Performance analysis of MIMO-OFDM systems using complex Gaussian quadratic forms

En este trabajo se proponen aportaciones originales para el análisis de prestaciones en sistemas multiantena con múltiples portadoras, mediante el desarrollo de nuevas técnicas matemáticas para el cálculo de probabilidades de error. Así, ha sido posible analizar el efecto de no idealidades (estimación de canal imperfecta, offset de continua, desbalanceo I/Q…) en las prestaciones de sistemas de comunicaciones móviles e inalámbricas

Optimal diversity performance of space time block codes in correlated distributed MIMO channels

This paper investigates optimal transmission of space-time block codes (STBCs) in distributed multiple-input multiple-output (D-MIMO) Rayleigh fading channels. The optimal diversity performance is achieved through transmit power allocation implemented at the receiver based on transmit and receive correlations to minimize the average symbol error rate (SER). Evaluation of SER performance of uncoded STBCs over a generalized distributed antenna (DA) topology is first presented, with exact analytical SER expressions derived for MQAM and MPSK symbols. SER upper bounds are also derived, based on which two criteria for complexity reduced antenna subset selection with sub-optimal power allocation are further proposed, whose performance approaches optimal over correlated D-MIMO channels. Moreover, a novel simplified but close SER approximation scheme is devised to significantly facilitate optimal SER calculation. We continue to thoroughly analyze how the optimal diversity is affected by large scale fading, targeted data rate, antenna correlations and transmit power. Finally, we develop a surprisingly close and useful analogy between open loop STBCs in co-located MIMO and optimal STBCs in D-MEVIO with minimum feedback (i.e., n bits for n DAs in Criterion 2 with power allocation scheme 2 which equally allocates power to the selected DAs). Extensive simulation results have been presented to demonstrate the effectiveness of our analysis. © 2008 IEEE.published_or_final_versio

Diversity receiver design and channel statistic estimation in fading channels

The main goal of this thesis is to provide an in-depth study of two important techniques that are effective in improving the performance, data rate, or bandwidth-efficiency in wireless communication systems. The two techniques are, first, diversity combining equipped with quadrature amplitude modulation (QAM), and second, the estimation of fading channel statistical properties;To effectively combat the adverse effect of fading and to improve the error rate performance in wireless communications, one of the major approaches is to employ diversity combining techniques. In the first part of this thesis, we focus on the equal gain combining (EGC) and hybrid-selection equal gain combining (HS/EGC) for bandwidth-efficient wireless systems (i.e. QAM systems). For EGC QAM systems, we propose the receiver structure and the corresponding decision variables, and then study the effects of imperfect channel estimation (ICE) and quantify the loss of the signal-to-noise ratio (SNR) gain caused by ICE. For HS/EGC QAM system, we develop a general approach to derive unified error rate and outage probability formulas over various types of fading channels based on the proposed HS/EGC receiver. The main contribution of this work lies in that it provides effective hybrid diversity schemes and new analytical approaches to enable thorough analysis and effective design of bandwidth efficient wireless communication systems which suffer from ICE and operate in realistic multipath channels;Channel statistic information is proven to be critical in determining the systems design, achievable data rate, and achievable performance. In the second part of this thesis, we study the estimation of the fading channel Statistics and Probability; We propose several iterative algorithms to estimate the first- and second-order statistics of general fading or composite fading-shadowing channels and derive the Cramer-Rao bounds (CRBs) for all the cases. We demonstrate that these iterative methods are efficient in the sense that they achieve their corresponding CRBs. The main contribution of this work is that it bridges the gap between the broad utilization of fading channel statistical properties and the lack of systematic study that makes such statistical properties available

Multiple-Input Multiple-Output Communications Systems Using Reconfigurable Antennas

RÉSUMÉ Depuis les années 1990, l'utilisation des systèmes de communications sans-fil à entrées multiples-sorties multiples (MIMO) a été introduit pour fournir des transmissions fiables à grande vitesse. Cette thèse porte sur l'application et l’étude des systèmes MIMO avec des antennes reconfigurables, qui sont ajustable électroniquement pour produire différents diagrammes de rayonnement d'un seul élément d'antenne et ainsi offrir une diversité de diagrammes de rayonnement. En particulier, nous étudions le comportement de la capacité de canal des systèmes MIMO à sélection de diagrammes de rayonnement (PS-MIMO), et nous proposons aussi des algorithmes de sélection du diagramme de rayonnement atteignant la capacité maximale. Tout d'abord, nous étudions l'application des antennes reconfigurables dans l'estimation des statistiques spatiales à long terme de canaux spatiaux avec grappes de multi-trajets (cluster). Nous proposons un estimateur de spectre de type Capon et une technique d'adaptation de la covariance (COMET) pour estimer conjointement l'angle moyen et l’étalement angulaire de la grappe spatiale avec des antennes reconfigurables. En second lieu, sur la base des statistiques à long terme du canal MIMO, nous proposons des algorithmes de sélection de diagramme de rayonnement MIMO (SPS-MIMO) pour atteindre la capacité maximale de canal ergodique. L'analyse de la maximisation de la capacité ergodique du système SPS-MIMO indique que le modèle statistique de sélection fournit des gains supplémentaires en améliorant la puissance du signal reçu et en décorrélant les signaux reçus avec différents diagrammes de rayonnement directionnels. Troisièmement, nous nous concentrons sur le modèle de sélection instantanée des diagrammes de rayonnement MIMO (IPS-MIMO) basé sur des informations instantanées d'état de canal (CSI) afin de maximiser la capacité instantanée pour chaque réalisation de canal. Nous démontrons que l’ordre de diversité des systèmes MIMO peut être multipliée par le nombre de diagrammes de rayonnement avec sélection de diagramme instantanée. Afin d'évaluer la capacité moyenne de l'IPS-MIMO, nous proposons un nouvel algorithme qui permet d’approximer étroitement la moyenne de la valeur maximale de la capacité du canal MIMO avec des trajets arbitrairement corrélés. Nous proposons également un algorithme pour sélectionner instantanément les diagrammes de rayonnement pour atteindre la capacité moyenne. En outre, sur la base d'une simple expression en forme fermée de la capacité coefficient de corrélation, nous sommes en mesure de proposer un algorithme de sélection de sous-ensemble de diagrammes qui offre un compromis entre performances et la complexité de l’algorithme de sélection. En conclusion, des gains de performance importants peuvent être obtenus grâce à la combinaison de l'utilisation d’antennes reconfigurables et de systèmes MIMO avec soit des algorithmes de sélection de diagramme de rayonnement statistique ou instantanée. La capacité des systèmes PS-MIMO à améliorer les performances du système, y compris la capacité et de l'ordre de la diversité, est démontrée par l'analyse théorique et des simulations numériques.----------ABSTRACT Since the 1990s, the use of multiple-input multiple-output (MIMO) systems has been introduced to modern wireless communications to provide reliable transmission at high data rates. This thesis focuses on the application of MIMO systems with reconfigurable antennas, which are electronically tunable to produce a number of radiation patterns at a single antenna element and provide pattern diversity. In particular, we investigate the capacity performance of the pattern selection MIMO (PS-MIMO) systems, and we also present maximum capacity achieving algorithms for radiation pattern selection. First, we investigate the application of reconfigurable antennas in estimating long term spatial statistics of spatial clustered channels. We propose a Capon-like spectrum estimator and a covariance matching technique (COMET) to jointly estimate the mean angle and the angular spread of the spatial cluster with reconfigurable antennas. Second, based on the long term statistics of the MIMO channel, we propose statistical pattern selection MIMO (SPS-MIMO) algorithms to achieve maximum ergodic channel capacity. Analysis of the ergodic capacity maximization of the SPS-MIMO indicates that the statistical pattern selection provides additional gains by enhancing received signal power and decorrelating received signals with different directional radiation patterns. Third, we focus on the instantaneous pattern selection MIMO (IPS-MIMO) based on instantaneous channel state information (CSI) in order to maximize the instantaneous capacity for every channel realization. We prove that the diversity order of MIMO systems can be multiplied by the number of radiation patterns with instantaneous pattern selection. In order to evaluate the mean capacity of the IPS-MIMO, we propose a novel algorithm which closely approximates the mean of the maximum of the channel capacity of arbitrarily correlated MIMO channels. We also propose an algorithm for instantaneously selecting radiation patterns to achieve the mean capacity. In addition, based on a simple closed-form approximation to the capacity correlation coefficient, we are able to propose a subset pattern selection algorithm which enables the trade-off between performances and complexity. In conclusion, important extra gains can be obtained as a result of combining the use of reconfigurable antennas and MIMO systems with either statistical or instantaneous radiation pattern selection. The capability of the PS-MIMO to improve system performances, including capacity and diversity order, is demonstrated through theoretical analysis and numerical simulations

Double spatial media based modulation.

Masters Degree. University of KwaZulu-Natal, Durban.Multiple-input multiple-out (MIMO) systems have become an increasingly popular technology in wireless communications due to their high data rates and increased reliability. However, several drawbacks degrade the performance of MIMO systems. Inter-channel interference, inter- antenna synchronization, low energy e ciency, and relatively high-complexity receive algorithms are several of the challenges that MIMO systems face. As such, spatial modulation (SM) was introduced as a scheme that is capable of exploiting the advantages of MIMO systems, while simultaneously mitigating its drawbacks. SM provided an excellent method of exploiting spatial diversity, which eventually replaced MIMO systems. However, as the use of SM became more prominent, its drawbacks became more apparent. The spectral e ciency of SM is limited by the logarithmic relationship between spectral efficiency and the number of transmit antennas. Several SM-based transmission schemes, such as quadrature spatial modulation and double spatial modulation (DSM), were introduced with the prospect of improving the spectral efficiency of SM. These schemes have a single radio frequency (RF) chain; therefore, relatively low-complexity receive algorithms are employed. Conventional transmission techniques are referred to as source-based modulation (SBM). Media-based modulation (MBM) is a new attractive transmission scheme that has been recently receiving increased research attention. MBM employs the use of RF mirrors to vastly improve the error performance and/or spectral efficiency of modulation schemes. It has been demonstrated that MBM, coupled with SBM techniques, vastly improves the error performance and can potentially increase the spectral efficiency of these systems. In this dissertation, DSM is extended to employ MBM, such as to improve error performance. The proposed transmission scheme is called double spatial media-based modulation (DSMBM). The theoretical average bit error probability (ABEP) of DSMBM over an independent and identically distributed Rayleigh frequency- at fading channel in the presence of additive white Gaussian noise is formulated. The theoretical ABEP of DSMBM is validated by Monte Carlo simulations, where the error performance matches the theoretical ABEP at high signal-to-noise ratios (SNRs). Lastly, coded channels are investigated. Typically soft-output detection coupled with soft-input channel decoding yields a signicant SNR gain. Motivated by this, this dissertation further proposes a soft-output maximum-likelihood detector for the DSM and DSMBM schemes.List of acronyms on pages xv-xvi

MIMO Systems

In recent years, it was realized that the MIMO communication systems seems to be inevitable in accelerated evolution of high data rates applications due to their potential to dramatically increase the spectral efficiency and simultaneously sending individual information to the corresponding users in wireless systems. This book, intends to provide highlights of the current research topics in the field of MIMO system, to offer a snapshot of the recent advances and major issues faced today by the researchers in the MIMO related areas. The book is written by specialists working in universities and research centers all over the world to cover the fundamental principles and main advanced topics on high data rates wireless communications systems over MIMO channels. Moreover, the book has the advantage of providing a collection of applications that are completely independent and self-contained; thus, the interested reader can choose any chapter and skip to another without losing continuity

Bit and power loading for MIMO systems with statistical channel knowledge at the transmitter

In MIMO (multiple input-multiple output) communication, the adaptation of the modulation and coding at the transmitter side according to the channel characteristics allows reducing the transmission power and/or enhancing the data rates. However, it is not always feasible to have instantaneous knowledge of the channel at the transmitter. This Thesis focuses on the case that the receiver has (perfect) instantaneous Channel State Information (CSIR) but the transmitter has only access to its distribution (CDIT). This is a practical case that applies, particularly, to situations where the channel varies rapidly. Under CDIT, the input cannot be adapted to the instantaneous state of the channel and thus SVD (singular value decomposition) cannot be used to diagonalize the channel. Achieving capacity requires a complex Gaussian input vector with a covariance that depends on the channel distribution. In practice, however, discrete constellations are used instead of Gaussian signals. Determining the optimum signalling strategy with discrete constellations is difficult in general, and thus a pragmatic approach is using the spatial signalling directions indicated by the capacityachieving covariance. Several classical practical bit and power loading algorithms are available for parallel-channel settings. To guarantee the quality of service, a certain average bit error probability (BER) is required at the receiver side. Different types of receiver correspond to differente relationships between the BER and the SINR. With the feedback of the parameters of the SINR (Signal-to-Interference-plus-Noise Ratio) distribution, two optimization problems for single user MIMO systems with correlation at the transmitter side can be solved, namely rate maximization with a total power constraint and power minimization with a target bit rate. The goal of this Thesis is to devise practical bit and power loading schemes for MIMO that can operate on the basis of CDIT only. For practical reasons, three typical receivers are considered, namely zero-forcing (ZF), minimum mean squared error (MMSE) and zero-forcing with successive interference cancellation (ZF-SIC). The following problems are addressed: • Maximization of the bit rates with discrete constellations, using the transmit directions given by the capacity achieving input covariance, at a certain average bit error probability (BER) and a constraint of total transmit power. • Minimization of the transmit power with discrete constellations, using the transmit directions given by the capacity achieving input covariance, at a certain average bit error probability (BER) and a target transmit bit rate. • Evaluation and comparison of the power gain when optimizing the transmission with the three mentioned types of receivers relative to a non-optimized transmission. In order to address these items, in this work it is essential to establish a relationship between the average BER corresponding to each of the three receivers and the powers allocated at the transmitter under the premise of CDIT. By utilizing these BER approximations, two dual optimization problems, bit maximization and power minimization, are solved for the practical case of statistical channel knowledge at the transmitter side and discrete constellations. Using a Gamma or a generalized Gamma distribution of the SINR, BER approximations can be obtained through integration. For a single user MIMO system with correlated channel, to accomplish the optimization process the mathematical methods used are a Levin-Campello algorithm for ZF, exhaustive search with additional constraints for MMSE and tree search with bit rate boundary for ZF-SIC. The accuracy of the developed expressions is verified with Monte Carlo simulations. The transmission environment is specified to be a Rayleigh flat-fading channel with correlation at the transmitter side. The Thesis is structured as follows. An introduction is presented at the first chapter, explaining the contents of this Thesis. Following a description of the basic process which takes place at the transmitter side, the second chapter presents the characteristics of the MIMO channel. Moreover, the system models of three typical receivers are described, namely ZF, MMSE and ZF-SIC. The third chapter starts with a review of capacity, and leads to the so-called waterfilling distribution. The dual optimization problems, bit rate maximization and power minimization, are defined with the objective of enhancing the performance via processing at the transmitter side. In some practical systems, Levin-Campello develops a solution for the dual optimization problems for discrete constellations that is described. Also, in order to further understand the power minimization problem for discrete constellations considering the loss of mutual information due to a given modulation, Mercury/Waterfilling is reviewed. In chapter IV, the BER of a ZF receiver is computed by using its SINR distribution, which is a Gamma distribution. For convenience, it is further accurately approximated at the high SNR regime. From the relationship between BER and power for different constellations, the two dual problems can be solved by a Levin-Campello algorithm, as the streams are independent with each other. To facilitate using the Levin-Campello algorithm, BER approximations are simplified to be established in convenient closedform equations. In chapter V, the BER of an MMSE receiver is also computed by using its SINR distribution, which can be modeled as a Gamma distribution or a generalized Gamma distribution. Some accurate closed-formed approximations are proposed and compared. In chapter VI, from these relationships between BER and power for different constellations, the two dual problems are solved by exhaustive search, as the streams are coupled with each other in the case of the MMSE receiver. In order to reduce the computational complexity, some additional constrains are added. For the two dual optimization problems, the total number of transmitted bits with an MMSE receiver cannot be less than those with a ZF receiver. Therefore, the starting point for the search is always the solution derived for ZF receivers, and the search progresses from that point towards higher loads until the constraints set in. The BER of MMSE can be approximated by the moment generating function (MGF), which includes the first three moments of SINR. Comparing two randomly selected antennas, when an increment of the number of bits is added to one of them, placing the increment in the antenna with better channel condition requires less total power to accomplish the transmission. Thus, it can be concluded that the better channel should be loaded with more bits. With this additional constraint, the computational complexity of the exhaustive search can be reduced even more reasonably. In chapter VII, taking into account the error propagation, a closed-form BER approximation can be derived for the ZF-SIC receiver by using the total probability theorem. Moreover, since the ordering of the decoding process can dramatically impact the system performance when using this receiver, a precoder is proposed to determine the decoder ordering to minimize the total power. Moreover, a boundary of possible bit rates for ZF-SIC is presented, considering the bit rate of ZF and ZF-PSIC (perfect SIC), for the two dual optimization problems. To make the search converge more efficiently, a tree search is implemented making use of this boundary. In the final chapter, the results obtained for the different receivers are compared to conclude the core of this Thesis. Then, some future work is outlined. ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------En los sistemas de comunicaciones multiantena (MIMO: multiple inputmultiple output), la adaptación de los esquemas de modulación y codificación en el extremo transmisor según las características del canal permite reducir la potencia de transmisión y/o aumentar la velocidad de transmisión. Sin embargo, no siempre es posible tener conocimiento instantáneo del canal en el transmisor. Esta Tesis se centra en el caso en que el receptor tiene (perfecta) información instantánea del canal (CSIR: Channel State Information at the Receiver), pero el transmisor únicamente tiene acceso a su distribución (CDIT: Channel Distribution Information at the Transmitter). Este es un caso práctico que sucede, en particular, en situaciones en las que el canal varía rápidamente. Con CDIT, la señal no se puede adaptar al estado instantáneo del canal y, por tanto, no es posible usar una descomposición en valores singulares para diagonalizar el canal. Alcanzar la capacidad requiere el uso de señales Gaussianas cuya correlación depende de la distribución del canal. En la práctica, sin embargo, se utilizan constelaciones discretas y no señales Gaussianas. Determinar la estrategia óptima de transmisión con constelaciones discretas es difícil en general y, por ello, tomaremos una aproximación pragmática consistente en utilizar las direcciones espaciales correspondientes a la matriz de covarianza que permite obtener la capacidad (con señales Gaussianas). Para constelaciones discretas y canales paralelos independientes existen varios algoritmos de carga adaptativa de bits y potencia (bit and power loading) clásicos, que no son directamente aplicables al sistema bajo estudio. Si deseamos garantizar la calidad de servicio, se requiere una cierta probabilidad de error promedio (BER: bit error rate) en el extremo receptor. A diferentes tipos de receptor corresponden relaciones distintas entre la BER y la relación señal a interferencia (SINR: signal to interference plus noise ratio). Con la realimentación de los parámetros de la distribución de SINR al transmisor es posible resolver dos problemas duales de optimización en sistemas MIMO de usuario único con canal con correlación en el extremo transmisor: maximización de la tasa binaria con una restricción de potencia y minimización de la potencia transmitida con una restricción de la tasa binaria objetivo. El objetivo de esta Tesis es diseñar esquemas prácticos de carga adaptativa de bits y potencia para sistemas MIMO, que puedan operar sobre la base de conocimiento estadístico del canal en el transmisor (CDIT) únicamente. Por motivos prácticos, consideramos tres tipos de receptores típicos: receptor de forzado a cero (ZF), receptor de mínimo error cuadrático medio (MMSE), y receptor ZF con cancelación sucesiva de interferencias (ZF-SIC). Para estos tres receptores se abordan los siguientes problemas: • Maximizar la tasa binaria con constelaciones discretas, usando las direcciones espaciales de transmisión dictadas por la matriz de covarianza que alcanza la capacidad, garantizando una cierta probabilidad de error promedio y con la restricción de la potencia total a transmitir. • Minimizar la potencia de transmisión con constelaciones discretas, usando las direcciones espaciales de transmisión dictadas por la matriz de covarianza que alcanza la capacidad, garantizando una cierta probabilidad de error promedio y satisfaciendo un requisito de tasa binaria. • Obtener y comparar la ganancia de potencia de los tres tipos de receptores mencionados en relación con una transmisión sin optimizar. Para abordar estos problemas, es esencial establecer una relación entre la probabilidad de error promedio de cada uno de los receptores y la potencia asignada en el transmisor a cada flujo de datos MIMO, bajo la premisa de conocimiento CDIT. A partir de la distribución Gamma o Gamma generalizada de la SINR, se obtienen aproximaciones para la probabilidad de error promedio mediante integración. Para un sistema MIMO de usuario único con canal correlado, los métodos matemáticos empleados para resolver los problemas de optimización son: algoritmo “Levin-Campello” para ZF, búsqueda exhaustiva con restricciones adicionales para MMSE, y búsqueda en árbol con tasa binaria acotada para ZF-SIC. La precisión de las aproximaciones y las prestaciones de los algoritmos desarrollados se evalúan mediante simulación de Monte Carlo. El entorno de transmisión viene dado por un canal MIMO con desvanecimiento tipo Rayleigh, plano en frecuencia y con correlación en el extremo transmisor. La estructura de la Tesis es la siguiente. En el primer capítulo se presenta una introducción y se describe el contenido de la Tesis. A continuación, tras una descripción del procesado básico que tiene lugar en el transmisor, el capítulo II presenta las características del canal MIMO. Además, se describen el modelo del sistema y los tres receptores que se van a tratar: ZF, MMSE y ZF-SIC. El capítulo III comienza con una revisión de la capacidad, lo que conduce a la denominada distribución de “waterfilling” en sistemas MIMO. Los dos problemas de optimización duales, maximización de la tasa binaria y minimización de la potencia, se definen para mejorar las prestaciones mediante procesado en el extremo transmisor. En algunos sistemas prácticos, el algoritmo de Levin-Campello constituye una solución para estos problemas de optimización duales con constelaciones discretas, por lo que se presenta una revisión del mismo. Con el fin de comprender mejor el problema de minimización de potencia para constelaciones discretas, considerando la pérdida de información mutua debida a una modulación concreta, se revisa a continuación la distribución conocida como “mercury/waterfilling”. En el capítulo IV, se estima la probabilidad de error promedio para un receptor ZF utilizando la distribución de la SINR, que corresponde a una función de densidad de probabilidad Gama, y se encuentra una aproximación para relación señal a ruido alta que resulta muy precisa. A partir de la relación entre la BER y la potencia requerida para diferentes constelaciones, los dos problemas duales se pueden resolver mediante un algoritmo tipo “Levin-Campello”, dado que los flujos de datos son independientes. Para facilitar el uso de este algoritmo, se mejoran las aproximaciones de la BER, obteniendo cómodas ecuaciones en forma compacta. En el capítulo V, se estima la probabilidad de error promedio para un receptor MMSE, también utilizando la distribución de la SINR, que ahora corresponde a una Gama o Gama generalizada. Se proponen y comparan varias expresiones en forma cerrada. En el capítulo VI, a partir de la relación entre la BER y la potencia requerida para diversas constelaciones, se resuelven los dos problemas duales mediante búsqueda exhaustiva, dado que en este caso los flujos de datos están acoplados debido a que el receptor MMSE no cancela la interferencia. Para reducir la carga computacional se añaden algunas restricciones. Para los dos problemas duales, el número total de bits que se pueden transmitir cuando el receptor es MMSE no puede ser menor que el correspondiente a un receptor ZF. Así pues, el punto de partida de la búsqueda es la solución para el receptor ZF y la búsqueda progresa desde ese punto hacia mayores tasas mientras lo permiten las restricciones. La probabilidad de error tras el receptor MMSE se puede aproximar a trav´es de la MGF (moment generating function) que incluye los tres primeros momentos de la SINR. Comparando dos antenas cualesquiera se demuestra que si hay que añadir un cierto incremento de bits en una de ellas, la antena con mejor canal es la que requiere menor incremento de potencia total para transmitirlo. Así, se puede concluir que los mejores canales deben llevar mayor número de bits y esto permite añadir una restricción adicional a la búsqueda, que conlleva, de este modo, una carga computacional razonable. En el capítulo VII, se obtiene una aproximación cerrada para la BER de un receptor ZF-SIC considerando la propagación de errores, a partir del teorema de la probabilidad total. Dado que el orden del proceso de decodificación tiene un impacto importante en las prestaciones del sistema con este receptor, se propone un precodificador que determina el orden que minimiza la potencia total. Por otra parte, se presentan unas cotas de las tasas binarias posibles con ZF-SIC, considerando las de ZF y ZF-PSIC (perfect SIC) para los dos problemas duales de optimización. Haciendo uso de estas cotas, se emplea una búsqueda en árbol para agilizar la convergencia

Design and Analysis of GFDM-Based Wireless Communication Systems

Le multiplexage généralisé par répartition en fréquence (GFDM), une méthode de traitement par blocs de modulation multiporteuses non orthogonales, est une candidate prometteuse pour les technologies de forme d'onde pour les systèmes sans fil au-delà de la cinquième génération (5G). La capacité du GFDM à ajuster de manière flexible la taille du bloc et le type de filtres de mise en forme des impulsions en fait une méthode appropriée pour répondre à plusieurs exigences importantes, comme une faible latence, un faible rayonnement hors bande (OOB) et des débits de données élevés. En appliquant aux systèmes GFDM la technique des systèmes à entrées multiples et sorties multiples (MIMO), la technique de MIMO massif ou des codes de contrôle de parité à faible densité (LDPC), il est possible d'améliorer leurs performances. Par conséquent, l'étude de ces systèmes combinés sont d'une grande importance théorique et pratique. Dans cette thèse, nous étudions les systèmes de communication sans fil basés sur le GFDM en considérant trois aspects. Tout d'abord, nous dérivons une borne d'union sur le taux d'erreur sur les bits (BER) pour les systèmes MIMO-GFDM, technique qui est basée sur des probabilités d'erreur par paires exactes (PEP). La PEP exacte est calculée en utilisant la fonction génératrice de moments(MGF) pour les détecteurs à maximum de vraisemblance (ML). La corrélation spatiale entre les antennes et les erreurs d'estimation de canal sont prises en compte dans l'environnement de canal étudié. Deuxièmement, les estimateurs et les précodeurs de canal de faible complexité basés sur une expansion polynomiale sont proposés pour les systèmes MIMO-GFDM massifs. Des pilotes sans interférence sont utilisés pour l'estimation du canal basée sur l'erreur quadratique moyenne minimale(MMSE) pour lutter contre l'influence de la non-orthogonalité entre les sous-porteuses dans le GFDM. La complexité de calcul cubique peut être réduite à une complexité d'ordre au carré en utilisant la technique d'expansion polynomiale pour approximer les inverses de matrices dans l'estimation MMSE conventionnelle et le précodage. De plus, nous calculons les limites de performance en termes d'erreur quadratique moyenne (MSE) pour les estimateurs proposés, ce qui peut être un outil utile pour prédire la performance des estimateurs dans la région de Eₛ/N₀ élevé. Une borne inférieure de Cramér-Rao(CRLB) est dérivée pour notre modèle de système et agit comme une référence pour les estimateurs. La complexité de calcul des estimateurs de canal proposés et des précodeurs et les impacts du degré du polynôme sont également étudiés. Enfin, nous analysons les performances de la probabilité d'erreur des systèmes GFDM combinés aux codes LDPC. Nous dérivons d'abord les expressions du ratio de vraisemblance logarithmique (LLR) initiale qui sont utilisées dans le décodeur de l'algorithme de somme de produits (SPA). Ensuite, basé sur le seuil de décodage, nous estimons le taux d'erreur de trame (FER) dans la région de bas E[indice b]/N₀ en utilisant le BER observé pour modéliser les variations du canal. De plus, une borne inférieure du FER du système est également proposée basée sur des ensembles absorbants. Cette borne inférieure peut agir comme une estimation du FER dans la région de E[indice b]/N₀ élevé si l'ensemble absorbant utilisé est dominant et que sa multiplicité est connue. La quantification a également un impact important sur les performances du FER et du BER. Des codes LDPC basés sur un tableau et construit aléatoirement sont utilisés pour supporter les analyses de performances. Pour ces trois aspects, des simulations et des calculs informatiques sont effectués pour obtenir des résultats numériques connexes, qui vérifient les méthodes proposées.8 372162\u a Generalized frequency division multiplexing (GFDM) is a block-processing based non-orthogonal multi-carrier modulation scheme, which is a promising candidate waveform technology for beyond fifth-generation (5G) wireless systems. The ability of GFDM to flexibly adjust the block size and the type of pulse-shaping filters makes it a suitable scheme to meet several important requirements, such as low latency, low out-of-band (OOB) radiation and high data rates. Applying the multiple-input multiple-output (MIMO) technique, the massive MIMO technique, or low-density parity-check (LDPC) codes to GFDM systems can further improve the systems performance. Therefore, the investigation of such combined systems is of great theoretical and practical importance. This thesis investigates GFDM-based wireless communication systems from the following three aspects. First, we derive a union bound on the bit error rate (BER) for MIMO-GFDM systems, which is based on exact pairwise error probabilities (PEPs). The exact PEP is calculated using the moment-generating function (MGF) for maximum likelihood (ML) detectors. Both the spatial correlation between antennas and the channel estimation errors are considered in the investigated channel environment. Second, polynomial expansion-based low-complexity channel estimators and precoders are proposed for massive MIMO-GFDM systems. Interference-free pilots are used in the minimum mean square error (MMSE) channel estimation to combat the influence of non-orthogonality between subcarriers in GFDM. The cubic computational complexity can be reduced to square order by using the polynomial expansion technique to approximate the matrix inverses in the conventional MMSE estimation and precoding. In addition, we derive performance limits in terms of the mean square error (MSE) for the proposed estimators, which can be a useful tool to predict estimators performance in the high Eₛ/N₀ region. A Cramér-Rao lower bound (CRLB) is derived for our system model and acts as a benchmark for the estimators. The computational complexity of the proposed channel estimators and precoders, and the impacts of the polynomial degree are also investigated. Finally, we analyze the error probability performance of LDPC coded GFDM systems. We first derive the initial log-likelihood ratio (LLR) expressions that are used in the sum-product algorithm (SPA) decoder. Then, based on the decoding threshold, we estimate the frame error rate (FER) in the low E[subscript b]/N₀ region by using the observed BER to model the channel variations. In addition, a lower bound on the FER of the system is also proposed based on absorbing sets. This lower bound can act as an estimate of the FER in the high E[subscript b]/N₀ region if the absorbing set used is dominant and its multiplicity is known. The quantization scheme also has an important impact on the FER and BER performances. Randomly constructed and array-based LDPC codes are used to support the performance analyses. For all these three aspects, software-based simulations and calculations are carried out to obtain related numerical results, which verify our proposed methods