k + 1), and successively design lower rate codes up to rate k/2^k corresponding to a Hadamard code. Using a full search for small binary codes we found that optimal or near-optimal codes of increasing length can be obtained in a nested manner by utilizing Hadamard matrix columns. The codes can be linear if the Hadamard matrix is linear and non-linear otherwise. The design methodology was extended to the generic complex codes by utilizing columns of newly derived or existing unitary codes. The inherent nested nature of the codes make them ideal for progressive transmission. Extensive comparisons to metric bounds and to previously designed codes show the optimality or near-optimality of the new codes, designed for the fading and the additive white Gaussian noise channel (AWGN). It was also shown that linear codes can be optimal or at least meeting the metric bounds; one example is the systematic pilot-based code of rate k/(k + 1) which was proved to meet the lower bound on the maximum cross-correlation. Further, the method was generalized such that good codes for arbitrary channels can be designed given the corresponding metric or the pairwise error probability. In synchronous multiple-access schemes it is common to use unitary block codes to transmit the multiple users’ information, especially in the downlink. In this work we suggest the use of newly designed non-unitary block codes, resulting in increased throughput efficiency, while the performance is shown not to be substantially sacrificed. The non-unitary codes are again developed through suitable nested searches. In addition, new multiple-access codes are introduced that optimize certain criteria, such as the sum-rate capacity. Finally, the introduction of the asymptotically optimum convolutional codes for a given constraint length, reduces dramatically the search size for good convolutional codes of a certain asymptotic performance, and the consequences to coded code-division multiple access (CDMA) system design are highlighted.

Tese de doutoramento. Engenharia Electrotécnica e de Computadores. Universidade do Porto. Faculdade de Engenharia. 2011

We address the problem of image denoising for additive white Gaussian noise (AWGN), Poisson noise, and Chi-squared noise scenarios. Thermal noise in electronic circuitry in camera hardware can be modeled as AWGN. Poisson noise is used to model the randomness associated with photon counting during image acquisition. Chi-squared noise statistics are appropriate in imaging modalities such as Magnetic Resonance Imaging (MRI). AWGN is additive, while Poisson noise is neither additive nor multiplicative. Although Chi-squared noise is derived from AWGN statistics, it is non-additive. Mean-square error (MSE) is the most widely used metric to quantify denoising performance. In parametric denoising approaches, the optimal parameters of the denoising function are chosen by employing a minimum mean-square-error (MMSE) criterion. However, the dependence of MSE on the noise-free signal makes MSE computation infeasible in practical scenarios. We circumvent the problem by adopting an MSE estimation approach. The ground-truth-independent estimates of MSE are Stein’s unbiased risk estimate (SURE), Poisson unbiased risk estimate (PURE) and Chi-square unbiased risk estimate (CURE) for AWGN, Poison and Chi-square noise models, respectively. The denoising function is optimized to achieve maximum noise suppression by minimizing the MSE estimates. We have chosen the bilateral filter as the denoising function. Bilateral filter is a nonlinear edge-preserving smoother. The performance of the bilateral filter is governed by the choice of its parameters, which can be optimized to minimize the MSE or its estimate. However, in practical scenarios, MSE cannot be computed due to inaccessibility of the noise-free image. We derive SURE, PURE, and CURE in the context of bilateral filtering and compute the parameters of the bilateral filter that yield the minimum cost (SURE/PURE/CURE). On processing the noisy input with bilateral filter whose optimal parameters are chosen by minimizing MSE estimates (SURE/PURE/CURE), we obtain the estimate closest to the ground truth. We denote the bilateral filter with optimal parameters as SURE-optimal bilateral filter (SOBF), PURE-optimal bilateral filter (POBF) and CURE-optimal bilateral filter (COBF) for AWGN, Poisson and Chi-Squared noise scenarios, respectively. In addition to the globally optimal bilateral filters (SOBF and POBF), we propose spatially adaptive bilateral filter variants, namely, SURE-optimal patch-based bilateral filter (SPBF) and PURE-optimal patch-based bilateral filter (PPBF). SPBF and PPBF yield significant improvements in performance and preserve edges better when compared with their globally-optimal counterparts, SOBF and POBF, respectively. We also propose the SURE-optimal multiresolution bilateral filter (SMBF) where we couple SOBF with wavelet thresholding. For Poisson noise suppression, we propose PURE-optimal multiresolution bilateral filter (PMBF), which is the Poisson counterpart of SMBF. We com-pare the performance of SMBF and PMBF with the state-of-the-art denoising algorithms for AWGN and Poisson noise, respectively. The proposed multiresolution-based bilateral filtering techniques yield denoising performance that is competent with that of the state-of-the-art techniques.