On Linear Transmission Systems

This thesis is divided into two parts. Part I analyzes the information rate of single antenna, single carrier linear modulation systems. The information rate of a system is the maximum number of bits that can be transmitted during a channel usage, and is achieved by Gaussian symbols. It depends on the underlying pulse shape in a linear modulated signal and also the signaling rate, the rate at which the Gaussian symbols are transmitted. The object in Part I is to study the impact of both the signaling rate and the pulse shape on the information rate. Part II of the thesis is devoted to multiple antenna systems (MIMO), and more specifically to linear precoders for MIMO channels. Linear precoding is a practical scheme for improving the performance of a MIMO system, and has been studied intensively during the last four decades. In practical applications, the symbols to be transmitted are taken from a discrete alphabet, such as quadrature amplitude modulation (QAM), and it is of interest to find the optimal linear precoder for a certain performance measure of the MIMO channel. The design problem depends on the particular performance measure and the receiver structure. The main difficulty in finding the optimal precoders is the discrete nature of the problem, and mostly suboptimal solutions are proposed. The problem has been well investigated when linear receivers are employed, for which optimal precoders were found for many different performance measures. However, in the case of the optimal maximum likelihood (ML) receiver, only suboptimal constructions have been possible so far. Part II starts by proposing new novel, low complexity, suboptimal precoders, which provide a low bit error rate (BER) at the receiver. Later, an iterative optimization method is developed, which produces precoders improving upon the best known ones in the literature. The resulting precoders turn out to exhibit a certain structure, which is then analyzed and proved to be optimal for large alphabets

Quantized Multimode Precoding in Spatially Correlated Multi-Antenna Channels

Multimode precoding, where the number of independent data-streams is adapted optimally, can be used to maximize the achievable throughput in multi-antenna communication systems. Motivated by standardization efforts embraced by the industry, the focus of this work is on systematic precoder design with realistic assumptions on the spatial correlation, channel state information (CSI) at the transmitter and the receiver, and implementation complexity. For spatial correlation of the channel matrix, we assume a general channel model, based on physical principles, that has been verified by many recent measurement campaigns. We also assume a coherent receiver and knowledge of the spatial statistics at the transmitter along with the presence of an ideal, low-rate feedback link from the receiver to the transmitter. The reverse link is used for codebook-index feedback and the goal of this work is to construct precoder codebooks, adaptable in response to the statistical information, such that the achievable throughput is significantly enhanced over that of a fixed, non-adaptive, i.i.d. codebook design. We illustrate how a codebook of semiunitary precoder matrices localized around some fixed center on the Grassmann manifold can be skewed in response to the spatial correlation via low-complexity maps that can rotate and scale submanifolds on the Grassmann manifold. The skewed codebook in combination with a lowcomplexity statistical power allocation scheme is then shown to bridge the gap in performance between a perfect CSI benchmark and an i.i.d. codebook design.Comment: 30 pages, 4 figures, Preprint to be submitted to IEEE Transactions on Signal Processin

Multiuser MIMO techniques with feedback

Kooperative Antennenanlagen haben vor kurzem einen heißen Forschungsthema geworden, da Sie deutlich höhere spektrale Effizienz als herkömmliche zelluläre Systeme versprechen. Der Gewinn wird durch die Eliminierung von Inter-Zelle Störungen (ICI) durch Koordinierung der-Antenne Übertragungen erworben. Vor kurzem, verteilte Organisation Methoden vorgeschlagen. Eine der größten Herausforderungen für das Dezentrale kooperative Antennensystem ist Kanalschätzung für den Downlink Kanal besonders wenn FDD verwendet wird. Alle zugehörigen Basisstationen im genossenschaftlichen Bereich müssen die vollständige Kanal Informationen zu Wissen, die entsprechenden precoding Gewicht Matrix zu berechnen. Diese Information ist von mobilen Stationen übertragen werden Stationen mit Uplink Ressourcen zu stützen. Wird als mehrere Basisstationen und mehreren mobilen Stationen in kooperativen Antennensysteme und jede Basisstation und Mobilstation beteiligt sind, können mit mehreren Antennen ausgestattet sein, die Anzahl der Kanal Parameter wieder gefüttert werden erwartet, groß zu sein. In dieser Arbeit wird ein effizientes Feedback Techniken der downlink Kanal Informationen sind für die Multi-user Multiple Input Multiple Output Fall vorgeschlagen, der insbesondere auf verteilte kooperative Antennensysteme zielt. Zuerst wird ein Unterraum-basiertes Kanalquantisierungsverfahren vorgeschlagen, das ein vorbestimmtes Codebuch verwendet. Ein iterativer Codebuchentwurfsalgorithmus wird vorgeschlagen, der zu einem lokalen optimalen Codebuch konvergiert. Darüber hinaus werden Feedback-Overhead-Reduktionsverfahren entwickelt, die die zeitliche Korrelation des Kanals ausnutzen. Es wird gezeigt, dass das vorgeschlagene adaptive Codebuchverfahren in Verbindung mit einem Datenkomprimierungsschema eine Leistung nahe an dem perfekten Kanalfall erzielt, was viel weniger Rückkopplungsoverhead im Vergleich zu anderen Techniken erfordert. Das auf dem Unterraum basierende Kanalquantisierungsverfahren wird erweitert, indem mehrere Antennen auf der Senderseite und/oder auf der Empfängerseite eingeführt werden, und die Leistung eines Vorcodierungs- (/Decodierungs-) Schemas mit regulierter Blockdiagonalisierung (RBD) wurde untersucht. Es wird ein kosteneffizientes Decodierungsmatrixquantisierungsverfahren vorgeschlagen, dass eine komplexe Berechnung an der Mobilstation vermeiden kann, während es nur eine leichte Verschlechterung zeigt. Die Arbeit wird abgeschlossen, indem die vorgeschlagenen Feedback-Methoden hinsichtlich ihrer Leistung, ihres erforderlichen Feedback-Overheads und ihrer Rechenkomplexität verglichen werden.Cooperative antenna systems have recently become a hot research topic, as they promise significantly higher spectral efficiency than conventional cellular systems. The gain is acquired by eliminating inter-cell interference (ICI) through coordination of the base antenna transmissions. Recently, distributed organization methods have been suggested. One of the main challenges of the distributed cooperative antenna system is channel estimation for the downlink channel especially when FDD is used. All of the associated base stations in the cooperative area need to know the full channel state information to calculate the corresponding precoding weight matrix. This information has to be transferred from mobile stations to base stations by using uplink resources. As several base stations and several mobile stations are involved in cooperative antenna systems and each base station and mobile station may be equipped with multiple antennas, the number of channel state parameters to be fed back is expected to be big. In this thesis, efficient feedback techniques of the downlink channel state information are proposed for the multi-user multiple-input multiple-output case, targeting distributed cooperative antenna systems in particular. First, a subspace based channel quantization method is proposed which employs a predefined codebook. An iterative codebook design algorithm is proposed which converges to a local optimum codebook. Furthermore, feedback overhead reduction methods are devised exploiting temporal correlation of the channel. It is shown that the proposed adaptive codebook method in conjunction with a data compression scheme achieves a performance close to the perfect channel case, requiring much less feedback overhead compared with other techniques. The subspace based channel quantization method is extended by introducing multiple antennas at the transmitter side and/or at the receiver side and the performance of a regularized block diagonalization (RBD) precoding(/decoding) scheme has been investigated as well as a zero-forcing (ZF) precoding scheme. A cost-efficient decoding matrix quantization method is proposed which can avoid a complex computation at the mobile station while showing only a slight degradation. The thesis is concluded by comparing the proposed feedback methods in terms of their performance, their required feedback overhead, and their computational complexity. The techniques that are developed in this thesis can be useful and applicable for 5G, which is envisioned to support the high granularity/resolution codebook and its efficient deployment schemes. Keywords: MU-MIMO, COOPA, limited feedback, CSI, CQ, feedback overhead reduction, Givens rotatio

Design and implimentationof Multi-user MIMO precoding algorithms

The demand for high-speed communications required by cutting-edge applications has put a strain on the already saturated wireless spectrum. The incorporation of antenna arrays at both ends of the communication link has provided improved spectral efficiency and link reliability to the inherently complex wireless environment, thus allowing for the thriving of high data-rate applications without the cost of extra bandwidth consumption. As a consequence to this, multiple-input multiple-output (MIMO) systems have become the key technology for wideband communication standards both in single-user and multi-user setups. The main difficulty in single-user MIMO systems stems from the signal detection stage at the receiver, whereas multi-user downlink systems struggle with the challenge of enabling non-cooperative signal acquisition at the user terminals. In this respect, precoding techniques perform a pre-equalization stage at the base station so that the signal at each receiver can be interpreted independently and without the knowledge of the overall channel state. Vector precoding (VP) has been recently proposed for non-cooperative signal acquisition in the multi-user broadcast channel. The performance advantage with respect to the more straightforward linear precoding algorithms is the result of an added perturbation vector which enhances the properties of the precoded signal. Nevertheless, the computation of the perturbation signal entails a search for the closest point in an in nite lattice, which is known to be in the class of non-deterministic polynomial-time hard (NP-hard) problems. This thesis addresses the difficulties that stem from the perturbation process in VP systems from both theoretical and practical perspectives. On one hand, the asymptotic performance of VP is analyzed assuming optimal decoding. Since the perturbation process hinders the analytical assessment of the VP performance, lower and upper bounds on the expected data rate are reviewed and proposed. Based on these bounds, VP is compared to linear precoding with respect to the performance after a weighted sum rate optimization, the power resulting from a quality of service (QoS) formulation, and the performance when balancing the user rates. On the other hand, the intricacies of performing an efficient computation of the perturbation vector are analyzed. This study is focused on tree-search techniques that, by means of an strategic node pruning policy, reduce the complexity derived from an exhaustive search and yield a close-to-optimum performance. To that respect, three tree-search algorithms are proposed. The xed-sphere encoder (FSE) features a constant data path and a non-iterative architecture that enable the parallel processing of the set of vector hypotheses and thus, allow for high-data processing rates. The sequential best-node expansion (SBE) algorithm applies a distance control policy to reduce the amount of metric computations performed during the tree traversal. Finally, the low-complexity SBE (LC-SBE) aims at reducing the complexity and latency of the aforementioned algorithm by combining an approximate distance computation model and a novel approach of variable run-time constraints. Furthermore, the hardware implementation of non-recursive tree-search algorithms for the precoding scenario is also addressed in this thesis. More specifically, the hardware architecture design and resource occupation of the FSE and K-Best xed-complexity treesearch techniques are presented. The determination of the ordered sequence of complexvalued nodes, also known as the Schnorr-Euchner enumeration, is required in order to select the nodes to be evaluated during the tree traversal. With the aim of minimizing the hardware resource demand of such a computationally-expensive task, a novel non-sequential and lowcomplexity enumeration algorithm is presented, which enables the independent selection of the nodes within the ordered sequence. The incorporation of the proposed enumeration technique along with a fully-pipelined architecture of the FSE and K-Best approaches, allow for data processing throughputs of up to 5 Gbps in a 4x4 antenna setup.Aplikazio abangoardistek beharrezko duten abiadura handiko komunikazioen eskaerak presio handia ezarri du dagoeneko saturatuta dagoen haririk gabeko espektruan. Komunikazio loturaren bi muturretan antena array-en erabilerak eraginkortasun espektral eta dagarritasun handiagoez hornitu du berez konplexua den haririk gabeko ingurunea, modu honetan banda zabalera gehigarririk gabeko abiadura handiko aplikazioen garapena ahalbidetuz. Honen ondorioz, multiple-input multiple output (MIMO) sistemak banda zabaleko komunikazio estandarren funtsezko teknologia bihurtu dira, erabiltzaile bakarreko ezarpenetan hala nola erabiltzaile anitzeko inguruneetan. Erabiltzaile bakarreko MIMO sistemen zailtasun garrantzitsuena hartzailean ematen den seinalearen detekzio fasean datza. Erabiltzaile anitzeko sistemetan, aldiz, erronka nagusiena datu jasotze ez kooperatiboa bermatzea da. Prekodi kazio teknikek hartzaile bakoitzaren seinalea kanalaren egoera orokorraren ezagutzarik gabe eta modu independiente baten interpretatzea ahalbidetzen dute estazio nagusian seinalearen pre-ekualizazio fase bat inposatuz. Azken aldian, prekodi kazio bektoriala (VP, ingelesez vector precoding) proposatu da erabiltzaile anitzeko igorpen kanalean seinalearen eskuratze ez kooperatiboa ahalbidetzeko. Perturbazio seinale baten erabilerak, prekodi katutako seinalearen ezaugarriak hobetzeaz gain, errendimenduaren hobekuntza nabarmen bat lortzen du prekodi kazio linearreko teknikekiko. Hala ere, perturbazio seinalearen kalkuluak sare in nitu baten puntu hurbilenaren bilaketa suposatzen du. Problema honen ebazpenaren konplexutasuna denbora polinomialean ez deterministikoa dela jakina da. Doktoretza tesi honen helburu nagusia VP sistemetan perturbazio prozesuaren ondorioz ematen diren zailtasun teoriko eta praktikoei irtenbide egoki bat ematea da. Alde batetik, seinale/zarata ratio handiko ingurunetan VP sistemen errendimendua aztertzen da, beti ere deskodetze optimoa ematen dela suposatuz. Perturbazio prozesuak VP sistemen errendimenduaren azterketa analitikoa oztopatzen duenez, data transmisio tasaren hainbat goi eta behe borne proposatu eta berrikusi dira. Borne hauetan oinarrituz, VP eta prekodi kazio linealaren arteko errendimendu desberdintasuna neurtu da hainbat aplikazio ezberdinen eremuan. Konkretuki, kanalaren ahalmen ponderatua, zerbitzu kalitatearen formulazio baten ondorioz esleitzen den seinale potentzia eta erabiltzaileen datu transmisio tasa orekatzean lortzen den errendimenduaren azterketa burutu dira. Beste alde batetik, perturbazio bektorearen kalkulu eraginkorra lortzeko metodoak ere aztertu dira. Analisi hau zuhaitz-bilaketa tekniketan oinarritzen da, non egitura sinple baten bitartez errendimendu ia optimoa lortzen den. Ildo horretan, hiru zuhaitz-bilaketa algoritmo proposatu dira. Alde batetik, Fixed-sphere encoder-aren (FSE) konplexutasun konstateak eta arkitektura ez errekurtsiboak datu prozesaketa abiadura handiak lortzea ahalbidetzen dute. Sequential best-node expansion (SBE) delako algoritmo iteratiboak ordea, distantzia kontrol politika baten bitartez metrika kalkuluen kopurua murriztea lortzen du. Azkenik, low-complexity SBE (LC-SBE) algoritmoak SBE metodoaren latentzia eta konplexutasuna murriztea lortzen du ordezko distantzien kalkuluari eta exekuzio iraupenean ezarritako muga aldakorreko metodo berri bati esker. Honetaz gain, prekodi kazio sistementzako zuhaitz-bilaketa algoritmo ez errekurtsiboen hardware inplementazioa garatu da. Zehazki, konplexutasun nkoko FSE eta K-Best algoritmoen arkitektura diseinua eta hardware baliabideen erabilera landu dira. Balio konplexuko nodoen sekuentzia ordenatua, Schnorr-Euchner zerrendapena bezala ezagutua, funtsezkoa da zuhaitz bilaketan erabiliko diren nodoen aukeraketa egiteko. Prozesu honek beharrezkoak dituen hardware baliabideen eskaera murrizteko, konplexutasun bajuko algoritmo ez sekuentzial bat proposatzen da. Metodo honen bitartez, sekuentzia ordenatuko edozein nodoren aukeraketa independenteki egin ahal da. Proposatutako zerrendapen metodoa eta estruktura fully-pipeline baten bitartez, 5 Gbps-ko datu prozesaketa abiadura lortu daiteke FSE eta K-Best delako algoritmoen inplementazioan.La demanda de comunicaciones de alta velocidad requeridas por las aplicaciones más vanguardistas ha impuesto una presión sobre el actualmente saturado espectro inalámbrico. La incorporación de arrays de antenas en ambos extremos del enlace de comunicación ha proporcionado una mayor e ciencia espectral y abilidad al inherentemente complejo entorno inalámbrico, permitiendo así el desarrollo de aplicaciones de alta velocidad de transmisión sin un consumo adicional de ancho de banda. Consecuentemente, los sistemas multiple-input multiple output (MIMO) se han convertido en la tecnología clave para los estándares de comunicación de banda ancha, tanto en las con guraciones de usuario único como en los entornos multiusuario. La principal di cultad presente en los sistemas MIMO de usuario único reside en la etapa de detección de la señal en el extremo receptor, mientras que los sistemas multiusuario en el canal de bajada se enfrentan al reto de habilitar la adquisición de datos no cooperativa en los terminales receptores. A tal efecto, las técnicas de precodi cación realizan una etapa de pre-ecualización en la estación base de tal manera que la señal en cada receptor se pueda interpretar independientemente y sin el conocimiento del estado general del canal. La precodifi cación vectorial (VP, del inglés vector precoding) se ha propuesto recientemente para la adquisición no cooperativa de la señal en el canal de difusión multiusuario. La principal ventaja de la incorporación de un vector de perturbación es una considerable mejora en el rendimiento con respecto a los métodos de precodi cación lineales. Sin embargo, la adquisición de la señal de perturbación implica la búsqueda del punto más cercano en un reticulado in nito. Este problema se considera de complejidad no determinística en tiempo polinomial o NP-complejo. Esta tesis aborda las di cultades que se derivan del proceso de perturbación en sistemas VP desde una perspectiva tanto teórica como práctica. Por un lado, se analiza el rendimiento de VP asumiendo una decodi cación óptima en escenarios de alta relación señal a ruido. Debido a que el proceso de perturbación di culta la evaluación analítica del rendimiento de los sistemas de VP, se proponen y revisan diversas cotas superiores e inferiores en la tasa esperada de transmisión de estos sistemas. En base a estas cotas, se realiza una comparación de VP con respecto a la precodi cación lineal en el ámbito de la capacidad suma ponderada, la potencia resultante de una formulación de calidad de servicio y el rendimiento obtenido al equilibrar las tasas de transmisión de los usuarios. Por otro lado, se han propuesto nuevos procedimientos para un cómputo e ciente del vector de perturbación. Estos métodos se basan en técnicas de búsqueda en árbol que, por medio de diferentes políticas de podado, reducen la complejidad derivada de una búsqueda exhaustiva y obtienen un rendimiento cercano al óptimo. A este respecto, se proponen tres algoritmos de búsqueda en árbol. El xed-sphere encoder (FSE) cuenta con una complejidad constante y una arquitectura no iterativa, lo que permite el procesamiento paralelo de varios vectores candidatos, lo que a su vez deriva en grandes velocidades de procesamiento de datos. El algoritmo iterativo denominado sequential best-node expansion (SBE) aplica una política de control de distancias para reducir la cantidad de cómputo de métricas realizadas durante la búsqueda en árbol. Por último, el low-complexity SBE (LC-SBE) tiene por objetivo reducir la complejidad y latencia del algoritmo anterior mediante la combinación de un modelo de cálculo aproximado de distancias y una estrategia novedosa de restricción variable del tiempo de ejecución. Adicionalmente, se analiza la implementación en hardware de algoritmos de búsqueda en árbol no iterativos para los escenarios de precodi cación. Más especí camente, se presentan el diseño de la arquitectura y la ocupación de recursos de hardware de las técnicas de complejidad ja FSE y K-Best. La determinación de la secuencia ordenada de nodos de naturaleza compleja, también conocida como la enumeración de Schnorr-Euchner, es vital para seleccionar los nodos evaluados durante la búsqueda en árbol. Con la intención de reducir al mínimo la demanda de recursos de hardware de esta tarea de alta carga computacional, se presenta un novedoso algoritmo no secuencial de baja complejidad que permite la selección independiente de los nodos dentro de la secuencia ordenada. La incorporación de la técnica de enumeración no secuencial junto con la arquitectura fully-pipeline de los algoritmos FSE y K-Best, permite alcanzar velocidades de procesamiento de datos de hasta 5 Gbps para un sistema de 4 antenas receptoras

Resource allocation and feedback in wireless multiuser networks

This thesis focuses on the design of algorithms for resource allocation and feedback in wireless multiuser and heterogeneous networks. In particular, three key design challenges expected to have a major impact on future wireless networks are considered: cross-layer scheduling; structured quantization codebook design for MU-MIMO networks with limited feedback; and resource allocation to provide physical layer security. The first design challenge is cross-layer scheduling, where policies are proposed for two network architectures: user scheduling in single-cell multiuser networks aided by a relay; and base station (BS) scheduling in CoMP. These scheduling policies are then analyzed to guarantee satisfaction of three performance metrics: SEP; packet delay; and packet loss probability (PLP) due to buffer overflow. The concept of the τ-achievable PLP region is also introduced to explicitly describe the tradeoff in PLP between different users. The second design challenge is structured quantization codebook design in wireless networks with limited feedback, for both MU-MIMO and CoMP. In the MU-MIMO network, two codebook constructions are proposed, which are based on structured transformations of a base codebook. In the CoMP network, a low-complexity construction is proposed to solve the problem of variable codebook dimensions due to changes in the number of coordinated BSs. The proposed construction is shown to have comparable performance with the standard approach based on a random search, while only requiring linear instead of exponential complexity. The final design challenge is resource allocation for physical layer security in MU-MIMO. To guarantee physical layer security, the achievable secrecy sum-rate is explicitly derived for the regularized channel inversion (RCI) precoder. To improve performance, power allocation and precoder design are jointly optimized using a new algorithm based on convex optimization techniques

Resource allocation and feedback in wireless multiuser networks

This thesis focuses on the design of algorithms for resource allocation and feedback in wireless multiuser and heterogeneous networks. In particular, three key design challenges expected to have a major impact on future wireless networks are considered: cross-layer scheduling; structured quantization codebook design for MU-MIMO networks with limited feedback; and resource allocation to provide physical layer security. The first design challenge is cross-layer scheduling, where policies are proposed for two network architectures: user scheduling in single-cell multiuser networks aided by a relay; and base station (BS) scheduling in CoMP. These scheduling policies are then analyzed to guarantee satisfaction of three performance metrics: SEP; packet delay; and packet loss probability (PLP) due to buffer overflow. The concept of the τ-achievable PLP region is also introduced to explicitly describe the tradeoff in PLP between different users. The second design challenge is structured quantization codebook design in wireless networks with limited feedback, for both MU-MIMO and CoMP. In the MU-MIMO network, two codebook constructions are proposed, which are based on structured transformations of a base codebook. In the CoMP network, a low-complexity construction is proposed to solve the problem of variable codebook dimensions due to changes in the number of coordinated BSs. The proposed construction is shown to have comparable performance with the standard approach based on a random search, while only requiring linear instead of exponential complexity. The final design challenge is resource allocation for physical layer security in MU-MIMO. To guarantee physical layer security, the achievable secrecy sum-rate is explicitly derived for the regularized channel inversion (RCI) precoder. To improve performance, power allocation and precoder design are jointly optimized using a new algorithm based on convex optimization techniques

Analysis and design of physical-layer network coding for relay networks

Physical-layer network coding (PNC) is a technique to make use of interference in wireless transmissions to boost the system throughput. In a PNC employed relay network, the relay node directly recovers and transmits a linear combination of its received messages in the physical layer. It has been shown that PNC can achieve near information-capacity rates. PNC is a new information exchange scheme introduced in wireless transmission. In practice, transmitters and receivers need to be designed and optimized, to achieve fast and reliable information exchange. Thus, we would like to ask: How to design the PNC schemes to achieve fast and reliable information exchange? In this thesis, we address this question from the following works: Firstly, we studied channel-uncoded PNC in two-way relay fading channels with QPSK modulation. The computation error probability for computing network coded messages at the relay is derived. We then optimized the network coding functions at the relay to improve the error rate performance. We then worked on channel coded PNC. The codes we studied include classical binary code, modern codes, and lattice codes. We analyzed the distance spectra of channel-coded PNC schemes with classical binary codes, to derive upper bounds for error rates of computing network coded messages at the relay. We designed and optimized irregular repeat-accumulate coded PNC. We modified the conventional extrinsic information transfer chart in the optimization process to suit the superimposed signal received at the relay. We analyzed and designed Eisenstein integer based lattice coded PNC in multi-way relay fading channels, to derive error rate performance bounds of computing network coded messages. Finally we extended our work to multi-way relay channels. We proposed a opportunistic transmission scheme for a pair-wise transmission PNC in a single-input single-output multi-way relay channel, to improve the sum-rate at the relay. The error performance of computing network coded messages at the relay is also improved. We optimized the uplink/downlink channel usage for multi-input multi-output multi-way relay channels with PNC to maximize the degrees of freedom capacity. We also showed that the system sum-rate can be further improved by a proposed iterative optimization algorithm