This thesis investigates the use of Maximum Likelihood Sequence Estimation (MLSE) in the presence of unknown channel parameters. MLSE is a fundamental problem that is closely related to many modern research areas like Space-Time Coding, Overloaded Array Processing and Multi-User Detection. Per-Survivor Processing (PSP) is a technique for approximating MLSE for unknown channels by embedding channel estimation into the structure of the Viterbi Algorithm (VA). In the case of successful acquisition, the convergence rate of PSP is comparable to that of the pilot-aided RLS algorithm. However, the performance of PSP degrades when certain sequences are transmitted. In this thesis, the blind acquisition characteristics of PSP are discussed. The problematic sequences for any joint ML data and channel estimator are discussed from an analytic perspective. Based on the theory of indistinguishable sequences, modifications to conventional PSP are suggested that improve its acquisition performance significantly. The effect of tree search and list-based algorithms on PSP is also discussed. Proposed improvement techniques are compared for different channels. For higher order channels, complexity issues dominate the choice of algorithms, so PSP with state reduction techniques is considered. Typical misacquisition conditions, transients, and initialization issues are reported. / Master of Science

In this thesis study, joint frequency offset and channel estimation methods for single-input single-output (SISO) systems are examined. The performance of maximum likelihood estimate of the parameters are studied for different training sequences. Conventionally training sequences are designed solely for the channel estimation purpose. We present a numerical comparison of different training sequences for the joint estimation problem. The performance comparisons are made in terms of mean square estimation error (MSE) versus SNR and MSE versus the total training energy metrics. A novel estimation scheme using complementary sequences have been proposed and compared with existing schemes. The proposed scheme presents a lower estimation error than the others in almost all numerical simulations. The thesis also includes an extension for the joint channel-frequency offset estimation problem to the multi-input multi-output systems and a brief discussion for multiple frequency offset case is also given.

Στο πρώτο μέρος της παρούσας Διπλωματικής Εργασίας εισάγονται οι βασικές έννοιες της Θεωρίας Κωδικοποίησης και των Τηλεπικοινωνιακών Συστημάτων. Για τη διόρθωση λαθών στην περίπτωση της μετάδοσης μέσω ενός θορυβώδους καναλιού εφαρμόζεται κωδικοποίηση καναλιού με Γραμμικούς Μπλοκ Κώδικες, και πιο συγκεκριμένα Κώδικες Χαμηλής Πυκνότητας Ελέγχου Ισοτιμίας (Low-Density Parity-Check Codes, LDPC). Ορίζεται η μαθηματική περιγραφή των κωδίκων αυτών και διατυπώνονται σχετικοί ορισμοί και θεωρήματα. Επίσης, διατυπώνεται το κριτήριο Μέγιστης Πιθανοφάνειας, στο οποίο βασίζεται η ανάπτυξη του αντίστοιχου αποκωδικοποιητή. Το δεύτερο μέρος περιλαμβάνει την εξομοίωση του αποκωδικοποιητή Μέγιστης Πιθανοφάνειας στο λογισμικό και την υλοποίησή του σε FPGA, στις περιπτώσεις όπου χρησιμοποιούνται Soft ή Hard είσοδοι στον αποκωδικοποιητή. Ακόμη, παρουσιάζεται η Αρχιτεκτονική του αποκωδικοποιητή και η Μεθοδολογία Σχεδίασής του. Παρουσιάζονται βελτιώσεις στη σχεδίαση του αποκωδικοποιητή που οδηγούν σε μείωση της απαιτούμενης επιφάνειας στο υλικό. Τα αποτελέσματα που προκύπτουν από τις μετρήσεις των δύο υλοποιήσεων συγκρίνονται με την περίπτωση αποκωδικοποιητή βασισμένο σε επαναλήψεις και εξάγονται τα διαγράμματα ρυθμού σφαλμάτων bit και τα αντίστοιχα συμπεράσματα. / In the first part of this thesis, the basic principles of Coding Theory and Communication Systems are introduced. In order to correct errors in the case of transmission through a noisy channel, channel coding with Linear Block Codes is applied, and more specifically Low-Density Parity-Check (LDPC) codes. The mathematical description of such codes is defined and useful definitions and theorems are specified. In addition, the Maximum Likelihood (ML) criterion is specified, on which the development of the relevant decoder is based. The second part consists of the simulation of the ML decoder in software and its hardware implementation on FPGA, in the cases where either Soft or Hard information is used as the decoder's input. Furthermore, the decoder's Architecture and the Design Methodology used are presented. Improvements concerning the implementation of the decoder are introduced, which lead to a reduction in the required area on chip. The experimental results of the two implementations are compared to the case of the iterative decoder and the Bit Error Rate plots are produced, as well as the appropriate conclusions.

<p>The Multiple-input and Multiple-output (MIMO) channel model is very useful for the presentation of a wide range of wireless communication systems. This thesis addresses the joint design of a precoder and a receiver for a MIMO channel model, in a scenario in which perfect channel state information (CSI) is available at both ends. We develop a novel framework for the transmitting-receiving procedure. Under the proposed framework, the receiver decomposes the channel matrix by using a block QR decomposition, where Q is a unitary matrix and R is a block upper triangular matrix. The optimal maximum likelihood (ML) detection process is employed within each diagonal block of R. Then, the detected block of symbols is substituted and subtracted sequentially according to the block QR decomposition based successive cancellation. On the transmitting end, the expression of probability of error based on ML detection is chosen as the design criterion to formulate the precoder design problem. This thesis presents a design of MIMO transceivers in the particular case of having 4 transmitting and 4 receiving antennas with full CSI knowledge on both sides. In addition, a closed-form expression for the optimal precoder matrix is obtained for channels satisfying certain conditions. For other channels not satisfying the specific condition, a numerical method is applied to obtain the optimal precoder matrix.</p> / Master of Applied Science (MASc)

Regression analysis is very popular among researchers in various fields but almost all the researchers use the classical methods which assume that X is nonstochastic and the error is normally distributed. However, in real life problems, X is generally stochastic and error can be nonnormal. Maximum likelihood (ML) estimation technique which is known to have optimal features, is very problematic in situations when the distribution of X (marginal part) or error (conditional part) is nonnormal. Modified maximum likelihood (MML) technique which is asymptotically giving the estimators equivalent to the ML estimators, gives us the opportunity to conduct the estimation and the hypothesis testing procedures under nonnormal marginal and conditional distributions. In this study we show that MML estimators are highly efficient and robust. Moreover, the test statistics based on the MML estimators are much more powerful and robust compared to the test statistics based on least squares (LS) estimators which are mostly used in literature. Theoretically, MML estimators are asymptotically minimum variance bound (MVB) estimators but simulation results show that they are highly efficient even for small sample sizes. In this thesis, Weibull and Generalized Logistic distributions are used for illustration and the results given are based on these distributions. As a future study, MML technique can be utilized for other types of distributions and the procedures based on bivariate data can be extended to multivariate data.

Cette thèse est dédié à l’étude de la problématique des interférences multi utilisateurs dans le système Argos et à la proposition des diverses techniques pour réduire les effets de ces interférences. Le système Argos est un système mondial de localisation et de collecte de données géo positionnées par satellite. Il permet à l’échelle mondiale de collecter et de traiter les données émises par des émetteurs installés sur la surface de terre. Ces émetteurs sont connus sous le nom de balises. Ces balises sont installées sur des voiliers, des stations météo, des bouées, ainsi que sur quelques animaux (phoques, penguins, etc.…). Le système Argos a été créé en 1978 par le Centre National des Études spatiales (CNES), l’agence spatiale américaine (NASA) et l’agence américaine d’étude de l’atmosphère et de l’océan (NOAA). Depuis sa création, le nombre de balises Argos n’a cessé d’augmenter afin de couvrir au mieux la couverture mondiale. Nous sommes orientés ainsi à la saturation de la bande d’émission et à la présence des interférences multi utilisateurs (MUI) provenant de la réception simultanée de plusieurs signaux émis par les balises. Cette MUI limite la capacité du système Argos et dégrade les performances en termes de Taux Erreur Bit (TEB). Actuellement, le système Argos n’est capable de traiter qu’un seul signal reçu à un instant donné. D’où, l’intérêt d’implanter des techniques au niveau du récepteur capable de réduire les effets des interférences et de traiter les signaux émis par toutes les balises. Plusieurs techniques de détection multi utilisateurs (MUD) ont été développées dans le cadre de cette problématique. Ces techniques sont principalement implantées dans les systèmes CDMA où des codes d’étalement sont utilisés afin de différencier entre les différents signaux. Ceci n’est pas le cas du système Argos où les signaux ne présentent pas des séquences d’étalement et que les bandes de fréquences pour ces différents signaux ne sont pas disjointes à cause de l’effet Doppler et donc, un recouvrement spectral au niveau du récepteur est très probable. Dans ce contexte, l’objectif du travail présenté dans cette thèse est d’étudier différentes techniques MUD appliquées au système Argos et d’évaluer ces techniques au niveau des performances en termes de TEB et de complexité d’implantation. Dans ce travail, nous présentons les différentes composantes du système Argos ainsi que son mode de fonctionnement. Ensuite, nous présentons la problématique dans le système Argos ainsi que les différentes solutions proposées. Parmi ces solutions, nous montrons celle basant sur l’implantation des techniques MUD au niveau du récepteur. Ces différentes techniques MUD sont alors présentées ainsi que les avantages et les inconvénients de chacune d’elles. Parmi les techniques possédant un bon compromis entre les performances d’une part et la complexité d’autre part, nous notons la technique d’annulation par série d’interférence (SIC). Dans cette technique, les signaux sont démodulés successivement suivant l’ordre décroissant des puissances. Cette technique nécessite une étape d’estimation des paramètres des signaux à chaque étape. L’impact d’une estimation imparfaite des différents paramètres est aussi étudié. Après l’étude des impacts des erreurs d’estimation, nous proposons des estimateurs adaptables au système Argos. Les performances de ces estimateurs sont obtenues en comparant les variances de leurs erreurs aux bornes de Cramer Rao (CRB). Enfin, nous terminons le travail par une conclusion générale des résultats obtenus et nous envisageons les perspectives des prochains travaux. / In our thesis, we investigate the application of multi user detection techniques to a Low Polar Orbit (LPO) satellite used in the Argos system. Argos is a global satellite-based location and data collection system dedicated for studying and protecting the environment. User platforms, each equipped with a Platform Transmitter Terminal (PTT), transmit data messages to a 850 km LPO satellite. An ARGOS satellite receives, decodes, and forwards the signals to ground stations. All PTTs transmit at random times in a 100 kHz bandwidth using different carrier frequencies. The central carrier frequency f0 is 401.65 MHz. Due to the relative motion between the satellite and the platforms, signals transmitted by PTTs are affected by both a different Doppler shift and a different propagation delay. Thus, the Argos satellite receives overlapping signals in both frequency and time domains inducing Multiple Access Interference (MAI). One common approach to mitigate the MAI problem is to implement Multi User Detection (MUD) techniques at the receiver. To tackle this problem, several MUD techniques have been proposed for the reception of synchronous and asynchronous users. In particular, the Successive Interference Cancelation (SIC) detector has been shown to offer a good optimality-complexity trade-off compared to other common approaches such as the Maximum Likelihood (ML) receiver. In an Argos SIC receiver, users are decoded in a successive manner, and the signals of successfully decoded users are subtracted from the waveform before decoding the next user. This procedure involves a parameter estimation step and the impact of erroneous parameter estimates on the performance of Argos SIC receiver has been studied. Argos SIC receiver has been shown to be both robust to imperfect amplitude and phase estimation and sensitive to imperfect time delay estimation. The last part of our work focuses on the implementation of digital estimators for the Argos system. In particular, we propose a time delay estimator, a frequency estimator, a phase estimator and an amplitude estimator. These estimators are derived from the ML principle and they have been already derived for the single user transmission. In our work, we adapt successfully these estimators for the multi user detector case. These estimators use the Non Data Aided (NDA) cases in which no a priori information for the transmitted bits is required. The performance of these different estimators are compared to the Cramer Rao Bound (CRB) values. Finally, we conclude in our work by showing the different results obtained during this dissertation. Also, we give some perspectives for future work on Argos system.

It is well known that communication using multiple antennas provides high data rate and reliability. Coding across space and time is necessary to fully exploit the gains offered by multiple input multiple output (MIMO) systems. One such popular method of coding for MIMO systems is space-time block coding. In applications where the terminals do not have enough physical space to mount multiple antennas, relaying or cooperation between multiple single antenna terminals can help achieve spatial diversity in such scenarios as well. Relaying techniques can also help improve the range and reliability of communication. Recently it has been shown that certain space-time block codes (STBCs) can be employed in a distributed fashion in single antenna relay networks to extract the same benefits as in point to point MIMO systems. Such STBCs are called distributed STBCs. However an important practical issue with STBCs and DSTBCs is its associated high maximum likelihood (ML) decoding complexity. The central theme of this thesis is to systematically construct STBCs and DSTBCs applicable for various scenarios such that are amenable for low decoding complexity. The first part of this thesis provides constructions of high rate STBCs from crossed product algebras that are minimum mean squared error (MMSE) optimal, i.e., achieves the least symbol error rate under MMSE reception. Moreover several previous constructions of MMSE optimal STBCs are found to be special cases of the constructions in this thesis. It is well known that STBCs from orthogonal designs offer single symbol ML decoding along with full diversity but the rate of orthogonal designs fall exponentially with the number of transmit antennas. Thus it is evident that there exists a tradeoff between rate and ML decoding complexity of full diversity STBCs. In the second part of the thesis, a definition of rate of a STBC is proposed and the problem of optimal tradeoff between rate and ML decoding complexity is posed. An algebraic framework based on extended Clifford algebras is introduced to study the optimal tradeoff for a class of multi-symbol ML decodable STBCs called ‘Clifford unitary weight (CUW) STBCs’ which include orthogonal designs as a special case. Code constructions optimally meeting this tradeoff are also obtained using extended Clifford algebras. All CUW-STBCs achieve full diversity as well. The third part of this thesis focusses on constructing DSTBCs with low ML decoding complexity for two hop, amplify and forward based relay networks under various scenarios. The symbol synchronous, coherent case is first considered and conditions for a DSTBC to be multi-group ML decodable are first obtained. Then three new classes of four-group ML decodable full diversity DSTBCs are systematically constructed for arbitrary number of relays. Next the symbol synchronous non-coherent case is considered and full diversity, four group decodable distributed differential STBCs (DDSTBCs) are constructed for power of two number of relays. These DDSTBCs have the best error performance compared to all previous works along with low ML decoding complexity. For the symbol asynchronous, coherent case, a transmission scheme based on orthogonal frequency division multiplexing (OFDM) is proposed to mitigate the effects of timing errors at the relay nodes and sufficient conditions for a DSTBC to be applicable in this new transmission scheme are given. Many of the existing DSTBCs including the ones in this thesis are found to satisfy these sufficient conditions. As a further extension, differential encoding is combined with the proposed transmission scheme to arrive at a new transmission scheme that can achieve full diversity in symbol asynchronous, non-coherent relay networks with no knowledge of the timing errors at the relay nodes. The DDSTBCs in this thesis are proposed for application in the proposed transmission scheme for symbol asynchronous, non-coherent relay networks. As a parallel to the non-coherent schemes based on differential encoding, we also propose non-coherent schemes for symbol synchronous and symbol asynchronous relay networks that are based on training. This training based transmission scheme leverages existing coherent DSTBCs for non-coherent communication in relay networks. Simulations show that this training scheme when used along with the coherent DSTBCs in this thesis outperform the best known DDSTBCs in the literature. Finally, in the last part of the thesis, connections between multi-group ML decodable unitary weight (UW) STBCs and groups with real elements are established for the first time. Using this connection, we translate the necessary and sufficient conditions for multi-group ML decoding of UW-STBCs entirely in group theoretic terms. We discuss various examples of multi-group decodable UW-STBCs together with their associated groups and list the real elements involved. These examples include orthogonal designs, quasi-orthogonal designs among many others.

Cette thèse porte sur l'étude des performances d'estimateurs en traitement du signal, et s'attache en particulier à étudier les bornes inférieures de l'erreur quadratique moyenne (EQM) pour l'estimation de points de rupture, afin de caractériser le comportement d'estimateurs, tels que celui du maximum de vraisemblance (dans le contexte fréquentiste), mais surtout du maximum a posteriori ou de la moyenne conditionnelle (dans le contexte bayésien). La difficulté majeure provient du fait que, pour un signal échantillonné, les paramètres d'intérêt (à savoir les points de rupture) appartiennent à un espace discret. En conséquence, les résultats asymptotiques classiques (comme la normalité asymptotique du maximum de vraisemblance) ou la borne de Cramér-Rao ne s'appliquent plus. Quelques résultats sur la distribution asymptotique du maximum de vraisemblance provenant de la communauté mathématique sont actuellement disponibles, mais leur applicabilité à des problèmes pratiques de traitement du signal n'est pas immédiate. Si l'on décide de concentrer nos efforts sur l'EQM des estimateurs comme indicateur de performance, un travail important autour des bornes inférieures de l'EQM a été réalisé ces dernières années. Plusieurs études ont ainsi permis de proposer des inégalités plus précises que la borne de Cramér-Rao. Ces dernières jouissent en outre de conditions de régularité plus faibles, et ce, même en régime non asymptotique, permettant ainsi de délimiter la plage de fonctionnement optimal des estimateurs. Le but de cette thèse est, d'une part, de compléter la caractérisation de la zone asymptotique (en particulier lorsque le rapport signal sur bruit est élevé et/ou pour un nombre d'observations infini) dans un contexte d'estimation de points de rupture. D'autre part, le but est de donner les limites fondamentales de l'EQM d'un estimateur dans la plage non asymptotique. Les outils utilisés ici sont les bornes inférieures de l’EQM de la famille Weiss-Weinstein qui est déjà connue pour être plus précise que la borne de Cramér-Rao dans les contextes, entre autres, de l’analyse spectrale et du traitement d’antenne. Nous fournissons une forme compacte de cette famille dans le cas d’un seul et de plusieurs points de ruptures puis, nous étendons notre analyse aux cas où les paramètres des distributions sont inconnus. Nous fournissons également une analyse de la robustesse de cette famille vis-à-vis des lois a priori utilisées dans nos modèles. Enfin, nous appliquons ces bornes à plusieurs problèmes pratiques : données gaussiennes, poissonniennes et processus exponentiels. / This thesis deals with the study of estimators' performance in signal processing. The focus is the analysis of the lower bounds on the Mean Square Error (MSE) for abrupt change-point estimation. Such tools will help to characterize performance of maximum likelihood estimator in the frequentist context but also maximum a posteriori and conditional mean estimators in the Bayesian context. The main difficulty comes from the fact that, when dealing with sampled signals, the parameters of interest (i.e., the change points) lie on a discrete space. Consequently, the classical large sample theory results (e.g., asymptotic normality of the maximum likelihood estimator) or the Cramér-Rao bound do not apply. Some results concerning the asymptotic distribution of the maximum likelihood only are available in the mathematics literature but are currently of limited interest for practical signal processing problems. When the MSE of estimators is chosen as performance criterion, an important amount of work has been provided concerning lower bounds on the MSE in the last years. Then, several studies have proposed new inequalities leading to tighter lower bounds in comparison with the Cramér-Rao bound. These new lower bounds have less regularity conditions and are able to handle estimators’ MSE behavior in both asymptotic and non-asymptotic areas. The goal of this thesis is to complete previous results on lower bounds in the asymptotic area (i.e. when the number of samples and/or the signal-to-noise ratio is high) for change-point estimation but, also, to provide an analysis in the non-asymptotic region. The tools used here will be the lower bounds of the Weiss-Weinstein family which are already known in signal processing to outperform the Cramér-Rao bound for applications such as spectral analysis or array processing. A closed-form expression of this family is provided for a single and multiple change points and some extensions are given when the parameters of the distributions on each segment are unknown. An analysis in terms of robustness with respect to the prior influence on our models is also provided. Finally, we apply our results to specific problems such as: Gaussian data, Poisson data and exponentially distributed data.