Limitations of Experimental Channel Characterisation

CONTENTS

Title

Abstract

Kurzfassung

Acknowledgements

Contents

List of Figures

List of Tables

1. Introduction
1.1 Channel Modelling and Experimental Channel Characterisation
1.2 Drawbacks of the Experimental Channel Characterisation and Motivation
1.3 Overview and Contributions

2. Channel Measurement
2.1 Channel Measurement Techniques
2.2 MIMO Channel Sounding Measurement Technique
2.3 Detailed Configuration of the Applied MIMO Sounder Systems
2.3.1 Tx/Rx Synchronisation in Remote Operation
2.3.2 Back-to-Back Calibration
2.3.3 Receiver Sensitivity
2.3.4 Phase Noise
2.3.5 Arrangement of External Amplifiers in the RF Signal Path
2.4 Antenna Arrays

3. Antenna Array Data Model
3.1 Broadband Model of a Single Antenna Element
3.2 Narrow Band Model of the Measured Radiation Pattern
3.3 The Effective Aperture Distribution Function
3.3.1 The Idea behind the EADF
3.3.2 Construction of the 2D Periodic Radiation Pattern
3.3.3 EADF calculated from the 2D Periodic Radiation Pattern
3.3.4 Analytic Expression for Radiation Patterns and Derivatives of an Antenna Array
3.3.5 Model Error Dependent on the Number of Relevant Samples Used for the EADF
3.4 Performance and Accuracy Comparison Between Different Interpolation Methods .
3.5 Minimum Angular Sampling Grid for Antenna Array Radiation Patterns

4. Antenna Array Calibration
4.1 Obtaining the Antenna Array Radiation Patterns from Measurement
4.1.1 Measurement System Setup
4.1.2 2D Antenna Positioning System
4.1.3 Back-to-Back Calibration of the Measurement System
4.1.4 Calibration of the Dual Polarised Reference Horn Antenna
4.1.5 Calibration of Channel Measurement Antenna Arrays
4.2 Estimation of EADFs from Measured Radiation Patterns
4.2.1 Data Model of the Measured Radiation Patterns Including a Collective Phase Change
4.2.2 EADF Estimation Algorithm
4.2.3 Algorithm performance dependent on SNR and number of elements
4.2.4 Measurement Example
4.2.5 Conclusion on EADF Estimation Algorithm
4.3 Measured Radiation Patterns and EADFs of Different Array Types . .
4.3.1 “Single Polarised” Antenna Array UCAx1x1x16
4.3.2 Polarimetric Antenna Array SPUCPAx2x4x24
4.3.3 Polarimetric Antenna Array PULPAx2x1x8

5. Channel Modelling and Parameter Estimation
5.1 Radio Channel Model
5.1.1 The Specular Path Model (SC)
5.1.2 The Dense Multipath Model (DMC)
5.2 Maximum Likelihood Parameter Estimator RIMAX
5.2.1 Formulation of the Estimation Problem
5.2.2 Global Search for New Paths
5.2.3 Local Search and Discussion of the Algorithmt’s Convergence
5.2.4 Estimation example
5.3 Discussion about the Limitations of the Estimator and its Model . .

6. Performance Evaluation of Practical Antenna Arrays
6.1 CRLB Based Evaluation Framework for Practical Antenna Arrays
6.1.1 Example: Comparison of a Theoretical and Measured CUBA
6.2 Verification of the Antenna Array Performance Evaluation Framework
6.2.1 Single Path Scenario
6.2.2 Coherent two path scenario
6.3 Conclusion Chapter 6

7. Consequences of Modelling Errors in Channel Parameter Estimation
7.1 Analysis Procedure and Definition of Basic Parameters Used in this Chapter
7.2 Antenna Array Related Model Mismatch
7.2.1 Systematic Error Related to the Quality of the Calibration Measurement and to the Narrow Band Model
7.2.1.1 Accuracy of the Narrow Band Model derived from Anechoic Chamber Measurements (Angular Domain)
7.2.1.2 Consequences of distorted Radiation Patterns on the Calculated EADFs
7.2.1.3 Simplified Reflection Model of the Positioning System and Distorted EADFs
7.2.1.4 Systematic Error of the Estimation Result Caused by Distorted EADFs
7.2.1.5 Concluding Remarks on Systematic Error Related to the Quality of the Calibration Measurement and to the Narrow Band Model
7.2.2 Systematic Error Due to Incomplete Data Models
7.2.2.1 Effect of Ignoring Elevation Characteristics
7.2.2.2 Ignoring Polarisation Characteristic
7.2.2.3 Consequences of the “Plane Wave Assumption”
7.2.2.4 Concluding Remarks on Systematic Error Due to Incomplete Data Models
7.3 System Related Consequences
7.3.1 Consequence of Phase Noise on the DoD/DoA Estimation
7.3.1.1 Long Term Phase Drift
7.3.1.2 Phase Noise
7.3.1.3 Estimation of Artefacts as Consequence of Phase Noise
7.3.2 Consequence of an Unsuitable Calibrated External LNA
7.3.3 Concluding Remarks on System Related Consequences
7.4 Conclusions Chapter 7 and Array Error Chart

8. Overall Limitations of Experimental Channel Characterisation
8.1 Definition of Metrics
8.1.1 Antenna Independent Metrics
8.1.2 Antenna Dependent Metrics
8.1.2.1 Relative Error of the MIMO Channel Diversity Metrics
8.2 Error Analysis Based on Ray-tracing
8.2.1 Description of the 3D Ray-tracer
8.2.2 Ray-tracing Based Analysis Procedure
8.2.3 Consequences of an Overall Model Accuracy Lower than the Maximum SNR in the CIR
8.2.3.1 Relevance of the Estimated DMC
8.2.3.2 Angular Power Spectrum of the SC
8.2.3.3 ECM Mismatch of the SC
8.2.3.4 MIMO Capacity Error
8.2.3.5 NPCG Error
8.2.4 Consequences of an Overall Model Accuracy Higher than the Maximum SNR in the CIR
8.2.4.1 Relevance of the Estimated DMC
8.2.4.2 Angular Power Spectrum of the SC
8.2.4.3 ECM Mismatch of the SC
8.2.4.4 MIMO Capacity Error
8.2.4.5 NPCG Error
8.3 Error Analysis Based on Measurements
8.3.1 Description of the Measurement
8.3.2 Measurement Based Analysis Procedure
8.3.3 Consequences of an Overall Model Accuracy Lower or Higher than the SNR in the CIR
8.3.3.1 Relevance of the Estimated DMC
8.3.3.2 MIMO Capacity Error
8.4 Conclusion Chapter 8

9. Conclusions and Future Prospects

Appendix A. Channel Measurement
A.1 Estimation of the Phase Noise Properties of the MIMO Sounders Used . .
A.2 Correction for the Switched Reference Attenuator

Appendix B. Antenna Array Data Model
B.1 Efficient Antenna Array Data Format
B.1.1 Compressed EADF for Single Antenna Element
B.1.2 Efficient Matrix Notation for Joint Description of All Antenna Elements .

Appendix C. A General Characterisation of the Antenna Arrays Used
C.1 Definition of Mean Antenna Array Element Parameters
C.1.1 Maximum Gain and Mean Gain of All Antennas
C.1.2 Mean XPD of All Antennas of the Array
C.1.3 3 dB beam width in azimuth and co-elevation
C.2 Overview of All Arrays

Appendix D. Performance Comparison of Practical Antenna Arrays
D.1 Settings for the Analysis
D.2 Constant SNR
D.3 Constant transmit power and receiver sensitivity
D.3.1 Single path scenario
D.3.2 Coherent two path scenario
D.3.2.1 Settings and Parameter Definition
D.3.2.2 Azimuth Results for Constant Co-Elevation
D.3.2.3 Co-elevation Results for Constant Azimuth

Appendix E. Glossary of Notations, Operators, Matrices, Symbols, and Acronyms
E.1 Notations
E.2 Mathematical operators
E.3 Special matrices
E.3.1 Fourier matrix
E.3.2 Noise matrix or vector
E.3.3 Reflection and Selection matrices
E.4 List of Frequently Used Symbols
E.5 Acronyms

Bibliography

Theses

ABSTRACT

This thesis deals with Experimental Channel Characterisation and its performance limits in real propagation environments. This includes recording of the multidimensional wideband channel matrix by using a Multiple-Input Multiple-Output (MIMO) channel sounder and antenna arrays at both sides of the link. High-resolution parameter estimation is finally applied to characterise the channel in terms of Direction of Departure (DoD), Direction of Arrival (DoA), Time Delay of Arrival (TDoA), and complex polarimetric path weights. The quality of these estimates in “real world” scenarios is degraded by several impairments of the practical antenna arrays and the measurement system used. The resulting estimation quality limits are investigated in detail by simulations and measurements. The entire processing chain is analysed in terms of possible error sources. To this end, measurement system impairments, antenna array calibration errors as well as limitations of the radio channel model applied by the high-resolution parameter estimation pro- cedure are investigated. Moreover, consequences of using these results to deduce and parameterise geometry based channel models are demonstrated.

Propagation measurements give us an antenna dependent description of the radio channel. For the antenna independent characterisation of the radio channel, high-resolution parameter estimation algorithms are applied to determine the DoD and DoA of the specular paths at the transmit and receive side respectively. The gradient based Maximum Likelihood (ML) parameter estimation framework RIMAX, which is reviewed in this thesis uses a data model that describes the radio channel and the measurement system including the antenna arrays. Contrary to other ML pa- rameter estimation algorithms, the model of the radio channel comprises two parts: specular like reflections and distributed diffuse scattering. For the model of the measurement system, an efficient and accurate description of the measured polarimetric antenna array radiation patterns is required. The proposed analytic description of antenna array radiation patterns, which is called Effective Aperture Distribution Function (EADF), is essentially a two dimensional (2D) Fourier transfor- mation of the periodic radiation patterns. As opposed to other models, radiation patterns and its derivatives can be easily calculated analytically from the EADF with low computational burden and high accuracy. A full polarimetric 2D array calibration procedure for the accurate measurement of the radiation patterns of antenna arrays is proposed. This procedure contains the calibration of the entire measurement setup including the MIMO channel sounder, the dual polarised reference horn antenna, and all devices in the Radio Frequency signal path.In this context, a new gradient based ML estimation algorithm is proposed to correct the measured radiation patterns for a phase offset, which occurs during the calibration measurement.

A powerful framework for the performance evaluation of practical antenna arrays in terms of an- gular resolution limits in the presence of additive independent and identically distributed (i.i.d.) Gaussian measurement noise is presented. It is based on the EADFs of measured radiation patterns, which allow us to calculate the Cramér-Rao Lower Bounds of the angular parameters of the spec- ular like reflections. The benefits of using the EADF to describe the radiation patterns including all “imperfections” of the measured antenna array is hereby exploited. The proposed antenna array performance evaluation framework is verified based on measurements in an anechoic chamber.

The derived model of the measurement system including the antenna arrays can only be determined within certain accuracy. A mismatch between the real measurement system and its model used for parameter estimation always exists. From the analysis of several estimation results of a wide range of measurements it was found that such a model mismatch partially may cause significant errors in the estimation results. In this thesis a distinction is made between antenna array related model mismatch and measurement system related model mismatch. Antenna array related model mismatch caused by systematic errors depending on the quality of antenna array calibration and systematic errors due to the usage of incomplete data models (e.g. ignoring polarisation charac- teristic of the antenna elements) are investigated. The consequence of phase noise and unsuitable calibrated measurement systems are presented in the context of model mismatch related to the measurement system. It is shown that the use of an inaccurate model of the measurement system inherently will result in biased and/or artificially spread angular estimates of the parameters of the specular reflections. Methods are proposed to correct/avoid model mismatch and to reduce the consequence of inaccurate/simplified models, whereas it is emphasised that some errors are unavoidable.

The consequences of all unavoidable errors on Experimental Channel Characterisation in complex propagation environments are investigated in the last part of this work. It is clearly shown un- der which circumstances the estimated specular reflections and distributed diffuse scattering are reliable and relevant. The investigations are based on realistic simulations of the radio channel (ray-tracing) and macro-cell propagation measurements. This synthesis of ray-tracing simulations and measurements guarantees the correctness and reliability of the accomplished results.

The contributions of this thesis are of interest for researchers dealing with high-resolution parameter estimation and channel modelling and can be summarised as follows:

- the efficient and accurate radiation pattern modelling of antenna arrays,
- the powerful performance evaluation framework for practical antenna arrays,
- the exposure of consequence of modelling errors on parameter estimation,
- and the demonstration of overall limitations of Experimental Channel Characterisation.

KURZFASSUNG

In dieser Dissertation wird die Experimentelle Kanalcharakterisierung und deren Grenzen in rea- len Ausbreitungsumgebungen untersucht. Dies beinhaltet die Aufzeichnung der mehrdimensionalen breitbandigen Kanalmatrix mit einem Multiple-Input Multiple-Output (MIMO) Channel-Sounder unter Verwendung von Antennenarrays auf der Sende- und Empfangsseite. Um den Funkkanal mit Hilfe der Parameter Sendewinkel (DoD), Empfangswinkel (DoA), Laufzeit (TDoA) und den komplexen polarimetrischen Pfadgewichten zu charakterisieren, werden hochauflösende Parame- terschätzverfahren verwendet. Die Genauigkeit dieser Parameterschätzergebnisse in ”realen“Mess- umgebungen wird durch eine Vielzahl von Fehlerquellen begrenzt. Diese Genauigkeitsgrenzen der Parameterschätzung werden anhand zahlreicher Simulationen und Messungen analysiert. Fehler- quellen im gesamten Verarbeitungsablauf werden untersucht. Dazu gehören die Einschränkungen durch das Messsystem, systematische Fehler bei der Kalibrierung praktischer Antennenarrays sowie Unzulänglichkeiten des Funkkanalmodells des hochauflösenden Parameterschätzers. Darüber hinaus werden die Auswirkungen der Parametrierung bzw. Ableitung geometrisch basierter Kanalmodelle auf der Grundlage von Parameterschätzergebnissen mit begrenzter Genauigkeit aufgezeigt.

Mit Messungen in typischen Ausbreitungsumgebungen kann der Funkkanal immer nur in Abhän- gigkeit der Messantennen beschrieben werden. Als Ziel wird jedoch eine antennenunabhängige Be- schreibung des Funkkanals angestrebt. Daher ist es notwendig, die Sende- und Empfangswinkel der spekularen Ausbreitungspfade mittels hochauflösender Parameterschätzverfahren zu bestimmen. Der gradientenbasierte Maximum Likelihood (ML) Parameterschätzer RIMAX, auf dem diese Ar- beit aufbaut, verwendet ein Datenmodell, das den Funkkanal und das Messsystem inklusive der Antennenarrays beschreibt. Im Gegensatz zu anderen ML-Parameterschätzern wird ein Funkanalm- odell angewendet, welches spekulare Reflektionen und verteilte diffuse Streuungen berücksichtigt. Für die Modellierung des Messsystems wird ein effizientes und exaktes Modell der gemessenen polarimetrischen Richtcharakteristika benötigt. Das hier vorgeschlagene Modell, die so genann- te Effective Aperture Distribution Function (EADF), beschreibt die Antennenrichtcharakteristika analytisch und basiert im Wesentlichen auf der zweidimensionalen (2D) Fouriertransformation der periodischen Richtcharakteristika. Im Gegensatz zu anderen Verfahren können auf der Grundlage der EADF die Antennencharakteristika und ihre Ableitungen mit geringem Aufwand und hoher Genauigkeit berechnet werden. Für eine exakte Messung der Richtcharakteristika eines Antennen- arrays wird ein vollpolarimetrisches 2D-Kalibrierverfahren vorgeschlagen. Mit diesem Verfahren wird der komplette Messaufbau kalibriert. Dazu gehören der MIMO Channel-Sounder, die dual polarisierte Referenzhornantenne und alle Hochfrequenzkomponenten außer dem zu untersuchen- den Antennenarray. Im Zusammenhang mit der Arraykalibrierung wird ein gradientenbasierter ML-Parameterschätzer entwickelt, mit dem eine bei der Kalibriermessung auftretende Phasenab- weichung korrigiert wird.

Des Weiteren wird ein leistungsstarkes Verfahren zur Bewertung praktischer Antennenarrays auf der Basis der EADFs gemessener Richtcharakteristika vorgeschlagen. Die Cramér-Rao-Schranken der Winkelparameter in Abhängigkeit des Signal-Rausch-Verhältnisses werden mit dem EADF-Modell analytisch berechnet. Der Vorteil des EADF-Modells besteht darin, dass die Richtcharakteristika eines realen Antennenarrays unter Einbeziehung aller störenden Einflussgrößen beschrieben wer- den. Das vorgeschlagene Bewertungsverfahren wird anhand von Messungen im Antennenmessraum verifiziert.

Das Modell des Messsystems inklusive der Antennenarrays, welches für die Parameterschätzung verwendet wird, kann das reale System nur begrenzt beschreiben. Es wurden Schätzergebnisse von zahlreichen Messungen analysiert. Hierbei musste festgestellt werden, dass Fehler bei der Model- lierung zu teilweise unglaubwürdigen Schätzergebnissen führen. Genauer untersucht werden Feh- ler in Bezug auf die Antennenarrays und das Messsystem. Erstere werden hervorgerufen durch systematische Fehler bei der Arraykalibrierung und durch die Verwendung unvollständiger Daten- modelle (z.B. Nichtberücksichtigung der polarimetrischen Eigenschaften der Antennen). Letztere entstehen einerseits durch Phasenrauschen und andererseits durch ungeeignete Kalibrierung. Es wird nachgewiesen, dass die Verwendung ungenauer Modelle zur Schätzung von Artefakten führt. Diese Schätzfehler äußern sich in Abweichungen und/oder in einer künstlichen Aufspreizung der Winkelschätzungen der spekularen Anteile. Es werden geeignete Methoden vorgeschlagen, um die Auswirkungen von Modellfehlern weitestgehend zu vermeiden bzw. zu korrigieren. Betont werden muss jedoch, dass einige Fehler unvermeidbar sind.

Die Auswirkungen aller unvermeidbaren Fehler auf die Experimentelle Kanalcharakterisierung in komplexen Ausbreitungsumgebungen werden im letzten Teil dieser Arbeit dargestellt. Es wird ge- zeigt, unter welchen Bedingungen die geschätzten spekularen Anteile sowie die geschätzten verteil- ten diffusen Streuanteile glaubwürdig und physikalisch relevant sind. Die Untersuchungen basieren auf ”realistischen“ Simulationen des Funkkanals(Ray-Tracing)und auf Messungen.Diese Synthese garantiert Glaubwürdigkeit und Aussagefähigkeit der in der Arbeit gewonnenen Ergebnisse.

Die Resultate dieser Dissertation sind speziell für Wissenschaftler auf dem Gebiet der Parame- terschätzung sowie Funkkanalmodellierung von Interesse und können wie folgt zusammengefasst werden:

- die Entwicklung eines Modells zur exakten und effizienten Beschreibung der Richtcharakteristika von Antennenarrays,
- ein Verfahren zur Bewertung praktischer Antennenarrays,
- die Sensibilisierung für Modellfehler und deren Auswirkungen auf die Parameterschätzergeb- nisse und
- die Bestimmung der Grenzen Experimenteller Kanalcharakterisierung unter Berücksichtigung aller unvermeidbarer Fehlerquellen.

ACKNOWLEDGEMENTS

The discussion with various people has made this thesis possible or complete. First, I want to thank Prof. Reiner Thomä for his continuous support and encouragement, both as a supervisor and as a colleague. Further, I thank all the colleagues in the department Elektronische Messtechnik at Technische Universität Ilmenau. I like to mention especially Gerd Sommerkorn, Milan Narandžić, Vadim Algeier, Christian Schneider, Karl Borkowski, Gitta Weber and Dr. Wim Kotterman who helped me in practical and scientific matters. I am very grateful for the fruitful cooperation with Dr. Andreas Richter during the time we developed the RIMAX parameter estimation framework.

I feel a special gratitude for Prof. Jun-ichi Takada, for his support during my time as visiting researcher at the Tokyo Institute of Technology and for the discussion with respect to my research.

The measurement campaign in Section 8.3 is supported by the National Institute of Information and Communications Technology (NICT) of Japan. Furthermore, I would like to thanks the members of the Takada Laboratory for their support during these measurements, especially Kriangsak Sivasondhivat, Mir Ghoraishi, Gilbert Siy Ching and Navarat Lertsirisopon.

I am very grateful for the help of Gilbert Siy Ching of the Takada Laboratory who was proofreading this work several times.

Furthermore, I thank Prof. Matthias Hein for reviewing my thesis.

The cooperation with MEDAV GmbH, Uttenreuth in the field of channel sounding was of crucial importance for this work. Special thanks go to the colleagues Dirk Brückner, Steffen Warzügel, Johannes Schramm, and Walter Wirnitzer for their continuous support.

The applied ray-tracer and its description in Section 8.2 was provided from Thomas Fügen and Jürgen Maurer of the Institut für Höchstfrequenztechnik und Elektronik of the University of Karl- sruhe.

A longer list of fellow researchers, not directly mentioned, of Bristol University, Lund University, Wien University of Technology and Helsinki University of Technology deserve my gratitude for the successful collaborations and interesting discussions.

Furthermore, I would like to thank Giovanni Del Galdo and Jörg Lotze for the research cooperation when comparing the radiation pattern descriptors EADF and VSH. I also would like to thank both for many useful tips in terms of applying LATEX to write this thesis.

My biggest gratitude goes indeed to my parents who always showed and allowed me to see the world from many different perspectives. My grandmother deserves special thanks for her continuous support, power and years of serving the best food. Furthermore, I have to thank my girlfriend Kotomi who encouraged me indirectly to finish my thesis.

Finally, I would like to thank all my friends who are a very important part of my life.

LIST OF FIGURES

1.1 Double directional Direction of Departure (DoD)/Direction of Arrival (DoA) struc- ture of a multipath radio channel

2.1 Multi-carrier spread spectrum signal in the time and frequency

2.2 MIMO sounder block diagram

2.3 MIMO sounder switching time frame

2.4 Key Features of the sounders used

2.5 Block diagram of the MIMO sounder

2.6 Back-to-back calibration setup

2.7 Characterisation of all RF parts dependent on the AGC level

2.8 Characterisation of the switched reference attenuator

2.9 Frequency bin SNR versus Delay bin SNR

2.10 Maximum achievable signal power and mean noise power ATM vs. HyEff

2.11 Random walk phase and phase noise correlation

2.12 Back-to-back calibration setup including external PA and LNA

2.13 Exemplary LNA characteristic for different input power levels

2.14 1D circular measurement antenna arrays

2.15 Reference and application antenna arrays/antennas

2.16 Planar measurement antenna arrays

2.17 2D circular measurement antenna arrays

2.18 Block diagram of an antenna array

3.1 Spherical coordinate system

3.2 Geometrical description of the m -th antenna element

3.3 Simulation layout of a dual polarised patch

3.4 Periodic radiation pattern

3.5 Fourier transform of the over-sampled radiation pattern

3.6 Mean interpolation error of a radiation pattern

3.7 Radiation pattern interpolation accuracy and time

3.8 Derivation of the minimum sampling grid UCAx1x1x16

3.9 Derivation of the minimum sampling grid PUCPAx2x1x24

3.10 Sampling grids for PUCPA2x1x24, UCA1x1x16 and SPUCPA2x4x24

4.1 Block diagram of the antenna array calibration measurement setup

4.2 Positioning system

4.3 Dual polarised reference horn antenna

4.4 Gains of the dual polarised reference horn antenna

4.5 Cross polarisation discrimination reference horn antenna

4.6 Frequency dependent gain of the dual polarised reference horn antenna

4.7 Simulated phase drift over azimuthal scan and 1D EADF

4.8 Flow chart of the estimation algorithm

4.9 Radiation pattern reconstruction error and error of estimated phases

4.10 Standard deviation of the estimated phase

4.11 Reconstruction error, corrected and uncorrected EADFs of a practical antenna array

4.12 Radiation patterns, EADFs, and XPD UCAx1x1x16

4.13 Cross polarisation discrimination SPUCPAx2x4x24

4.14 Cross polarisation discrimination PULPAx2x1x8

4.15 Radiation pattern and EADF SPUCPAx2x4x24

4.16 Radiation pattern and EADF PULPAx2x1x8

5.1 Multidimensional specular components data model

5.2 Dense multipath model in the delay time domain

5.3 RIMAX block diagram

5.4 Correlation function for global search applying the minimum sampling grid N95

5.5 Convergence behaviour of SAGE and RIMAX

5.6 Convergence behaviour of SAGE and RIMAX shown in a cost function

5.7 Convergence rate SAGE and RIMAX

5.8 CIR measurement example and parameter estimates

6.1 Pattern of inverse FIM of a single path and a coherent two path scenario . .

6.2 EADFs of of a theoretical and measured CUBA

6.3 Radiation patterns of a theoretical and measured CUBA

6.4 CRLB comparison of of a theoretical and measured CUBA for SNR of 25 dB

6.5 Estimated azimuth variance vs. calculated CRLB

6.6 Ratio between estimated variance and calculated CRLB

6.7 Coherent two path scenario measurement setup

6.8 Azimuth CRLB vs. estimated azimuth variance in a two path scenario

6.9 Distribution of the ratios r q in azimuth for a two path scenario

7.1 Parasitic reflections in the anechoic chamber lateral view

7.2 Parasitic reflections in the anechoic chamber top view

7.3 Measured IR and error IR anechoic chamber UCAx1x1x16

7.4 Illustration of the parameter model accuracy

7.5 Model accuracy UCAx1x1x6 and PULPAx2x1x8

7.6 Maximum measurable co-elevation angle

7.7 Positioning system verification measurement setups

7.8 Radiation patterns and 1D EADFs for positioning system verification measurements

7.9 Illustration of the simplified scattering and diffraction model of the positioning system

7.10 Undistorted, distorted and measured EADFs PUCPAx2x1x24

7.11 Estimated artefacts using the distorted complete or windowed EADFs

7.12 SRR in case of using the distorted complete or windowed EADFs

7.13 DoA ambiguity in case of using an ideal ULA

7.14 Phase over 16 element UCA

7.15 Estimation results ignoring elevation characteristic PULPAx2x1x8

7.16 Estimated artefacts ignoring elevation characteristic PULPAx2x1x8

7.17 Estimation results ignoring elevation characteristic UCAx1x1x16

7.18 Error of the estimated azimuth and its standard deviation ignoring elevation char- acteristic UCAx1x1x

7.19 Estimation results ignoring polarisation characteristic of the UCAx1x1x16

7.20 Estimated artefacts ignoring polarisation characteristic of the UCAx1x1x16

7.21 Wave front curvature for different source distances

7.22 Antenna position dependent model error for different wave front curvatures

7.23 Estimation results for different wave front curvatures simulated PUCPA and ULA

7.24 Estimated artefacts for different wave front curvatures

7.25 Estimated artefacts when considering wave front curvature during estimation

7.26 Consequences of long term phase drift with respect to the number of antennas . .

7.27 Consequences of long term phase drift for a set of practical antenna arrays

7.28 Consequences of uncorrelated phase noise for a simulated ULA, UCA, PUCPA . . .

7.29 Consequences of correlated phase noise in comparison to uncorrelated phase noise .

7.30 Consequences of uncorrelated phase noise for practical antenna arrays dependent on the phase noise standard deviation

7.31 Consequences of uncorrelated phase noise for a set of practical antenna arrays and the HyEff system as function of azimuth

7.32 Consequences of uncorrelated phase noise for a set of practical antenna arrays and the HyEff system as function of co-elevation

7.33 Estimated artefacts as consequence of uncorrelated and correlated phase noise, ATM system

7.34 Estimated artefacts as consequence of uncorrelated phase noise, HyEff system

7.35 Consequences of an unsuitable calibrated LNA and system

7.36 UCAx1x1x16 error chart

8.1 Illustration of the SNRIR of the SC and DMC

8.2 CDF of relative error in terms of NPCG for an example measurement route

8.3 3D ray-tracer environment and exemplary impulse response

8.4 Procedure for the ray-tracing based error analysis

8.5 Alignment of the application antenna array PPDA related to the Rx moving direction

8.6 Simulation route and SNR MT12 to MT14

8.7 Estimated SNRIR of SC and DMC for the measurement route MT12 to MT14

8.8 “True” and estimated Rx azimuth power spectra route MT12 to MT14

8.9 ECM mismatch of four different estimation setups route MT12 to MT

8.10 Error in terms of capacity for the route MT12 to MT14

8.11 Error in terms of NPCG for the route MT12 to MT14

8.12 Simulation route and SNR MT59 to MT34

8.13 Estimated SNRIR of SC and DMC for the measurement route MT59 to MT34

8.14 “True” and estimated Rx azimuth power spectra route MT59 to MT34

8.15 ECM mismatch of four different estimation setups route MT59 to MT34

8.16 Error in terms of capacity for the route MT59 to MT34

8.17 Error in terms of NPCG for the route MT59 to MT34

8.18 Measurement scenario

8.19 Portion of SC power

8.20 Block diagram of the analysis procedure in case of measurements

8.21 Antenna subset selection from the measurement antenna array

8.22 Comparison of the SNRIR of the SC and DMC in case of measurements

8.23 Mean capacity error and its standard deviation SC+DMC+Noise

8.24 Mean capacity error and its standard deviation SC+Noise

A.1 Phase noise estimation for the ATM and HyEff system

A.2 Magnitude and phase offset dependent on the Tx power attenuation level for the corrected and uncorrected data

B.1 Illustration of the calculation of GK1 to GK4

B.2 Matrices Γ13 and Γ24 of antenna array data format

D.1 Comparison of azimuth standard deviation and relative variance of the path weights for a single path and constant SNR for different arrays

D.2 Array comparison in case of single path for constant co-elevation and constant trans- mit power

D.3 Array comparison in case of single path for constant azimuth and constant transmit power

D.4 Performance comparison SPUCPAx2x4x24 and UCAx1x1x16 in terms of az- imuth resolution

D.5 Performance comparison between SPUCPAx2x4x24 and UCAx1x1x16 in terms of azimuth resolution for different path lengths

D.6 Array comparison in terms of resolution capability in azimuth

D.7 Relation between maximum separation error and relative variances

D.8 Array comparison in terms of resolution capability in co-elevation

D.9 Relation between[Abbildung in dieser Leseprobe nicht enthalten]and[Abbildung in dieser Leseprobe nicht enthalten]in the best case in co-elevation

LIST OF TABLES

2.1 Receiver sensitivity of the HyEff and ATM system

7.1 Mean model accuracy ς120MHz in dB for different polarisation combinations and an- tenna arrays

8.1 Observation model vs. Estimation model

C.1 Array Characterisation

1. INTRODUCTION

The design of future mobile radio networks (i.e., beyond third generation (3G)) requires research towards new air interfaces which are characterised by highest bandwidth efficiency and unprece- dented flexibility. It is commonly understood that radio systems equipped with multiple antennas at both the Mobile Station (MS) and the Base Station (BS) have a huge potential to increase the bit-rates of wireless links. This is possible thanks to a simultaneous transmission of multiple data streams³⁵. This multi-antenna technique is called Multiple-Input Multiple-Output (MIMO) and can optimally exploit the spatial diversity of the multiple propagation paths existing in a rich scattering environment. Conceptually, the multipath propagation of the radio channel gives rise to different spatio-temporal signatures for the different transmit data streams, which permits a receiver equipped with multiple antennas to separate those data streams that are otherwise not orthogonal in any of the conventional communication signal dimensions, i.e., in time, frequency, or code. Keeping this in mind, it is not really surprising that the performance of a MIMO system will strongly depend on the radio channel conditions. A key question for a system design and implemen- tation is therefore, whether it is possible to find practically feasible schemes which are sufficiently robust for this task. Another related issue is determining what specific features are required for a practical MIMO system to work reliably under a wealth of various propagation conditions.

1.1 State of the Art Channel Modelling and Experimental Channel Characterisation

The thorough investigation of the multidimensional wave propagation mechanisms is a prerequisite for understanding the spatial and temporal structure of the channel transfer function, and thus, for optimum design and realistic performance evaluation of multiple antenna systems. There are many ways to simulate the input-output behaviour of the radio channel. Basically, channel modelling activities can be divided into deterministic and stochastic approaches.

Examples of deterministic modelling are Finite-Difference Time-Domain (FDTD) and ray-tracing. Ray-tracing is a physically motivated approach and is based on electromagnetic wave propagation analysis (e.g. Uniform Geometrical Theory of Diffraction (UTD)) and uses ray-optical models [36-38]. These models can be very exact and can also describe the time variant channel in certain propagation environments [39, 40]. In case of ray-tracing or ray-launching, a detailed database (i.e., a precise description of the environment) and high computation times are required. To balance the complexity of ray-tracing, stochastic modelling approaches for diffuse scattering are proposed in [41-45].

There are also completely statistical models trying to reproduce the input/output behaviour in a statistical sense by formal assumptions of correlation coefficients and distributions resulting at the transmit antenna and receive antenna ports disregarding the geometrical distribution of the reflectors. A disadvantage of these non-geometric models is that they are inherently specific for a certain antenna characteristic.

For antenna independent modelling (which allows antenna de-embedding and embedding), geome- try based channel models are a must⁴⁶. Hereby, the position and the distribution of the scattering areas are generated according to statistical assumptions. In the European forum for cooperative scientific research COST 259⁴⁷, COST 273⁴⁸, and in standardisation bodies (e.g. 3GPP⁴⁹, WINNER⁵⁰ ) Geometry-Based Stochastic Channel Models (GBSCM) were extensively discussed. These models are parametrised based on measurements in typical mobile radio environments. Since the geometry of the propagation environment is taken into account, the influence of the character- istic of the antenna system, such as inter element coupling and polarisation dependent radiation patterns can be included in GBSCM based system simulations. Hereby, the directions of the trans- mitted and received waves need to be considered ([51, 52], Double Directional Channel Model).

Since the complexity of wave reflection, scattering, diffraction, etc. in real propagation environ- ments can never be completely reproduced by electromagnetic simulation and due to the strong simplifications of the statistical approaches, all models have to be verified and/or parametrised by propagation measurements. So called real-time channel sounders [53, 54] with huge mem- ory capacity and flexibility in using various antenna arrays are employed for such measurements. Directional channel models can be deduced directly from measurements in real propagation en- vironments estimating the geometric parameters of the paths from the recorded data. Given a ray-optical path model, the parameters normally used to model a propagation path are Direction of Arrival (DoA) at the receiver array, Direction of Departure (DoD) at the transmitter array, Time Delay of Arrival (TDoA), Doppler shift, and the complex polarimetric path weight matrix. Fig- ure 1.1 highlights the double directional structure of the multipath channel. Specifically, a double directional measurement, which includes joint DoD/DoA estimation, allows the separation of the directional and polarisation dependent influence of the antennas from the measurements which is a prerequisite of antenna independent channel characterisation. This approach, which has the poten- tial to characterise the radio channel in an antenna independent fashion based on measurements, will be called Experimental Channel Characterisation.

A channel modelling approach that is directly based on the results of Experimental Channel Char- acterisation is proposed in¹. This so called Measurement Based Parametric Channel Modelling (MBPCM) is essentially a two-step procedure with an Experimental Channel Characterisation step and a follow-up synthesis step. With the estimated path parameters from Experimental Channel Characterisation an antenna independent description of the radio channel is given. The synthesis step gives us the flexibility to generate realistic MIMO channel transfer functions employing arbi- trary application antenna arrays based on the estimated path parameters. However, the estimated path parameters are only valid in a limited area around the original antenna position (during mea- surement). To cope with this problem the MBPCM approach is extended in⁵⁵ and additionally to the path parameters (described before), the reflection points of each path are estimated from the results of Experimental Channel Characterisation. With the knowledge of the reflection points it is possible to extend the valid area around the original antenna position for the syntheses step of the MBPCM approach.

Note that ray-tracing, GBSCM, and MBPCM are mainly verified or parametrised via Experimental Channel Characterisation. Consequently, the accuracy of these modelling approaches are limited to the accuracy of the Experimental Channel Characterisation itself.

illustration not visible in this excerpt

Fig. 1.1: Double directional DoD/DoA structure of a multipath radio channel.

The radio channel responses can, in general, be observed only within a limited aperture volume which is defined by the array size, frequency bandwidth and temporal observation window. This strictly limits the achievable resolution and accuracy with respect to the angular, delay, and Doppler domain, respectively, when classical non-parametric estimation algorithms are applied. Therefore, high-resolution parameter estimation algorithms have to be envisaged to enhance the resolution by fitting an appropriate data model of the radio channel and measurement system to the measured data. Mainly two different methods are discussed in literature⁵⁶: subspace methods like Estima- tion of Signal Parameters via Rotational Invariance Techniques (ESPRIT) [57, 58], Root-Multiple Signal Classification (MUSIC)⁵⁹ and Maximum Likelihood (ML) methods like Space Alternat- ing Generalized Expectation Maximisation (SAGE) [60, 61]. In these cases the radio channel is modelled by a number of specular propagation paths (Specular Components (SC)) that are de- scribed by the parameters DoA, DoD, TDoA, Doppler shift, and the complex polarimetric path weights, which are independent from the antennas used during the measurement. The resolution of these parameters is limited by the measurement Signal to Noise Ratio (SNR), antenna and device imperfections, calibration quality, and the limited validity of the model of the measurement sys- tem. The angular resolution performance mainly depends on the antenna array architecture and its manufacturing quality, which includes low electromagnetic coupling, high electrical and mechanical stability. In this context, also the definition of the data model is crucial. It has to be accurate enough to represent the wave propagation and the influence of the measurement system. On the other hand, the radio channel model must not be excessively detailed since the amount of informa- tion gathered by the MIMO sounder is always limited and may not be enough to estimate all model parameters precisely. A proper choice of the model structure and order can dramatically reduce the algorithmic complexity and enhance the accuracy and resolution as well as the reliability of the results. It was observed that with the specular paths only 20% to 80% of the received channel sounding signal power can be described. To solve this, the ML algorithm RIMAX² using a hybrid radio channel model was proposed. The word hybrid is used to indicate that the radio channel is described by a superposition of SC that result from specular-like reflection and Dense Multipath Components (DMC). Up to now (see⁶² ) it is assumed that only SC which could not be estimated (unresolved SC) and distributed diffuse scattering are contributing to the DMC. The DMC can be described by a few parameters that essentially parameterise an exponential decaying function in the delay domain. Other causes for the DMC such as model errors related to the measurement system and practical antenna arrays were not considered up to the present.

1.2 Drawbacks of the Experimental Channel Characterisation and Motivation

The accuracy and limits of high-resolution parameter estimation techniques are commonly evaluated theoretically by computing the Cramér-Rao Lower Bound (CRLB), which defines the fundamental limitations on the achievable parameter variance. In most publications (e.g. in [60, 63, 64]), high- resolution parameter estimation techniques are verified based on the CRLBs, simulated antenna arrays, and synthetic radio channels. It is assumed that white Gaussian measurement noise is the only error source. Furthermore, it is assumed that the model of the antenna arrays and the radio channel data model matches reality exactly. Based on this verification, most of the parameter estimation techniques that are well known from theory are applied in practice in a straightfor- ward manner without further considerations (e.g. in [57, 60, 65-71]). Partially unsustainable assumptions are intentionally or unintentionally made with respect to the measurement systems and parameter estimation models applied. For the measurement systems, e.g., the impact of phase noise or unproper calibrated systems are often ignored. For the data models, a common approach is to use incomplete data models (e.g. ignoring full polarisation characteristic and/or elevational characteristic of antenna elements) or to ignore the finite accuracy of the antenna array calibration measurements. Nevertheless, the results of parameter estimation with unsustainable assumptions are used for further processing such as clustering algorithms, channel capacity calculations and parametrisation of GBSCMs. Contrary to the above mentioned publications only a few publi- cations are found that at least try to avoid unsustainable assumptions while estimating the radio channel parameters [3, 4, 72, 73] or try to evaluate practical antenna arrays based on measurements [74-76]. From the above discussion and from a significant experience with measurement analysis [1-3, 5-20] we observed that the reliability, the accuracy, and the limitations of Experimental Chan- nel Characterisation using high-resolution parameter estimation techniques are not clearly defined.

This work deals in detail with the limitations of Experimental Channel Characterisation. Methods for accurate and efficient modelling and performance evaluation of practical antenna arrays are proposed. The entire processing chain is analysed in terms of possible error sources. To this end, measurement system impairments, antenna array calibration errors as well as limitations of the radio channel model applied by the high-resolution parameter estimation procedures are investigated. The resulting estimation quality limits are analysed in detail by simulations and measurements. Finally, the impact of parametrising the geometry based channel modelling approach MBPCM with the results of Experimental Channel Characterisation is shown.

The major contribution of the work is a clear answer to five crucial questions:

1. What are the resolution limits of practical antenna arrays?
2. How can we obtain reliable estimates of the radio channel parameters from propagation measurements?
3. What are the fundamental limitations of Experimental Channel Characterisation?
4. Do the DMC result only from unresolved SC and distributed diffuse scattering, strictly speak- ing are they related to the real propagation conditions only?
5. What is the consequence when parametrising geometry based channel modelling approaches in particular MBPCM with the results of Experimental Channel Characterisation?

The following section illustrates the outline of the work.

1.3 Overview and Contributions

Chapter 2 reviews the most commonly used measurement techniques to characterise a radio chan- nel. Furthermore, it briefly introduces the functionality of the MIMO channel sounding systems applied in the measurements discussed in this thesis. The major sources of error when using such measurement systems are emphasised. Measurement setups are proposed for accurate calibration of the applied measurement systems. System parameters such as phase noise, phase drift, and receiver sensitivity are obtained from measurements. These system parameters are especially relevant in terms of reliability and accuracy of the measurement data and define the limits of the Experimental Channel Characterisation. The purpose and some basic design considerations of high-resolution antenna arrays are discussed. The practical antenna arrays used in this work are presented.

Chapter 3 deals in detail with the efficient and the accurate modelling of measured polarimetric antenna array radiation patterns, which is a prerequisite for an antenna independent description of the radio channel and performance evaluation of practical antenna arrays. A novel and ana- lytic description of measured antenna array radiation patterns by means of the Effective Aperture Distribution Function (EADF) is proposed. As opposed to other methods, the derivatives of the radiation patterns dependent on the DoD/DoA can be easily calculated analytically based on the EADFs. It is shown that the proposed EADF outperforms the Spline interpolation method as well as the vector spherical harmonics (Vector Spherical Harmonics (VSH),²¹ ) in terms of calculation time by achieving the same interpolation accuracy. The EADF’s low computational complexity, the analytic description of the radiation patterns and its derivatives, and the performance advantage is already exploited in several applications such as the IST-WINNER Channel Model²², IlmProp (geometry-based Multi-User MIMO Channel Modelling tool) [55, 77]) and the RIMAX parameter estimation framework⁵³.

An angular sampling grid with a minimum number of samples for the efficient calculation of the radiation patterns of practical antenna arrays is proposed since it is often required for Experimen- tal Channel Characterisation. This grid is based on the idea of the EADF and fulfils the Nyquist theorem in the angular domain.

Parts of the material dealt in this chapter have been published in [13, 21, 23-28].

Chapter 4 proposes a full polarimetric two dimensional (2D) array calibration procedure for the accurate measurement of the radiation patterns of practical antenna arrays. The procedure involves the calibration of the entire measurement setup by means of the MIMO channel sounder, the dual polarised reference horn antenna, and all devices in the Radio Frequency (RF) signal path that do not correspond to the antenna array under test.

Due to the employment of a MIMO channel sounder, we have to cope with a varying phase offset during the 2D antenna array calibration measurement time of several hours (with a Network Analyser (NWA) it would be several days!). These phase offsets prohibit the direct derivation of the EADF model from measurements. A novel gradient based ML estimation algorithm is proposed to correct the measured radiation patterns for the collective phase offset, which consequently allows the accurate derivation of the EADF model.

Applying both the array calibration procedure and the correction for the phase offset the radiation patterns and their EADFs for three different array types are discussed. With this discussion the necessity of accurate full-polarimetric 2D array calibration for Experimental Channel Characterisation and channel modelling is emphasised.

The authors’s contribution related to some of the topics of this chapter has been published in²⁹.

Chapter 5 reviews the radio channel model applied for the gradient based ML parameter esti- mation framework RIMAX. The theory of this framework was developed in cooperation with An- dreas Richter⁶². In this work the practical implementation of the RIMAX for arbitrary practical antenna arrays and measurement environments was carried out. For the RIMAX implementation, a deep knowledge in estimation theory and handling of measurement data was required.

The radio channel model of the RIMAX comprises two components, the specular (SC) and the dense multipath components (DMC). The SC result mainly from specular-like reflections and the DMC are assumed as unresolved SC and distributed diffuse scattering. As opposed to other parameter estimation algorithms this hybrid model preserves the balance between the maximum information we can gather from measurements and the number of estimated parameters. Further advantages of the RIMAX e.g. the convergence also in the presence of closely spaced propagation paths and the internal reliability check of the estimated paths during the iterative estimation process are highlighted.

However, the drawback of most parameter estimation frameworks is that the impact of error sources other than additive Gaussian measurement noise are neglected. The fundamental limitations of the data model used for parameter estimation with respect to the practical measurement system and practical antenna arrays is briefly introduced.

Own contributions related to the topics of this chapter have been published in [2, 8, 9, 13, 30, 31].

Chapter 6 deals in detail with a powerful framework for the performance evaluation of prac- tical antenna arrays with respect to their angular resolution limits. The framework is based on the calculation of the CRLB of the parameters of the SC. The method can provide information about the DoD/DoA resolution limits of multiple propagation paths and its parameter variances. As opposed to other publications the framework is applicable to any practical antenna array. The advantage of the EADF model using the measured radiation patterns including all imperfections of the antenna array is hereby exploited. Time consuming performance evaluation measurements other than the antenna array calibration become unnecessary with the proposed framework.

For the verification of the proposed antenna array performance evaluation framework, the simple single path and coherent two paths scenario (considering worst and best case phase constellations between the two paths) are measured with a practical antenna array in the anechoic chamber. The results of the measurement and parameter estimation are compared with the theoretical calculated CRLB of the applied practical antenna array. With this verification the capability of the proposed performance evaluation framework is clearly shown.

Parts of the material dealt in this chapter have been published in [23, 24, 26-28].

Chapter 7 explores the major causes of mismatch between the model of the SC applied by the parameter estimator and the “real” radio channel. The investigations were initiated by the observation of partially implausible estimation results that were found analysing a wide range of measurements.

A distinction is made between model mismatch related to the antenna arrays:

- bias related to quality of antenna array calibration,
- bias related to incomplete data models

and model mismatch related to the measurement system:

- consequences of phase noise,
- consequences of a unsuitable calibrated measurement system.

The proprietary parameter estimator RIMAX is used to demonstrate the consequences of the dif- ferent error sources in case of the simple single path scenario. Notice that the results can be generalised, as any ML parameter estimator using the same data models would render similar re- sults.

It is shown that the use of an inaccurate/simplified data model inherently will result in biased and/or artificially spread angular estimates. It is not inconceivable that the popular approach of clustering multi-paths components for channel modelling is spurred by the artefacts resulting from data model choices as described in this chapter.

For some antenna array types and error sources, estimation bias is even unavoidable, irrespective of the used data model. But for some error sources solutions are highlighted to correct/avoid model mismatch and to reduce the consequences of inaccurate/simplified data models.

Parts of the author’s contribution given in this chapter have been published in [18, 32, 33].

Chapter 8 deals with the overall consequences of practical measurement systems, practical an- tenna arrays, and unavoidable model errors on Experimental Channel Characterisation in complex propagation environments. It is shown that the estimated SC are most reliable (in well defined limits) if the DMC estimation is incorporated in the estimation framework. As opposed to the estimated SC, the estimated DMC are partially unreliable or can not be considered as feature of the radio channel. Especially for measurements with a maximum SNR of the impulse response higher than the overall accuracy of the model of the measurement system and antenna arrays, the estimated DMC describe mainly model error. Thus, the DMC can not be assumed as unresolved SC or distributed diffuse scattering only. In this case they are not related to the propagation conditions of the measured environment. Nevertheless it is shown that the estimated DMC are reasonable if the maximum SNR is lower or equal to the overall model accuracy. In this case the estimated DMC are related to the “real” propagation.

The results are of crucial importance when parametrising GBSCMs with the estimated SC and DMC of Experimental Channel Characterisation. Based on the MBPCM approach and the calculation of the error of MIMO channel diversity metrics it is shown that:

- in case of measurement SNRs higher than the overall model accuracy, the error increases drastically if additionally to the SC, the DMC are assumed as feature of the measured channel, consequently the DMC have to be discarded when parameterising the MBPCM approach,
- in case of measurement SNRs lower or equal to the overall model accuracy, the error is acceptable if both the SC and the DMC are assumed as feature of the measured channel.

Some topics dealt in this chapter have been published in⁴.

Chapter 9 summarises the key issues covered in this work, emphasising their impact on the international scientific community.

2. CHANNEL MEASUREMENT

Several techniques exist to characterise the mobile radio channel based on measurements. In Section 2.1 an overview of existing measurement techniques are given, discussing their advantages and disadvantages. The preferred measurement method of this thesis is based on the MIMO channel sounding technique, which is discussed in Section 2.2. The measurement systems that were used for channel measurements presented in this work are introduced in Section 2.3. General and also system specific properties of these kind of measurement devices are discussed. As the results of any measurement analysis procedure will be affected by the analysed system properties, such as measurement noise, phase noise, etc., this discussion is of major importance in this thesis. The purpose and the basic construction of the high resolution antenna arrays used in this thesis are presented in Section 2.4.

2.1 Channel Measurement Techniques

From a historical perspective, the first sounding experiments have been carried out using single tone Continuous Wave (CW) signals⁷⁸. This was appropriate as long as only the narrow-band channel behaviour was of interest. Single tone CW sounding, however, gives us no information to resolve path time delays. To this end, we need a frequency domain bandwidth, which is roughly the inverse of the desired delay resolution. Sequential sounding at a number of different frequencies is the easiest approach to achieve even very high delay resolution, since standard vector network analyser techniques can be applied. The drawback is the resulting huge measurement time, which precludes mobile measurements. The only solution to this problem is to keep the environment fixed during one series of frequency sampling measurements. This actually has its equivalent in sequential sampling of the antenna array geometry and may be considered as an equivalent to the synthetic antenna aperture approach in the frequency domain. Sustained measurement along some longer trajectory is clearly prohibitive. Network analyser application also requires a direct cable connection between Transmitter (Tx) and Receiver (Rx) sites.

Short duration repetitive pulses together with envelope detectors have been used in early broadband real-time sounding experiments⁷⁸. The main drawback of this method is the high peak-to-mean power ratio at the transmitter and only power delay profiles can be measured. To achieve the maximum SNR at the receiver, excitation signals with a minimum crest factor are required. The crest factor is given by the ratio of the peak value of the signal to its root mean square (r.m.s.) amplitude. Minimum crest factor signals are distinguished by a constant magnitude envelope in the time domain. At the same time, they must have a constant spectrum, which leads to a short autocorrelation function. This pulse compression approach is well known from spread spectrum technology and makes these signals very useful for real-time identification of time delay systems since all frequencies are instantaneously excited and a considerable SNR processing gain is achieved in the time domain by correlation processing.

Pulse compression requires noise-like structured signals. Periodic pseudo-random excitation signals are of special importance since they can be processed in integer periods. The time-period must be at least as long as the maximum path excess time-delay τmax to avoid TDoA ambiguities. With a maximum delay-Doppler spreading factor S = τmax B max of a typical mobile radio channel well below 0.01, the period of the received time-variant channel response signal is still almost the same as of the excitation signal. This presumes that the minimum signal period time is chosen. Then, the channel output can be transformed to the frequency domain by Discrete Fourier Transformation (DFT)/Fast Fourier Transformation (FFT) processing without any significant leakage variance.

Probably, the most well known examples of these excitation signals are periodic Pseudo Random Bit Sequence (PRBS)⁷⁹. PRBS can be very easily generated by a shift register since only digital circuits are required. This makes it possible to generate broadband excitation signals, even suitable for ultra-wideband sounding⁸⁰. Another advantage of PRBS is that they can be repeated in the receiver with a slightly slower clock rate. This is applied in the classical swept time-delay cross- correlation sounder implementation as originally proposed by Cox⁷⁸. This “sliding correlation” sounder requires only slow AD converters. The disadvantage of this principle, working sequentially in delay, is again the long measurement time which prohibits real-time operation.

The shape of the power spectrum of PRBS follows a [sinc(.)]² function. For system identification purposes it can only be used up to a frequency of about 0.4 f c, f c being the clock rate⁸¹. Even though the spectrum decays rather slowly, a very high sampling rate or a suitable anti-aliasing filter at the receiver are required to avoid aliasing. Moreover, the system under test is excited in a frequency band which is not used. This effectively wastes transmit power. Most experimental transmit spectrum permissions given by regulation authorities will require strict band-limited spec- tra. Then, the signal must be filtered at the transmitter to remain within a finite bandwidth. Any filtering and phase slope modification, however, will increase the crest factor of the PRBS, which is supposed to be unity in the ideal case.

A much more flexible excitation signal concept is known as the periodic multi-sine signal. This approach is well known from frequency domain system identification in measurement engineering⁸¹. In communication engineering this signal may be called a Multi-Carrier Spread Spectrum Signal (MCSSS). The MCSSS is defined by its complex Fourier coefficients X(µ Δ f):

illustration not visible in this excerpt

with[Abbildung in dieser Leseprobe nicht enthalten]. Once designed in the frequency domain, the corresponding time domain waveform x(nt 0) is stored in an arbitrary waveform generator memory and periodically transmitted at the Tx. Therefore, it includes all the advantages which are discussed above for periodic signals. The difference in comparison to PRBS is that phases and magnitudes of X(µ Δ f) can be arbitrarily chosen in order to optimize the system performance. As an example, in Fig. 2.1 a MCSSS excitation signal with uniform power spectrum is shown. The phases of the Fourier coefficients are chosen to minimize the crest factor of the signal waveform. Although a quadratic phase slope typically results in a crest factor below 2, numerical optimization can even further reduce the crest factor to about 1.4. Another advantage of this signal design is that analogue hardware phase distortion (e.g. from the filters) and even non-linear distortion (from the power amplifier) can be mitigated. This means that a predefined ideal transmit signal is iteratively predistorted throughout a calibration procedure where the real output signal is measured and optimised.

Regarding the overall spectral shape, the main advantage of MCSSS is its “brickwall-type” shape, which allows us to concentrate the signal energy precisely into the band of interest. This is also possible for multiple bands. One exemplary application is FDD sounding which means that the sounder simultaneously excites both the up-link and the down-link band. Note that the desired full flexibility of the excitation signal requires quadrature up-conversion at the transmitter. At the

illustration not visible in this excerpt

Fig. 2.1: Broadband multi-carrier spread spectrum signal (MCSSS) in the time and frequency domain (top row) and estimated CIR and received signal spectrum (bottom row)

receiver side the signal is filtered, down converted, and demodulated via a quadrature demodulator. An efficient architecture is based on low IF analogue down conversion, IF sampling and final digital down conversion. For example for a bandwidth of 240 MHz, 160 MHz IF frequency and 640 MHz ADC sampling rate is adequate. For real-time processing, Nyquist sampling at the receiver in most cases is a must. One integer period of the received time-variant channel response y(t, nt 0) is sampled and transformed into the frequency domain by FFT processing. The final quadrature down conversion is accomplished by cyclic FFT-shifting of the result, which finally gives the baseband representation Y(t, µ Δ f) of the received signal. In case of multipath transmission, frequency selective fading as shown for example in Fig. 2.1(bottom row, right) shapes the power spectrum of the received signal. An estimate of the time-variant channel frequency response is calculated from input-output cross correlation as:

illustration not visible in this excerpt

The uniform shape of the excitation signal spectrum and its low crest factor at the transmitter maximises the SNR. With integer period data acquisition there is no additional estimation vari- ance resulting from leakage noise⁸¹. Therefore, the required data acquisition time is minimal and the estimation variance is as small as possible. With Nyquist sampling at the receiver, the highest possible measurement repetition rate for a channel with a maximum excess time-delay τmax can be achieved, namely 1/τmax. The lower limit is given by the Doppler bandwidth B max. It results from the Nyquist sampling criterion of the fast fading channel response. However, since the delay-Doppler spreading factor S = τmax · B max of a typical mobile radio channel is well below 0.01, there are large gaps allowed between successive measured channel response functions without sacrificing the Nyquist criterion. Normally, there is no need to measure faster since additional CIRs (which may be required for link level simulation) can always be calculated via bandlimited interpolation. Nevertheless, faster measurement speed may be desirable if we aim at further noise reduction by synchronous averaging of a temporal sequence y(t, nt 0). Only when the averaging window approaches or exceeds 1/ B max would this act as a Doppler low-pass filter and potentially suppress fast fading.

Fig. 2.1 shows the impulse response which would result from an inverse Fourier transform of H(t, µ Δ f). Calculating the impulse response in this way requires a tapering window function in the frequency domain, which effectively wastes measured data and, hence, reduces the SNR and limits the resolution. A better choice is to use H(t, µ Δ f) as an observation vector in the frequency domain for high-resolution TDoA parameter estimation described in Section 5. H(t, µ Δ f) repre- sents the sum-of-exponentials model describing the delay spectrum. A second frequency domain dimension can be constructed from time-limited sections of the observed sequence H(t, µ Δ f) with the sum-of-exponentials in t describing the Doppler spectrum. The 2D Fourier transform approx- imates the joint delay-Doppler frequency response. A Single-Input Single-Output (SISO) sounder just relies on this principle.

2.2 MIMO Channel Sounding Measurement Technique

A MIMO channel sounder measures the channel response matrix between all M Tx antennas at the transmit side and all M Rx antennas at the receiver side. This could be carried out by applying a parallel multiple channel transmitter and receiver. True parallel systems are not only extremely expensive, they lack also of versatility (when considering changing the number of antenna channels) and are susceptible to phase drift errors. Moreover, parallel operation of the transmitter channels would cause additional problems, as the M Tx transmitted signals have to be separated at the receiver. A much more suitable sounder architecture is based on switched antenna access. A switched antenna sounder contains only one physical transmitter and receiver channel. Only the antennas and the switching channels are parallel. This reduces the sensitivity to channel imbalance. As an example for such a sounder architecture the simplified block diagram of the sounders used in this thesis is given in Fig. 2.2.

Fig. 2.3 shows the switching time frame⁷⁸ of the sequential MIMO sounders used, where antenna arrays at both sides of the link are present. Any rectangular block in the figure represents one period of the transmit/receive signal. Synchronous switching at the Rx and Tx is required in order to clearly assign the received signal periods to any input-output combination of the channel matrix. Timing and switching frame synchronisation is established during an initial synchronisation process prior to measurement data recording and must be maintained over the complete measurement time even in the case of remote operation of Tx and Rx. This is accomplished by rubidium or caesium reference oscillators at both Rx and Tx. The total snapshot time length is now given by t s = 2τmax M Tx M Rx, where M Tx and M Rx are the number of antennas at the Tx and the Rx site, respectively. The factor two comes from the blank period inserted at the receiver after every period acting as a guard interval to avoid switching transients. Similar to Orthogonal Frequency Division Multiplex (OFDM), this Complex Impulse Response (CIR) estimation principle relies on a periodic signal model for excitation and reception. Therefore, the guard interval has to cope with the channel and the device response. For some signal processing operations based upon the recorded data, it may be a disadvantage that the antenna channels are not sampled at strictly the same time instant. If the maximum Doppler bandwidth for real-time sounding is less than 1/ t s, the antenna channels can be individually interpolated resulting in MIMO channel responses with aligned sampling time for all channels.

illustration not visible in this excerpt

Fig. 2.2: MIMO sounder block diagram

2.3 Detailed Configuration of the Applied MIMO Sounder Systems

In this subsection, the two MIMO sounders used are described. The sounders were developed in cooperation with the company MEDAV GmbH⁵³ under the BMBF (Federal Ministry of Education and Research) projects ATMmobile (Broadband Mobile Multimedia Communication using ATM) and HyEff (High Spectral Efficiency Mobile Networks). Therefore, in the following discussion the

illustration not visible in this excerpt

Fig. 2.3: MIMO sounder switching time frame

sounders will be called ATM and HyEff, respectively. Both systems are based on the MIMO channel sounding technique described in the previous section. However, they differ in terms of the practical realisation. The resulting key features of the two sounders are compared in Fig. 2.4. In Fig. 2.5, a

illustration not visible in this excerpt

Fig. 2.4: Key Features of the sounders used

block diagram of the MIMO sounders used is shown. The RF parts are indicated with black colour and the RF signal flow is indicated by black arrows. The RF signal path includes the up converter at Tx, the Tx Power Amplifier (PA), the internal Low Noise Amplifier (LNA) at the Rx, and the Radio Frequency Tuner (RFT) at the Rx. The RFT is a complicated system of multi-level down converters, controllable attenuators, and amplifiers. The attenuators and amplifiers at the receiver are controlled by the Automatic Gain Control (AGC) to ensure maximum signal level throughout the receiver chain from the antenna to the analogue digital converter (ADC) input. At the same time it avoids overloading. The AGC covers a range of 0 dB to 51 dB in steps of 3 dB. The AGC setting is implemented on the basis of instantaneous peak value estimation. To avoid uncontrolled transients, the AGC timing control is synchronised to the MIMO switching time frame (Fig. 2.3). If low received signal power is expected, the internal LNA can be used (RF switch setting ○). Note that in case of the ATM system, the internal LNA is always included in the RF signal path. In case of the HyEff system the internal LNA can be excluded by selecting the input RF In (RF switch setting ○). The input RF In can handle a larger input power than the input RF In LNA. This means that additional external LNAs may be used, when connected to the input RF In.

The golden parts in Fig. 2.5 are related to the 10 MHz clock signal distribution, which is provided from the rubidium references included in the Tx and Rx. The transmission of the periodic multisine signal (arbitrary wave form generator), the MUX switching control at Tx and Rx, the AGC at the receiver, and the ADC are synchronised to the 10 MHz clock signals. Consequently, the synchronisation of the Tx and Rx clock signals in remote operation mode are an important issue and will be discussed in Section 2.3.1.

Section 2.3.2 is related to back-to-back calibration. Back-to-back calibration means, that the overall system frequency response is measured and stored for equalisation purposes. The Tx and Rx are directly connected via a reference attenuator. The calibration includes the absolute device power gain as well. This is achieved throughout the back-to-back calibration when operating the transmitter with its nominal output power to the reference attenuator. For a calibration of the system for a certain AGC level, the input power at the receiver is adjusted by the reference attenuator. Therefore, the reference attenuator is a switched reference attenuator. The attenuation can be varied in the range of 0 dB to 120 dB. In case of the HyEff system, the attenuation settings are software controllable, whereas it is only manually adjustable in case of the ATM system. Based on the given system designs, two back-to-back calibration procedures will be considered: a back-to- back calibration for only one AGC level (ATM) and an AGC dependent back-to-back calibration (HyEff). AGC dependent back-to-back calibration indicates the measurement and storage of the overall system frequency responses for all possible AGC levels.

Further considerations concerning the hardware operation of the sounder systems refer to receiver sensitivity (Section 2.3.3) and phase noise (Section 2.3.4).

If external amplifiers are used, their arrangement in the RF signal path is crucial for the back- to-back calibration and measurement. Therefore, different arrangements are discussed in Section 2.3.5.

Note that all topics discussed here are directly related to the achievable quality of measurement based channel characterisation using parameter estimation schemes and are therefore of crucial importance in most chapters of this thesis.

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Fig. 2.5: Block diagram of the transmitter and receiver of the MIMO sounders used. Control units are in blue, RF parts in black, and golden parts are related to the 10 MHz clock signal distribution.

2.3.1 Tx/Rx Synchronisation in Remote Operation

Remote operation means that there is no synchronisation link applied between Tx and Rx. In this case, distinct rubidium reference sources at both Tx and Rx are required and the Local Oscillator (LO) signals have to be generated at both sides. This makes a sounder fundamentally different from a standard network analyser. The synchronisation of the Tx and Rx clock signals is achieved by manual or automatic (1 PPS synchronisation signal) adjustment of the two separate rubidium frequency references. This synchronisation normally takes place before the back-to-back system calibration is carried out. The synchronisation has to be maintained throughout the whole measurement cycle. For DoD/DoA estimation, full coherent operation is necessary during the snapshot period t s. If we aim at Doppler estimation or if a sequence of snapshots is to be averaged for SNR enhancement, the period of coherent operation must be extended to multiples of t s. This sets the limits for phase noise parts (see also Section 2.3.4) having a coherence time below this time interval. However, a long term phase drift can normally be accepted as long as the reference offset is smaller than the specified Doppler bandwidth. A small reference frequency offset would be measured as a respective Doppler shift. Note that for specific measurements, such as antenna array calibration measurements, a coherent operation period of several hours is necessary, which may require a direct Tx/Rx synchronisation by cable (Section 4.1).

2.3.2 Back-to-Back Calibration

As already mentioned in the previous section, two calibration procedures will be considered: 1. the back-to-back calibration for only one AGC level and 2. the AGC dependent back-to-back calibration. In Fig. 2.6 the back-to-back calibration setup for both procedures is shown. Note that for the HyEff system both procedures can be applied, whereas the ATM system is limited to the first one. For the first back-to-back calibration procedure, all frequency responses of a measurement

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Fig. 2.6: Back-to-back calibration setup

campaign will be equalised with the same system frequency response, because from the calibration only a single frequency response for a fixed AGC level is available. The magnitude is corrected with the nominal AGC level which is set during measurement, but the system frequency characteristic in terms of phase and magnitude changes between the different AGC levels is ignored.

If the second procedure is applied, then each frequency response measured is equalised with the corresponding system frequency response for AGC level set.

Let us discuss the consequence of each calibration procedure by analysing the system frequency responses for the different AGC levels. For each AGC level, a unique chain of amplifiers and attenuators in the RFT are linked by the AGC. Therefore, the frequency response depends on the AGC level. In Fig. 2.7(a) the magnitude of the frequency responses normalised to the corresponding nominal AGC levels are shown. The differences in magnitude for different AGC levels are almost negligible. On the contrary, the combination of the attenuators for different AGC levels results in a different electrical length of the receiver chain, the phase offset between the different AGC levels is significant (see Fig. 2.7(b)). For DoD/DoA estimation, the phase differences between the different

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Fig. 2.7: Joint characterisation of all RF parts dependent on the AGC level set (HyEff system)

antenna channels are used. Consequently, the first calibration procedure calibrating only one AGC level is acceptable only when the AGC level is fixed while measuring all antenna channels in one snapshot. Thus, the phase offset is the same for all antenna channels and the DoD/DoA can be estimated correctly. The disadvantage of the fixed AGC setting becomes obvious especially when the received power strongly varies depending on the measured antenna channels. As the AGC level is adjusted to the peak power over all channels, the channels with a lower received power will be measured with a significantly worse SNR. On the other hand, if the AGC level is set for each channel and the stored complex frequency responses of the AGC dependent back-to-back calibration are used for equalisation, then all channels are measured with the same SNR. Consequently, the second calibration procedure is preferable. Nevertheless, if the back-to-back calibration setup described in

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Fig. 2.8: Characterisation of the switched reference attenuator

Fig. 2.6 is used to obtain the system frequency responses for each AGC level, then it has to be taken into account that also the switched reference attenuator has different electrical lengths dependent on the attenuation set. Therefore, the measured system frequency responses have to be corrected accordingly. Appendix A.2 shows the characteristics of the switched reference attenuator and the consequence of ignoring them in the AGC dependent back-to-back calibration.

2.3.3 Receiver Sensitivity

The sensitivity S in a receiver is normally defined as the minimum input signal power required to produce a specified output signal having a certain signal-to-noise ratio (SNRmin):

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where F is the noise figure of the receiver and P N the measurement noise power at the input of the receiver (related to the thermal noise of the source resistor). The noise power is defined as:

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where [Abbildung in dieser Leseprobe nicht enthalten] J/K is the Boltzmann’s constant, T is the resistor’s absolute temperature in Kelvin and B is the bandwidth in Hz. In case of the MIMO channel sounder different definitions of the desired SNR can be applied. One could ask for a certain SNRFR,min at one frequency bin or alternatively, for the SNRIR,min in the delay domain. The latter can be defined as the ratio between the peak power and mean noise power in the Impulse Response (IR). Note that the SNRIR,min also includes the correlation gain, which is related to the number of frequency bins M f used during the measurement. Using the back-to-back calibration setup shown in Fig. 2.6, the receiver sensitivity of

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Fig. 2.9: Mean signal and noise power at one frequency bin (a) in comparison to the maximum achievable signal power and noise power at one delay bin (b) for different impulse response lengths τmax (Hyeff system using internal LNA)

the Hyeff system (including and excluding the internal LNA) can be determined. This means that the switched reference attenuator is used to vary the total input power at the receiver. For both MIMO channel sounders used, the total transmitted power in the fixed frequency band of 120 MHz is constant, even when the number of used frequency bins M f in this band is changed to adjust the maximum length of the impulse response τmax. Consequently, the mean signal power at one frequency bin for a small M f is higher than in case of a larger M f. However, with a decreasing M f (decreasing τmax) in the fixed band of 120 MHz the mean noise power at one frequency bin increases as the noise bandwidth which is related to the distance between two frequency bins increases. Thus, the mean SNRFR defined at one frequency bin for a certain total input power is independent of the impulse response length (number of frequency bins M f) used. This leads us to a sensitivity definition for one frequency bin independent of the total number of frequency bins used:

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In case of the delay domain we define the minimum detectable signal after impulse compression by means of applying the inverse Fourier transformation to the measured data in the frequency domain. As the Tx and Rx are directly connected, in the calibration setup used, all signal power will be concentrated in one delay bin, where the noise power at one delay bin is equal to the noise power at one frequency bin. With an increasing length τmax of the periodic multi-sine signal (increasing M f) the SNRIR of the strongest delay bin (peak) increases (see Fig. 2.9(b)). The achievable SNR gain of 10 · log10(M f) dB is commonly called correlation gain in other publications. Thus, the receiver

sensitivity seen in the delay domain is dependent on the number of frequency bins used:

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In Table 2.1, the system specific measured values of 10·log10(k B · B · T · F System) for room temperature and a bandwidth of B = 120 MHz are listed for the HyEff and the ATM system. The difference of the measured values between the HyEff system with and without the internal LNA are related to the resulting noise figure F of the amplifier chain used. From this table and from Fig. 2.10 it can be seen that the ATM system has the same performance as the HyEff system using internal LNA. It

Tab. 2.1: System dependent measured values of 10 · log10(k B · B · T · F System) [dBm] for room temperature and bandwidth of B = 120 MHz, the variation being related to the resulting noise figures F, when using the different inputs at the receiver.

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should be noted that the SNRIR remains constant for a larger total input power (see Fig. 2.9). This effect is related to the AGC, which adds attenuation to avoid overloading of the receiver amplifiers and keep the input signal at the analogue digital converter (ADC) in its dynamic range. However, the noise figure F of the receiver is consequently increased by the additional attenuation of the AGC. Figure 2.9(b) is divided by a dashed line into two parts to specify the range where the AGC attenuation level is higher than 0 dB.

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Fig. 2.10: Maximum achievable signal power and mean noise power at one delay bin Hyeff system

(a) and ATM system (b)

2.3.4 Phase Noise

In principle, the phase noise (pn) depends on the characteristics of the Phase Locked Loop (PLL) used at the transmit and receive side. The output signals of the separate local oscillators at the transmitter and receiver, denoted by O Tx and O Rx respectively, for the desired local frequency f LO are given by:

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and

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where ϕTx(t) and ϕRx(t) are the phase noises at the Tx and Rx local oscillators, respectively. For the modelling of the phase-distorted channel matrix it is assumed that the phase noise affects all frequency sub-channels of the multi-carrier spread spectrum test signal equally. This means that the coherence time of the phase noise is assumed to be larger than the cycle duration of the periodic multi-sine test signal. Herewith, the phase noise affected and time-variant channel frequency response can be written as:

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The phase noise is commonly modelled as an uncorrelated stationary Gaussian process with zero mean and σ² variance ([82-84]). Additionally, long term phase drift affects (random walk phase ⁸⁵ ) and correlated phase noise dependent on the characteristics of the PLLs have been reported ⁸⁶. Therefore, the phase noise is assumed here as a superposition of a long term phase drift ϕpnL(t) and phase noise ϕpnS(t) modelled as a correlated Gaussian process with zero mean and σ² pnS variance, which leads us to:

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We assume that for the period t s = 2 · τmax · M Rx · M Tx of one snapshot the long term phase drift ϕpnL(t) can be approximated by a linear function. Thus, it can be written as:

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where [Abbildung in dieser Leseprobe nicht enthalten] is the phase gradient. For the long term phase drift basically two cases can be considered:

- if the system is phase-locked (e.g., transmitter and receiver are connected and use a common reference (denoted by 1 Ref.)) the resulting gradient ΔϕpnL(t s, t) is expected to be small (basically depends on the temperature stability of the rubidium reference),
- if the system is in remote operation, which means that the system is only frequency-locked and 2 references are used (2 Ref.).

In the second case, the gradient[Abbildung in dieser Leseprobe nicht enthalten]can be larger, which is mainly dependent on the quality of synchronisation of the 2 rubidium references. Here, the temperature stability of the references used plays a major role, as a constant temperature of the surrounding area can not always be guaranteed, especially in case of outdoor measurements. Figure 2.11(a) shows a CDF, estimated from measurement results, of the magnitude of the gradient ΔϕpnL(t s = 3.2ms) using one or two separate rubidium references for an indoor and outdoor measurement. Note that these results only refer to the phase gradient for a specific test measurement, whereas it is not necessarily guaranteed that in an outdoor measurement the phase gradient is always smaller than [Abbildung in dieser Leseprobe nicht enthalten]This basically depends on how much time is spent for a proper synchronisation and how constant the temperature of the references can be kept. Nevertheless, the results illustrate in which range the phase gradient can be expected.

The phase noise standard deviation σpnS and the phase noise covariance matrix Σ of the correlated Gaussian phase noise process are obtained from measurements. The analysis procedure is discussed in appendix A.1. Finally, the phase noise standard deviation σpnS is 5.69◦ for the ATM system and 2.94◦ for HyEff system. The estimated auto correlation functions of the phase noise process of both MIMO sounders are shown in Fig. 2.11(b).

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Fig. 2.11: CDF of the random walk phase gradient ΔϕpnL(t s = 3.2ms) using 1 or 2 rubidium references in different environments (a) and auto correlation function (ACF) of the Gaussian phase noise process for the HyEff and ATM system (b)

2.3.5 Arrangement of External Amplifiers in the RF Signal Path

Regarding the arrangement of antenna switches and amplifiers in the RF signal path, a trade- off always exists between sensitivity and phase stability. Separate LNAs after each Rx antenna and/or separate PAs before each Tx antenna are mostly inadequate because of the increase in phase drift between antenna channels. Also, the usage of separate filters in each antenna channel is not appropriate, as the phase drift between the antenna channels increases due to the differences between the filters. Differences are related to the manufacturing and also to the ageing process stage of each filter.

To avoid such differences it is better to use a single PA and LNA before the Tx antenna switch and after the Rx antenna switch respectively. Consequently, all antenna channels are collectively biased with the same phase drift. This phase offset that is equal for all channels will not affect the quality of the DoD/DoA estimation. The corresponding back-to-back calibration setup is shown in Fig. 2.12.

The external PA or LNA is required to compensate for the attenuation of the RF cables between the transmitter and the Tx array (Tx cable 1) or between the Rx array and the receiver (Rx cable 1). This is especially the case if RF cables with a larger attenuation need to be used. To minimise the signal attenuation which can not be compensated, the cable between the output of the external PA and the Tx antenna switch (Tx cable 2) and the cable between the output of the Rx antenna switch and the input of the LNA (Rx cable 2) should be as short as possible (see Fig. 2.12). Furthermore, the amplification of the external LNA should be in the range of the attenuation of the Rx cable 1. If a LNA with a large amplification or a LNA with a better noise figure than the internal LNA is used, the input RF In that is less sensitive against non-linear distortions should be selected. For the single PA at the Tx, the corresponding Tx antenna switch has to handle the full output power which may exceed 2...10 W for broadband urban measurements. Using the proposed arrangement of the PA and LNA in the RF signal path, it is necessary to include them in the back-to-back system frequency response calibration, as these kind of amplifiers (which may also include filters) are normally frequency dependent. Furthermore, the frequency responses of LNAs or PAs depend on the input power level. As an example, the magnitude and phase of the normalised frequency responses of an LNA used in this thesis are shown in Fig. 2.13, the colour indicating the different input power levels in dBm. It is clear that the frequency responses differ with respect to the different input power levels. Even though the magnitude differences seem to be small (0.5 ... 3dB), the differences of the phase are not negligible. Therefore, the appropriate arrangement of the LNA or PA in the RF signal path during back-to-back calibration is an important issue. As the output power of the transmitter does not change, the PA is always used at the same input power. Consequently, the PA needs to be calibrated only for one power input level and the frequency response remains stable (except phase drift) during the whole measurement time. For the LNA a constant power input level is not given. Therefore, the frequency response of the LNA has to be determined dependent on the input power level (LNA calibration). Using the back-to-back calibration setup shown in Fig. 2.12 the LNA and the different AGC levels can be jointly calibrated. To avoid that the receiver amplifiers are used in their non-linear region, it is important that the input power at the receiver is within the specified dynamic range. Note that in case of the ATM system the LNA can not be calibrated dependent on the power input level. Therefore, it has to be decided before the measurement at which power input level the system should be calibrated. This assumes that the power which will be received in a measurement is already known in advance. Since it is an often made mistake that the LNA is calibrated for a inappropriate power input level, the consequences of an unsuitable calibrated external LNA on the parameter estimation results will be discussed in Section 7.3.2 of Chapter 7.

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Fig. 2.12: Back-to-back calibration setup including external PA and LNA

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Fig. 2.13: Magnitude (a) and phase (b) of the normalised frequency response of an exemplary LNA for different input power levels (denoted with different colour).

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