Currently, the 3rd Generation Partnership Project (3GPP) standards body is working actively to specify Voice services over Adaptive Multi-user channels on One Slot (VAMOS), an enhanced transmission scheme to double the voice service capacity in existing Global System for Mobile communications (GSM) system. Capacity increase is achieved by multiplexing two users in the same timeslot within the same radio frequency channel. With this new transmission scheme, several characteristics of VAMOS downlink signals can be taken into account in mobile station equalizer design. Firstly, the base station maps a pair of bits from the two VAMOS users to a quaternary symbol whose I/Q amplitude ratio may vary burst by burst. When the ratio is not unity, the VAMOS downlink signal is improper because its pseudo-covariance does not vanish. Secondly, in the baseband modulation stage, the symbol sequence is processed by ??/2 progressive symbol rotation and linearized Gaussian minimum shift keying (LGMSK) pulse shaping. Hence, intersymbol interference (ISI) is introduced. Lastly, due to tight frequency reuse in most GSM networks today, mobile stations also experience co-channel interference (CCI) from other base stations transmitting various types of signals such as GMSK, 8 phase shift keying (8PSK), or VAMOS. In order to achieve network capacity increase, advanced equalizers in mobile stations are required to offer superior bit error rate (BER) performance in this challenging mobile radio system. Unlike uplink transmission where a base station is typically equipped with an antenna array to enhance the desired signal and suppress CCI, equalizer design in downlink direction is more challenging because most mobile stations have one antenna only. In the past decade, various single antenna interference cancellation (SAIC) solutions have been developed to mitigate the CCI effect. While these solutions can be straightforwardly reused to obtain acceptable performance in VAMOS, in this work a novel equalizer is proposed to achieve better BER performance by addressing the forementioned characteristics of VAMOS downlink signals. This equalizer consists of a widely linear multiple-input multiple-output (MIMO) minimum mean square error (MMSE) filter and a joint maximum likelihood sequence estimator (JMLSE). In the first stage, since the transmitted signal and the received signal may not be jointly proper, a widely linear filter is more effective in suppressing interference from other base stations plus background noise while preserving the two paired VAMOS users??? signal energy. In the next stage, further interference cancellation is achieved by jointly detecting the two users??? symbol sequences using JMLSE. Optimality of the proposed equalizer is justified by theoretical proof and simulation in this work.

Abstract A recent World Health Organisation study conducted in 26 countries found substantial disagreement in the prescribing information available in those countries, as well as significant disparity between brands within the same country. This appears to be a common experience in other countries. This may mislead prescribers, patients and those comparing drug-use patterns across countries, and have serious safety implications. This study was carried out to investigate the variability of prescribing information currently available within South Africa, comparing generic and originator brands. It also investigated the extent of variability between the Standardised Package Insert (SPI) mandated by the Medicines Control Council, versus internationally approved prescribing information for given drug substances. Five drug substances were selected that are widely used in South Africa. The package inserts of the originator product were compared in terms of the indications, dosage, cautions, side-effects and drug interactions versus five generic brands of each drug substance registered in South Africa, using a comprehensive method adapted from the WHO study. The SPI was also compared against the South African originator brand package insert and those approved in four international MCC Reference Countries (ie. USA, EU, Canada & Australia) for each drug substance. Substantial disagreement was found between the originator and generic products for each drug substance, which may be due, in part, to the absence of a mandatory periodic updating requirement for package inserts in the post-registration phase in South Africa. This may result in divergence between materials from companies that voluntarily submit safety updates over the life of the product, and those that do not. There was also substantial disagreement between the SPI and the originator and international reference country materials. The reason is less simple to explain. The SPI project is in its early stages, and requires validation to ensure that the texts are in fact, entirely in line with latest best clinical practice and with the reference countries with which MCC aligns itself. These findings are comparable with those found in international WHO study. Regulatory authorities have key responsibility in ensuring that prescribing information is current and consistent across originator, generic and international materials. It is recommended that the MCC implement a mandatory updating requirement for all registered medicines with specified timelines. Secondly, a validation step should be introduced in the MCC SPI project to ensure consistency with international materials. Additional recommendations are made to improve the quality and practicality of prescribing information to ensure that it remains relevant in the South African and regional context. vThese findings are comparable with those found in international WHO study. Regulatory authorities have key responsibility in ensuring that prescribing information is current and consistent across originator, generic and international materials. It is recommended that the MCC implement a mandatory updating requirement for all registered medicines with specified timelines. Secondly, a validation step should be introduced in the MCC SPI project to ensure consistency with international materials. Additional recommendations are made to improve the quality and practicality of prescribing information to ensure that it remains relevant in the South African and regional context.

Au cours des vingt dernières années, le débit croissant des communications radiofréquences a imposé la mise en œuvre de techniques d'égalisation de plus en plus complexes. Pour résoudre ce problème, les modulations multi-porteuses ont été massivement employées dans les standards de communications à très haut débit. Un exemple caractéristique de la démocratisation de ces formes d'ondes est l'utilisation de l'OFDM (Orthogonal Frequency Division Multiplexing) sur le lien descendant des réseaux 4G. Toutefois, pour les futurs réseaux 5G, l'émergence prévue des communications M2M (Machine-to-Machine) impose aux formes d'ondes une grande tolérance aux asynchronismes au sein de ces réseaux et ne permet pas l'emploi de l'OFDM qui nécessite une synchronisation stricte en temps et en fréquence. Egalement, l'utilisation efficace du spectre par les techniques de la radio cognitive est incompatible avec l'OFDM en raison de la mauvaise localisation en fréquence de cette forme d'onde.Dans ce contexte, la forme d'onde FBMC-OQAM (Filter Bank Multi-Carrier - Offset Quadrature Amplitude Modulation) est apparue comme une solution potentielle à ces problèmes. Toutefois, l'égalisation des signaux FBMC-OQAM en canal sélectif en fréquence et/ou canal MIMO (Multiple Input Multiple Output) est rendue difficile par la subsistance d'interférences entre les sous-porteuses du schéma FBMC-OQAM. Cette thèse étudie donc l'égalisation de ces liaisons. L'étude de récepteurs WL (Widely Linear) qui permettent la suppression d'interférences, sans diversité d'antenne en réception, au sein des réseaux utilisant des signaux noncirculaires au second ordre (e.g. signaux ASK, GMSK, OQAM) est privilégiée. Cette technique nommée SAIC (Single Antenna Interference Cancellation) et utilisée dans les réseaux GSM pour la suppression d'interférences co-canal est envisagée pour une extension à la suppression des interférences entre porteuses des formes d'ondes FBMC-OQAM. La technologie SAIC, qui a été étendue pour plusieurs antennes en réception (MAIC - Multiple Antenna Interference Cancellation) a l'avantage de sa faible complexité et ne génère pas de propagation d'erreur à faible SNR contrairement aux solutions de suppression successive d'interférences. Une approche progressive est adoptée, depuis l'élaboration du SAIC pour la suppression d'interférences co-canal où nous démontrons l'importance de considérer le caractère cyclostationnaire des signaux OQAM. Basée sur cette constatation, une nouvelle structure de réception utilisant un filtre WL-FRESH (FREquency-SHift) est proposée et ses meilleures performances comparé au récepteur WL standard sont présentées analytiquement et par simulations numériques. L'extension du SAIC pour la suppression d'une interférence décalée en fréquence est ensuite menée et différentes structures de réception sont proposées et analysées en détail. L'aptitude des traitements SAIC utilisant des filtres WL-FRESH à supprimer 2 interférences décalées en fréquence est présentée. Dans le contexte des signaux FBMC-OQAM qui utilisent généralement le filtre de mise en forme PHYDYAS, chaque sous-porteuse est polluée par ses deux sous-porteuses adjacentes. Cependant, pour évaluer les traitements SAIC sans devoir prendre en compte la contribution des sous-porteuses voisines à ces sous-porteuses adjacentes, un filtre doit précéder le traitement de réception. Pour cette raison, l'analyse de l'impact d'un filtre de réception sur les performances des traitements SAIC proposés est effectuée et les conditions sur la bande passante du filtre nécessaires pour justifier l'intérêt d'un traitement SAIC par filtrage WL sont présentées. Dans un dernier temps, une approche alternative d'égalisation des signaux FBMC-OQAM est présentée. Elle consiste à démoduler conjointement les sous-porteuses interférentes après filtrage. Cette technique est abordée dans le contexte de liaisons MIMO Alamouti FBMC-OQAM. / During the last two decades, the increase of wireless communications throughput has necessitated more and more complex equalization techniques. To solve this issue, multicarrier modulations have been massively adopted in high data rates wireless communications standards. A typical example of the wide use of these waveforms is the adoption of OFDM (Orthogonal Frequency Division Multiplexing) for the downlink of 4G mobile networks. However, for next-generation 5G networks, the expected increase of M2M (Machine-to-Machine) communications forbids the use of OFDM because of the tight time and frequency synchronization constraints imposed by this waveform. Additionally, efficient spectrum occupation through cognitive radio strategies are incompatible with the poor spectral localization of OFDM. In this context, FBMC-OQAM (Filter Bank Multi-Carrier - Offset Quadrature Amplitude Modulation) waveforms appeared as a potential solution to these issues. However, equalization of FBMC-OQAM in frequency selective channels and/or MIMO (Multiple Input Multiple Output) channels is not straightforward because of residual intrinsic interferences between FBMC-OQAM subcarriers. Thus, this thesis considers equalization techniques for these links. In particular, the study of WL (Widely Linear) receivers allowing the mitigation of interferences, with only a single antenna, among networks using second-order noncircular waveforms (e.g. ASK, GMSK, OQAM signals) is privileged. This work studied this technique, named SAIC (Single Antenna Interference Cancellation) and applied for the suppression of co-channel interferences in GSM networks in order to adapt it for the cancellation of FBMC-OQAM intercarrier interferences. SAIC, which was further extended to multiple receive antennas (MAIC - Multiple Antenna Interference Cancellation) benefits from its low complexity and does not generate error propagation at low SNR contrary to successive interference cancellation based solutions. A progressive approach is adopted, from SAIC/MAIC for the suppression of co-channel interferences where we emphasize the importance of considering the cyclostationary nature of OQAM communication signals. Based on this, the proposal of a new WL-FRESH (FREquency-SHift) filter based receiver for OQAM-like signals is made and its performance is characterized analytically and by numerical simulations asserting its superior performance with respect to the standard WL receiver. The extension of SAIC/MAIC for the mitigation of a frequency-shifted interference is then considered and reception structures are proposed and analyzed in detail. The ability of WL-FRESH filter based SAIC receivers to perform the suppression of multiple frequency-shifted interferences is assessed. In the context of FBMC-OQAM signals which frequently utilize the PHYDYAS pulse-shaping prototype filter, each subcarrier is polluted only by its adjacent subcarriers. However, to evaluate SAIC processing without having to consider neighboring subcarriers of the adjacent ones, a filtering operation prior to the SAIC processing is needed. For this reason, the impact of a reception filter on the performance gain provided by the SAIC processing was conducted and conditions on the filter bandwidth have been established which governs the potential performance gain of a WL filter based processing for SAIC of frequency-shifted interferences.In a last step, an alternative equalization approach for FBMC-OQAM is investigated. This proposed technique consists in the per-subcarrier joint demodulation of the subcarrier of interest and its interfering adjacent ones after a filtering step. This proposal is considered in the context of MIMO Alamouti FBMC-OQAM links.

Cette thèse est consacrée à l’exploitation des propriétés de non-circularité et de non-gaussianité des signaux d’intérêt (SOI) et/ou des interférences pour les transmissions sans fil et l’écoute passive. Dans une première partie de cette thèse, nous nous intéressons à l’extension des récepteurs SIMO-MLSE conventionnels vers de nouvelles architectures exploitant la potentielle non-circularité au second ordre des interférences co-canal (CCI), pour la démodulation de signaux rectilignes (BPSK, ASK), quasi-rectilignes (MSK, GMSK et OQAM) et à symboles complexes (QAM). L’architecture générale des récepteurs développés est basée sur un prétraitement avec une extension widely linear (WL) du filtre adapté spatio-temporel, ramenant le traitement de démodulation à un problème scalaire, un échantillonnage au rythme symbole et ensuite un organe de décision basé sur une version modifiée de l’algorithme de Viterbi. Pour le cas particulier des signaux quasi-rectiligne, on intercale un traitement de dérotation entre l’échantillonneur et l’organe de décision. Un travail de modélisation à temps discret des SOI, brouilleurs et du bruit de fond a été mené afin de créer des modèles de simulations pour la validation des expressions SINR analytiques interprétables, via l’évaluation des probabilités d’erreur symboles. Dans une deuxième partie, nous nous intéressons à la formation de voies (Beamforming) non-linéaire à travers des structures de Volterra complexe du troisième ordre. Ces dernières permettent l’exploitation de la non-circularité jusqu’au sixième ordre ainsi que du caractère non-gaussien des SOI et/ou des interférences. Dans le contexte de l’écoute passive, nous avons introduit un beamformer MVDR de Volterra du troisième ordre utilisant la seule information a priori du vecteur directionnel du SOI et implémentable grâce à une structure équivalente GSC. Nous avons étudié ses performances en particulier par l’évaluation analytique des expressions du SINR en fonction des statistiques de l’interférence, et par sa vitesse d’apprentissage, démontrant ainsi sa supériorité par rapport aux beamformers MVDR linéaire et WL classiques. Dans un contexte de radiocommunications, nous avons étudié une version MMSE de ce beamformer de Volterra complexe du troisième ordre qui prend lui en compte les propriétés statistiques de non-circularité jusqu’au sixième ordre et de non-gaussianité du SOI et du CCI. La dernière partie de cette thèse est consacrée à la robustesse de tests de détection de rectilinéarité de signaux en présente d’offsets de fréquence. Ces tests sont importants pour ajuster la nature du traitement (linéaire ou WL) en fonction de la rectilinéarité des signaux, afin de garantir le meilleur rapport performance/temps de convergence des algorithmes / This thesis is devoted to exploit the non-circularity and non-gaussianity properties of signals of interest (SOI) and/or interference for wireless transmissions and passive listening. In the first part of this thesis, we are interested in the extension of conventional SIMO-MLSE receivers to new architectures exploiting the potential second order non-circularity of co-channel interference (CCI), for the demodulation of rectilinear signals (BPSK, ASK), quasi-rectilinear (MSK, GMSK and OQAM) and quadrature amplitude modulation (QAM). The general architecture of the developed receivers is based on a pre-processing with a widely linear (WL) extension of the spatio-temporal matched filter, bringing the demodulation processing back to a scalar problem, a sampling at the symbol rate and then a decision block based on a modified version of the Viterbi algorithm. For the particular case of the quasi-rectilinear signals, a derotation processing is interposed between the sampler and the decision block. A work on equivalent discrete time modeling of SOI, interferers and background noise has been carried out in order to create simulation models as for the validation of the interpretable analytic SINR expressions, by the evaluation of the symbol error rates. In a second part, we are interested to the beamforming through complex Volterra structures of the third order. These structures allow us the exploitation of the non-circularity up to the sixth order as well as the non-gaussian nature of the SOI and/or the interferences. For passive listening applications, we have introduced a third-order Volterra MVDR beamformer using only a priori information of SOI steering vector and implemented by an equivalent GSC structure. We have studied its performance, in particular by interpretable closed-form expressions as functions of statistics of the interference, and by its speed of learning, thus proving its advantages with respect to the conventional linear and WL MVDR beamformers. For wireless communications applications, we have studied an MMSE version of this complex Volterra beamformer of the third order that takes into account of the non-circularity up to the sixth order as well as the non-gaussian nature of the SOI and interference. The last part of this thesis is devoted to the robustness of rectilinearity tests in the presence of frequency offset. These tests are important for adjusting the processing (linear or WL) as a function of the rectilinearity of the signals in order to guarantee the best performance/convergence rate ratio of algorithms

In this thesis, new precoding and equalization techniques for multicarrier systems were proposed and analyzed.First, the error performance of precoded filterbank multicarrier (FBMC) systems was analyzed. It was found out that this performance is highly sensitive to complete subchannel equalization. When there is residual intersymbol interference (ISI) stemming from imperfect subchannel equalization there is a loss of diversity; this loss can be prevented with the adoption of a number of subchannels large enough so that each subchannel suffers flat fading or with the utilization of a subchannel equalizer with sufficient length to compensate the subchannel frequency response.After that, an approximation for the signal to interference-plus-noise ratio (SINR) distribution of SC-FDE systems using linear MMSE equalization was proposed. This approximation uses the lognormal distribution with the smallest Kullback-Leibler distance to the true distribution, and was shown to be precise in the error performance sense; it serves as a system abstraction. With this abstraction, a precise method to obtain the analytical coded error performance of these systems was proposed.Finally, widely linear Tomlinson-Harashima precoders and equalizers (linear and decision-feedback) for SC-FDE systems were proposed. These precoders and equalizers have better error performance when compared to their strictly linear versions if signals coming from an improper constellation are transmitted. Their error performance when decision-feedback equalizers are used is less sensitive to the length of the feedback filter. When widely linear precoders are used, this error performance becomes less sensitive to channel estimation errors.

Dans cette thèse, de nouvelles techniques d'égalisation et de précodage pour des systèmes multiporteuses ont été proposées et analysées. D'abord, la performance d'erreur des systèmes multiporteuses à base de bancs de filtres (FBMC) précodées a été analysée. Il a été découvert que cette performance est très sensible à l'égalisation complète des sous-canaux. Quand il y a de l'interference inter-symbole residuel qui vient de l'égalisation imparfaite du sous-canaux, il y a une perte de diversité; cette diversité peut être recuperée avec l'adoption d'un nombre de sous-canaux assez grand pour que chaque sous-canaux subisse de l'évanouissement plat ou avec l'utilisation d'un égaliseur de sous-canaux avec une longueur assez suffisante pour compenser cette réponse en fréquence. Après, une approximation pour la distribution du rapport signal/bruit-plus-interfèrence (SINR) des systèmes SC-FDE qui utilisent égalisation MMSE linéaire a été proposée. Cette approximation utilise la distribution lognormal avec la plus petit distance de Kullback-Leibler vers la vraie distribution, et il s'est révélé qu'elle est precise dans la performance d'erreur; elle sert aussi comme une abstraction de cette système. Avec cette abstraction, une méthode précise pour obtenir la performance d'erreur analytique codée de ces systèmes a été proposée. Finalement, des précodeurs Tomlinson-Harashima (THP) et égaliseurs (linéaires et à retour de décision) largement linéaires pour des systèmes SC-FDE ont été proposés. Ces précodeurs et égaliseurs ont une performance d'erreur mieux quand comparés avec ses versions strictement linéaires si des signaux de constellations impropres sont transmises. Aussi, la performance d'erreur quand des égaliseurs à retour de décision sont utilisés est moins sensible au longueur du filtre de retour. Quand des précodeurs largement linéaires sont utilisés, cette performance devient moins sensible à des erreurs d'estimation du canaux. / In this thesis, new precoding and equalization techniques for multicarrier systems were proposed and analyzed.First, the error performance of precoded filterbank multicarrier (FBMC) systems was analyzed. It was found out that this performance is highly sensitive to complete subchannel equalization. When there is residual intersymbol interference (ISI) stemming from imperfect subchannel equalization there is a loss of diversity; this loss can be prevented with the adoption of a number of subchannels large enough so that each subchannel suffers flat fading or with the utilization of a subchannel equalizer with sufficient length to compensate the subchannel frequency response.After that, an approximation for the signal to interference-plus-noise ratio (SINR) distribution of SC-FDE systems using linear MMSE equalization was proposed. This approximation uses the lognormal distribution with the smallest Kullback-Leibler distance to the true distribution, and was shown to be precise in the error performance sense; it serves as a system abstraction. With this abstraction, a precise method to obtain the analytical coded error performance of these systems was proposed.Finally, widely linear Tomlinson-Harashima precoders and equalizers (linear and decision-feedback) for SC-FDE systems were proposed. These precoders and equalizers have better error performance when compared to their strictly linear versions if signals coming from an improper constellation are transmitted. Their error performance when decision-feedback equalizers are used is less sensitive to the length of the feedback filter. When widely linear precoders are used, this error performance becomes less sensitive to channel estimation errors.

Neste texto são propostos algoritmos de filtragem adaptativa de baixo custo computacional para o processamento de sinais lineares no sentido amplo e para beamforming. Novas técnicas de filtragem adaptativa com baixo custo computacional são desenvolvidas para o processamento de sinais lineares no sentido amplo, representados por números complexos ou por quaternions. Os algoritmos propostos evitam a redundância de estatísticas de segunda ordem na matriz de auto correlação, o que é obtido por meio da substituição do vetor de dados original por um vetor de dados real contendo as mesmas informações. Dessa forma, evitam-se muitas operações entre números complexos (ou entre quaternions), que são substituídas por operações entre reais e números complexos (ou entre reais e quaternions), de menor custo computacional. Análises na media e na variância para qualquer algoritmo de quaternions baseados na técnica least-mean squares (LMS) são desenvolvidas. Também é obtido o algoritmo de quaternions baseado no LMS e com vetor de entrada real de mais rápida convergência. Uma nova versão estável e de baixo custo computacional do algoritmo recursive least squares (RLS) amplamente linear também é desenvolvida neste texto. A técnica é modificada para usar o método do dichotomous coordinate descent (DCD), resultando em uma abordagem de custo computacional linear em relação ao comprimento N do vetor de entrada (enquanto o algoritmo original possui custo computacional quadrático em N). Para aplicações em beamforming, são desenvolvidas novas técnicas baseadas no algoritmo adaptive re-weighting homotopy. As novas técnicas são aplicadas para arrays em que o número de fontes é menor do que o número de sensores, tal que a matriz de auto correlação se torna mal-condicionada. O algoritmo DCD é usado para obter uma redução adicional do custo computacional. / In this text, low-cost adaptive filtering techniques are proposed for widely-linear processing and beamforming applications. New reduced-complexity versions of widely-linear adaptive filters are proposed for complex and quaternion processing. The low-cost techniques avoid redundant secondorder statistics in the autocorrelation matrix, which is obtained replacing the original widely-linear data vector by a real vector with the same information. Using this approach, many complex-complex (or quaternion-quaternion) operations are substituted by less costly real-complex (or real-quaternion) computations in the algorithms. An analysis in the mean and in the variance is performed for quaternion-based techniques, suitable for any quaternion least-mean squares (LMS) algorithm. The fastest-converging widely-linear quaternion LMS algorithm with real-valued input is obtained. For complex-valued processing, a low-cost and stable version of the widely-linear recursive least-squares (RLS) algorithm is also developed. The widely-linear RLS technique is modified to apply the dichotomous coordinate descent (DCD) method, which leads to an algorithm with computational complexity linear on the data vector length N (in opposition to the original WL technique, for which the complexity is quadratic in N). New complex-valued techniques based on the adaptive re-weighting homotopy algorithm are developed for beamforming. The algorithms are applied to sensor arrays in which the number of interferer sources is less than the number of sensors, so that the autocorrelation matrix is ill-conditioned. DCD iterations are applied to further reduce the computational complexity.

Neste texto são propostos algoritmos de filtragem adaptativa de baixo custo computacional para o processamento de sinais lineares no sentido amplo e para beamforming. Novas técnicas de filtragem adaptativa com baixo custo computacional são desenvolvidas para o processamento de sinais lineares no sentido amplo, representados por números complexos ou por quaternions. Os algoritmos propostos evitam a redundância de estatísticas de segunda ordem na matriz de auto correlação, o que é obtido por meio da substituição do vetor de dados original por um vetor de dados real contendo as mesmas informações. Dessa forma, evitam-se muitas operações entre números complexos (ou entre quaternions), que são substituídas por operações entre reais e números complexos (ou entre reais e quaternions), de menor custo computacional. Análises na media e na variância para qualquer algoritmo de quaternions baseados na técnica least-mean squares (LMS) são desenvolvidas. Também é obtido o algoritmo de quaternions baseado no LMS e com vetor de entrada real de mais rápida convergência. Uma nova versão estável e de baixo custo computacional do algoritmo recursive least squares (RLS) amplamente linear também é desenvolvida neste texto. A técnica é modificada para usar o método do dichotomous coordinate descent (DCD), resultando em uma abordagem de custo computacional linear em relação ao comprimento N do vetor de entrada (enquanto o algoritmo original possui custo computacional quadrático em N). Para aplicações em beamforming, são desenvolvidas novas técnicas baseadas no algoritmo adaptive re-weighting homotopy. As novas técnicas são aplicadas para arrays em que o número de fontes é menor do que o número de sensores, tal que a matriz de auto correlação se torna mal-condicionada. O algoritmo DCD é usado para obter uma redução adicional do custo computacional. / In this text, low-cost adaptive filtering techniques are proposed for widely-linear processing and beamforming applications. New reduced-complexity versions of widely-linear adaptive filters are proposed for complex and quaternion processing. The low-cost techniques avoid redundant secondorder statistics in the autocorrelation matrix, which is obtained replacing the original widely-linear data vector by a real vector with the same information. Using this approach, many complex-complex (or quaternion-quaternion) operations are substituted by less costly real-complex (or real-quaternion) computations in the algorithms. An analysis in the mean and in the variance is performed for quaternion-based techniques, suitable for any quaternion least-mean squares (LMS) algorithm. The fastest-converging widely-linear quaternion LMS algorithm with real-valued input is obtained. For complex-valued processing, a low-cost and stable version of the widely-linear recursive least-squares (RLS) algorithm is also developed. The widely-linear RLS technique is modified to apply the dichotomous coordinate descent (DCD) method, which leads to an algorithm with computational complexity linear on the data vector length N (in opposition to the original WL technique, for which the complexity is quadratic in N). New complex-valued techniques based on the adaptive re-weighting homotopy algorithm are developed for beamforming. The algorithms are applied to sensor arrays in which the number of interferer sources is less than the number of sensors, so that the autocorrelation matrix is ill-conditioned. DCD iterations are applied to further reduce the computational complexity.

Le récepteur SAIC/MAIC introduit récemment est capable de séparer jusqu'à 2N utilisateurs synchronisés avec N antennes pour les réseaux de radiocommunications utilisant des modulations rectilignes ou quasi-rectilignes. Un tel récepteur, opérationnel dans les téléphones GSM depuis 2006, exploite la non-circularité du second ordre des signaux et met en œuvre un filtre optimal linéaire au sens large (widely linéaire WL). Il s'est montré performant pour les utilisateurs synchrones en absence de résidu de porteuse (l'effet doppler par exemple), mais son comportement en présence d'utilisateurs asynchrones ayant des résidus de porteuse potentiellement non nuls, omniprésents dans de nombreuses applications radio, n'a pas encore fait l'objet d'études théoriques, ce qui ne permet pas d'en connaître les dégradations. Le but de la 1e partie de ce travail consiste à présenter une analyse des performances du SAIC/MAIC, implanté via une approche MMSE avec séquence d'apprentissage, en présence de deux utilisateurs non nécessairement synchronisés et ayant des dérives de fréquence. Pour simplifier, nous avons limité l'analyse théorique à quelques cas particuliers avec des modulations rectilignes. Ainsi des expressions analytiques simples et interprétables ont été données et analysées. Nous avons prouvé que les performances sont moins dégradées dans le cas d'une dérive sur l'utile qu'en présence d'une dérive sur le brouilleur. En outre, la dégradation augmente avec la désynchronisation des deux signaux. Afin de préciser le domaine de validité des approximations analytiques, des illustrations numériques ont été réalisées en prenant comme paramètres ceux du standard GSM dans le but d'appliquer cette étude à ce standard et aux réseaux cellulaires. L'extension de l'analyse aux modulations quasi-rectilignes a nécessité la mise en œuvre d'un filtrage spatio-temporel. Nous avons ainsi étudié l'impact de la taille du filtre spatio-temporel sur les performances du MMSE SAIC/MAIC pour des modulations quasi-rectilignes (MSK et GMSK) en présence de résidus de porteuse. L'étude révèle qu'avec des résidus de porteuse standards, ce récepteur reste relativement robuste et ne nécessite pas de compensation. La 2e partie de ce travail considère des canaux sélectifs en fréquence et consiste à développer un SIMO MLSE pour un signal utile à modulation linéaire quelconque en présence de bruit additif gaussien centré stationnaire coloré temporellement et spatialement et potentiellement non circulaire, en partant d'un problème général de détection d'une forme d'onde. Nous avons démontré que le SIMO MLSE est constitué d'un filtre WL, d'un échantillonneur au rythme symbole et d'une minimisation récursive d'une métrique qui peut se mettre en oeuvre par l'algorithme de Viterbi. Le cas des modulations quasi rectilignes a aussi été considéré. Dans ce cadre, nous avons démontré que le SIMO MLSE a la même structure moyennant un prétraitement de dérotation. Tous ces filtres WL sont interprétés comme des filtres WL adaptés multidimensionnels (WL MMF) au sens où ils maximisent le rapport SNR sur le symbole courant en sortie. Nous avons ensuite étendu la structure du MLSE développée au cas d'un bruit gaussien non circulaire mais cyclostationnaire, de manière à se rapprocher des applications cellulaires. Nous appelons ce nouveau récepteur "pseudo-MLSE" car sa structure a été imposée. En conjecturant que les performances en probabilité d'erreur par symbole sont directement reliées au SNR sur le symbole courant, des expressions générales de celui-ci ont été données pour des MLSE et pseudo-MLSE dans le cadre d'interférences stationnaires et cyclostationnaires potentiellement non circulaires. Des formules interprétables de ces SNR ont été données dans des cas particuliers et des simulations numériques ont été présentées pour montrer les gains en performance des récepteurs introduits par rapport aux MLSE classiques dérivés sous hypothèse de bruit stationnaire circulaire / The SAIC/MAIC (Single/Multiple Antenna Interference Cancellation) receiver, recently introduced, is able to separate up to 2N synchronous users with N antennas for the radiocommunications networks using rectilinear or quasi-rectilinear modulations. A such receiver, operational in GSM handsets since 2006, exploits the second order non-circularity of signals and gives rise to an optimal widely linear (WL) filter. This receiver has been shown to be powerful for synchronous users without any frequency offsets (for example Doppler shift), but its behaviour in the presence of asynchronous users having potentially non zero carrier residues, omnipresent in many radio applications, has not yet been the subject of theoretical studies, which doesn't allow us to know their damage. For this reason, the purpose of the first part of this work is to present an analysis of SAIC/MAIC receiver performances, implemented via an MMSE approach with training sequence, with two users not necessarily synchronized with frequency shifts. To simplify the analytical developments, we limited the theoretical analysis to some particular cases with rectilinear modulations. Hence, simple and interpretable analytical expressions were given and analyzed. We proved in particular that the performance is less degraded in the case of a shift on the useful than in the presence of a drift on the jammer. Furthermore, the degradation increases with desynchronization of the two signals. To precise the range of validity of analytical approximations, numerical illustrations were made using as parameters those of the GSM standard in order to apply this study to this standard in particular and cellular networks in general. Extending the analysis to quasi-rectilinear modulations had required the implementation of a spatio-temporal filtering. We have studied the impact of the size of the spatio-temporal filter on the performance of MMSE SAIC/MAIC receiver for quasi-rectilinear modulations (GMSK and MSK) in the presence of residual frequencies. The study reveals that with standard carrier residues, this receiver remains relatively robust and doesn't require a compensation. The second part of this work considers frequency-selective channels and is developing a SIMO MLSE receiver for a useful signal with any linear modulation in the presence of an additive Gaussian centered stationary temporally and spatially colored and potentially non-circular noise, starting from a general problem of detection of a waveform. We have shown that SIMO MLSE receiver consists of a WL filter, a sampler at the symbol rate and a recursive minimization of a metric that can be solved by the Viterbi algorithm. The case of quasi-rectilinear modulations is also considered. Within this framework, we had proved that the SIMO MLSE receiver has the same structure through a postreatment derotation. All these filters are interpreted as WL multidimensional matched filters (WL MMF) in the sense that they maximize the SNR of the current symbol at output. Then, we extended the MLSE receiver structure developed in case of a noncircular gaussian noise but this time cyclostationary, so as to approximate radio cellular applications. We call this new receiver "pseudo-MLSE" because its structure was imposed. By conjecturing that the performances by per symbol error probability are directly related to the SNR of the current symbol, general expressions of this SNR are given for MLSE and pseudo MLSE receivers with stationary and cyclostationary potentially noncircular interferences. Interpretable formulas of these SNR were given in special cases and numerical simulations were presented to show performance gains of the receivers we have introduced relative to conventional MLSE receivers derived under the assumption of circular stationary noise

The number of secure data streams a relay-assisted interference channel can support has been an intriguing problem. The problem is not solved even for a fundamental scenario with a single antenna at each transmitter, receiver and relay. In this paper, we study the achievable secure degrees of freedom of instantaneous relay-assisted interference channels with real and complex coefficients. The study of secure degrees of freedom with complex coefficients is not a trivial multiuser extension of the scenarios with real channel coefficients as in the case for the degrees of freedom, due to secrecy constraints. We tackle this challenge by jointly designing the improper transmit signals and widely-linear relay processing strategies.