Analysis of Error in the Estimation of the Temporal ACF of Ergodic Sum-of-Cisoids Simulators for Mobile Fading Channels

Abstract-Mobile fading channel simulators based on ergodic sum-of-cisoids (SOC) processes have been proposed in several papers as a solution to accurately approximate the channel's autocorrelation function (ACF) in a single simulation run. However, despite the encouraging results presented in the literature, it is not clear whether the ergodicity of this type of simulators is meaningful in practice, where in contrast to what theory assumes, the waveforms generated by the simulator have finite lengths. To clarifying this issue, we present in this paper a comprehensive analysis of the random error observed when the temporal ACF (TACF) of ergodic SOC processes is estimated from waveforms of finite duration. We start by computing the instantaneous error produced by three different estimators, namely the biased, the unbiased, and the half-interval estimators. We then derive compact expressions for some insightful statistical quantities of the estimation error, such as the mean, the variance, and the mean-squared value. Based on the obtained results, we discuss the conditions under which an ergodic SOC simulator can be considered to perform similarly in theory and practice. The analysis presented in this paper can be used as a framework for testing, calibration, and performance validation of new ergodic SOC channel simulators

Design of Mobile Radio Channel Simulators Using the Iterative Nonlinear Least Square Approximation Method with Applications in Vehicle-to-X Communications

Doktorgradsavhandling i informasjons- og kommunikasjonsteknologi, Universitetet i Agder, 2015Vehicle-to-X (V2X) communication systems are expected to provide tremendous benefits associated with the safety and traffic efficiency on roads. The successful deployment of emerging technologies like V2X requires channel models accurately representing fading statistics in environments where those technologies are used. The accuracy is, of course, a major concern when adapting or developing a suitable channel model for test and evaluation purposes. However, it is also important to take into account the simplicity of a channel model, which is crucial for efficient numerical computations and computer simulations. Reconciling simplicity and accuracy is a rather complex task to accomplish, which requires sophisticated parameter computation methods. To the best of our knowledge, only a limited number of investigations address the channel modelling and parametrization problems for vehicular propagation scenarios in the literature. In order to fill this gap, we concentrate on the development of new sophisticated channel modelling approaches and efficient parameter computation methods for the design of V2X communication systems in this dissertation. In general, there are two main applications of channel models: (1) for the design and test of wireless communication systems and (2) for the optimization of existing communication systems. For the design and test purposes, more general statistical models such as Rice and Rayleigh channel models are preferred. Those channel models provide a fundamental insight into propagation phenomena and at the same time they greatly simplify the theoretical and numerical computations to assess the performance of wireless communication systems. For the optimization purposes, however, measurement-based channel models are commonly used. The main advantage of such channel models is that they always accurately reflect the physical reality. In this dissertation, we will focus on the channel models designed for both of those application purposes. A significant part of this dissertation will be devoted to the thorough analysis and design of Rayleigh and Rice fading channel models. We investigate the correlation properties of those channels assuming asymmetrical shapes of Doppler power spectral densities (PSDs). In fact, this is what we often observe in real-world propagation scenarios. In this regard, we will present an analytical expression for the autocorrelation function (ACF) of Rice processes that captures such realistic scenarios. Another important contribution to this topic is the novel iterative nonlinear least square approximation method for the design of Rice and Rayleigh channel simulators based on sum-of-sinusoids (SOS), as well as sum-of-cisoids (SOC) approaches. The idea behind the proposed method is very simple. The parameters of the simulation model are extracted from the reference model, such as the stochastic Rice and Rayleigh channel models, by fitting the statistical properties of interest, e.g. the ACF and the probability density function (PDF). We show that the proposed method outperforms several other methods in designing channel simulators with desired distribution and correlation properties. We also show that the proposed method provides a subtle balance between channel model’s simplicity and accuracy in designing Rayleigh and Rice channel simulators. The parametrization is a process of determining the key parameters specifying the channel model. This process has a great influence on the reliability of the developed channel model. It is therefore highly desirable if those parameters are extracted from measurements. In fact, this idea constitutes the fundamental concept behind measurement-based channel modelling approach. The measurement-based models are important in the sense that they can be used for the optimizations of the wireless communication system. Hence, the problem of computing the channel model parameters from the measurements is of special interest. In this regard, we propose iterative nonlinear least square approximation method for the design of measurementbased channel simulators. Through detailed investigations and comparative studies, we demonstrate that the proposed method is highly flexible and outperforms several other conventional methods in terms of reproducing the correlation characteristics obtained from several measurements. In addition, we introduce a new approach for the design of channel models for V2X communications in tunnel environments, where the number of scatterers contributing to the total received power is relatively small

Channel simulation models for mobile broadband communication systems

Mobile broadband wireless communication systems (MBWCS) are emerging as a solution to provide broadband services to users on the move. These systems are expected to operate in a wide variety of propagation scenarios, at different mobile speeds, and at various frequency bands. Under such a variety of requirements, flexible and efficient channel simulation models will prove fundamental for the laboratory analysis of MBWCS. Currently, most of the existing channel simulation models are either too complex as to allow for an efficient performance investigation of MBWCS, or they cannot be applied to the simulation of some relevant classes of mobile fading channels. To overcome these limitations, we present in this doctoral a flexible and efficient methodology for the design of channel simulation models for MBWCS. Such a methodology is based on the sum-of-cisoids (SOC) approach, an approach that is closely in line with the electromagnetic plane-wave propagation model. We build our channel simulators upon a class of ergodic SOC simulation models. For the computation of the SOC model parameters, we introduce two simple methods that enable the design of simulation models for mobile fading channels characterized by any type of Doppler power spectral densities (DPSDs). The proposed methods are well-suited for the simulation of both single-input single-output (SISO) and multiple-input multiple-output (MIMO) channels. We evaluate the methods’ performance with respect to their accuracy for emulating important statistical functions of the channel, such as the autocorrelation function (ACF), the envelope probability density function (PDF), and the ACF of the squared envelope. In the case of MIMO channels, we evaluate the methods’ performance in terms of the approximation of the channel temporal ACF and spatial cross-correlation function (SCCF). The obtained results demonstrate the excellent performance of the proposed methods. This dissertation is also intended to provide a comprehensive treatise of the theory behind the design of SOC simulation models for mobile fading channels. In this respect, the statistical properties of SOC channel simulators are thoroughly analyzed. Important contribution are given concerning the correlation properties of the square envelope of SOC simulators. Such contributions include the derivation of closed-form expressions for the squared envelope ACF of the SOC simulation model, and the analysis of the ergodicity properties of the SOC model’s squared envelope. We also revisit here the concept of the symbol-spaced tapped line model (SSTDL) for WSSUS channels. In this regard, we present a discussion on the problems of SSTDL models, and we propose a simple solution to avoid them. The usefulness of such a solution is exemplary demonstrated by analyzing the bit error probability of a multi-carrier code division multiple access (MC-CDMA) system

The Design of Sum-of-Cisoids Rayleigh Fading Channel Simulators Assuming Non-Isotropic Scattering Conditions

Published version of an article from the journal: IEEE Transactions on Wireless Communications. .(c) 2010 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. Article also available from the publisher: http://dx.doi.org/10.1109/twc.2010.04.091198n this letter, we introduce the Riemann sum method (RSM) as an effective tool for the design of sum-of-cisoids (SOC) simulators for narrowband mobile Rayleigh fading channels under non-isotropic scattering conditions. We compare the performance of the RSM with that of the generalized method of equal areas (GMEA) and the L-p-norm method (LPNM), which were until now the only methods available for the design of SOC simulators for non-isotropic scattering channels. The obtained results indicate that the RSM is better suited than the GMEA and the LPNM to emulate the channel's autocorrelation function (ACF), whereas the latter two methods are more precise regarding the approximation of the envelope distribution. The results also show that the benefits of increasing the number of cisoids are more significant in the case of the RSM than in the case of the GMEA and LPNM. Owing to its simplicity and good performance, the RSM can be used to design flexible simulation platforms for the laboratory analysis of mobile communication systems operating in non-isotropic scattering environments

Geometry-Based Channel Models for Car-to-Car Communication Systems and Applications

In last two decades, intelligent transportation systems (ITS) have received considerable attention due to new road traffic safety applications that significantly improve the efficiency of traffic flow and reduce the number of road accidents. Consequently, there has been an increased interest in studying and developing car-to-car (C2C) communication systems, which play a key role in ITS. C2C communications has also gained the attention of standardization bodies, such as the IEEE1 and 3GPP LTE2, which aim to provide improvements in C2C communication systems. As it follows from the title, in this dissertation, we present the state-of-the-art regarding the modeling and analysis of different C2C channels in C2C communication systems. In C2C communication systems, the underlying radio channel differs from the conventional fixed-to-mobile (F2M) and fixed-to-fixed (F2F) channels in the way that both the mobile transmitter and the mobile receiver are in motion. In this regard, reliable and robust traffic telematic systems have to be designed, developed and tested. This leads to a demand for new radio channel models for C2C communication systems. Therefore, this dissertation is devoted to design, develop and validate new geometry-based channel models for C2C communication systems. In particular, two goals are aimed, which are study and investigation of the propagation characteristics of C2C fading channels and analyzing the performance of C2C communication systems over those fading channels correlated in time and space.publishedVersio

Millimeter wave radio channels: properties, multipath modeling and simulations

Based on the characterization of realistic radio channels, results presented in this dissertation lead towards an understanding that when moving up to the higher frequencies, frequency itself does not play a significant role in defining the channel modeling methodology. In fact, how a propagation channel is illuminated is of fundamental importance. Therefore, millimeter wave (mmWave) system properties such as a high antenna directivity and system bandwidth are shown to have a great influence on the channel model definition. In this thesis, a fundamental assumption made in the state-of-the-art millimeter wave wireless channel models is challenged. It has been shown that Rayleigh-Rice fading assumption made in the state-of-the-art channel models for resolvable channel taps does not remain valid. This is mainly due to the sparse multipath illumination caused by high antenna directivity and high bandwidth of a mmWave system.Studies presented in this thesis are based on the characterization of realistic radio channels obtained from exhaustive channel sounding campaigns. Mainly, three fundamental problems of wireless channel modelling have been investigated for millimetre wave (mmWave) radio channel modelling application, namely (i) Frequency dependence of propagation, (ii) Impact of antenna directivity on the channel model definition, and (iii) Impact of system bandwidth on the radio channel modelling. A detailed description of these problems is as follows: (i) Frequency Dependence of Propagation. Multi-band measurement campaigns arecarried out using directional antennas which do an omni-directional scan of the propagation environment. During the measurements, Tx-Rx systems are placed at fixed positions and the propagation environment remained as static as possible. Using synthesized omni-directional power delay profiles (PDPs), we aim to investigate if there exists a frequency dependency in the multipath dispersion statistics, e.g. delay and angular spreads. (ii) Impact of Antenna Directivity on the Channel Model Definition. Small-scale fading measurements are carried out which emulate a scenario, where a radio communication link is established through a single multipath cluster which is illuminated using antennas with different Half Power Beam Widths (HPBW). The major goal here is to investigate the impact of spatial multipath filtering on the small-scale fading due to high antenna directivity. In particular, the impact on variations in the receive signal strength and the validity of narrowband wide-sense stationary assumption (both in time and frequency domains) is investigated. (iii) Impact of System Bandwidth on the Radio Channel Modelling. Small-scale fading measurements are used to illuminate multipath clusters in a lecture room scenario. The primary objective is to investigate the impact of high system bandwidth on variations in the receive signal strength, randomness in the cross-polarization power ratio (XPR) and richness of the multipath scattering. Based on the characterization of realistic radio channels, results presented in this dissertation lead towards an understanding that when moving up to the higher frequencies, frequency itself does not play a significant role in defining the channel modelling methodology. In fact, how a propagation channel is illuminated is of fundamental importance. Therefore, mmWave system properties such as a high antenna directivity and system bandwidth are shown to have a high influence on the channel model definition. In general, fade depth scaling as a function of system bandwidth is quite well understood. We demonstrate that, the high antenna directivity of mmWave systems result in a further reduction in the fading depth. In addition, we explore some new directions to this line of research which are based on the second-order statistical analysis of the channel impulse response (CIR) vector. Our results emphasize that, fading statistics of resolvable channel taps in a mmWave radio channel cannot be modelled as Rayleigh-Rice distributed random variables. This is primarily due to the fact that channels with sparse scattering conditions are illuminated due to high antenna directivity and bandwidth of mmWave systems. Consequently, the complex Gaussian random variable assumption associated with Rayleigh-Rice fading distributions does not remain valid. Further, it has been demonstrated that, high antenna directivity and bandwidth of mmWave systems also raise a question mark on the validity of wide-sense stationary (WSS) assumption in the slow-time domain of mmWave radio channels. Results presented in this contribution are novel and they provide theoretically consistent insights into the measured radio channel.In dieser Arbeit werden drei grundlegende Probleme der Modellierung von Drahtloskanalen fur die Anwendung bei der Funkkanalmodellierung im Millimeterwellenbereich (mmWave) untersucht, namlich (i) die Frequenzabhangigkeit der Ausbreitung, (ii) der Einfluss der Antennenrichtwirkung auf die Definition des Kanalmodells und (iii) der Einfluss der Systembandbreite auf die Funkkanalmodellierung. Die detaillierte Beschreibung dieser Probleme lautet wie folgt: (i) Frequenzabhangigkeit der Ausbreitung. Mehrband-Messkampagnen werden mitRichtantennen durchgefuhrt, die eine omnidirektionale Abtastung der Ausbreitungsumgebung vornehmen. Wahrend der Messungen werden die Tx-Rx-Systeme an festen Positionen platziert und die Ausbreitungsumgebung bleibt so statisch wie moglich. Mit Hilfe von synthetisierten omnidirektionalen Verzogerungs-Leistungsprofilen soll untersucht werden, ob es eine Frequenzabhangigkeit in der Mehrwegeausbreitungsstatistik gibt, z.B. in der Verzogerung und der Winkelspreizung. (ii) Einfluss der Antennenrichtwirkung auf die Definition des Kanalmodells. Es werden Messungen des schnellen Schwunds durchgefuhrt, die ein Szenario emulieren, bei dem eine Funkverbindung uber ein einzelnes Mehrwege-Cluster aufgebaut wird, das mit Antennen mit unterschiedlichen Strahlbreiten ausgeleuchtet wird. Das Hauptzielist hier die Untersuchung des Einflusses der raumlichen Filterung auf den schnellen Schwund aufgrund der hohen Antennenrichtwirkung. Insbesondere wird die Auswirkung auf Variationen der Empfangssignalstarke und die Gultigkeit der Annahme der schmalbandigen Stationaritat im weiteren Sinne (sowohl im Zeit- als auch im Frequenzbereich) untersucht. (iii) Einfluss der Systembandbreite auf die Funkkanalmodellierung. Messungen desschnellen Schwunds werden verwendet, um Mehrwege-Cluster in einem Horsaal-Szenario auszuleuchten. Das primare Ziel ist es, den Einfluss einer hohen Systembandbreite auf die Variationen der Empfangssignalstarke, die Zufalligkeit des Kreuzpolarisationsverhaltnisses und die Reichhaltigkeit der Mehrwegstreuung zu untersuchen. Basierend auf der Charakterisierung realistischer Funkkanäle führen die in dieser Dissertation vorgestellten Ergebnisse zu dem Verständnis, dass beim Ubergang zu höheren Frequenzen die Frequenz x selbst keine signifikante Rolle bei der Definition der Kanalmodellierungsmethodik spielt. Vielmehr ist es von grundlegender Bedeutung, wie ein Ausbreitungskanal ausgeleuchtet wird. Daher zeigt sich, dass mmWave-Systemeigenschaften wie eine hohe Antennenrichtcharakteristik und Systembandbreite einen hohen Einfluss auf die Definition des Kanalmodells haben. Im Allgemeinen ist die Skalierung der Schwundtiefe als Funktion der Systembandbreite ziemlich gut verstanden. Wir zeigen, dass die hohe Antennenrichtwirkung von mmWave-Systemen zu einer weiteren Reduzierung der Schwundtiefe führt. Zusätzlich erforschen wir einige neue Richtungen in diesem Forschungsbereich, die auf der Analyse der Statistik zweiter Ordnung des Kanalimpulsantwort-Vektors basieren. Unsere Ergebnisse unterstreichen, dass die Schwund-Statistiken der auflösbaren Kanalabgriffe in einem mmWave-Funkkanal nicht als Rayleigh-Rice-verteilte Zufallsvariablen modelliert werden können. Dies liegt vor allem daran, dass durch die hohe Antennenrichtwirkung und Bandbreite von mmWave-Systemen Kanale mit spärlichen Streubedingungen ausgeleuchtet werden. Folglich ist die Annahme komplexer Gaus’scher Zufallsvariablen, die mit Rayleigh-Rice Schwundverteilungen verbunden ist, nicht mehr gültig. Des Weiteren wird gezeigt, dass die hohe Antennenrichtwirkung und Bandbreite von mmWave-Systemen auch die Gültigkeit der Annahme von Stationarität im weiteren Sinne im Slow-Time-Bereich von mmWave-Funkkanälen in Frage stellt. Die in diesem Beitrag vorgestellten Ergebnisse sind neuartig und bieten theoretisch konsistente Einblicke in den gemessenen Funkkanal

Modelling, Analysis, and Simulation of Underwater Acoustic Channels : Doctoral Dissertation for the Degree Philosophiae Doctor (PhD) at the Faculty of Engineering and Science, Specialization in Information and Communication Technology

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Statistical analysis of the capacity of mobile radio channels

Doktorgradsavhandling i informasjons- og kommunikasjonsteknologi, Universitetet i Agder, Grimstad, 201

Massive MIMO channel models for 5G wireless communication systems and beyond

The recently standardised 5th generation (5G) wireless communication technologies and their evolution towards the 6th generation (6G) will enable low-latency, highdensity, and high-capacity communications across a wide variety of scenarios under tight constraints on energy consumption and limited availability of radio electromagnetic spectrum. Massive multiple-input multiple-output (MIMO) technologies will be key to achieve some of these goals and cover the ever-growing demand of data rates, reliability and seamless connectivity. Nowadays, the design and evaluation of new wireless communication technologies heavily rely on computationally-efficient channel models that can accurately capture essential propagation phenomena and flexibly adapt to a wide variety of scenarios. Thus, this thesis aims at providing methods of analysis of massive MIMO channels and developing advanced massive MIMO channel models that will help assess the 5G wireless communication technologies and beyond. First, key aspects of massive MIMO channels are investigated through a stochastic transformation method capable of modelling the space-time varying (STV) distribution of the delay and angle of arrival (AoA) of multi-path components (MPCs). The proposed method is followed by a channel modelling approach based on STV parameters of the AoA distribution that leads to closed-form expressions of key massive MIMO channel statistical properties. These methods are employed to analyse widelyused channel models and reveal some of their limitations. This investigation provides fundamental insights about non-stationary properties of massive MIMO channels and paves the way for developing subsequent efficient and accurate channel models. Second, three-dimensional (3D) non-stationary wideband geometry-based stochastic models (GBSMs) for massive MIMO communication systems are proposed. These models incorporate a novel approach to capture near-field effects, namely, the parabolic wavefront, that presents a good accuracy-complexity trade-off when compared to other existing techniques. In addition to cluster of MPCs (re)appearance, a Log-normal cluster-level shadowing process complements the modelling of large-scale fading over the array. Statistical properties of the models are derived and validated through simulations and measurements extracted from the available literature. Third, a highly-flexible and efficient 3D space-time non-stationary wideband massive MIMO channel model based on an ray-level evolution approach is proposed as a candidate for the design and assessment of 5G and beyond 5G (B5G) massive MIMO wireless communication technologies. The model can capture near-field effects, (dis)appearance, and large-scale fading of both clusters and individual MPCs by employing a single approach. Its efficiency relies upon a more realistic wavefront selection criterion, namely, the effective Rayleigh distance, which accounts for the limited lifespan of MPCs over the array. This novel criterion can help improve the efficiency of both existing and B5G massive MIMO channel models by greatly reducing the need for spherical wavefronts