Analysis of the Local Quasi-Stationarity of Measured Dual-Polarized MIMO Channels

It is common practice in wireless communications to assume strict or wide-sense stationarity of the wireless channel in time and frequency. While this approximation has some physical justification, it is only valid inside certain time-frequency regions. This paper presents an elaborate characterization of the non-stationarity of wireless dual-polarized channels in time. The evaluation is based on urban macrocell measurements performed at 2.53 GHz. In order to define local quasi-stationarity (LQS) regions, i.e., regions in which the change of certain channel statistics is deemed insignificant, we resort to the performance degradation of selected algorithms specific to channel estimation and beamforming. Additionally, we compare our results to commonly used measures in the literature. We find that the polarization, the antenna spacing, and the opening angle of the antennas into the propagation channel can strongly influence the non-stationarity of the observed channel. The obtained LQS regions can be of significant size, i.e., several meters, and thus the reuse of channel statistics over large distances is meaningful (in an average sense) for certain algorithms. Furthermore, we conclude that, from a system perspective, a proper non-stationarity analysis should be based on the considered algorithm

Stationarity analysis of V2I radio channel in a suburban environment

Due to rapid changes in the environment, vehicular communication channels no longer satisfy the assumption of wide-sense stationary uncorrelated scattering. The non-stationary fading process can be characterized by assuming local stationarity regionswith finite extent in time and frequency. The local scattering function (LSF) and channel correlation function (CCF) provide a framework to characterize the mean power and correlation of the non-stationary channel scatterers, respectively. In this paper, we estimate the LSF and CCF from measurements collected in a vehicle-to-infrastructure radio channel sounding campaign in a suburban environment in Lille, France. Based on the CCF, the stationarity region is evaluated in time as 567 ms and used to capture the non-stationary fading parameters. We obtain the time-varying delay and Doppler power profiles fromthe LSF, and we analyze the corresponding root-mean-square delay and Doppler spreads. We show that the distribution of these parameters follows a lognormal model. Finally, application relevance in terms of channel capacity and diversity techniques is discussed. Results show that the assumption of ergodic capacity and the performance of various diversity techniques depend on the stationarity and coherence parameters of the channel. The evaluation and statistical modeling of such parameters can provide away of tracking channel variation, hence, increasing the performance of adaptive schemes

A Group-Theoretic Approach to the WSSUS Pulse Design Problem

We consider the pulse design problem in multicarrier transmission where the pulse shapes are adapted to the second order statistics of the WSSUS channel. Even though the problem has been addressed by many authors analytical insights are rather limited. First we show that the problem is equivalent to the pure state channel fidelity in quantum information theory. Next we present a new approach where the original optimization functional is related to an eigenvalue problem for a pseudo differential operator by utilizing unitary representations of the Weyl--Heisenberg group.A local approximation of the operator for underspread channels is derived which implicitly covers the concepts of pulse scaling and optimal phase space displacement. The problem is reformulated as a differential equation and the optimal pulses occur as eigenstates of the harmonic oscillator Hamiltonian. Furthermore this operator--algebraic approach is extended to provide exact solutions for different classes of scattering environments.Comment: 5 pages, final version for 2005 IEEE International Symposium on Information Theory; added references for section 2; corrected some typos; added more detailed discussion on the relations to quantum information theory; added some more references; added additional calculations as an appendix; corrected typo in III.

Efficient Channel Modeling Methods for Mobile Communication Systems

Siirretty Doriast

Extending TDL based non-WSSUS vehicle-to-everything channel model

In den vergangenen Jahrzehnten haben drahtlose Kommunikationssysteme eine rasante Entwicklung durchgemacht und es wurden viele Untersuchungen durchgeführt, seit Maxwell die Existenz von elektromagnetischer Wellen vorausgesagt hat. In den letzten Jahren hat die Forschung im Bereich der vehicle to X (V2X)-Kommunikation stetig zugenommen. V2X beschreibt die Fähigkeit, Daten zwischen einem Fahrzeug oder vehicle (V) und “allem” zu übertragen. In Zukunft könnten Fahrzeuge mit ihrer Umgebung kommunizieren, um Verkehrsunfälle zu vermeiden und Staus zu verringern. Dazu werden sie ihr Geschwindigkeits- und Positionsdaten über Ad-hoc-Fahrzeugnetze senden und empfangen können. Um die Verkehrssicherheit zu erhöhen, ist eine zuverlässige Kommunikationsverbindung notwendig. Die größte Herausforderung bei der Fahrzeugkommunikation besteht darin, dass sich die Eigenschaften des Physical Layers aufgrund der inhärenten Mobilität innerhalb des Kanals, der hohen Fahrzeuggeschwindigkeiten, der unterschiedlichen Antennenpositionen und der vielen Handover aufgrund kleinerer Zellen schnell ändern. Dies bringt eine Reihe von Herausforderungen in Bezug auf die Kanalcharakterisierung mit sich. Es handelt sich um einen Kanal mit starker Zeitvarianz und es treten viele Übergänge auf. Somit handelt es sich um einen nicht-stationärer (non-stationary) Kanal. Das Hauptziel dieser Untersuchung ist es, eine Methode zu finden, mit der der Kanal einer komplexen Umgebung in einer einfachen Form mit weniger strengen Beziehungen zur Geometrie dargestellt werden kann. Dabei werden die statistischen Eigenschaften ähnlich der Messdaten beibehalten. In dieser Arbeit werden nichtstationäre tapped delay line (TDL)-Modelle verwendet, um vehicle to infrastructure (V2I)-Kanäle zu beschreiben. Es wird eine neue Strategie zur Extraktion von TDL-Kanalmodellparametern aus Messdaten vorgeschlagen. Dieser Ansatz basiert auf einer bestehenden Methode zur Ableitung von Parametern für ein TDLModell. Es wird gezeigt, dass mit einer anderen Methode zur Auswahl der Taps die Anzahl der Abgriffe, die zur Rekonstruktion der root mean square delay spread (RMS-DS) eines Kanals erforderlich sind, erheblich reduziert werden kann. Ein neuer Ansatz zur überprüfen der Korrektheit der Ableitung der Kanalmodellparameter wird aufgezeigt. Die Durchführbarkeit der Methode wird anhand von Channel Sounding Messungen bestätigt. In dieser Dissertation wird ein Generator zur Erzeugung von Kanalimpulsantworten entwickelt und das nichtstationäre Verhalten der Kanäle durch die Verwendung eines ON/OFF-Prozesses beschrieben. Es werden Markov-Ketten unterschiedlicher Ordnung modelliert, um das nicht-stationäre Verhalten besser zu erfassen. Die Untersuchung zeigt, dass Markov-Ketten erster Ordnung mit zwei Zuständen vorzuziehen sind, um das häufige ON/OFF-Verhalten von Mehrwegpfaden darzustellen, und dass die Markov-Modelle zweiter und dritter Ordnung keine großen Auswirkungen haben. Eine Methode zur Erweiterung eines single input single output (SISO)-TDL-Modells auf multiple input multiple output (MIMO) unter der non-wide sense stationary uncorrelated scattering (non-WSSUS)-Annahme wird eingeführt, um TDL-Kanalmodelle für V2I MIMO-Systeme zu entwickeln. Die Analyse bewertet die SISO- mit der MIMO-Konfiguration in Bezug auf die Kanalkapazität. Es werden verschiedene MIMO-Konfigurationen untersucht, und es wird gezeigt, dass die Position der Antennen eine wichtige Rolle spielt. Die Verwendung von nur vier Antennen am transmitter (Tx) und receiver (Rx), die in unterschiedliche Richtungen abstrahlen, führt zu einem qualitativen Sprung in der Leistungsfähigkeit des Systems.In the past decades, wireless communication systems have undergone rapid development, and many investigations have been done since Maxwell predicted the existence of electromagnetic waves. In recent years, vehicle to X (V2X) communication research has been growing steadily. V2X describes the ability to transmit data between a vehicle (V) and “everything”. In the future, vehicles might be able to communicate with their environment to prevent traffic accidents and reduce congestion by allowing vehicles to transmit and receive data through a vehicular ad hoc network at their speed and position. In order to achieve the ultimate goal of enhancing transportation safety, it is crucial to establish reliable communication links. The main challenge of vehicular communications introduces new properties because the physical layer properties are rapidly changing due to inherent mobility within the channel, high vehicle speeds, varying antenna positions, and many handovers due to smaller cells. This brings up a number of challenges in terms of channel characterization because it is a strong time-variant channel and many transitions occur; therefore, it is a non-stationary channel. In this thesis, non-stationary tapped delay line (TDL) models are used to describe the vehicle to infrastructure (V2I) channels. This thesis proposes a new strategy to extract TDL channel model parameters from measurement data. The proposed approach is based on an existing method to derive parameters for a TDL model. It will be shown that with a different method of choosing taps, the number of taps necessary to regenerate the root mean square delay spread (RMS-DS) of a channel can be significantly reduced. An approach is proposed to verify the correctness of the channel model parameters derivation. The feasibility of the method will be confirmed using channel-sounding measurements. This dissertation devises a generator to produce channel impulse responses (CIRs) and describes the non-stationary behavior of the channels via employing an ON/OFF process. Different order Markov chains are modeled with the aim of better capturing the non-stationary behavior. The investigation shows that first-order two-state Markov chains are preferable to represent multipath’s frequent ON/OFF behavior, and the second- and third-order Markov models do not make enormous effects. A method for extending a single input single output (SISO)-TDL model to multiple input multiple output (MIMO) under non-wide sense stationary uncorrelated scattering (non-WSSUS) assumption is introduced to develop TDL channel models for the V2I MIMO systems. The analysis evaluates SISO- with MIMO configuration in terms of channel capacity. Different MIMO configurations are explored, and it will be illustrated that the position of antennas plays an important role. Using only four antennas at the transmitter (Tx) and receiver (Rx) that radiate towards different directions will make a qualitative leap in the performance of the system

Noncoherent Capacity of Underspread Fading Channels

We derive bounds on the noncoherent capacity of wide-sense stationary uncorrelated scattering (WSSUS) channels that are selective both in time and frequency, and are underspread, i.e., the product of the channel's delay spread and Doppler spread is small. For input signals that are peak constrained in time and frequency, we obtain upper and lower bounds on capacity that are explicit in the channel's scattering function, are accurate for a large range of bandwidth and allow to coarsely identify the capacity-optimal bandwidth as a function of the peak power and the channel's scattering function. We also obtain a closed-form expression for the first-order Taylor series expansion of capacity in the limit of large bandwidth, and show that our bounds are tight in the wideband regime. For input signals that are peak constrained in time only (and, hence, allowed to be peaky in frequency), we provide upper and lower bounds on the infinite-bandwidth capacity and find cases when the bounds coincide and the infinite-bandwidth capacity is characterized exactly. Our lower bound is closely related to a result by Viterbi (1967). The analysis in this paper is based on a discrete-time discrete-frequency approximation of WSSUS time- and frequency-selective channels. This discretization explicitly takes into account the underspread property, which is satisfied by virtually all wireless communication channels.Comment: Submitted to the IEEE Transactions on Information Theor