Indoor building materials structural analysis through non-destructive near-field penetration loss measurements

Indoor building materials structural analysis through non-destructive near-field penetration loss measurements Degree Thesis submitted to the Faculty of the Escola T`ecnica d’Enginyeria de Telecomunicaci´o de Barcelona Universitat Polit`ecnica de Catalunya by Mart´ı Xargay i Ferrer In partial fulfillment of the requirements for the degree in TELECOMMUNICATIONS TECHNOLOGIES AND SERVICES ENGINEERING Advisor: Prof. Dr. Katsuyuki Haneda and Prof. Dr. Juan Manuel Rius Barcelona, 19/06/2023 Abstract Non-destructive material measurements for structural analysis of building elements are a valuable tool in situations where invasive techniques are unfeasible. In this work, a free-space penetration loss measurement technique is applied to the study of wall structure, relying on educated guesses about the internal composition of the material under test (MUT). Using a setup with antennas and a vector network analyzer (VNA), the sample’s transmission coefficients are captured in the 1-18 GHz frequency range and compared to the loss model presented in the ITU-R (International Telecommunication Union-Radiocommunication Sector) Recommendation. Tests are run in a laboratory environment on three wood samples, and in the field on two internal partitions of a standard office building in Finland. The method’s limitations and operation are assessed in terms of root mean squared error (RMSE), and the results allow for detection of material anomalies and discontinuities and a general understanding of the MUT’s electrical behavior. 3 Resum Les mesures no destructives per a l’an`alisi estructural d’elements de construcci´o suposen una eina valuosa en situacions on les t`ecniques invasives s´on inviables. En aquest treball s’aplica una t`ecnica de mesurament de p`erdues de penetraci´o en espai lliure a l’estudi estructural de parets, basant-se en suposicions fonamentades sobre la composici´o interna del material sota estudi (MUT). Utilitzant una configuraci´o amb antenes i un analitzador de xarxes vectorial (VNA), es capturen els coeficients de transmissi´o de la mostra en la banda de 1 a 18 GHz i es comparen amb el model de p`erdues presentat en les Recomanacions de la UIT-R (Uni´o Internacional de Telecomunicacions-Sector de Radiocomunications). Els tests es realitzen en un entorn de laboratori amb tres mostres de fusta, i en el camp amb dos tabics interns d’un edifici d’oficines est`andard a Finl`andia. Les limitacions i el funcionament del m`etode s’avaluen en termes d’error quadr`atic mitj`a de l’arrel (RMSE); els resultats permeten detectar anomalies i discontinu¨ıtats del material, i entendre el comportament el`ectric del MUT en general. 4 Resumen Las medidas no destructivas para el an´alisis estructural de elementos de construcci´on representan una herramienta valiosa en situaciones donde las t´ecnicas invasivas son inviables. En este trabajo se aplica una t´ecnica de medici´on de p´erdidas de penetraci´on en espacio libre al estudio estructural de paredes, bas´andose en suposiciones fundamentadas sobre la composici´on interna del material bajo estudio (MUT). Utilizando una configuraci´on con antenas y un analizador de redes vectorial (VNA), se capturan los coeficientes de transmisi´on de la muestra en la banda de 1 a 18 GHz y se comparan con el modelo de p´erdidas presentado en las Recomendaciones de la UIT-R (Uni´on Internacional de Telecomunicaciones-Sector de Radiocomunicaciones). Las pruebas se realizan en un entorno de laboratorio con tres muestras de madera, y en campo con dos tabiques internos de un edificio de oficinas est´andar en Finlandia. Las limitaciones y el funcionamiento del m´etodo se eval´uan en t´erminos de error cuadr´atico medio de la ra´ız (RMSE); los resultados permiten detectar anomal´ıas y discontinuidades del material, y comprender el comportamiento el´ectrico del MUT en general. 5 Dedico aquest treball als meus avis, Maria i Ramon. 6 Acknowledgements I would like to thank my advisors at the School of Electrical Engineering at Aalto University, Pasi Koivum¨aki and Prof. Dr. Katsuyuki Haneda, who have actively supervised and supported my work and helped with all the technical details, directing me through the right path towards successful completion of the project. I am also very grateful to my co-advisor at UPC-ETSETB, Prof. Dr. Juan Manuel Rius, whose reaffirming support has been crucial to the proper finalization of the work. I would like to show my appreciation to ELEC Aalto University, for hosting and allowing the author to use the necessary equipment to carry out my final thesis in Espoo. To UPC-ETSETB for their support during the stay and allowing the Bachelor’s Thesis defence in Barcelona. Specially, I am very grateful to Sasha Spurn´a and Araceli Ortiz and all other involved people whose work has materialized this exchange mobility experience. Amb aquest treball tanco els meus estudis de grau, posant punt i final a una meravellosa experi`encia. Una etapa plena de vida i d’aprenentatge, que no hauria estat la mateixa sense la millor companyia i orientaci´o. Per aix`o vull donar les gr`acies a tots aquells mentors que, directament o indirecta, m’han guiat en algun punt d’aquest viatge: Prof. Dr. Alba Pag`es, Dr. Jordi Andilla, Prof. Dr. David Artigas, Dr. Pablo Loza-Alvarez, David Sariol, Dr. Benjamin Izquierdo, Prof. Dr. Adriano Camps, i tants m´es. Finalment, i potser el m´es important, vull agrair a la meva fam´ılia i amics el seu suport durant els millors i pitjors moments, que m’ha ajudat a seguir endavant, animant-me i inspirant-me a donar el millor de mi mateix. 7 Revision history and approval record Revision Date Purpose 0 16/05/2023 Document creation 1 02/06/2023 Document revision 2 11/06/2023 Document revision 3 13/06/2023 Document revision 4 17/06/2023 Document revision DOCUMENT DISTRIBUTION LIST Name e-mail Mart´ı Xargay Ferrer [email protected] Pasi Koivum¨aki pasi.k[email protected] Prof. Dr. Katsuyuki Haneda k[email protected] Prof. Dr. Juan Manuel Rius Casals [email protected] Written by: Reviewed and approved by: Date 17/06/2023 Date 17/06/2023 Name Mart´ı Xargay Ferrer Name Prof. Dr. Katsuyuki Haneda, Prof. Dr. Juan Manuel Rius and Pasi Koivum¨aki Position Project Author Position Project Supervisor 8 Contents Abstract 3 Resum 4 Resumen 5 Acknowledgements 6 Contents 9 List of Figures 11 List of Tables 12 List of Abbreviations 13 1 Introduction 14 1.1 Motivation ......................................... 14 1.2 Statementofpurpose.................................... 14 1.3 Requirements and specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.4 Methodsandprocedures.................................. 15 1.5 Workplan.......................................... 15 1.5.1 Work Packages, Tasks and Milestones . . . . . . . . . . . . . . . . . . . . . . 15 1.5.2 Timeplan...................................... 17 1.6 Deviations from the original work plan . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2 State of the art 18 2.1 Material electrical properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2 Models for material simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.1 Models for frequency dependence . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.2 Models for calculating transmission coefficients . . . . . . . . . . . . . . . . . 19 2.2.2.1 Simplified method for a single-layer slab . . . . . . . . . . . . . . . . 19 2.2.2.2 Iterative method for a multi-layer slab . . . . . . . . . . . . . . . . . 19 2.3 Free-space measurement techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.4 Free-space path loss method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.4.1 Setup ........................................ 21 2.4.2 Environment .................................... 21 2.4.3 Materials ...................................... 22 2.4.4 Frequencies ..................................... 22 2.4.5 Fieldproximity................................... 22 2.5 Walls electromagnetic behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3 Methodology and project development 24 3.1 Laboratory measurement campaign . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.1.1 Setup ........................................ 24 3.1.1.1 Samples.................................. 24 3.1.1.2 Equipment ................................ 25 3.1.2 Procedure...................................... 26 3.1.3 Post-processing................................... 27 3.1.3.1 Time-gating ............................... 27 3.1.3.2 Calibration................................ 28 3.1.3.3 RMSEcalculation ............................ 28 9 WP2 Title: Test measurements Major constituent: laboratory measurements Planned start: 03/03/2023 Planned end: 26/04/2023 Start event: 03/03/2023 End event: 26/04/2023 Perform comprehensive measurements of penetration loss on samples with known dielectric properties and post-process and analyze the results using possible measurement setups that will be used on site: antennas covering different frequency ranges and at different distances from the sample. - Internal task T1: Get to know the Microwave lab and its equipment. Configure all devices and prepare the setup. - Internal task T2: Perform the measurements on different samples. - Internal task T3: Post-process results and assess its proper functioning. WP3 Title: Measurement campaign Major constituent: on-site measurements Planned start: 07/03/2023 Planned end: 07/04/2023 Start event: 07/03/2023 End event: 23/03/2023 Carry out an extensive measurement campaign of the interior walls of the location of interest, in former Nokia Espoo Campus. Different walls in different positions shall be tested in frequency ranges of interest. - Internal task T1: Contact individuals responsible for the building. Check for availability of the space. Agree on experiment day. - Internal task T2: Go to Karaportti building to assess the feasibility of the measurements and design the experiment with on-site information. - Internal task T3: Mounting and calibrating the setup. - Internal task T4: Measurement campaign in Karaportti. WP4 Title: Post-processing Major constituent: software Planned start: 08/04/2023 Planned end: 26/04/2023 Start event: 24/03/2023 End event: 26/04/2023 Process the measurement data to extract background noise and undesired effects. - Internal task T1: Study given code and techniques. - Internal task T2: Time-gating of results. - Internal task T3: Calibration with free line of sight measurements. - Internal task T4: Clean up noise and refine the results to extract the necessary information. Generate all the graphs. WP5 Title: Analysis and discussion Major constituent: software and reasoning Planned start: 27/04/2023 Planned end: 31/05/2023 Start event: 27/04/2023 End event: 31/05/2023 Analyze the results and make an educated prediction of the structure and internal composition of the sample in question using criteria of minimizing mean square error. - Internal task T1: Make informed hypotheses on wall structure (that is, researching common wall structures and materials in Finnish buildings). - Internal task T2: Create MATLAB script implementing an algorithm to find wall structure (number of layers, their thickness and composition) based on minimizing the mean squared error. - Internal task T3: Assess and discuss results. Improve the algorithm as much as possible. - Internal task T4: Present comparison between theoretical and measured results. WP6 Title: Documentation Major constituent: writing and documentation Planned start: 27/02/2023 Planned end: 19/06/2023 Start event: 27/02/2023 End event: 18/06/2023 An important part of the educational value of the bachelor’s thesis lies in the abilities of writing, reasoning, as well as critical thinking, discussing the results, and drawing conclusions. Therefore, an entire work package is dedicated to the preparation of the documents required by the UPC: Project Proposal and Work Plan, Project Critical Review, and Final Report, as well as any complementary reports that may be necessary during the project. - Internal task T1: Writing “Project Proposal and Work Plan”. - Internal task T2: Writing “Critical Review”. - Internal task T3: Writing “Final Review”. WP# Task# Short title for the task Milestone / deliverable Date T1 Search for papers that measure penetration loss using techniques similar to our List of publications 09/02/2023 T3 Sorting articles according to different techniques used Paper grid classification 25/02/2023WP1 T4 Writing a comprehensive state-of-the-art report State-of-the-art report 02/03/2023 T1 Familiarize with equipment from Microwave Lab Equipment list 05/03/2023 WP2 T3 Post-process sample results and assess the functioning of the technique Sample results analysis report 26/04/2023 T2 Go to the site to assess the feasibility of the measurements and design the experiment Experiment design plan 14/03/2023 WP3 T4 Measurement campaign Raw results from measurement 23/03/2023 WP4 T3 Clean up noise and refine the results to extract the necessary information. Generate all the graphs. Report with final plots 26/04/2023 16 T1 Make informed hypotheses on wall structure (that is, researching common wall structures and materials in Finnish buildings) Research background report 05/05/2023 WP5 T3/T4 Assess and discuss results. Present comparison between theoretical and measured results. Final results assessment report 31/05/2023 T1 Project Proposal and Work Plan Project Proposal and Work Plan 07/03/2023 T2 Critical Review Critical Review 14/04/2023WP6 T3 Final Review Final Review 19/06/2023 1.5.2 Time plan February March April May June 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 WP1 T1 T2 T3 T4 WP2 T1 T2 T3 WP3 T1 T2 T3 T4 WP4 T1 T2 T3 T4 WP5 T1 T2 T3 T4 WP6 T1 T2 T3 Figure 1: Gantt diagram of the project 1.6 Deviations from the original work plan Overall, the progress of the Final Degree Project has been smooth and there have only been minor incidents in its development. The project has adapted to time limitations, like the one presented during the measurement campaign at Nokia Espoo Campus: the authors’ time was restricted to the availability of their contact in the company, meaning there was only time for a few measurements on a couple of walls. Material limitations, such as sharing equipment with other users, and the risk of failure or malfunction, also posed challenges. Ultimately, the results obtained were not as precise as initially expected, and only basic information on the type of material and structure could be obtained. On the other hand, work plan modifications are minimal, mainly centered on temporal perception of work packages. Many tasks can be carried out in parallel, which is particularly noticeable in WP4 for post-processing: previously envisioned as a sequential process, tasks often require revisiting or overlapping with other tasks. Laboratory measurements and associated post-processing have been extended due to logistical difficulties. Measurements at Nokia are advanced because of the availability of the authors’ contact within the company, and more time has been dedicated to obtaining accurate graphs expressing results. The time for the results discussion remains the same, but more time has been allocated to writing the Bachelor’s Thesis, considering the content complexity and density. The Critical Review demanded however less time than anticipated. A task has been added to WP4: the Group had codes that implemented a part of the scattering parameter data processing, and their study was crucial in developing the final code. 17 2 State of the art This section provides background theory on various transmission measurement techniques and explains how these techniques have been utilized in literature to estimate certain parameters of the MUT. 2.1 Material electrical properties The fundamental constants of interest are the frequency-dependant electrical permittivity, ε, and conductivity, σ. In the literature, several methods exist for quantifying these parameters. Therefore, this section aims to clarify the different representations and their interconnections. Considering non-ionized, non-magnetic materials (free charge density is zero, ρf= 0, and permeability of the material is that of free-space, µ=µ0), the electric field wave equation can be derived from Maxwell’s equations: ∇2 E−εµ0 ∂2 E ∂2t=µ0σ∂ E ∂t (1) where  E(V/m) is the electric field intensity vector, ε(F/m) is the dielectric’s permittivity, µ0 (N/A2) is the permeability of free space and σ(S/m) is the conductivity. Writing  Ein exponential notation:  E= E0ej(ωt− k·r)(2) where  E0(V/m) is the value of  Efor t= 0 and r = 0,  k(m-1) is the wave number vector, ω(s-1) is the angular frequency and r (m) is the spatial distance vector. Considering Equation 1 and further developing gives the dispersion equation, as described in [10]: k2−εµ0ω2+jωµ0σ= 0 (3) where k= 2π/λ is the magnitude of  k. With the velocity of propagation defined as v=ω/k , the velocity of light in free space defined as c= 1/√ε0µ0, and material permittivity defined as ε=εrε0, where εris the relative dielectric permittivity of the medium, Equation 3 gives: c2 v2=εr−jσ ωε0 (4) The second part of the Equation 4 can be renamed as εrwith a complex value: εr=ε′ r−jσ ωε0 =ε′ r−jε′′ r(5) with ε′ rand ε′′ rbeing the real and imaginary parts of the real permittivity. So can then Equation 4 be used to express the velocity of propagation: v=c √εr =c n(6) where nis the refractive index of the medium. In case of a non-conducting dielectric (σ= 0), the wave does not attenuate as it propagates, and the relative permittivity has a real value, εr∈R. In case of a conducting dielectric (σ= 0), the wave attenuates as it propagates, and the relative permittivity has a complex value, εr∈C. In this case, the loss tangent can be defined as tan(δ) = ε′′ r ε′ r. 18 2.2 Models for material simulations 2.2.1 Models for frequency dependence As stated before, both the real (ε′ r) and imaginary (ε′′ r) part of the permittivity are frequencydependant. In this work, International Telecommunication Union (ITU)’s approach for frequency dependency [9] is used. For both the real part of the permittivity and the conductivity (i.e. imaginary part of permittivity), there is statistically significant evidence for an increase with frequency, so an exponential trend line is the best fit to all available data: ε′ r=afb GHz (7) σ=cfd GHz (8) Where a,b,cand dare constants characterizing each material. The ITU-R Recommendation [9] provides standardized values of these constants for several materials in their Table 3 1. 2.2.2 Models for calculating transmission coefficients This work’s model considers a plane wave incident (transverse electric (TE) polarization) upon a planar interface between two homogeneous and isotropic media with different electric properties that are far enough apart from other interfaces to have negligible effects. The section, based on the ITU-R’s Recommendations [9], provides techniques to compute transmission coefficients for both single-layer and multi-layer slabs. It is assumed that the MUT is in air, i.e. εr= 1. 2.2.2.1 Simplified method for a single-layer slab Considering a slab consisting of a single layer of building material of thickness dat an incidence (and emergence) angle θ0and wavelength λ, the transmission coefficient, T, can be expressed as: T=(1 −R2 eT E)e−jq 1−R2 eT Ee−j2q(9) where and ReT E is the E-field reflection coefficient for TE polarization for oblique incidence on a plane media interface. q=2πd λpεr−sin2θ0(10) ReT E =cos θ−pεr−sin2θ0 cos θ+pεr−sin2θ0 (11) 2.2.2.2 Iterative method for a multi-layer slab Considering a slab of N≥1 layers, perfectly planar and parallel to one another. Each layer n (1 ≤n≤N) has the corresponding relative permittivity εrnand thickness dn. The first layer is n= 1, being n= 0 the air before the first layer, and n=N+ 1 the air after the last layer. The incidence (and emergence) angle is θ0, being θnthe direction of propagation in each layer n. Needless to say, in this work, θ0= 0. The values are first initialized: AN+1 = 1 BN+1 = 0 (12) 1An error has been spotted in the Recommendation ITU-R P.2040-2 (09/2021). The concrete a,b,cand dcoefficients had been updated with respect to the previous Recommendation edition. However, Figure 6 of latest Recommendation has not been accordingly updated, and the transmission coefficient plot for a concrete slab at 1 GHz with TE polarization do not match the a,b,cand dvalues from Table 3. This mistake has been duly reported to its author. 19 And then for n=N, N −1, ..., 1,0: An= 0.5ejkndncos θn[An+1(1 + Yn+1) + Bn+1(1 −Yn+1)] (13a) Bn= 0.5e−jkndncos θn[An+1(1 −Yn+1) + Bn+1(1 + Yn+1)] (13b) where Yn+1 =cos θn+1 cos θnrεr,n+1 εr,n (14a) sin θn=sin θ0 √εr,n (14b) kn=2π λ√εr,n (14c) After layer n= 0 is reached, the E-field transmission coefficient with TE polarization can be calculated by: TT E =1 A0 (15) This is the method that has been used in this work. It can also be applied to transverse magnetic (TM) polarizations, or for reflection coefficients, adding the corresponding equations ([9] gives the full algorithm). The ITU-R Recommendation [9] offers an analogue technique, ”Matrix method for multi-layer slab”, explained in the Annexes (Section A.1). 2.3 Free-space measurement techniques The free-space (FS) material measurements refer to techniques used to measure the properties of a material without physically contacting it, many of which rely on electromagnetic waves. In this work, FS material measurements are used to determine the penetration loss of a material, which refers to the amount of electromagnetic energy that is absorbed or reflected by the material as it passes through it. FS measurement methods can be classified following different criteria. Based on the type of electromagnetic waves (frequency, wavelength) used in the measurement: X-ray (30 PHz - 30 EHz, 0.01 to 10 nm), optical (300 GHz to 30 PHz, 10 nm to 1 mm), terahertz (0.1 to 10 THz, 30 to 300 µm) or microwave (300 MHz to 300 GHz, 1 mm to 1 m). Based on the way electromagnetic waves interact with the MUT: •Resonant techniques measure energy absorption or reflection at specific frequencies and are used for materials with high dielectric constants. These materials can cause significant energy loss at certain frequencies. Cavity perturbation is a common resonant technique where a sample is placed in a resonant cavity, and changes in the cavity’s resonant frequency due to the sample’s presence are measured. The changes are related to the energy absorbed or reflected by the sample, providing information about its dielectric properties. Resonant techniques are suitable for materials with specific dielectric properties, where resonant frequencies can offer insight into the material’s composition and structure. Techniques involving nested reverberation chambers have been widely researched in literature in the study of shielding effectiveness (SE) of different building materials, like carbon fiber [11], wood and marble [12] and different composites [13]. •Non-resonant techniques involve measuring the amount of energy that passes through a material at different frequencies: they do not rely on specific resonant frequencies. These techniques like the free-space path loss (FSPL) method are more commonly used for measuring penetration loss, as they can provide information over a wide frequency range. Analysis of SE of modern energy-saving windows is made in [14] and then again in [15] comparing a resonant technique like the near isotropic irradiation in a nested reverberation chamber, with a non-resonant technique like the irradiation at normal incidence in a semi-anechoic chamber, obtaining similar results in the 1-18 GHz band. 20 2.4 Free-space path loss method In this work, the non-resonant technique of FSPL method is utilized to measure penetration losses of materials in the microwave band. This method involves transmitting a known amount of electromagnetic energy through FS from a transmitter (TX) to a receiver (RX) in line-of-sight (LOS) and measuring the energy received. The material under test is then placed between the transmitter and receiver, no line-of-sight (NLOS), and the measurement is repeated to determine the energy lost due to the material’s presence. By repeating these measurements over a frequency band, the frequency dependence of penetration losses can be captured, providing more information about the material’s internal structure. This section aims to provide information in the current state-of-the-art research for this method. 2.4.1 Setup The experimental setup utilized in this work is a well-established approach that has been widely used in the literature. It typically involves two directive antennas (e.g., horn-type) arranged in a bore-sight aligned bi-static configuration (although some studies have employed a mono-static approach [16]), with the sample placed between them. The choice of measurement equipment used can vary considerably, depending on the frequency range of interest. When conducting measurements over a broad frequency band, a vector network analyzer (VNA) is commonly employed due to its practicality and versatility. In this project, a VNA was used as the primary measuring device. In some cases, alternative measurement methods are employed when studying very specific narrowband frequencies, or when the frequency can be stepped manually. These methods involve using a signal generator at the TX to generate microwave continuous wave (CW) signals, along with a RX capable of measuring power at the desired frequency. Such RX can either be a spectrum analyzer (like in [8]’s second method, or [17–23]), a standard power-meter (like Ragulis et. al. in [24–26]) or even an oscilloscope [27, 28]. All setups provide similar results and are often used interchangeably: in [24], material SE are studied using a VNA to perform measurements in the 1-18 GHz range, while a tunable microwave generator and averaging power sensors were used in the 3-20 GHz range. Other publications also use more elaborate channel sounding systems based on wideband sliding correlator, like T. S. Rappaport’s group in [29, 30] or [31]. 2.4.2 Environment The measurement setup is strongly influenced by the environment in which it is carried out. For accurate and reliable results, it is recommended to use a laboratory environment, which offers a controlled setting with quantifiable errors and biases. Although complex samples can also be analyzed, laboratory setups are typically used to test relatively simple MUT. In contrast, a field environment allows for more realistic measurements of materials under real-life conditions. However, it is important to note that measurements obtained in a laboratory can differ significantly from those obtained in the field due to the environmental effects and unknown external factors. The laboratory studies are carried out inside an anechoic chamber (both TX and RX are inside), a semi-anechoic chamber (only the RX is in an anechoic chamber, and generally the sample is the only exit point of the chamber) or without a chamber. The presence of an anechoic chamber provides an environment devoid of reflections from the surroundings, which means that the received multipath component (MPC) only come from the sample. [24] uses both anechoic and semi-anechoic chambers, while [21] compares measurements on site and in lab. In this project, measurements are taken without an anechoic chamber nor absorbing material: external MPC are nonetheless generally removed by the time gating process, and measurement accuracy is increased through averaging. 21 2.4.3 Materials The scope of literature on materials can be quite extensive and varies depending on their intended use and the goals of the study. While there are numerous studies that conduct general research on materials, many are specifically focused on radio coverage and are primarily interested in building materials. One notable example of this is the study conducted by National Institute of Standards and Technology (NIST) [32]. Glass is one of the most studied materials, as recent improvements in energy efficiency have worsened its propagation conditions. In a laboratory environment, single glass slabs [27, 31, 33–36], double and triple-glazed windows [14, 15, 20, 24, 25, 37–40] and clear and metal-coated windows [14, 25, 26, 41, 42] have been studied. In a on-site environment, windows and glass doors have also been analyzed [8, 18, 28–30, 43–45]. Concrete is also a very studied material, both in lab environments [16, 27, 36, 39, 46–48] and on-site campaigns with concrete [22] (this one actually studies indoor concrete partitions) and reinforced concrete [18, 19] walls. In lab environments, all kinds of building materials like brick walls [17], marble, plywood, chipboard and plasterboard are studied in [21, 27, 31, 33–36, 39, 40, 42, 49–51]. Even textile has been studied several times, like in [52]. In on-site environments, several studies measure walls, partitions and doors of varied materials (mainly drywall, wood, brick, metal, etc.) in [18, 22, 28–30, 53] in far-field propagation. 2.4.4 Frequencies Most studies on penetration losses through building materials are focused on research in radio coverage. For this reason, the frequency range from 100 MHz to 6 GHz is extensively studied in a wide variety of materials [54], with both laboratory and on-site measurements. It is expected that upcoming wireless networks will be able to handle high-throughput connections to meet an increasingly diverse range of applications. However, the available spectrum in the sub-6 GHz range will not be sufficient to support new requirements. As new generations of mobile technologies increase in frequency in search of greater bandwidth, losses in the above-6 GHz bandwidth are becoming a subject of significant research [55], with particular interest in exploiting the millimeter-wave (mm-wave) bands in the 30-300 GHz range [2], expected to provide the necessary communication bandwidth for 5G and beyond. 2.4.5 Field proximity This method works particularly well in the propagation of a plane wavefront. The surroundings of an antenna can be divided in three regions, namely reactive near-field, radiating near-field (Fresnel) an the far-field (Fraunhofer) [56, 57], and only in the last region can the radiated wavefront be considered planar. Distance separating the radiating near-field from the far-field is called Fraunhofer distance, or far-field distance, and is described by Equation 16. d= 2D2/λ (16) where Dis the maximum dimension of the diffracting object, and λis the incident light wavelength. However, the fact that radiation is in the near or far field seems to have relatively little effect on the quality of the results. For this reason, the choice between near-field and far-field measurements depends on the objectives or spatial feasibility of the measurements. Greater distance generally provides a larger footprint on the sample, which can be useful for obtaining an average result of its losses. However, if spatial precision is required for the electromagnetic behavior of a particular position, the antennas will be positioned closer to the sample. [8] compares different techniques in near and far field measurements. 22 While it is preferred to work in far field, the distance is usually chosen to minimize the width of the spread of the transmitted wave upon the material [29]. This is important not only for accuracy but also to avoid edge diffraction effects, which can be particularly relevant in small laboratory samples. In order to make diffraction low and time-gateable, antenna distance from sample has to be small compared to distance from antenna to sample edge. The far-field versus near-field issue is somewhat crucial in this work, as measurements made in the near field are compared with theoretical models [9] designed for the far field. 2.5 Walls electromagnetic behavior When measuring a wall with FSPL technique, several material and structural anomalies within the wall can affect the results, including: •Moisture: it can significantly worsen radio wave propagation conditions for materials, especially at higher frequencies [58]. Water molecules can cause electric and magnetic fields to lose energy through absorption and scattering, reducing the strength and quality of radio signals. This is a common issue in humid climates, such as in Finland, and in older buildings with humidity problems. •Metal objects: such as pipes, conduits, reinforcement bars [59], and electrical wiring can affect radio propagation measurements due to their conductor nature, causing significant shielding and unpredictable effects. Load-bearing walls may also contain reinforcement bars distributed in the concrete, making them difficult to predict without a detailed blueprint of the building’s plumbing. •Structural defects: defects such as cracks or gaps within a wall can have an impact on the absorption or reflection of energy. Older buildings may also have irregularities due to natural wear and tear over time, causing imperfections to appear. Additionally, environmental factors can contribute to material degradation in walls, such as alumina cement. •Surface finish: the surface finish of a wall, whether it is painted or textured, can have a significant impact on the amount of energy absorbed or reflected by the wall [60]. This is especially true if the surface irregularities are in the order of the wavelength used for analysis. Rough or porous surfaces tend to scatter and reflect radio waves, whereas smooth and reflective surfaces can cause specular reflection. Moreover, some paints may contain metallic particles, which can act as a shield and block electromagnetic waves. •Energy efficiency: improving the energy efficiency of buildings can significantly impact the electromagnetic properties of walls and consequently, indoor radio coverage. This effect may be particularly evident in colder countries like Finland, as shown in [40], where thermal insulation is a crucial aspect of building design. – Insulating gaps: air gaps or cavities within walls can affect the energy absorbed or reflected by the wall, and if they are filled with insulating materials, it can change the dielectric properties of the wall. This can cause variations in the way radio waves propagate through the partitions, leading to changes in signal strength and quality. – Metallic coatings: energy-efficient films applied to walls can impact the electromagnetic properties by acting as conductive shields that block or reflect radio waves and cause attenuation of the signal [14]. The thickness and composition of the films can affect the degree of attenuation, similar to the way thin metal coatings between multiple layers of glass in windows can provide thermal insulation but also worsen propagation properties. •Other material and structural irregularities: Interior partitions are not designed with electromagnetic uniformity in mind, but rather physical stability and usefulness. This can result in structural designs with air gaps for ventilation or support elements like wooden bars, concrete columns, and pillars, which can cause variations in the electrical behavior of the wall. 23 3 Methodology and project development Taking into account all the factors that affect walls’ electromagnetic behavior, commented in the State-of-the-art (Section 2), conducting a blind study of walls presents a challenge. Therefore, a comprehensive analysis of material samples is first conducted in a controlled laboratory environment, with the intention of familiarizing with the method and the type of results that will be obtained. 3.1 Laboratory measurement campaign The laboratory measurement campaign is carried out in the Microwave Laboratory from Aalto University School of Electrical Engineering on 3 different dates, due to time and logistical limitations: March 6th, March 8th and March 21st 2023. The goal of the study is to analyze the structure (i.e. thickness) of a series of readily available material samples in the laboratory, in a manner similar to how it is done afterwards with the walls. The study involves taking measurements of the scattering parameters for each material: more accurately, the transmission coefficient parameter S21. This is done for two frequency ranges (1-10 GHz and 10-18 GHz), which respectively include the frequencies of interest (4 GHz and 14 GHz), utilized for measurements in [5]. Two different dispositions are applied to better understand the effects of the proximity of the antenna to the sample: at a distance of 2 cm (distance 1) and 0 cm (distance 2) from the MUT. After obtaining these measurements, they are post-processed to assess the accuracy of the ITU-R’s model [9] for this particular material, measured in terms of RMSE. 3.1.1 Setup A setup similar to the one used by Karttunen et. al. in [8]’s ”third method” is built, as it is a known and effective approach. Similar versions have been used in multiple literature examples. 3.1.1.1 Samples Tables 5 and 6 (both in the Annexes, Section B.1), and Table 1 provide information about the studied materials, their dimensions, and tentative composition. Table 5 presents measurements conducted in the laboratory at 4 GHz on March 6th and March 21st 2023, while Table 6 presents measurements conducted in the laboratory at 14 GHz on March 8th. Table 1 combines measurements from both frequencies, and its samples are of particular interest because they have a known or assumed composition, measurable penetration losses for their thickness, and can be easily combined to observe the effects of each part. Not all measurements are repeated at both frequency bands: only those in Table 1. -Sample 1, or Wood 1, is the first material studied, and it is a pale, dry piece of wood measuring 60 x 60 cm with a thickness of 1.51 cm. Figure 22 shows how it appears to be an engineered wood, possibly plywood, made by bonding several thin layers (or plies) of wood veneer together. The wood’s origin and tree species are unknown. -Sample 2, or Wood 2, is the second material studied, and it is a piece of wood measuring 49.5 x 59 cm with a thickness of 1.92 cm. In Figure 23, it can bee seen that it is a warm-colored wood, of medium humidity, and has possibly undergone varnishing treatment at some point. It is also of unidentified origin and tree species. -Sample 3 involves a combination of the previous two types of wood, Wood 1 and Wood 2, to measure their combined penetration losses. In this case, the two wooden slabs are joined together, with Wood 1 closest to the RX antenna (port 1 of the VNA) and Wood 2 closest to the TX antenna (port 2 of the VNA). It is important to note that any air gap between the two layers is considered negligible and not taken into account during the experiment. By measuring the losses in this configuration, valuable insights into the behavior of the materials and their impact on signal penetration is gained. 24 The two wooden slabs are both modeled according to the ITU-R’s ”wood” standard [9]. However, the fact that they are made of different types of wood implies that they have different permittivity values, which is clear from the data presented in the Results section (Section 4). Although Table 1 provides the most comprehensive analysis considering the thoroughness of the measurements, other materials are also analyzed at 10-18 GHz (14 GHz wide-band): - The fourth measurement involves using Wood 1 and Wood 2 with a 1.7 cm air gap between them, allowing for the experimentation with structures similar to those expected in the analysis of walls in the Nokia Campus. However, a lack of materials prevent the construction of a symmetrical ”wall” (with two slabs of the same thickness) that would provide valuable information for subsequent measurements. - The fifth measurement examines a 50 x 50 cm sample of expanded polystyrene (EPS) that is 3 cm thick. One of its faces is coated with a black paint that appears to be metallized, based on the transmission coefficient analysis. - The final measurement is conducted as a control using a metallic plane. It serves to confirm the system’s performance and demonstrate a low transmission coefficient through the conductive plane. Additionally, it provides insights into the amount of power captured from diffraction at the sample’s edges. Some measurements are excluded from the tables as they provide minimal information about the material and offer no insight into the effectiveness of the technique. For instance, a single-slab sample of 1 cm thick styrofoam is tested, but the propagation loss at 4 GHz is negligible or non-existent, meaning the data is not usable for this work’s purpose. Additional studies are performed with the EPS sample, in which it is combined with other slabs and materials. Unfortunately, these tests show that the EPS’s conductive properties result in significant losses, rendering any information gleaned from analyzing such stack-up of materials unusable. Measurement carried out at both 4 and 14 GHz in the laboratory Material Dimensions Dist. 1 Dist. 2 4 GHz meas. (.s2p) 14 GHz meas. (.s2p) sampl1 d1 vna1 sampl1 d1 vna22 cm 5.51 cm ref1 d1 vna1 ref1 d1 vna2 sampl1 d2 vna1 sampl1 d2 vna2 1 Plywood Height = 60 cm Width = 60 cm Thick. = 1.51 cm 0 cm 1.51 cm ref1 d2 vna1 ref1 d2 vna2 sampl2 d1 vna1 sampl2 d1 vna22 cm 5.92 cm ref2 d1 vna1 ref2 d1 vna2 sampl2 d2 vna1 sampl2 d2 vna2 2 Wood Height = 49.5 cm Width = 59 cm Thick. = 1.92 cm 0 cm 1.92 cm ref2 d2 vna1 ref2 d2 vna2 sampl3 d1 vna1 sampl3 d1 vna22 cm 7.43 cm ref3 d1 vna1 ref3 d1 vna2 sampl3 d2 vna1 sampl3 d2 vna2 3Wood + plywood Sample 1 and 2 together 0 cm 3.43 cm ref3 d2 vna1.s2p ref3 d2 vna2 Table 1: Table collecting all laboratory measurements. 3.1.1.2 Equipment Figure 2: Laboratory measurements setup diagram. 25 3.2.3 Procedure To capture the transmission coefficient throughout the frequency band, two VNA configurations are used, one at 4 GHz and the other at 14 GHz, in a similar manner to laboratory measurements. The antenna set is adjusted accordingly for each VNA configuration. The first VNA configuration (VNA1) uses a frequency range from 1 to 10 GHz with an IF BW of 10 kHz and no averaging. The second configuration (VNA2) uses a frequency range from 10 to 18 GHz with a narrower IF BW of 2 kHz, and an averaging factor of 8 sweeps for Wall 1 and 3 sweeps for Wall 2. These different configurations allow for different levels of precision and accuracy in the measurements. The narrower frequency range and IF BW from VNA2 allow for more precise measurements at higher frequencies, while the averaging factor helps to reduce noise and improve the accuracy of the measurements. Considering the small role distance between samples and antennas is seen to play in the laboratory results, and with the aim to speed up the measurement campaign, measurements are taken at a fixed distance for each frequency band and for each wall. The exact distances can be found in Table 2. These measurements are taken in near-field propagation as the distance is below the Fraunhofer bound (Equation 16). During the measurement campaign, time-gating is used to eliminate reflections from the environment, while the VNA averaging factor is used to reduce noise in the measurement. This factor is determined based on the variability observed in the frequency domain S21 values. Multiple measurements are taken for each wall at different positions, to allow for the averaging of the results and to have representative values for the entire wall. The number of measurements is limited by the time available in the site. For Wall 1, measurements are taken at 5 equidistant positions 50 cm apart, starting 2 m from the load-bearing column touching the window. For Wall 2, measurements are taken at 9 equidistant positions 25 cm apart, starting 1 m from the window wall, avoiding vertical metal supports. All measurement points are at the same height: approximately 95 cm. Because these measurements are made on real walls, each antenna has to be placed in a different room, making it difficult to bore-sight align them with a wall in-between. Prior to the measurements, a laser distance measuring device is used to find the measurement positions on each side of the wall, which are marked with painter’s tape. The necessary NLOS measurements can then be taken by moving the carts to target the marks on the wall. Needless to say, the painter’s tape is transparent electromagnetically. In this field experiment, it is not possible to take a reference LOS capture for each measurement position because the wall between the antennas cannot be removed at will, unlike in laboratory experiments. As a result, only sample measurements are taken for each position and VNA configuration. A single reference measurement is used for all positions on the same wall with the same VNA configuration (a total of 4 references). The reference is obtained by measuring air between the two antennas, ensuring the same distance between the antenna apertures, which is calculated as the sum of the wall thickness and the distances of each antenna to the wall. The measurement is made in a room in the same building’s office, and the distances are 24 cm for Wall 1 @ VNA1, 22 cm for Wall 1 @ VNA2, 17 cm for Wall 2 @ VNA1 and 11 cm for Wall 2 @ VNA2. In this way, with the LOS reference, it is not possible to eliminate all reflections from the immediate environment, as it is possible to do in the laboratory, but all external or inherent elements of the propagation medium can be corrected. Just like in the laboratory, VNA results can be saved in an .s2p file format on a USB drive. This can then be connected to a computer with MATLAB for post-processing. 32 3.2.4 Post-processing 3.2.4.1 Time-gating Time-gating is used to remove unwanted MPC from the environment in Karaportti measurements. This is done by performing a series of steps: taking the S21 frequency plot, calculating the inverse fast Fourier transform (IFFT) to obtain the CIR, windowing the peak of interest, and returning to the frequency domain by calculating the FFT. Both the sample and reference measurements are time-gated with the gating window centered at the peak of each CIR. The chosen VNA configurations have a time resolution (1/BW) of 0.111 and 0.125 ns for VNA1 and VNA2, respectively, which is the same as in the laboratory. Unfortunately, these temporal steps are not sufficient to resolve different internal reflections within the wall, which have a similar delay as the steps: this is can be explained noticing that the utilized wavelength is in the same order of magnitude as the thickness of the layers to be measured. Although obtaining this information would have been interesting, the BW cannot be increased beyond the VNA and antenna limitations. The maximum visible delay of the CIR, defined as τmax =N/BW (where Nis the number of frequency points), is increased in comparison to the laboratory measurements. It is important to extend the range of the CIR in order to capture the main reflection peak from the wall, which can appear with a considerable delay, considering that the distance to be covered through the optical fiber is over 100 m. For this reason, the maximum number of frequency points allowed by the VNA, N= 10,001, is chosen, resulting in a minimum value of τmax = 1.111µs. After examining the laboratory results, a Gaussian window is directly applied to the CIR, as it has a lesser impact on the frequency results. The width of the window is FWHM = 3.333ns (i.e. 1 m). It is chosen larger than in the laboratory post-processing, in order to capture all propagation paths coming from thicker walls, resulting in a wider-spread CIR. This choice balances the limitations of the frequency band and the elimination of unwanted reflections. 3.2.4.2 Calibration As done with the laboratory results, each S21 measurement at each wall position is normalized to a single reference measurement per wall and per VNA configuration, for a total of four reference measurements (2 walls, 2 VNA configurations). Normalization is done by dividing each S21 sample by its corresponding reference value for a specific frequency, in order to compensate for all irregularities of the medium and the measurement system. The result is the transmission coefficient solely due to the wall. 3.2.4.3 Averaging and RMSE calculation The measurements of several positions on each wall are obtained for each VNA configuration. These measurements are considered as realizations of a random variable, and the S21 dB values for each measurement position at the same frequency are averaged to obtain a result closer to the variable’s expected value. The average trace is then compared to the ITU-R model [9] by calculating the RMSE in the useable frequency band after time-gating, as in Equation 17 . The RMSE values are studied with ITU-R models of different materials to check which structures offer more reasonable results. 33 4 Results and discussion As it has been commented in the Introduction (Section 1), these results aim to provide further insight on the walls influencing the measurements from [5] publication. In such publication, 500 MHz bandwidth channel sounding measurements at 4 and 14 GHz are conducted. In this work, the wall structure is studied through not only wide-band (1-10 GHz and 10-18 GHz), but also narrow(er)- band measurements (3.75 to 4.25 GHz and 13.75 to 14.25 GHz). These narrow-band measurements come from the same VNA sweep, but the studied band is limited to the frequencies of interest. From the thickness sweeps used to assess the quality of the structure guesses it can straight-forwardly be noticed the performance of a narrow-band measurement is very notably decreased, so only the full wide-band frequency range is used in the end. The plots obtained through the narrow-band approach can still be visualized in the Annexes (Section 8). 4.1 Laboratory measurement campaign Penetration loss measurements are conducted in the laboratory for two antenna-sample distances: 0 and 2 cm. As expected, little difference is observed between the results, meaning the diffraction effect is minimal at that distance, and the differences observed may only be due to alignment defects, human movement or calibration errors. All results presented here are thus at 2 cm (distance 1). The laboratory results are initially analyzed through thickness sweeps. This method involves comparing the measured penetration losses (in dB) across a range of frequencies to the theoretical losses of a single slab of a specific material with a certain thickness in the same frequency range. The RMSE is calculated for different typical construction materials, as defined in the ITU-R Recommendation [9], and for different probable thicknesses of the sample. Ideally, the thickness sweep should reveal a distinct minimum in the RMSE plot at the thickness that matches the actual width of the sample and for the material that corresponds to the slab. The different thickness sweeps can be seen in Figures 7, 8, and 9 for Sample 1, 2, and 3 respectively. RMSE is represented in linear. Figure 7: Thickness sweep of laboratory Sample 1 in @ VNA1, 1-10 GHz (left) and @ VNA2, 10-18 GHz (right) at distance 1 in wide-band. Figure 8: Thickness sweep of laboratory Sample 2 in @ VNA1 (left) and @ VNA2 (right) at distance 1 in wide-band. 34 Figure 9: Thickness sweep of laboratory Sample 3 in @ VNA1 (left) and @ VNA2 (right) at distance 1 in wide-band. Sample 1, a wooden slab with a thickness of 1.51cm, shows reasonable results in the laboratory measurements. As can be seen in Figure 7, both in the high and low frequency bands, the material model that achieves a RMSE minimum closest to the real thickness of the sample is the generic wood ITU-R permittivity model. Specifically, these minima are found at 1.75 and 1.6 cm for the frequency bands of 1-10 GHz and 10-18 GHz, respectively. While the result is conclusive in the high frequency band, there is some ambiguity in the low frequency band, where the material could be mistaken for plasterboard. The two materials are quite similar electromagnetically, and thus behave similarly in the ITU-R model: therefore, it should not be surprising that they yield such similar results. They both suggest that the sample is relatively lightweight and electromagnetically transparent. It is worth noting that Sample 1 is not an untouched wooden sample, but rather an artificially treated type similar to plywood. However, it can be observed that its electrical behavior is very different from the model proposed by the ITU-R for this type of material (which would only require a thickness of 2-3cm to exhibit similar losses to Sample 1). Instead, its behavior is much closer to the wood model, which already raises concerns about the wide variability and generality that the ITU-R loss models exhibit. This initial result allows to verify the proper functioning of the free-space method used and confirm the suitability of the ITU-R’s wood model for the sample, while also providing insight into the acceptable degree of variability and error. Sample 2, a wooden sample with a thickness of 1.92 cm, according to the results in the 1-10 GHz frequency band, the ITU-R’s wood model fits well with the losses of the sample, with a minimum RMSE at 2.1 cm. However, the same cannot be said for the high frequency band, which shows the minimum at 3.2 cm. The observed discrepancy indicates that the ITU-R’s loss model for wood may not be entirely suitable for this particular sample, and the obtained results are not as accurate as desired. It is worth noting that despite this observation, the results still confirm the low-loss performance of the sample, which aligns well with prior knowledge of its composition. Sample 3, which is a composite of the previous two samples with a total thickness of 3.43 cm, yields results that are consistent with the previous observations. The low frequency range shows more favorable outcomes, while the high frequency range suggests that the ITU-R’s permittivity model may not be an accurate fit for this sample. To better understand these behaviors from Sample 2 and 3, a permittivity sweep (Figure 10) is performed with the intention of determining the actual permittivity of the studied samples, in contrast to the permittivity values provided by the ITU-R frequency-dependant model (based on abcd values). To achieve this goal, the loss plots obtained from measurements are compared with simulations considering a single slab of the same thickness as the sample. The RMSE is calculated for different values of permittivity, scanning a specific range of possible values for the real and imaginary parts 35 of εr(Equation 5). However, this process relies on a key assumption: that neither the real nor the imaginary part of the permittivity varies within the studied frequency range. While this assumption is typically valid for the real part, it is often incorrect for the imaginary part, as presented in the ITU-R Recommendation [9]. Nevertheless, it is still an acceptable approach for a narrow frequency band and for materials with minimal frequency variability. Figure 10: Permittivity sweep from laboratory Sample 1 (left), 2 (center), 3 (right) in @ VNA2 (left) at distance 1 in wide-band. The simulations exhibit a noticeable lack of precision in their results, with multiple values of εr yielding reasonable RMSE. While it is possible to extract a range of values for the imaginary part (ε′′ r) that offers minimal errors, the same cannot be said for the real part (ε′ r). The latter offers minimal errors throughout its entire range of values, making it almost impossible to identify a specific range with significantly good accuracy. One can observe the small role that the real part plays in penetration losses, and how difficult it is to determine its value based on RMSE values. Therefore, taking into account the limitations that restrict this assumption, it can be considered that MUT’s ε′ rwill not significantly deviate from its study wood model, only in order to narrow down the range of values of the imaginary part and specify a more accurate ε′′ r. Assuming, according to the ITU-R model, a value of 1.99 for the frequency-invariant ε′ r, and averaging the minima from @VNA1 and @VNA2 measurements, ε′′ r values equal to 0.11, 0.155 and 0.142 are obtained for Sample 1, 2 and 3 respectively. By considering these values frequency-invariant, the corresponding thickness sweeps can be observed in Figures 7, 8 and 9, respectively. The ITU-R permitivity model for wood shows that the imaginary part ranges from 0.0845 to 0.104 across 1 to 18 GHz, respectively. This indicates that, particularly for wood, the permittivity does not vary much within these frequency ranges. Although the disparities of the thickness sweep are notable, the tuned εrvalues obtained through the permittivity sweep do not differ significantly from those of the ITU-R model. This underscores the important role played by conductivity in the measured losses, a parameter that ITU-R provides in tables of a non-specific nature: many types of wood are grouped under a single value, which leads to significant variability in the results. The chosen values that minimize the permittivity sweep reveal interesting insights. For Sample 1, εr= 1.99 −j0.11 closely matches the ITU-R model, suggesting that the laboratory sample closely resembles the one used by ITU-R in terms of electrical properties. In contrast, Sample 2 with εr= 1.99 −j0.155 has a significantly larger ε′′ r, indicating higher losses. This could be due to a higher degree of moisture in the sample or the effect of varnishing. Sample 3, on the other hand, with εr= 1.99 −j0.142, has a permittivity that falls in between Sample 1 and Sample 2, reflecting its composition as a combination of the two wooden slabs. 36 4.2 Site measurement campaign Figure 11: Wall models with (right) and without (left) air gap. Considering the most common construction practices, two wall models can be assumed (Figure 11). One defined as a singleslab of uniform material with indefinite permittivity and known thickness t, and the other defined as two layers of the same uniform material with indefinite permittivity and an unknown thickness s, with an air gap in between of thickness t−2s, where tis the total known thickness of the wall. This air gap can be made of insulating foam or some other material similar to air. While these models are highly simplified, they should allow for an reasonable modeling of most partition walls. One of the educated guesses on which this work is based is the assumption of symmetry in interior walls: as opposed to external walls, there is no reason to assume that internal partitions should have asymmetrical sides. However, strictly speaking, it is known that the walls under study are indeed uneven, as the south face of Wall 1 has a cork board, and both faces of Wall 2 have asymmetrically distributed metallic supports. 4.2.1 Wall 1 As mentioned in the Methodology (Section 3), up to 5 positions are measured in both VNA configurations, 1-10 GHz and 10-18 GHz, which are presented in Figure 12. The first thing that draws attention is the significant variability in the results, with a range exceeding 5 dB. It can also be observed that losses are higher at higher frequencies, and in any case, they are lower than the reference LOS air measurement. Once all positions are normalized to the LOS reference, wall losses oscillate between approximately 0 and 15 dB @VNA1, and between 15 and 40 dB @VNA2. An unusual behavior is observed in position 5 @VNA2, which seems to exhibit resonances around 13 GHz, difficult to explain with the available knowledge of the wall and the setup. Nevertheless, the overall results vary little including or excluding this measurement, so it is in the end taken into account. The gray vertical lines indicate boundaries where the time gating effect is considered negligible: it can be verified that there are indeed strange behaviors beyond these boundaries. Figure 12: Frequency plots of Wall 1 measured and time gated S21 for different positions at @ VNA1 (left) and @ VNA2 (right). Raw measurements (up) and calibrated measurements (down). 37 Once these values are obtained, a thickness sweep similar to the one performed in the laboratory measurements can be carried out. Figures 13 and 14 compare the time-gated and calibrated measured losses in terms of the RMSE with the two previously presented wall models, considering different materials according to the ITU-R permittivity model and sweeping the slab thicknesses t for the no-air-gap model and sfor the air-gap model. In this way, the dashed lines correspond to an air-gap model where the value of tis fixed to the real wall thickness and the value of scan be observed on the upper axis, while the solid lines correspond to a no-air-gap model where the value of tcan be observed on the lower axis. To do this, the thickness sweeps of each position have been averaged to obtain a mean trace for each frequency band and for each material (in the Annexes, Section C.3.1, a visual example of this averaging is presented). Figure 13: Thickness sweep of Wall 1 @ VNA1 in wide-band. RMSE in linear. Figure 14: Thickness sweep of Wall 1 @ VNA2 in wide-band. RMSE in linear. If the wall is assumed to be solid (single slab model, solid lines, lower x-axis), the material used to construct it should offer the lowest RMSE error when compared to the 18.5cm-thick singleslab model (which is the thickness measured for Wall 1). Although there is no trace that shows a minimum for this thickness, the materials that most resemble it for @VNA1 are plasterboard and wood, and to a lesser extent chipboard, while for @VNA2 they are chipboard and somewhat less plasterboard and wood. In any case, the three are electromagnetically very similar materials, but equally improbable as the material that makes up the wall, since the wall is visibly solid and heavy. The construction materials that are most likely to make up the wall are concrete or bricks, both of which either offer a significantly higher RMSE or have losses that are either too large or too small, corresponding to a much thinner wall (5-10 cm for concrete) or a much thicker wall (brick @VNA2). These unsatisfactory results lead to the conclusion that the wall is likely to have some kind of air gap, which would explain why the measured losses are much smaller than those for a concrete wall of the same thickness. If the wall is assumed with an air gap (dashed lines, upper x-axis), it should be made of the material that provides the lowest RMSE error for both frequency bands, for a model with an air gap where the thickness of the slabs (s) is around 3-5 cm. Knowing that the slab material is most likely solid and heavy, like concrete or bricks, it would not be reasonable to expect sthicknesses smaller than 2 cm, nor would it make sense to have an air gap smaller than 5 cm. Therefore, it is found that the only reasonable materials for @VNA1 are concrete and chipboard, and for @VNA2 are plywood and concrete. Based on the available knowledge of the wall, chipboard and plywood can be discarded, leaving only concrete as the plausible option with a thickness of sbetween 2 and 4.5 cm. These results, although reasonable, are not very conclusive. The minimum values of RMSE still seem quite high compared to other materials, and the possible range of slab thicknesses (s) in case it is concrete is very wide. Moreover, 2 centimeters of concrete with an air gap is a relatively absurd structure. For this reason, it would make more sense for the wall not to follow a 2-layer model with an air gap in between, but rather to be made of 18.5cm-thick concrete blocks. These concrete blocks 38 traditionally already have an air cavity inside, which would explain the low losses. Additionally, this type of composition also makes sense from a structural engineering standpoint: if there are loadbearing columns at each end of the wall, it does not make sense for the wall to also be of load-bearing reinforced concrete. Instead, it is more reasonable for it to be a partition type, relatively lightweight and easy to construct, as would be the case if it were built using concrete blocks. On the other hand, this could also explain the resonances and variability observed in the losses for different positions: some positions may fall on block end points, where there is more thickness of material (more losses), while other positions may capture more air (less losses). Another aspect that would be sensible to consider is the great variability in permittivity and therefore losses offered by concrete [46]. To begin with, there are many types of concrete, with different compositions in the mix and therefore with different electrical properties (e.g. ITU-R permittivity model does not match with [61]). The exact composition or type of concrete that could compose the wall is not known, making it difficult to refine the results any further. It has also been found that the age of the concrete can be closely related to the losses it presents, as older, and therefore drier, concrete can present fewer losses than more recent concrete with a higher concentration of water [58]. In addition, in the case of a wall made of concrete blocks, the repetition pattern, height, or size of the internal cavity is also unknown. It is also worth mentioning the role that the board on the south face of the wall may have played, which has been omitted in the models. 4.2.2 Wall 2 For Wall 2, up to 9 positions have been measured for penetration loss in both frequency bands, as shown in Figure 15. The outliers that stand out the most are positions 4 and 6, which exhibit significantly higher losses than the rest for @VNA1. These higher losses only occur in the 1-10 GHz band, with no trace of them in the 10-18 GHz band. Referring back to the map of measurement positions (and Annex Figures 25 and 26), it can be observed that positions 4 and 6 are very close to the vertical metallic supports of the wall, whose conductive behavior is responsible for these losses. These values are only observed for the low frequency band because larger antennas (in the order of the wavelength) are used very close to the MUT, which means the ETS Lindgren antenna has a much larger footprint on the sample than the one from Quinstar technology. These results have therefore not been used in subsequent calculations nor charts for neither @VNA1 nor @VNA2. Figure 15: Frequency plots of Wall 2 measured and time gated S21 for different positions at @ VNA1 (left) and @ VNA2 (right). Raw measurements (up) and calibrated measurements (down). 39 On the other hand, still on Figure 15, the high variability in the measured losses for the different positions (even excluding positions 4 and 6) should also be mentioned, with variations over 5 dB. However, losses in general are lower than those measured for Wall 1, indicating that it is a much lighter wall. The losses range from -2 to 4 dB in the low frequency band, and from 3 to 12 dB in the high frequency band. Similarly to what has been done with Wall 1, a thickness sweep can be performed by comparing, in terms of RMSE, the measured losses for each frequency band with the no-air-gap model and with the air-gap model. In this way, different materials are compared with the ITU-R permittivity model for different thicknesses in each of the wall models: over t(lower x-axis) for the single-slab model, and over s(upper x-axis) with tfixed to the actual thickness of the wall, for the model with air gap. Figure 16: Thickness sweep of Wall 2 @ VNA1 in wide-band. RMSE in linear. Figure 17: Thickness sweep of Wall 2 @ VNA2 in wide-band. RMSE in linear. Assuming the wall to be a solid single-slab structure (represented by solid lines on the lower x-axis), its material should exhibit the lowest RMSE error when compared to the ITU-R single-slab model with a tthickness of 9 cm, which is the thickness measured for Wall 2. However, as seen in @VNA1, this is clearly not the case for any material, as there are no traces with an absolute minimum at tgreater than 1.5 cm. This means that any construction material would have to be unreasonably thin to exhibit the same penetration losses as Wall 1. As for @VNA2, the results are not as clear, as lightweight and low-loss materials such as plasterboard or wood with thicknesses of t= 5.2 cm and t= 6 cm, respectively, already exhibit similar losses to those of the MUT. These results still deviate greatly from the ideal thickness of t= 9 cm and are not supported by the low-frequency band, suggesting that the internal structure of the wall more closely resembles a hollow wall model. If the wall is assumed with an air gap (dashed lines, upper x-axis), it should be made of the material that provides the lowest RMSE error for both frequency bands, for a model with an air gap where the slabs’ thickness (s) is around 1-2 cm. In this case, the material expected to compose the wall, according to visual inspection, should be a lightweight material such as wood or plasterboard, slabs of which typically do not exceed 2 cm in thickness. Looking at @VNA1, the wooden wall model shows an RMSE absolute minimum at s= 1.2 cm, while the plasterboard and, with more error, chipboard models have considerable minima at s= 1.1 and s= 1 cm, respectively. Other materials such as concrete would need to be unrealistically thin to achieve the same losses. Looking at @VNA2, the results are more diverse, although common points can be found with the low frequency band plots. The only material that shows minima in the 1-2cm range of sis chipboard, with 1.35 cm, but lightweight materials such as plasterboard also have local minima not far off, at 1.85 cm. In any case, taking into account both bands, it can be inferred that light materials give sensible thicknesses and low errors. Therefore, Wall 2 can be characterized as a hollow wall of light materials such as wood,chipboard or plasterboard. 40 5 Budget This section provides an overview of the estimated budget required to execute the project. The amortizations account for the initial and residual value of the equipment utilized, which is provided by the Department of Electronics and Nanoengineering from Aalto University. It has been assumed that they have been used throughout the entire project duration. As they are available for the entire department, distributing the amortized time among users taking into account their individual usage intensity (which can be particularly critical for electronic elements like the VNA or the computer) is unfeasible. AMORTIZATIONS Element Initial value (e) Residual value (%) Residual value (e) Amort. years Yearly amort. (e) 5-month amort. (e) MATLAB license 2,000.00 0 0.00 1 2,000.00 833.33 PC 1,000.00 15 150.00 5 170.00 70.83 Trolley 200.00 25 50.00 25 6.00 2.50 Antenna ETS-Lindgren 400.00 20 80.00 20 16.00 6.67 Antenna Quinstar 500.00 20 100.00 20 20.00 8.33 VNA 12,000.00 15 1,800.00 15 680.00 283.33 Battery 75.00 5 3.75 5 14.25 5.94 Power supply 150.00 10 15.00 15 9.00 3.75 O/E & E/O converters 500.00 10 50.00 12 37.50 15.63 Fiber optic cable 2,000.00 10 200.00 8 225.00 93.75 Coaxial cables set 80.00 20 16.00 10 6.40 2.67 TOTAL 3,184.15 1,326.73 Table 3: Amortizations table. For the purpose of this budget study, a realistic working environment is assumed, in which the author’s economic conditions align with those of a junior engineer of equivalent expertise. The author’s average hourly salary in the hosting country (Finland) would be 13 e/hour. The calculation takes into account the number of hours corresponding to the workload of 18 credits for this project. Additionally, the worker’s social security contributions are factored in. Amortizations, based on Table 3, are also included, considering the number of units being amortized. As per the direct costing approach, costs such as office supplies and transportation (for the measurement campaign) are accordingly considered. In this way, the total cost of the project is approximately 9,100 e. DIRECT COSTING Element People - units Cost/unit (e) Cost (e) Junior engineer 1 5,850.00 5,850.00 Junior engineer SS 1 1,755.00 1,755.00 MATLAB license 1 833.33 833.33 PC 1 70.83 70.83 Trolleys 2 2.50 5.00 Antennas ETS-Lindgren 2 6.67 13.33 Antennas Quinstar 2 8.33 16.67 VNA 1 283.33 283.33 Batteries 2 5.94 11.88 Power supply 1 3.75 3.75 O/E & E/O converters 2 15.63 31.25 Fiber optic cable 1 93.75 93.75 Coaxial cables set 1 2.67 2.67 Office and supplies 20 Transportation 100.00 TOTAL 9,090.79 Table 4: Costing table. 41 Appendices A State-of-the-art appendix A.1 Matrix method for calculating transmission coefficients in a multi-layer slab This annex describes an alternative approach for computing transmission coefficients in multi-layer slabs when a TE-polarized plane wave is directed at a planar interface separating two homogeneous and isotropic media with distinct electric properties. The method is based on ITU-R Recommendations [9] and assumes that the media are sufficiently separated from other interfaces to have minimal impact. The results are the same as the ones given by the ”Iterative method”. Additionally, the MUT is assumed to be in air, with an electric permittivity of 1. In order to calculate the transmission coefficient, T, for a building material consisting of Nparallel dielectric slabs, this alternative approach is based on the ABCD matrix formulation: A B C D=A1B1 C1D1.A2B2 C2D2... AiBi CiDi... ANBN CNDN(18) where Ai=cos(βidi) (19a) Bi=jZisin(βidi) (19b) Ci=j1 Zi sin(βidi) (19c) Di=Ai(19d) and βi=kicosθi(20a) sinθi=sinθ0 √εri (20b) k0=2π λ(20c) km=k0√εri(20d) Zi=120π √εricosθi (20e) Note that λis the free-space wavelength, k0is the free-space wave number, εriis the complex relative permittivity in the i’th layer, kiis the wave number in the i’th layer, βiis the propagation constant in the direction perpendicular to the slab plane in the i’th layer and diis the i’th layer width. Also, ε0=εN+1 = 1 θ0=θN+1 = 0 Z0=ZN+1 (21) From the A,B,Cand Dcoefficients, the transmission coefficient can be calculated as T=2 2A+B/Z0+CZ0 2(22) 2A typographical error has been spotted in the Recommendation ITU-R P.2040-2 (09/2021). In that document, the transmission coefficient formula has a Tinstead of a 2 in the Equation 22 numerator. This error has been duly reported to its author. 48 B Methodology appendix Antennas used for the 1-10 GHz measurements (VNA1) and the 10-18 GHz measurements (VNA2): ETS Lindgren and Quinstar Technology antennas, respectively. Figure 18: ETS Lindgren 3164-08 antennas. Figure 19: Quinstar Technology 15 GHz antennas. B.1 Laboratory measurement campaign Setup for laboratory measurements: Figure 20: VNA1 configuration setup for laboratory measurements. Figure 21: VNA2 configuration setup for laboratory measurements. Wooden slabs used as samples in the laboratory measurement campaign: Figure 22: Wood sample number 1. Figure 23: Wood sample number 2. 49 Samples measured under the VNA1 configuration: Measurements carried out at 4 GHz in the laboratory Material Dimensions Dist. 1 Dist. 2 VNA 1 (.s2p) 4 GHz meas. sampl1 d1 vna12 cm 5.51 cm ref1 d1 vna1 sampl1 d2 vna1 1 Plywood Height = 60 cm Width = 60 cm Thick. = 1.51 cm 0 cm 1.51 cm ref1 d2 vna1 sampl2 d1 vna12 cm 5.95 cm ref2 d1 vna1 sampl2 d2 vna1 2 Wood Height = 49.5 cm Width = 59 cm Thick. = 1.92 cm 0 cm 2 cm ref2 d2 vna1 sampl3 d1 vna12 cm 7.43 cm ref3 d1 vna1 sampl3 d2 vna1 3Wood + plywood Sample 1 and 2 together 0 cm 3.43 cm ref3 d2 vna1 Table 5: Table collecting all laboratory VNA1 measurements. Samples measured under the VNA2 configuration: Measurements carried out at 14 GHz in the laboratory Material Dimensions Dist 1. Dist 2. VNA 2 (.s2p) 14 GHz meas. sampl1 d1 vna22 cm 5.51 cm ref1 d1 vna2 sampl1 d2 vna2 1 Plywood Height = 60 cm Width = 60 cm Thick. = 1.51 cm 0 cm 1.51 cm ref1 d2 vna2 sampl2 d1 vna22 cm 5.92 cm ref2 d1 vna2 sampl2 d2 vna2 2 Wood Height = 49.5 cm Width = 59 cm Thick. = 1.92 cm 0 cm 1.92 cm ref2 d2 vna2 sampl3 d1 vna22 cm 7.43 cm ref3 d1 vna2 sampl3 d2 vna2 3Wood + plywood Sample 1 and 2 together 0 cm 3.43 cm ref3 d2 vna2 sampl4 d1 vna22 cm 9.13 cm ref4 d1 vna2 sampl4 d2 vna2 4 Plywood + gap (1.7 cm) + wood Sample 1 and 2 together with a 1.7 cm air gap in-between 0 cm 5.13 cm ref4 d2 vna2 sampl5 d1 vna22 cm 7 cm ref5 d1 vna2 sampl5 d2 vna2 5EPS + black paint Height = 50 cm Width = 50 cm Thick. = 3 cm 0 cm 3 cm ref5 d2 vna2 sampl6 d1 vna22 cm 4.15 cm ref6 d1 vna2 sampl6 d2 vna2 6Metallic plate Height = 50 cm Width = 95 cm Thick. = 0.15 cm 0 cm 0.15 cm ref6 d2 vna2 Table 6: Table collecting all laboratory VNA2 measurements. 50 B.2 Site measurement campaign Setup for site measurements: Figure 24: TX (upper left) and RX (upper right) setups for VNA1 configuration Wall 1 measurements. TX (lower left) and RX (lower right) setups for VNA2 configuration Wall 2 measurements. Analyzed walls in the Nokia Espoo Campus measurement campaign. Figure 25: Analyzed wall number 1. Figure 26: Analyzed wall number 2. 51 C Results and discussion appendix C.1 ITU-R loss models Here, the S21 results measured in the laboratory for the three samples, at distance 1 and for both VNA configurations, are compared with the curves simulated using the ITU-R transmission model for a single-slab of the same thickness for different materials. Each of these penetration loss lines is compared with the actual measured data, and the corresponding RMSE is presented in the legend. Figure 27: Comparison of measured S21 for Sample 1 in @ VNA1 (left) and @ VNA2 (right) at distance 1 with ITU-R models for different materials. Figure 28: Comparison of measured S21 for Sample 2 in @ VNA1 (left) and @ VNA2 (right) at distance 1 with ITU-R models for different materials. Figure 29: Comparison of measured S21 for Sample 3 in @ VNA1 (left) and @ VNA2 (right) at distance 1 with ITU-R models for different materials. 52 C.2 Laboratory measurement campaign Figure 30: Thickness sweep of laboratory Sample 1 in @ VNA1 (left) and @ VNA2 (right) at distance 1 in narrow-band. Figure 31: Thickness sweep of laboratory Sample 2 in @ VNA1 (left) and @ VNA2 (right) at distance 1 in narrow-band. Figure 32: Thickness sweep of laboratory Sample 3 in @ VNA1 (left) and @ VNA2 (right) at distance 1 in narrow-band. 53 C.3 Site measurement campaign C.3.1 Averaging of position thickness sweeps Figure 33: Averaging of thickness sweep for all Wall 1 positions, assuming a single slab of concrete w/o air gap @ VNA1 in wide-band. Figure 34: Averaging of thickness sweep for all Wall 2 positions, assuming a wooden structure with air gap @ VNA1 in wide-band. C.3.2 Wall 1 Figure 35: Thickness sweep of Wall 1 @ VNA1 in narrow-band. Figure 36: Thickness sweep of Wall 1 @ VNA2 in narrow-band. C.3.3 Wall 2 Figure 37: Thickness sweep of Wall 2 @ VNA1 in narrow-band. Figure 38: Thickness sweep of Wall 2 @ VNA2 in narrow-band. 54