Limited Feedback Precoding for Massive MIMO

The large-scale array antenna system with numerous low-power antennas deployed at the base station, also known as massive multiple-input multiple-output (MIMO), can provide a plethora of advantages over the classical array antenna system. Precoding is important to exploit massive MIMO performance, and codebook design is crucial due to the limited feedback channel. In this paper, we propose a new avenue of codebook design based on a Kronecker-type approximation of the array correlation structure for the uniform rectangular antenna array, which is preferable for the antenna deployment of massive MIMO. Although the feedback overhead is quite limited, the codebook design can provide an effective solution to support multiple users in different scenarios. Simulation results demonstrate that our proposed codebook outperforms the previously known codebooks remarkably

Beamforming in MISO Systems: Empirical Results and EVM-based Analysis

We present an analytical, simulation, and experimental-based study of beamforming Multiple Input Single Output (MISO) systems. We analyze the performance of beamforming MISO systems taking into account implementation complexity and effects of imperfect channel estimate, delayed feedback, real Radio Frequency (RF) hardware, and imperfect timing synchronization. Our results show that efficient implementation of codebook-based beamforming MISO systems with good performance is feasible in the presence of channel and implementation-induced imperfections. As part of our study we develop a framework for Average Error Vector Magnitude Squared (AEVMS)-based analysis of beamforming MISO systems which facilitates comparison of analytical, simulation, and experimental results on the same scale. In addition, AEVMS allows fair comparison of experimental results obtained from different wireless testbeds. We derive novel expressions for the AEVMS of beamforming MISO systems and show how the AEVMS relates to important system characteristics like the diversity gain, coding gain, and error floor.Comment: Submitted to IEEE Transactions on Wireless Communications, November 200

Coherence Optimization and Best Complex Antipodal Spherical Codes

Vector sets with optimal coherence according to the Welch bound cannot exist for all pairs of dimension and cardinality. If such an optimal vector set exists, it is an equiangular tight frame and represents the solution to a Grassmannian line packing problem. Best Complex Antipodal Spherical Codes (BCASCs) are the best vector sets with respect to the coherence. By extending methods used to find best spherical codes in the real-valued Euclidean space, the proposed approach aims to find BCASCs, and thereby, a complex-valued vector set with minimal coherence. There are many applications demanding vector sets with low coherence. Examples are not limited to several techniques in wireless communication or to the field of compressed sensing. Within this contribution, existing analytical and numerical approaches for coherence optimization of complex-valued vector spaces are summarized and compared to the proposed approach. The numerically obtained coherence values improve previously reported results. The drawback of increased computational effort is addressed and a faster approximation is proposed which may be an alternative for time critical cases

Coding on Flag Manifolds for Limited Feedback MIMO Systems

The efficiency of the physical layer in modern communication systems using multi-input multi-output (MIMO) techniques is largely based on the availability of channel state information (CSI) at the transmitter. In many practical systems, CSI needs to be quantized at the receiver side before transmission through a limited rate feedback channel. This is typically done using a codebook-based precoding transmission, where the receiver transmits the index of a codeword from a pre-designed codebook shared with the transmitter. To construct such codes one has to discretize complex flag manifolds. For single-user MIMO with a maximum likelihood receiver, the spaces of interest are Grassmann manifolds. With a linear receiver and network MIMO, the codebook design is related to discretization of Stiefel manifolds and more general flag manifolds. In this thesis, coding in flag manifolds is studied. In a first part, flag manifolds are defined as metric spaces corresponding to subsurfaces of hyperspheres. The choice of distance defines the geometry of the space and impacts clustering and averaging (centroid computation) in vector quantization, as well as coding theoretical packing bounds and optimum constructions. For two transmitter antenna systems, the problem reduces to designing spherical codes. A simple isomorphism enables to analytically derive closed-form codebooks with inherent low-implementation complexity. For more antennas, the concept of orbits of symmetry groups is investigated. Optimum codebooks, having desirable implementation properties as described in industry standardization, can be obtained using orbits of specific groups. For large antenna systems and base station cooperation, a product codebook strategy is also considered. Such a design requires to jointly discretize the Grassmann and Stiefel manifolds. A vector quantization algorithm for joint Grassmann-Stiefel quantization is proposed. Finally, the pertinence of flag codebook design is illustrated for a MIMO system with linear receiver

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

Mehrdimensionale Kanalschätzung für MIMO-OFDM

DIGITAL wireless communication started in the 1990s with the wide-spread deployment of GSM. Since then, wireless systems evolved dramatically. Current wireless standards approach the goal of an omnipresent communication system, which fulfils the wish to communicate with anyone, anywhere at anytime. Nowadays, the acceptance of smartphones and/or tablets is huge and the mobile internet is the core application. Given the current growth, the estimated data traffic in wireless networks in 2020 might be 1000 times higher than that of 2010, exceeding 127 exabyte. Unfortunately, the available radio spectrum is scarce and hence, needs to be utilized efficiently. Key technologies, such as multiple-input multiple-output (MIMO), orthogonal frequency-division multiplexing (OFDM) as well as various MIMO precoding techniques increase the theoretically achievable channel capacity considerably and are used in the majority of wireless standards. On the one hand, MIMO-OFDM promises substantial diversity and/or capacity gains. On the other hand, the complexity of optimum maximum-likelihood detection grows exponentially and is thus, not sustainable. Additionally, the required signaling overhead increases with the number of antennas and thereby reduces the bandwidth efficiency. Iterative receivers which jointly carry out channel estimation and data detection are a potential enabler to reduce the pilot overhead and approach optimum capacity at often reduced complexity. In this thesis, a graph-based receiver is developed, which iteratively performs joint data detection and channel estimation. The proposed multi-dimensional factor graph introduces transfer nodes that exploit correlation of adjacent channel coefficients in an arbitrary number of dimensions (e.g. time, frequency, and space). This establishes a simple and flexible receiver structure that facilitates soft channel estimation and data detection in multi-dimensional dispersive channels, and supports arbitrary modulation and channel coding schemes. However, the factor graph exhibits suboptimal cycles. In order to reach the maximum performance, the message exchange schedule, the process of combining messages, and the initialization are adapted. Unlike conventional approaches, which merge nodes of the factor graph to avoid cycles, the proposed message combining methods mitigate the impairing effects of short cycles and retain a low computational complexity. Furthermore, a novel detection algorithm is presented, which combines tree-based MIMO detection with a Gaussian detector. The resulting detector, termed Gaussian tree search detection, integrates well within the factor graph framework and reduces further the overall complexity of the receiver. Additionally, particle swarm optimization (PSO) is investigated for the purpose of initial channel estimation. The bio-inspired algorithm is particularly interesting because of its fast convergence to a reasonable MSE and its versatile adaptation to a variety of optimization problems. It is especially suited for initialization since no a priori information is required. A cooperative approach to PSO is proposed for large-scale antenna implementations as well as a multi-objective PSO for time-varying frequency-selective channels. The performance of the multi-dimensional graph-based soft iterative receiver is evaluated by means of Monte Carlo simulations. The achieved results are compared to the performance of an iterative state-of-the-art receiver. It is shown that a similar or better performance is achieved at a lower complexity. An appealing feature of iterative semi-blind channel estimation is that the supported pilot spacings may exceed the limits given the by Nyquist-Shannon sampling theorem. In this thesis, a relation between pilot spacing and channel code is formulated. Depending on the chosen channel code and code rate, the maximum spacing approaches the proposed “coded sampling bound”.Die digitale drahtlose Kommunikation begann in den 1990er Jahren mit der zunehmenden Verbreitung von GSM. Seitdem haben sich Mobilfunksysteme drastisch weiterentwickelt. Aktuelle Mobilfunkstandards nähern sich dem Ziel eines omnipräsenten Kommunikationssystems an und erfüllen damit den Wunsch mit jedem Menschen zu jeder Zeit an jedem Ort kommunizieren zu können. Heutzutage ist die Akzeptanz von Smartphones und Tablets immens und das mobile Internet ist die zentrale Anwendung. Ausgehend von dem momentanen Wachstum wird das Datenaufkommen in Mobilfunk-Netzwerken im Jahr 2020, im Vergleich zum Jahr 2010, um den Faktor 1000 gestiegen sein und 100 Exabyte überschreiten. Unglücklicherweise ist die verfügbare Bandbreite beschränkt und muss daher effizient genutzt werden. Schlüsseltechnologien, wie z.B. Mehrantennensysteme (multiple-input multiple-output, MIMO), orthogonale Frequenzmultiplexverfahren (orthogonal frequency-division multiplexing, OFDM) sowie weitere MIMO Codierverfahren, vergrößern die theoretisch erreichbare Kanalkapazität und kommen bereits in der Mehrheit der Mobil-funkstandards zum Einsatz. Auf der einen Seite verspricht MIMO-OFDM erhebliche Diversitäts- und/oder Kapazitätsgewinne. Auf der anderen Seite steigt die Komplexität der optimalen Maximum-Likelihood Detektion exponientiell und ist infolgedessen nicht haltbar. Zusätzlich wächst der benötigte Mehraufwand für die Kanalschätzung mit der Anzahl der verwendeten Antennen und reduziert dadurch die Bandbreiteneffizienz. Iterative Empfänger, die Datendetektion und Kanalschätzung im Verbund ausführen, sind potentielle Wegbereiter um den Mehraufwand des Trainings zu reduzieren und sich gleichzeitig der maximalen Kapazität mit geringerem Aufwand anzunähern. Im Rahmen dieser Arbeit wird ein graphenbasierter Empfänger für iterative Datendetektion und Kanalschätzung entwickelt. Der vorgeschlagene multidimensionale Faktor Graph führt sogenannte Transferknoten ein, die die Korrelation benachbarter Kanalkoeffizienten in beliebigen Dimensionen, z.B. Zeit, Frequenz und Raum, ausnutzen. Hierdurch wird eine einfache und flexible Empfängerstruktur realisiert mit deren Hilfe weiche Kanalschätzung und Datendetektion in mehrdimensionalen, dispersiven Kanälen mit beliebiger Modulation und Codierung durchgeführt werden kann. Allerdings weist der Faktorgraph suboptimale Schleifen auf. Um die maximale Performance zu erreichen, wurde neben dem Ablauf des Nachrichtenaustausches und des Vorgangs zur Kombination von Nachrichten auch die Initialisierung speziell angepasst. Im Gegensatz zu herkömmlichen Methoden, bei denen mehrere Knoten zur Vermeidung von Schleifen zusammengefasst werden, verringern die vorgeschlagenen Methoden die leistungsmindernde Effekte von Schleifen, erhalten aber zugleich die geringe Komplexität des Empfängers. Zusätzlich wird ein neuartiger Detektionsalgorithmus vorgestellt, der baumbasierte Detektionsalgorithmen mit dem sogenannten Gauss-Detektor verknüpft. Der resultierende baumbasierte Gauss-Detektor (Gaussian tree search detector) lässt sich ideal in das graphenbasierte Framework einbinden und verringert weiter die Gesamtkomplexität des Empfängers. Zusätzlich wird Particle Swarm Optimization (PSO) zum Zweck der initialen Kanalschätzung untersucht. Der biologisch inspirierte Algorithmus ist insbesonders wegen seiner schnellen Konvergenz zu einem akzeptablen MSE und seiner vielseitigen Abstimmungsmöglichkeiten auf eine Vielzahl von Optimierungsproblemen interessant. Da PSO keine a priori Informationen benötigt, ist er speziell für die Initialisierung geeignet. Sowohl ein kooperativer Ansatz für PSO für Antennensysteme mit extrem vielen Antennen als auch ein multi-objective PSO für Kanäle, die in Zeit und Frequenz dispersiv sind, werden evaluiert. Die Leistungsfähigkeit des multidimensionalen graphenbasierten iterativen Empfängers wird mit Hilfe von Monte Carlo Simulationen untersucht. Die Simulationsergebnisse werden mit denen eines dem Stand der Technik entsprechenden Empfängers verglichen. Es wird gezeigt, dass ähnliche oder bessere Ergebnisse mit geringerem Aufwand erreicht werden. Eine weitere ansprechende Eigenschaft von iterativen semi-blinden Kanalschätzern ist, dass der mögliche Abstand von Trainingssymbolen die Grenzen des Nyquist-Shannon Abtasttheorem überschreiten kann. Im Rahmen dieser Arbeit wird eine Beziehung zwischen dem Trainingsabstand und dem Kanalcode formuliert. In Abhängigkeit des gewählten Kanalcodes und der Coderate folgt der maximale Trainingsabstand der vorgeschlagenen “coded sampling bound”