Feedback of channel state information in multi-antenna systems based on quantization of channel Gram matrices

This dissertation deals with the proper design of efficient feedback strategies for Multiple-Input Multiple-Output (MIMO) communication systems. MIMO systems outperform single antenna systems in terms of achievable throughput and are more resilient to noise and interference, which are becoming the limiting factors in the current and future communications. Apart from the clear performance advantages, MIMO systems introduce an additional complexity factor, since they require knowledge of the propagation channel in order to be able to adapt the transmission to the propagation channel’s characteristics and achieve optimum performance. This channel knowledge, also known as Channel State Information (CSI), is estimated at the receiver and sent to the transmitter through a limited feedback link. In this dissertation, first, the minimum channel information necessary at the transmitter for the optimum precoding design is identified. This minimum information for the optimum design of the system corresponds to the channel Gram matrix. It is essential for the design of optimized systems to avoid the transmission of redundant feedback information. Following this idea, a quantization algorithm that exploits the differential geometry of the set of Gram matrices and the correlation in time present in most propagation channels is developed in order to greatly improve the feedback performance. This scheme is applied first to single-user MIMO communications, then to some particular multiuser scenarios, and finally it is extended to general multiuser broadcast communications. To conclude, the feedback link sizing is studied. An analysis of the tradeoff between size of the forward link and size of the feedback link isformulated and the radio resource allocation problem, in terms of transmission energy, time, and bandwidth of the forward and feedback links is presented.En un mundo cada vez más interconectado, donde hay una clara tendencia hacia un mayor número de comunicaciones inalámbricas simultáneas (comunicaciones M2M: Machine to Machine, redes de sensores, etc.) y en el que las necesidades de capacidad de transmisión de los enlaces de comunicaciones aumentan de manera vertiginosa (audio, video, contenidos multimedia, alta definición, etc.) el problema de la interferencia se convierte en uno de los factores limitadores de los enlaces junto con los desvanecimientos del nivel de señal y las pérdidas de propagación. Por este motivo los sistemas que emplean múltiples antenas tanto en la transmisión como en la recepción (los llamados sistemas MIMO: Multiple-Input Multiple-Output) se presentan como una de las soluciones más interesantes para satisfacer los crecientes requisitos de capacidad y comportamiento relativo a interferencias. Los sistemas MIMO permiten obtener un mejor rendimiento en términos de tasa de transmisión de información y a su vez son más robustos frente a ruido e interferencias en el canal. Esto significa que pueden usarse para aumentar la capacidad de los enlaces de comunicaciones actuales o para reducir drásticamente el consumo energético manteniendo las mismas prestaciones. Por otro lado, además de estas claras ventajas, los sistemas MIMO introducen un punto de complejidad adicional puesto que para aprovechar al máximo las posibilidades de estos sistemas es necesario tener conocimiento de la información de estado del canal (CSI: Channel State Information) tanto en el transmisor como en el receptor. Esta CSI se obtiene mediante estimación de canal en el receptor y posteriormente se envía al transmisor a través de un canal de realimentación. Esta tesis trata sobre el diseño del canal de realimentación para la transmisión de CSI, que es un elemento fundamental de los sistemas de comunicaciones del presente y del futuro. Las técnicas de transmisión que consideran activamente el efecto de la interferencia y el ruido requieren adaptarse al canal y, para ello, la realimentación de CSI es necesaria. En esta tesis se identifica, en primer lugar, la mínima información sobre el estado del canal necesaria para implementar un diseño óptimo en el transmisor, con el fin de evitar transmitir información redundante y obtener así un sistema más eficiente. Esta información es la matriz de Gram del canal MIMO. Seguidamente, se desarrolla un algoritmo de cuantificación adaptado a la geometría diferencial del conjunto que contiene la información a cuantificar y que además aprovecha la correlación temporal existente en los canales de propagación inalámbricos. Este algoritmo se implementa y evalúa primero en comunicaciones MIMO punto a punto entre dos usuarios, después se implementa para algunos casos particulares con múltiples usuarios, y finalmente se amplía para el caso general de sistemas broadcast multi-usuario. Adicionalmente, esta tesis también estudia y optimiza el dimensionamiento del canal de realimentación en función de la cantidad de recursos radio disponibles, en términos de ancho de banda, tiempo y potencia de transmisión. Para ello presenta el problema de la distribución óptima de dichos recursos radio entre el enlace de transmisión de datos y el enlace de realimentación para transmisión de información sobre estado del canal como un problema de optimización

Estimation and detection techniques for doubly-selective channels in wireless communications

A fundamental problem in communications is the estimation of the channel. The signal transmitted through a communications channel undergoes distortions so that it is often received in an unrecognizable form at the receiver. The receiver must expend significant signal processing effort in order to be able to decode the transmit signal from this received signal. This signal processing requires knowledge of how the channel distorts the transmit signal, i.e. channel knowledge. To maintain a reliable link, the channel must be estimated and tracked by the receiver. The estimation of the channel at the receiver often proceeds by transmission of a signal called the 'pilot' which is known a priori to the receiver. The receiver forms its estimate of the transmitted signal based on how this known signal is distorted by the channel, i.e. it estimates the channel from the received signal and the pilot. This design of the pilot is a function of the modulation, the type of training and the channel. [Continues.

Signal processing for future MIMO-OFDM wireless communication systems

The combination of multiple-input multiple-output (MIMO) technology and orthogonal frequency division multiplexing (OFDM) is likely to provide the air-interface solution for future broadband wireless systems. A major challenge for MIMO-OFDM systems is the problem of multi-access interference (MAI) induced by the presence of multiple users transmitting over the same bandwidth. Novel signal processing techniques are therefore required to mitigate MAI and thereby increase link performance. A background review of space-time block codes (STBCs) to lever age diversity gain in MIMO systems is provided together with an introduction to OFDM. The link performance of an OFDM system is also shown to be sensitive to time-variation of the channel. Iterative minimum mean square error (MMSE) receivers are therefore proposed to overcome such time-variation. In the context of synchronous uplink transmission, a new two-step hard-decision interference cancellation receiver for STBC MIMO-OFDM is shown to have robust performance and relatively low complexity. Further improvement is obtained through employing error control coding methods and iterative algorithms. A soft output multiuser detector based on MMSE interference suppression and error correction coding at the first stage is shown by frame error rate simulations to provide significant performance improvement over the classical linear scheme. Finally, building on the "turbo principle", a low-complexity iterative interference cancellation and detection scheme is designed to provide a good compromise between the exponential computational complexity of the soft interference cancellation linear MMSE algorithm and the near-capacity performance of a scheme which uses iterative turbo processing for soft interference suppression in combination with multiuser detection.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Transmitter precoding for multi-antenna multi-user communications

Emerging wireless sensor networks and existing wireless cellular and ad hoc networks motivate the design of low-power receivers. Multi-user interference drastically reduces the energy efficiency of wireless multi-user communications by introducing errors in the bits being detected at the receiver. Interference rejection algorithms and multiple antenna techniques can significantly reduce the bit-error-rate at the receiver. Unfortunately, while interference rejection algorithms burden the receiver with heavy signal processing functionalities, thereby increasing the power consumption at the receiver, the small size of receivers, specifically in sensor networks and in downlink cellular communications, prohibits the use of multiple receive antennas. In a broadcast channel, where a central transmitter is transmitting independent streams to decentralized receivers, it is possible for the transmitter to have a priori knowledge of the interference. Multiple antennas can be used at the transmitter to enhance energy efficiency. In some systems, the transmitter has access to virtually an infinite source of power. A typical example would be the base station transmitter for the downlink of a cellular system. The power consumption at receivers can be reduced if some of the signal processing functionality of the receiver is moved to the transmitter.;In this thesis, we consider a wireless broadcast channel with a transmitter equipped with multiple antennas and having a priori knowledge of interference. Our objective is to minimize the receiver complexity by adding extra signal processing functions to the transmitter. We need to determine the optimal signal that should be transmitted so that interference is completely eliminated, and the benefits that can be obtained by using multiple transmit antennas can be maximized. We investigate the use of linear precoders, linear transformations made on the signal before transmission, for this purpose

MIMO equalization.

Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, Durban, 2005.In recent years, space-time block co'des (STBC) for multi-antenna wireless systems have emerged as attractive encoding schemes for wireless communications. These codes provide full diversity gain and achieve good performance with simple receiver structures without the additional increase in bandwidth or power requirements. When implemented over broadband channels, STBCs can be combined with orthogonal frequency division multiplexing (OFDM) or single carrier frequency domain (SC-FD) transmission schemes to achieve multi-path diversity and to decouple the broadband frequency selective channel into independent flat fading channels. This dissertation focuses on the SC-FD transmission schemes that exploit the STBC structure to provide computationally cost efficient receivers in terms of equalization and channel estimation. The main contributions in this dissertation are as follows: • The original SC-FD STBC receiver that bench marks STBC in a frequency selective channel is limited to coherent detection where the knowledge of the channel state information (CSI) is assumed at the receiver. We extend this receiver to a multiple access system. Through analysis and simulations we prove that the extended system does not incur any performance penalty. This key result implies that the SC-FD STBC scheme is suitable for multiple-user systems where higher data rates are possible. • The problem of channel estimation is considered in a time and frequency selective environment. The existing receiver is based on a recursive least squares (RLS) adaptive algorithm and provides joint equalization and interference suppression. We utilize a system with perfect channel state information (CSI) to show from simulations how various design parameters for the RLS algorithm can be selected in order to get near perfect CSI performance. • The RLS receiver has two modes of operation viz. training mode and direct decision mode. In training mode, a block of known symbols is used to make the initial estimate. To ensure convergence of the algorithm a re-training interval must be predefined. This results in an increase in the system overhead. A linear predictor that utilizes the knowled~e of the autocorrelation function for a Rayleigh fading channel is developed. The predictor is combined with. the adaptive receiver to provide a bandwidth efficient receiver by decreasing the training block size.· The simulation results show that the performance penalty for the new system is negligible. • Finally, a new Q-R based receiver is developed to provide a more robust solution to the RLS adaptive receiver. The simulation results clearly show that the new receiver outperforms the RLS based receiver at higher Doppler frequencies, where rapid channel variations result in numerical instability of the RLS algorithm. The linear predictor is also added to the new receiver which results in a more robust and bandwidth efficient receiver

Spatial diversity in MIMO communication systems with distributed or co-located antennas

The use of multiple antennas in wireless communication systems has gained much attention during the last decade. It was shown that such multiple-input multiple-output (MIMO) systems offer huge advantages over single-antenna systems. Typically, quite restrictive assumptions are made concerning the spacing of the individual antenna elements. On the one hand, it is typically assumed that the antenna elements at transmitter and receiver are co-located, i.e., they belong to some sort of antenna array. On the other hand, it is often assumed that the antenna spacings are sufficiently large, so as to justify the assumption of independent fading. In this thesis, the above assumptions are relaxed. In the first part, it is shown that MIMO systems with distributed antennas and MIMO systems with co-located antennas can be treated in a single, unifying framework. In the second part this fact is utilized, in order to develop appropriate transmit power allocation strategies for co-located and distributed MIMO systems. Finally, the third part focuses on specific synchronization problems that are of interest for distributed MIMO systems

Transmission strategies for wireless energy harvesting nodes

Over the last few decades, transistor miniaturization has enabled a tremendous increase in the processing capability of commercial electronic devices, which, combined with the reduction of production costs, has tremendously fostered the usage of the Information and communications Technologies (ICTs) both in terms of number of users and required data rates. In turn, this has led to a tremendous increment in the energetic demand of the ICT sector, which is expected to further grow during the upcoming years, reaching unsustainable levels of greenhouse gas emissions as reported by the European Council. Additionally, the autonomy of battery operated devices is getting reduced year after year since battery technology has not evolved fast enough to cope with the increase of energy consumption associated to the growth of the node¿s processing capability. Energy harvesting, which is known as the process of collecting energy from the environment by different means (e.g., solar cells, piezoelectric generators, etc.), has become a potential technology to palliate both of these problems. However, when energy harvesting modules are placed in wireless communication devices (e.g., sensor nodes or hand-held devices), traditional transmission strategies are no longer applicable because the temporal variations of the node¿s energy availability must be carefully accounted for in the design. Apart from not considering energy harvesting, traditional transmission strategies assume that the transmission radiated power is the unique energy sink in the node. This is a reasonable assumption when the transmission range is large, but it no longer holds for low consumption devices such as sensor nodes that transmit to short distances. As a result, classical transmission strategies become suboptimal in short-range communications with low consumption devices and new strategies should be investigated. Consequently, in this dissertation we investigate and design transmission strategies for Wireless Energy Harvesting Nodes (WEHNs) by paying a special emphasis on the different sinks of energy consumption at the transmitter(s). First, we consider a finite battery WEHN operating in a point-to-point link through a static channel and derive the transmission strategy that minimizes the transmission completion time of a set of data packets that become available dynamically over time. The transmission strategy has to satisfy causality constrains in data transmission and energy consumption, which impose that the node cannot transmit data that is not yet available nor consume energy that has not yet been harvested. Second, we consider a WEHN that has an infinite backlog of data to be transmitted through a point-to-point link in a time-varying linear vector Gaussian channel and study the linear precoding strategy that maximizes the mutual information given an arbitrary distribution of the input symbols while satisfying the Energy Causality Constraints (ECCs) at the transmitter. Next, apart from the transmission radiated power, we take into account additional energy sinks in the power consumption model and analyze how these energy sinks affect to the transmission strategy that maximizes the mutual information achieved by a WEHN operating in a point-to-point link. Finally, we consider multiple transmitter and receiver pairs sharing a common channel and investigate a distributed power allocation strategy that aims at maximizing the network sum-rate by taking into account the energy availability in the different transmitters and a generalized power consumption model.Durant les últimes dècades, la miniaturització del transistor i la reducció dels seus costos de fabricació han provocat un augment substancial del nombre de terminals de comunicacions i del tràfic de dades requerit per aquests dispositius. Així doncs, el consum energètic del sector de les Tecnologies de la Informació i Comunicacions ha incrementat notablement. A més a més, s’espera que aquest consum segueixi creixent durant els propers anys arribant a nivells insostenibles d’emissions de gasos d’efecte hivernacle segons ha informat el Consell Europeu. D’altra banda, la tecnologia de les bateries no ha evolucionat suficientment ràpid com per fer front a l’augment del consum energètic associat al creixement de la capacitat de processament dels dispositius. Això ha ocasionat que l’autonomia dels dispositius que operen amb bateries empitjori any rere any. Les energies renovables (per exemple, energia solar, cinètica, etc.) s’han convertit en una solució potencial per pal•liar aquests dos problemes. No obstant això, quan els dispositius de comunicació sense fils incorporen mòduls de captació d’energies renovables, les estratègies tradicionals de transmissió deixen de ser vàlides, ja que les variacions temporals de la disponibilitat d’energia en el dispositiu han de ser considerades en el disseny. A més a més, les estratègies de transmissió tradicionals assumeixen que la potència radiada és l’única font de consum energètic del node. Aquesta és una suposició raonable per distàncies de transmissió llargues, però deixa de ser vàlida quan es consideren dispositius de baix consum que transmeten en distàncies curtes. Com a resultat, les estratègies de transmissió clàssiques són subòptimes en comunicacions de curt abast amb dispositius de baix consum i per això, s’han d’investigar noves estratègies. En conseqüència, en aquesta tesi doctoral s’investiguen i es dissenyen noves estratègies de transmissió per nodes sense fils que operen amb energies renovables (WEHN) posant un èmfasi especial en les diferents fonts de consum d’energia en el transmissor. En primer lloc, la tesi investiga l’estratègia de transmissió en un enllaç¸ punt a punt a través d’un canal estàtic que minimitza el temps de transmissió d’un conjunt de paquets de dades que s’adquireixen al llarg del temps. L’estratègia de transmissió ha de satisfer les limitacions per causalitat en la transmissió de dades i en el consum d’energia les quals imposen que el node no pot transmetre dades que no han estat encara obtingudes o utilitzar energia que encara no ha estat adquirida. En segon lloc, es considera un WEHN que sempre disposa de dades per a transmetre a través d’un enllaç¸ punt a punt en un canal lineal Gaussià amb variacions temporals. En aquest escenari i, també, donada una distribució arbitrària dels símbols d’entrada, s’estudia l’estratègia de precodificació lineal que maximitza la informació mútua alhora que satisfà la causalitat d’energia en el transmissor. A continuació, a part de la potència radiada en transmissió, s’inclouen en el model de consum energètic els costos d’activació per accés al canal i per portadora. Donat aquest model, s’analitza com aquestes fonts de consum addicionals afecten a l’estratègia de transmissió que maximitza la informació mútua d’un WEHN que opera en un enllaç punt a punt. Finalment, la tesi considera diversos parells transmissor i receptor que comparteixen un canal comú i investiga una estratègia d’assignació de potència distribuïda la qual té com a objectiu maximitzar la suma de les taxes de transmissió dels diferents nodes tenint en compte la disponibilitat energètica en cada transmissor que està basada en un model de consum energètic generalitzat

Convergence of packet communications over the evolved mobile networks; signal processing and protocol performance

In this thesis, the convergence of packet communications over the evolved mobile networks is studied. The Long Term Evolution (LTE) process is dominating the Third Generation Partnership Project (3GPP) in order to bring technologies to the markets in the spirit of continuous innovation. The global markets of mobile information services are growing towards the Mobile Information Society. The thesis begins with the principles and theories of the multiple-access transmission schemes, transmitter receiver techniques and signal processing algorithms. Next, packet communications and Internet protocols are referred from the IETF standards with the characteristics of mobile communications in the focus. The mobile network architecture and protocols bind together the evolved packet system of Internet communications to the radio access network technologies. Specifics of the traffic models are shortly visited for their statistical meaning in the radio performance analysis. Radio resource management algorithms and protocols, also procedures, are covered addressing their relevance for the system performance. Throughout these Chapters, the commonalities and differentiators of the WCDMA, WCDMA/HSPA and LTE are covered. The main outcome of the thesis is the performance analysis of the LTE technology beginning from the early discoveries to the analysis of various system features and finally converging to an extensive system analysis campaign. The system performance is analysed with the characteristics of voice over the Internet and best effort traffic of the Internet. These traffic classes represent the majority of the mobile traffic in the converged packet networks, and yet they are simple enough for a fair and generic analysis of technologies. The thesis consists of publications and inventions created by the author that proposed several improvements to the 3G technologies towards the LTE. In the system analysis, the LTE showed by the factor of at least 2.5 to 3 times higher system measures compared to the WCDMA/HSPA reference. The WCDMA/HSPA networks are currently available with over 400 million subscribers and showing increasing growth, in the meanwhile the first LTE roll-outs are scheduled to begin in 2010. Sophisticated 3G LTE mobile devices are expected to appear fluently for all consumer segments in the following years

Advanced Algebraic Concepts for Efficient Multi-Channel Signal Processing

Unsere moderne Gesellschaft ist Zeuge eines fundamentalen Wandels in der Art und Weise wie wir mit Technologie interagieren. Geräte werden zunehmend intelligenter - sie verfügen über mehr und mehr Rechenleistung und häufiger über eigene Kommunikationsschnittstellen. Das beginnt bei einfachen Haushaltsgeräten und reicht über Transportmittel bis zu großen überregionalen Systemen wie etwa dem Stromnetz. Die Erfassung, die Verarbeitung und der Austausch digitaler Informationen gewinnt daher immer mehr an Bedeutung. Die Tatsache, dass ein wachsender Anteil der Geräte heutzutage mobil und deshalb batteriebetrieben ist, begründet den Anspruch, digitale Signalverarbeitungsalgorithmen besonders effizient zu gestalten. Dies kommt auch dem Wunsch nach einer Echtzeitverarbeitung der großen anfallenden Datenmengen zugute. Die vorliegende Arbeit demonstriert Methoden zum Finden effizienter algebraischer Lösungen für eine Vielzahl von Anwendungen mehrkanaliger digitaler Signalverarbeitung. Solche Ansätze liefern nicht immer unbedingt die bestmögliche Lösung, kommen dieser jedoch häufig recht nahe und sind gleichzeitig bedeutend einfacher zu beschreiben und umzusetzen. Die einfache Beschreibungsform ermöglicht eine tiefgehende Analyse ihrer Leistungsfähigkeit, was für den Entwurf eines robusten und zuverlässigen Systems unabdingbar ist. Die Tatsache, dass sie nur gebräuchliche algebraische Hilfsmittel benötigen, erlaubt ihre direkte und zügige Umsetzung und den Test unter realen Bedingungen. Diese Grundidee wird anhand von drei verschiedenen Anwendungsgebieten demonstriert. Zunächst wird ein semi-algebraisches Framework zur Berechnung der kanonisch polyadischen (CP) Zerlegung mehrdimensionaler Signale vorgestellt. Dabei handelt es sich um ein sehr grundlegendes Werkzeug der multilinearen Algebra mit einem breiten Anwendungsspektrum von Mobilkommunikation über Chemie bis zur Bildverarbeitung. Verglichen mit existierenden iterativen Lösungsverfahren bietet das neue Framework die Möglichkeit, den Rechenaufwand und damit die Güte der erzielten Lösung zu steuern. Es ist außerdem weniger anfällig gegen eine schlechte Konditionierung der Ausgangsdaten. Das zweite Gebiet, das in der Arbeit besprochen wird, ist die unterraumbasierte hochauflösende Parameterschätzung für mehrdimensionale Signale, mit Anwendungsgebieten im RADAR, der Modellierung von Wellenausbreitung, oder bildgebenden Verfahren in der Medizin. Es wird gezeigt, dass sich derartige mehrdimensionale Signale mit Tensoren darstellen lassen. Dies erlaubt eine natürlichere Beschreibung und eine bessere Ausnutzung ihrer Struktur als das mit Matrizen möglich ist. Basierend auf dieser Idee entwickeln wir eine tensor-basierte Schätzung des Signalraums, welche genutzt werden kann um beliebige existierende Matrix-basierte Verfahren zu verbessern. Dies wird im Anschluss exemplarisch am Beispiel der ESPRIT-artigen Verfahren gezeigt, für die verbesserte Versionen vorgeschlagen werden, die die mehrdimensionale Struktur der Daten (Tensor-ESPRIT), nichzirkuläre Quellsymbole (NC ESPRIT), sowie beides gleichzeitig (NC Tensor-ESPRIT) ausnutzen. Um die endgültige Schätzgenauigkeit objektiv einschätzen zu können wird dann ein Framework für die analytische Beschreibung der Leistungsfähigkeit beliebiger ESPRIT-artiger Algorithmen diskutiert. Verglichen mit existierenden analytischen Ausdrücken ist unser Ansatz allgemeiner, da keine Annahmen über die statistische Verteilung von Nutzsignal und Rauschen benötigt werden und die Anzahl der zur Verfügung stehenden Schnappschüsse beliebig klein sein kann. Dies führt auf vereinfachte Ausdrücke für den mittleren quadratischen Schätzfehler, die Schlussfolgerungen über die Effizienz der Verfahren unter verschiedenen Bedingungen zulassen. Das dritte Anwendungsgebiet ist der bidirektionale Datenaustausch mit Hilfe von Relay-Stationen. Insbesondere liegt hier der Fokus auf Zwei-Wege-Relaying mit Hilfe von Amplify-and-Forward-Relays mit mehreren Antennen, da dieser Ansatz ein besonders gutes Kosten-Nutzen-Verhältnis verspricht. Es wird gezeigt, dass sich die nötige Kanalkenntnis mit einem einfachen algebraischen Tensor-basierten Schätzverfahren gewinnen lässt. Außerdem werden Verfahren zum Finden einer günstigen Relay-Verstärkungs-Strategie diskutiert. Bestehende Ansätze basieren entweder auf komplexen numerischen Optimierungsverfahren oder auf Ad-Hoc-Ansätzen die keine zufriedenstellende Bitfehlerrate oder Summenrate liefern. Deshalb schlagen wir algebraische Ansätze zum Finden der Relayverstärkungsmatrix vor, die von relevanten Systemmetriken inspiriert sind und doch einfach zu berechnen sind. Wir zeigen das algebraische ANOMAX-Verfahren zum Erreichen einer niedrigen Bitfehlerrate und seine Modifikation RR-ANOMAX zum Erreichen einer hohen Summenrate. Für den Spezialfall, in dem die Endgeräte nur eine Antenne verwenden, leiten wir eine semi-algebraische Lösung zum Finden der Summenraten-optimalen Strategie (RAGES) her. Anhand von numerischen Simulationen wird die Leistungsfähigkeit dieser Verfahren bezüglich Bitfehlerrate und erreichbarer Datenrate bewertet und ihre Effektivität gezeigt.Modern society is undergoing a fundamental change in the way we interact with technology. More and more devices are becoming "smart" by gaining advanced computation capabilities and communication interfaces, from household appliances over transportation systems to large-scale networks like the power grid. Recording, processing, and exchanging digital information is thus becoming increasingly important. As a growing share of devices is nowadays mobile and hence battery-powered, a particular interest in efficient digital signal processing techniques emerges. This thesis contributes to this goal by demonstrating methods for finding efficient algebraic solutions to various applications of multi-channel digital signal processing. These may not always result in the best possible system performance. However, they often come close while being significantly simpler to describe and to implement. The simpler description facilitates a thorough analysis of their performance which is crucial to design robust and reliable systems. The fact that they rely on standard algebraic methods only allows their rapid implementation and test under real-world conditions. We demonstrate this concept in three different application areas. First, we present a semi-algebraic framework to compute the Canonical Polyadic (CP) decompositions of multidimensional signals, a very fundamental tool in multilinear algebra with applications ranging from chemistry over communications to image compression. Compared to state-of-the art iterative solutions, our framework offers a flexible control of the complexity-accuracy trade-off and is less sensitive to badly conditioned data. The second application area is multidimensional subspace-based high-resolution parameter estimation with applications in RADAR, wave propagation modeling, or biomedical imaging. We demonstrate that multidimensional signals can be represented by tensors, providing a convenient description and allowing to exploit the multidimensional structure in a better way than using matrices only. Based on this idea, we introduce the tensor-based subspace estimate which can be applied to enhance existing matrix-based parameter estimation schemes significantly. We demonstrate the enhancements by choosing the family of ESPRIT-type algorithms as an example and introducing enhanced versions that exploit the multidimensional structure (Tensor-ESPRIT), non-circular source amplitudes (NC ESPRIT), and both jointly (NC Tensor-ESPRIT). To objectively judge the resulting estimation accuracy, we derive a framework for the analytical performance assessment of arbitrary ESPRIT-type algorithms by virtue of an asymptotical first order perturbation expansion. Our results are more general than existing analytical results since we do not need any assumptions about the distribution of the desired signal and the noise and we do not require the number of samples to be large. At the end, we obtain simplified expressions for the mean square estimation error that provide insights into efficiency of the methods under various conditions. The third application area is bidirectional relay-assisted communications. Due to its particularly low complexity and its efficient use of the radio resources we choose two-way relaying with a MIMO amplify and forward relay. We demonstrate that the required channel knowledge can be obtained by a simple algebraic tensor-based channel estimation scheme. We also discuss the design of the relay amplification matrix in such a setting. Existing approaches are either based on complicated numerical optimization procedures or on ad-hoc solutions that to not perform well in terms of the bit error rate or the sum-rate. Therefore, we propose algebraic solutions that are inspired by these performance metrics and therefore perform well while being easy to compute. For the MIMO case, we introduce the algebraic norm maximizing (ANOMAX) scheme, which achieves a very low bit error rate, and its extension Rank-Restored ANOMAX (RR-ANOMAX) that achieves a sum-rate close to an upper bound. Moreover, for the special case of single antenna terminals we derive the semi-algebraic RAGES scheme which finds the sum-rate optimal relay amplification matrix based on generalized eigenvectors. Numerical simulations evaluate the resulting system performance in terms of bit error rate and system sum rate which demonstrates the effectiveness of the proposed algebraic solutions