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.

Low-Rank Channel Estimation for Millimeter Wave and Terahertz Hybrid MIMO Systems

Massive multiple-input multiple-output (MIMO) is one of the fundamental technologies for 5G and beyond. The increased number of antenna elements at both the transmitter and the receiver translates into a large-dimension channel matrix. In addition, the power requirements for the massive MIMO systems are high, especially when fully digital transceivers are deployed. To address this challenge, hybrid analog-digital transceivers are considered a viable alternative. However, for hybrid systems, the number of observations during each channel use is reduced. The high dimensions of the channel matrix and the reduced number of observations make the channel estimation task challenging. Thus, channel estimation may require increased training overhead and higher computational complexity. The need for high data rates is increasing rapidly, forcing a shift of wireless communication towards higher frequency bands such as millimeter Wave (mmWave) and terahertz (THz). The wireless channel at these bands is comprised of only a few dominant paths. This makes the channel sparse in the angular domain and the resulting channel matrix has a low rank. This thesis aims to provide channel estimation solutions benefiting from the low rankness and sparse nature of the channel. The motivation behind this thesis is to offer a desirable trade-off between training overhead and computational complexity while providing a desirable estimate of the channel

Fast and Robust Parametric Estimation of Jointly Sparse Channels

We consider the joint estimation of multipath channels obtained with a set of receiving antennas and uniformly probed in the frequency domain. This scenario fits most of the modern outdoor communication protocols for mobile access or digital broadcasting among others. Such channels verify a Sparse Common Support property (SCS) which was used in a previous paper to propose a Finite Rate of Innovation (FRI) based sampling and estimation algorithm. In this contribution we improve the robustness and computational complexity aspects of this algorithm. The method is based on projection in Krylov subspaces to improve complexity and a new criterion called the Partial Effective Rank (PER) to estimate the level of sparsity to gain robustness. If P antennas measure a K-multipath channel with N uniformly sampled measurements per channel, the algorithm possesses an O(KPNlogN) complexity and an O(KPN) memory footprint instead of O(PN^3) and O(PN^2) for the direct implementation, making it suitable for K << N. The sparsity is estimated online based on the PER, and the algorithm therefore has a sense of introspection being able to relinquish sparsity if it is lacking. The estimation performances are tested on field measurements with synthetic AWGN, and the proposed algorithm outperforms non-sparse reconstruction in the medium to low SNR range (< 0dB), increasing the rate of successful symbol decodings by 1/10th in average, and 1/3rd in the best case. The experiments also show that the algorithm does not perform worse than a non-sparse estimation algorithm in non-sparse operating conditions, since it may fall-back to it if the PER criterion does not detect a sufficient level of sparsity. The algorithm is also tested against a method assuming a "discrete" sparsity model as in Compressed Sensing (CS). The conducted test indicates a trade-off between speed and accuracy.Comment: 11 pages, 9 figures, submitted to IEEE JETCAS special issue on Compressed Sensing, Sep. 201

Inductive Matrix Completion and Root-MUSIC-Based Channel Estimation for Intelligent Reflecting Surface (IRS)-Aided Hybrid MIMO Systems

This paper studies the estimation of cascaded channels in passive intelligent reflective surface (IRS)- aided multiple-input multiple-output (MIMO) systems employing hybrid precoders and combiners. We propose a low-complexity solution that estimates the channel parameters progressively. The angles of departure (AoDs) and angles of arrival (AoAs) at the transmitter and receiver, respectively, are first estimated using inductive matrix completion (IMC) followed by root-MUSIC based super-resolution spectrum estimation. Forward-backward spatial smoothing (FBSS) is applied to address the coherence issue. Using the estimated AoAs and AoDs, the training precoders and combiners are then optimized and the angle differences between the AoAs and AoDs at the IRS are estimated using the least squares (LS) method followed by FBSS and the root-MUSIC algorithm. Finally, the composite path gains of the cascaded channel are estimated using on-grid sparse recovery with a small-size dictionary. The simulation results suggest that the proposed estimator can achieve improved channel parameter estimation performance with lower complexity as compared to several recently reported alternatives, thanks to the exploitation of the knowledge of the array responses and low-rankness of the channel using low-complexity algorithms at all the stages.Comment: Submitted to IEE

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”

Deep learning-based space-time coding wireless MIMO receiver optimization.

Doctoral Degree. University of KwaZulu-Natal, Durban.With the high demand for high data throughput and reliable wireless links to cater for real-time or low latency mobile application services, the wireless research community has developed wireless multiple-input multiple-output (MIMO) architectures that cater to these stringent quality of service (QoS) requirements. For the case of wireless link reliability, spatial diversity in wireless MIMO architectures is used to increase the link reliability. Besides increasing link reliability using spatial diversity, space-time block coding schemes may be used to further increase the wireless link reliability by adding time diversity to the wireless link. Our research is centered around the optimization of resources used in decoding space-time block coded wireless signals. There are two categories of space-time block coding schemes namely the orthogonal and non-orthogonal space-time block codes (STBC). In our research, we concentrate on two non-orthogonal STBC schemes namely the uncoded space-time labeling diversity (USTLD) and the Golden code. These two non-orthogonal STBC schemes exhibit some advantages over the orthogonal STBC called Alamouti despite their non-linear optimal detection. Orthogonal STBC schemes have the advantage of simple linear optimal detection relative to the more complex non-linear optimal detection of non-orthogonal STBC schemes. Since our research concentrates on wireless MIMO STBC transmission, for detection to occur optimally at the receiver side of a space-time block coded wireless MIMO link, we need to optimally perform channel estimation and decoding. USTLD has a coding gain advantage over the Alamouti STBC scheme. This implies that the USTLD can deliver higher wireless link reliability relative to the Alamouti STBC for the same spectral efficiency. Despite this advantage of the USTLD, to the best of our knowledge, the literature has concentrated on USTLD wireless transmission under the assumption that the wireless receiver has full knowledge of the wireless channel without estimation errors. We thus perform research of the USTLD wireless MIMO transmission with imperfect channel estimation. The traditional least-squares (LS) and minimum mean squared error (MMSE) used in literature, for imperfect pilot-assisted channel estimation, require the full knowledge of the transmitted pilot symbols and/or wireless channel second order statistics which may not always be fully known. We, therefore, propose blind channel estimation facilitated by a deep learning model that makes it unnecessary to have prior knowledge of the wireless channel second order statistics, transmitted pilot symbols and/or average noise power. We also derive an optimal number of pilot symbols that maybe used for USTLD wireless MIMO channel estimation without compromising the wireless link reliability. It is shown from the Monte Carlo simulations that the error rate performance of the USTLD transmission is not compromised despite using only 20% of the required number of Zadoff-Chu sequence pilot symbols used by the traditional LS and MMSE channel estimators for both 16-QAM and 16-PSK baseband modulation. The Golden code is a STBC scheme with spatial multiplexing gain over the Alamouti scheme. This implies that the Golden code can deliver higher spectral efficiencies for the same link reliability with the Alamouti scheme. The Alamouti scheme has been implemented in the modern wireless standards because it adds time diversity, with low decoding complexity, to wireless MIMO links. The Golden code adds time diversity and improves wireless MIMO spectral efficiency but at the cost of much higher decoding complexity relative to the Alamouti scheme. Because of the high decoding complexity, the Golden code is not widely adopted in the modern wireless standards. We, therefore, propose analytical and deep learning-based sphere-decoding algorithms to lower the number of detection floating-point operations (FLOPS) and decoding latency of the Golden code under low- and high-density M-ary quadrature amplitude modulation (M-QAM) baseband transmissions whilst maintaining the near-optimal error rate performance. The proposed sphere-decoding algorithms achieve at most 99% reduction in Golden code detection FLOPS, at low SNR, relative to the sphere-decoder with sorted detection subsets (SD-SDS) whilst maintaining the error rate performance. For the case of high-density M-QAM Golden code transmission, the proposed analytical and deep learning sphere-decoders reduce decoding latency by at most 70%, relative to the SD-SDS decoder, without diminishing the error rate performance

Compressive Sensing for Multi-channel and Large-scale MIMO Networks

Compressive sensing (CS) is a revolutionary theory that has important applications in many engineering areas. Using CS, sparse or compressible signals can be recovered from incoherent measurements with far fewer samples than the conventional Nyquist rate. In wireless communication problems where the sparsity structure of the signals and the channels can be explored and utilized, CS helps to significantly reduce the number of transmissions required to have an efficient and reliable data communication. The objective of this thesis is to study new methods of CS, both from theoretical and application perspectives, in various complex, multi-channel and large-scale wireless networks. Specifically, we explore new sparse signal and channel structures, and develop low-complexity CS-based algorithms to transmit and recover data over these networks more efficiently. Starting from the theory of sparse vector approximation based on CS, a compressive multiple-channel estimation (CMCE) method is developed to estimate multiple sparse channels simultaneously. CMCE provides a reduction in the required overhead for the estimation of multiple channels, and can be applied to estimate the composite channels of two-way relay channels (TWRCs) with sparse intersymbol interference (ISI). To improve end-to-end error performance of the networks, various iterative estimation and decoding schemes based on CS for ISI-TWRC are proposed, for both modes of cooperative relaying: Amplify-and-Forward (AF) and Decode-and-Forward (DF). Theoretical results including the Restricted Isometry Property (RIP) and low-coherent condition of the discrete pilot signaling matrix, the performance guarantees, and the convergence of the schemes are presented in this thesis. Numerical results suggest that the error performances of the system is significantly improved by the proposed CS-based methods, thanks to the awareness of the sparsity feature of the channels. Low-rank matrix approximation, an extension of CS-based sparse vector recovery theory, is then studied in this research to address the channel estimation problem of large-scale (or massive) multiuser (MU) multiple-input multiple-output (MIMO) systems. A low-rank channel matrix estimation method based on nuclear-norm regularization is formulated and solved via a dual quadratic semi-definite programming (SDP) problem. An explicit choice of the regularization parameter and useful upper bounds of the error are presented to show the efficacy of the CS method in this case. After that, both the uplink channel estimation and a downlink data recoding of massive MIMO in the interference-limited multicell scenarios are considered, where a CS-based rank-q channel approximation and multicell precoding method are proposed. The results in this work suggest that the proposed method can mitigate the effects of the pilot contamination and intercell interference, hence improves the achievable rates of the users in multicell massive MIMO systems. Finally, various low-complexity greedy techniques are then presented to confirm the efficacy and feasibility of the proposed approaches in practical applications

Compressive Sensing for Multi-channel and Large-scale MIMO Networks

Compressive sensing (CS) is a revolutionary theory that has important applications in many engineering areas. Using CS, sparse or compressible signals can be recovered from incoherent measurements with far fewer samples than the conventional Nyquist rate. In wireless communication problems where the sparsity structure of the signals and the channels can be explored and utilized, CS helps to significantly reduce the number of transmissions required to have an efficient and reliable data communication. The objective of this thesis is to study new methods of CS, both from theoretical and application perspectives, in various complex, multi-channel and large-scale wireless networks. Specifically, we explore new sparse signal and channel structures, and develop low-complexity CS-based algorithms to transmit and recover data over these networks more efficiently. Starting from the theory of sparse vector approximation based on CS, a compressive multiple-channel estimation (CMCE) method is developed to estimate multiple sparse channels simultaneously. CMCE provides a reduction in the required overhead for the estimation of multiple channels, and can be applied to estimate the composite channels of two-way relay channels (TWRCs) with sparse intersymbol interference (ISI). To improve end-to-end error performance of the networks, various iterative estimation and decoding schemes based on CS for ISI-TWRC are proposed, for both modes of cooperative relaying: Amplify-and-Forward (AF) and Decode-and-Forward (DF). Theoretical results including the Restricted Isometry Property (RIP) and low-coherent condition of the discrete pilot signaling matrix, the performance guarantees, and the convergence of the schemes are presented in this thesis. Numerical results suggest that the error performances of the system is significantly improved by the proposed CS-based methods, thanks to the awareness of the sparsity feature of the channels. Low-rank matrix approximation, an extension of CS-based sparse vector recovery theory, is then studied in this research to address the channel estimation problem of large-scale (or massive) multiuser (MU) multiple-input multiple-output (MIMO) systems. A low-rank channel matrix estimation method based on nuclear-norm regularization is formulated and solved via a dual quadratic semi-definite programming (SDP) problem. An explicit choice of the regularization parameter and useful upper bounds of the error are presented to show the efficacy of the CS method in this case. After that, both the uplink channel estimation and a downlink data precoding of massive MIMO in the interference-limited multicell scenarios are considered, where a CS-based rank-q channel approximation and multicell precoding method are proposed. The results in this work suggest that the proposed method can mitigate the effects of the pilot contamination and intercell interference, hence improves the achievable rates of the users in multicell massive MIMO systems. Finally, various low-complexity greedy techniques are then presented to confirm the efficacy and feasibility of the proposed approaches in practical applications

MIMO Systems

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