This thesis is targeted at precoding methods and resource allocation for the downlink of fixed multi-user multi-antenna broadband wireless systems. We explore different utilizations of precoders in transmission over frequency-selective channels. We first consider the weighted sum-rate (WSR) maximization problem for multi-carrier systems using linear precoding and propose a low complexity algorithm which exhibits near-optimal performance. Moreover, we offer a novel rate allocation method that utilizes the signalto- noise-ratio (SNR) gap to capacity concept to choose the rates to allocate to each data stream. We then study a single-carrier transmission scheme that overcomes known impairments associated with multi-carrier systems. The proposed scheme utilizes timereversal space-time block coding (TR-STBC) to orthogonalize the downlink receivers and performs the required pre-equalization using Tomlinson-Harashima precoding (THP).We finally discuss the strengths and weaknesses of the proposed method.

La mayor parte de los sistemas de comunicaciones requieren el conocimiento previo del canal, el cual se suele estimar a partir de una secuencia de entrenamiento. Sin embargo, la transmisión de símbolos piloto se traduce en una reducción de la eficiencia espectral del sistema, lo que imposibilita que se alcancen los límites predichos por la Teoría de la Información. Este problema ha motivado el desarrollo de un gran número de técnicas para la estima e igualación ciega de canal, es decir, para la obtención del canal o la fuente sin necesidad de transmitir una señal de entrenamiento. Normalmente, estas técnicas se basan en el conocimiento previo de ciertas características de la señal, tales como su pertenencia a un alfabeto finito, o sus estadísticos de orden superior. Sin embargo, en el caso de sistemas de múltiples entradas y salidas (MIMO), se ha demostrado que los estadísticos de segundo orden de las observaciones proporcionan la información suficiente para resolver el problema ciego.El objetivo de esta Tesis consiste en la obtención de nuevas técnicas para la estima e igualación ciega de canales MIMO, tanto en sistemas con redundancia espacial, como en casos más generales en los que las fuentes no presentan ningún tipo particular de estructura. De manera general, los métodos propuestos se basan en los estadísticos de segundo orden de las observaciones. Sin embargo, las técnicas se presentan desde un punto de vista determinista, es decir, los algoritmos propuestos explotan directamente la estructura de las matrices de datos, lo que permite obtener resultados más precisos cuando se dispone de un número reducido de observaciones. Adicionalmente, la reformulación de los criterios propuestos como problemas clásicos del análisis estadístico de señales, ha permitido la obtención de algoritmos adaptativos eficientes para la estima e igualación de canales MIMO. En primer lugar se aborda el caso de sistemas sin redundancia. Más concretamente, se analiza el problema de igualación ciega de canales MIMO selectivos en frecuencia, el cual se reformula como un conjunto de problemas de análisis de correlaciones canónicas (CCA). La solución de los problemas CCA se puede obtener de manera directa mediante un problema de autovalores generalizado. Además, en esta Tesis se presenta un algoritmo adaptativo basado en la reformulación de CCA como un conjunto de problemas de regresión lineal acoplados. De esta manera, se obtienen nuevos algoritmos bloque y adaptativos para la igualación ciega de canales MIMO de una manera sencilla. Finalmente, el método propuesto se basa, como muchas otras técnicas ciegas, en el conocimiento a priori del orden del canal, lo que constituye un problema casi tan complicado como el de la estima o igualación ciega. Así, en el caso de canales de una entrada y varias salidas (SIMO), la combinación de la técnica propuesta con otros métodos para la estima ciega del canal permite obtener un nuevo criterio para extracción del orden de este tipo de canalesEn segundo lugar se considera el problema de estima ciega de canal en sistemas con algún tipo de redundancia o estructura espacial, con especial interés en el caso de sistemas con codificación espacio-temporal por bloques (STBC). Específicamente, se propone una nueva técnica para la estima ciega del canal, cuya complejidad se reduce a la extracción del autovector principal de una matriz de correlación modificada. El principal problema asociado a este tipo de sistemas viene dado por la existencia de ciertas ambigüedades a la hora de estimar el canal. En esta Tesis se plantea el problema de identificabilidad de una manera general, y en el caso de códigos ortogonales (OSTBCs) se presentan varios nuevos teoremas que aseguran la identificabilidad del canal en un gran número de casos. Adicionalmente, se proponen varias técnicas para la resolución de las ambigüedades, tanto en el caso OSTBC como para códigos más generales. En concreto, se introduce el concepto de diversidad de código, que consiste en la combinación de varios códigos STBC. Esta técnica permite resolver las indeterminaciones asociadas a un gran número de problemas, y en su versión más sencilla se reduce a una precodificación no redundante consistente en una simple rotación o permutación de las antenas transmisoras.En definitiva, en esta Tesis se abordan los problemas de estima e igualación ciega de canal en sistemas MIMO, y se presentan varias técnicas ciegas, cuyas prestaciones se evalúan mediante un gran número de ejemplos de simulación. / The majority of communication systems need the previous knowledge of the channel, which is usually estimated by means of a training sequence. However, the transmission of pilot symbols provokes a reduction in bandwidth efficiency, which precludes the system from reaching the limits predicted by the Information Theory. This problem has motivated the development of a large number of blind channel estimation and equalization techniques, which are able to obtain the channel or the source without the need of transmitting a training signal. Usually, these techniques are based on the previous knowledge of certain properties of the signal, such as its belonging to a finite alphabet, or its higher-order statistics. However, in the case of multiple-input multiple-output (MIMO) systems, it has been proven that the second order statistics of the observations provide the sufficient information for solving the blind problem.The aim of this Thesis is the development of new blind MIMO channel estimation and equalization techniques, both in systems with spatial redundancy, and in more general cases where the sources do not have any particular spatial structure. In general, the proposed methods are based on the second order statistics of the observations. However, the techniques are presented from a deterministic point of view, i.e., the proposed algorithms directly exploit the structure of the data matrices, which allows us to obtain more accurate results when only a reduced number of observations is available. Additionally, the reformulation of the proposed criteria as classical statistical signal processing problems is exploited to obtain efficient adaptive algorithms for MIMO channel estimation and equalization.Firstly, we consider the case of systems without spatial redundancy. Specifically, we analyze the problem of blind equalization of frequency selective MIMO channels, which is reformulated as a set of canonical correlation analysis (CCA) problems. The solution of the CCA problems can be obtained by means of a generalized eigenvalue problem. In this Thesis, we present a new adaptive algorithm based on the reformulation of CCA as a set of coupled linear regression problems. Therefore, new batch and adaptive algorithms for blind MIMO channel equalization are easily obtained. Finally, the proposed method, as well as many other blind techniques, is based on the previous knowledge of the channel order, which is a problem nearly as complicated as the blind channel estimation or equalization. Thus, in the case of single-input multiple-output (SIMO) channels, the combination of the proposed technique with other blind channel estimation methods provides a new criterion for the order extraction of this class of channels.Secondly, we consider the problem of blind channel estimation in systems with some kind of redundancy or spatial structure, with special interest in space-time block coded (STBC) systems. Specifically, a new blind channel estimation technique is proposed, whose computational complexity reduces to the extraction of the principal eigenvector of a modified correlation matrix. The main problem in these cases is due to the existence of certain ambiguities associated to the blind channel estimation problem. In this Thesis the general identifiability problem is formulated and, in the case of orthogonal codes (OSTBCs), we present several new theorems which ensure the channel identifiability in a large number of cases. Additionally, several techniques for the resolution of the ambiguities are proposed, both in the OSTBC case as well as for more general codes. In particular, we introduce the concept of code diversity, which consists in the combination of several STBCs. This technique avoids the ambiguities associated to a large number of problems, and in its simplest version it reduces to a non-redundant precoding consisting of a single rotation or permutation of the transmit antennas.In summary, in this Thesis the blind MIMO channel estimation and equalization problems are analyzed, and several blind techniques are presented, whose performance is evaluated by means of a large number of simulation examples.

En la última década, la cooperación entre usuarios ha generado un gran interés por la posibilidad de mejorar la velocidad de transmisión en las redes de comunicaciones inalámbricas. El objetivo es formar un array con las antenas de todos los dispositivos y, de esta forma, aplicar técnicas de procesado espacio-temporal. El esquema de cooperación más sencillo es el canal con relays: todos los terminales que escuchen una comunicación entre dos puntos pueden ayudar a la fuente retransmitiendo lo que hayan recibido.En un sistema realista, los relays no disponen de información sobre el canal en trasmisión. En este escenario, los códigos espacio-temporales (STC, del inglés space-time coding) son la alternativa más eficiente para aprovechar la diversidad introducida por los relays. Sin embargo, los STC clásicos están diseñados para un número limitado y fijo de antenas transmisoras y no se adaptan bien a sistemas cooperativos donde el número de relays puede ser elevado y, sobretodo, puede variar en el tiempo, según los usuarios entren o salgan de la red. El problema principal es la necesidad de usar un código nuevo cada vez que cambie la configuración de la red, generando un importante tráfico de señalización.Esta tesis analiza un código espacio-temporal a bloques de dispersión lineal (LD-STBC, del inglés linear-dispersion space-time block coding), aleatorio y distribuido: a cada relay se le asigna una matriz aleatoria que aplica una transformación lineal al vector que contiene los símbolos de la fuente. Cada matriz se genera de forma independiente y sin ninguna relación con el número de usuarios involucrados. De esta manera, el número de nodos puede variar sin necesidad de modificar los códigos existentes.La forma más intuitiva de construir matrices de dispersión lineal independientes es que sus elementos sean variables aleatorias independientes e idénticamente distribuidas (i.i.d.). Por esta razón, se estudia primero la eficiencia espectral obtenida por este tipo de LD-STBC. Es importante remarcar que la eficiencia espectral es una cantidad aleatoria, ya que es una función de los códigos aleatorios anteriormente descritos. Sin embargo, cuando las dimensiones de las matrices crecen infinitamente pero manteniendo constante la tasa del código (relación entre número de símbolos de la fuente sobre el número de símbolos de los relays), la eficiencia espectral converge rápidamente hacia una cantidad determinista. Este resultado se demuestra usando la teoría de las matrices aleatorias. Por esta razón, el sistema se analiza aproximando la eficiencia espectral con su limite. Por ejemplo, la comparación con el canal directo entre fuente y destino permite definir unas condiciones suficientes en donde el sistema con relays es superior a la comunicación punto a punto.Posteriormente se debe analizar la probabilidad de outage, es decir la probabilidad de que, debido a la baja calidad del canal, la eficiencia espectral sea menor que la velocidad de transmisión solicitada por el sistema. Como ya se ha mencionado anteriormente, los relays se introducen para aumentar la diversidad del canal y, con ella, el número de caminos independientes entre la fuente y el receptor, reduciendo la probabilidad de outage. Para los LD-STBC i.i.d. las prestaciones en términos de outage dependen del tipo de relay (amplify and forward o decode and forward) y son función de la tasa del código, que debe ser cuidadosamente elegida para maximizar el orden de diversidad sin desperdiciar demasiados recursos.Finalmente, en el último capítulo de la tesis se considera otro tipo de LD-STBC, distinto del i.i.d. analizado hasta ahora. En este caso, las matrices de dispersión lineal siguen siendo independientes la una de la otra pero se añade la restricción de que cada una tenga columnas (o filas, según la tasa del código) ortogonales. Así, se consigue que el código siga siendo flexible con respecto a las variaciones en el número de usuarios, pero su estructura permite reducir la interferencia generada por cada relay, como se puede notar comparando su eficiencia espectral con la eficiencia espectral obtenida por el código i.i.d. Cabe destacar que el análisis asintótico de estos códigos (llamados isométricos) se basa en herramientas matemáticas más sofisticadas que las anteriores y, por lo tanto, es necesario un estudio más profundo para poder entender cómo se comporta en términos de outage. / In the last decade, cooperation among multiple terminals has been seen as one of the more promising strategies to improve transmission speed in wireless communications networks. Basically, the idea is to mimic an antenna array and apply distributed versions of well-known space-diversity techniques. In this context, the simplest cooperative scheme is the relay channel: all the terminals (relays) that overhear a point-to-point communication between a source and a destination may decide to aid the source by forwarding (relaying) its message.In a mobile system, it is common to assume that the relays do not have any information about the channel between them and the destination. Under this hypothesis, the best solution to exploit the diversity offered by multiple transmitting antennas is to use space-time coding (STC). However, classical STC's are designed for systems with a fixed and usually low number of antennas. Thus, they are not suitable for relaying in most mobile communications systems where the number of terminals is potentially large and may vary as users join or leave the network. For each new configuration, a new code has to be chosen and notified to the relays, introducing a set-up overhead of signaling traffic.In this dissertation we will propose and analyze a randomized distributed linear-dispersion space-time block code (LD-STBC): each relay is assigned a specific matrix which linearly transforms (left-multiplies) the column vector of source symbols. Each matrix is independently generated and does not depend on the total number of transmitters, which can thus change without interrupting data transmission for a new code--relay assignment.The more intuitive way to build independent linear-dispersion matrices is to fill them with independent and identically distributed (i.i.d.) random variables. Therefore, we will first consider these i.i.d. codes and characterize the resulting spectral efficiency. In order to analyze the performance achieved by the system, we consider a large-system analysis based on random matrix theory. We will show that the random spectral efficiency (function of the random linear-dispersion matrices) converges almost surely to a deterministic quantity when the dimensions of the code grow indefinitely while keeping constant the coding rate. Since convergence is very fast, the random spectral efficiency will be approximated by the deterministic limit in the subsequent analysis. By comparison with the direct link, sufficient conditions are derived for the superiority of relaying.Next, we will analyze the outage probability of the system, that is the probability that the spectral efficiency falls below a given target rate due to channel fading. The main purpose of diversity techniques is to introduce alternative paths from the source to the destination, so that data transmission does not fail when the direct link undergoes deep fading. We will show that the diversity behavior of LD-STBC relaying mainly depends on both the coding rate and the relaying strategy (amplify and forward or decode and forward). It is then important to choose the coding rate that maximizes the diversity order without wasting too many resources.To conclude the dissertation, we will consider a different code based on independent isometric Haar-distributed random linear-dispersion matrices. Thenew code maintains the flexibility of the previous one with respect to variations in the number of relays. However, the more complex structure of the codes allows a noticeable reduction of the interference generated by the relays. Unfortunately, isometric codes also require more sophisticated mathematical tools for their asymptotic analysis. For this reason, we simply introduce the problem by showing that it is possible to have some spectral-efficiency gain with respect to i.i.d. codes. The outage-probability analysis requires a more thorough understanding and will be the subject of future work.

This thesis is on the space--time variational multiscale (ST-VMS) computation of wind-turbine rotor and tower aerodynamics. The rotor geometry is that of the NREL 5MW offshore baseline wind turbine. We compute with a given wind speed and a specified rotor speed. The computation is challenging because of the large Reynolds numbers and rotating turbulent flows, and computing the correct torque requires an accurate and meticulous numerical approach. The presence of the tower increases the computational challenge because of the fast, rotational relative motion between the rotor and tower. The ST-VMS method is the residual-based VMS version of the Deforming-Spatial-Domain/Stabilized ST (DSD/SST) method, and is also called ``DSD/SST-VMST'' method (i.e., the version with the VMS turbulence model). In calculating the stabilization parameters embedded in the method, we are using a new element length definition for the diffusion-dominated limit. The DSD/SST method, which was introduced as a general-purpose moving-mesh method for computation of flows with moving interfaces, requires a mesh update method. Mesh update typically consists of moving the mesh for as long as possible and remeshing as needed. In the computations reported here, NURBS basis functions are used for the temporal representation of the rotor motion, enabling us to represent the circular paths associated with that motion exactly and specify a constant angular velocity corresponding to the invariant speeds along those paths. In addition, temporal NURBS basis functions are used in representation of the motion and deformation of the volume meshes computed and also in remeshing. We name this ``ST/NURBS Mesh Update Method (STNMUM).'' The STNMUM increases computational efficiency in terms of computer time and storage, and computational flexibility in terms of being able to change the time-step size of the computation. We use layers of thin elements near the blade surfaces, which undergo rigid-body motion with the rotor. We compare the results from computations with and without tower, and we also compare using NURBS and linear finite element basis functions in temporal representation of the mesh motion.

The reliability and data rate of wireless communication have traditionally been limited by the presence of multipath fading in wireless channels. However, dramatic performance improvements can be obtained by the use of multiple transmit and receive antennas. Specifically, multiple antennas increase reliability by providing diversity gain, namely greater immunity to deep channel fades. They also increase data rates by providing multiplexing gain, i.e., the ability to multiplex multiple symbols in one signaling interval. Harvesting the potential benefits of multiple antennas requires the use of specially designed space-time codes at the transmitter front-end. Space-time codes introduce redundancy in the transmitted signal across two dimensions, namely multiple transmit antennas and multiple signaling intervals. In this work, we focus on linear space-time codes, which linearly combine the real and imaginary parts of their complex inputs to obtain transmit vectors for multiple signaling intervals. We aim to design optimum linear space-time codes. Optimality metrics and design principles for space-time codes are shown to depend strongly on the codes' function in the overall transmitter architecture. We consider two cases, depending on whether or not the space-time code is complemented by a powerful outer error-control code. In the absence of an outer code, the multiplexing gain of a space-time code is measured by its rate, while its diversity gain is measured by its raw diversity order. To maximize multiplexing and diversity gains, the space-time code must have maximum possible rate and raw diversity order. We show that there is an infinite set of maximum-rate codes, almost all of which also have maximum raw diversity order. However, different codes in this set have different error rate for a given input alphabet and SNR. Therefore, we develop analytical and numerical optimization techniques to find the code in this set which has the minimum union bound on error rate. Simulation results indicate that optimized codes yield significantly lower error rates than unoptimized codes, at the same data rate and SNR. In a concatenated architecture, a powerful outer code introduces redundancy in the space-time code inputs, obtaining additional diversity. Thus, the raw diversity order of the space-time inner code is only a lower limit to the total diversity order of the concatenated transmitter. On the other hand, we show that the rate of the space-time code places an upper limit on the multiplexing ability of the concatenated architecture. We conclude that space-time inner codes should have maximum possible rate but need not have high raw diversity order. In particular, the serial-to-parallel converter, which introduces no redundancy at all, is a near-optimum space-time inner code. This claim is supported by simulation results. On the receiver side, we generalize the well known sphere decoder to develop new detection algorithms for stand-alone space-time codes. These new algorithms are extended to obtain efficient soft-output decoding algorithms for space-time inner codes.

In todays society, a growing number of users are demanding more sophisticated services from wireless communication devices. In order to meet these rising demands, it has been proposed to increase the capacity of the wireless channel by using more than one antenna at the transmitter and receiver, thereby creating multiple-input multiple-output (MIMO) channels. Using MIMO communication techniques is a promising way to improve wireless communication technology because in a rich-scattering environment the capacity increases linearly with the number of antennas. However, increasing the number of transmit antennas also increases the complexity of detection at an exponential rate. So while MIMO channels have the potential to greatly increase the capacity of wireless communication systems, they also force a greater computational burden on the receiver. Even suboptimal MIMO detectors that have relatively low complexity, have been shown to achieve unprecedented high spectral efficiency. However, their performance is far inferior to the optimal MIMO detector, meaning they require more transmit power. The fact that the optimal MIMO detector is an impractical solution due to its prohibitive complexity, leaves a performance gap between detectors that require reasonable complexity and the optimal detector. The objective of this research is to bridge this gap and provide new solutions for managing the inherent performance-complexity trade-off in MIMO detection. The optimally-ordered decision-feedback (BODF) detector is a standard low-complexity detector. The contributions of this thesis can be regarded as ways to either improve its performance or reduce its complexity - or both. We propose a novel algorithm to implement the BODF detector based on noise-prediction. This algorithm is more computationally efficient than previously reported implementations of the BODF detector. Another benefit of this algorithm is that it can be used to easily upgrade an existing linear detector into a BODF detector. We propose the partial decision-feedback detector as a strategy to achieve nearly the same performance as the BODF detector, while requiring nearly the same complexity as the linear detector. We propose the family of Chase detectors that allow the receiver to trade performance for reduced complexity. By adapting some simple parameters, a Chase detector may achieve near-ML performance or have near-minimal complexity. We also propose two new detection strategies that belong to the family of Chase detectors called the B-Chase and S-Chase detectors. Both of these detectors can achieve near-optimal performance with less complexity than existing detectors. Finally, we propose the double-sorted lattice-reduction algorithm that achieves near-optimal performance with near-BODF complexity when combined with the decision-feedback detector.

As the size of an adaptive antenna array grows, the system is able to resist interference signals of increasing bandwidth. This is a result of the transmit pattern gain increasing, which raises the target's return power, and a greater number of degrees of freedom. However, once the interference signal decorrelates completely from one channel to the next, increasing array size will cease to improve detection capability. The use of tapped delay-line processing to improve correlation between channels has been studied for smaller arrays with single element antennas, but previous analyses have not considereded larger systems that are partitioned into subarrays. This thesis quantifies the effect that subarrays have on performance, as measured by the interference bandwidth that can be handled, and explains how tapped delay-line processing can maintain the ability to detect targets in an environment with high bandwidth interference. The analysis begins by deriving equations to estimate the half-power bandwidth of an array with no taps. Then we find that a single delay with optimal spacing is sufficient to completely restore performance if the interference angle is known exactly. However, in practice, the tap spacing will never be optimal because this angle will not be known exactly, so further consideration is given to this non-ideal case and possible solutions for arbitrary interference scenarios are presented. Simulations indicate that systems with multiple taps have more tolerance to increasing interference bandwidth and unknown directions of arrival. Finally, the tradeoffs between ideal and practical configurations are explained and suggestions are given for the design of real-world systems.

Orthogonal frequency division multiplexing (OFDM) systems with cyclic prefix (CP) can be used to protect signal from the time-variant multipath channel induced distortions. However, the presence of CP could greatly decrease the effective data rate, thus many recent research works have been focused on the multiple-input multiple-output (MIMO) OFDM systems without CP (CP-free), equipped with the space-time block codes (ST-BC). The constraint of the conventional MIMO-OFDM (without using the ST-BC) system is that the number of receive-antenna has to be greater than the transmit-antenna. In this thesis, we first consider the ST-BC MIMO-OFDM system and show that the above-mentioned constraint can be removed, such that the condition become that the receive antenna should be greater than one, that is the basic requirement for MIMO system. It is particular useful and confirm to the recently specification, e.g., 3GPP LTE (Long Term Evolution) where the system deploy the 2¡Ñ2 or 4¡Ñ4 antennas systems. This thesis also considers the effects of peak-to-average power ratio (PAPR) in the transmitter and In-phase/ Quadrature-phase (IQ) imbalance in the receiver, and solves them by using the adaptive Volterra predistorter and blind adaptive filtering approach of the nonlinear parameters estimation and compensation, along with the power measurement, respectively. After the compensator of IQ imbalance in the receiver, an equalizer under the framework of generalized sidelobe canceller (GSC) is derived for interference suppression. To further reduce the complexity of receiver implementation, the partially adaptive (PA) scheme is applied by exploiting the structural information of the signal and interference signature matrices. As demonstrated from computer simulation results, the performance of the proposed CP-free ST-BC MIMO-OFDM receiver is very similar to that obtained by the conventional CP-based ST-BC MIMO-OFDM system under either the predistortion or compensation scenario.

The phenomenon of fading constitutes a fundamental problem in wireless communications. Researchers have proposed many methods to improve the reliability of communication over wireless channels in the presence of fading. Many studies on this topic have focused on diversity techniques. Transmit diversity is a common diversity type in which multiple antennas are employed at the transmitter. Space-time coding is a technique based on transmit diversity introduced by Tarokh et alii in 1998. In this thesis, various types of space-time codes are examined. Since they were originally introduced in the form of trellis codes, a major part is devoted to space-time trellis codes where the fundamental design criteria are established. Then, space-time block coding, which presents a different approach, is introduced and orthogonal spacetime block codes are analyzed in some detail. Lastly, rank codes from coding theory are studied and their relation to space-time coding are investigated.

In this thesis study, an overview of MIMO radar is presented. The differences in radar cross section, channel and received signal models in different MIMO radar configurations are examined. The performance improvements that can be achieved by the use of waveform diversity in coherent MIMO radar and by the use of angular diversity in statistical MIMO radar are investigated. The optimal detector under Neyman-Pearson criterion for Coherent MIMO radar when the interfering signal is white Gaussian noise is developed. Detection performance of phased array radar, coherent MIMO radar and Statistical MIMO radar are compared through numerical simulations. A detector for MIMO radar that contains the space time codes explicitly is also examined.