Absorption cross section of building materials at mm wavelength in a reverberation chamber

The reverberation chamber (RC) method is used to estimate the average absorption cross section of building materials at mm wave frequencies. Analysed samples include concrete, travertine and bricks of different types. The investigation is carried out in the frequency range between 50 GHz and 68 GHz, which is of interest in the next generation of mobile telecommunication system. A cylindrical cavity is transformed into a RC through the use of a mechanical model stirrer. The chamber field is statistically homogeneous and depolarized; therefore it can be used to probe the average response of the sample under test. In particular, through a differential measure of the average quality factor (average insertion loss) it is possible estimate the fraction of power absorbed by the sample under test. Several cube-shape samples have been characterized and compared. Obtained results show that analysed samples have remarkably different levels of the electromagnetic wave absorption, depending on both material density and chemical composition. The absorption of pure water is used as a baseline to determine the dynamic range of the measurement.


Introduction
The next generation of mobile networks will make use of millimeter frequency bands. At those frequencies, the electro magnetic (EM) wave propagation mechanisms must be charac terized and understood. This is very important in the planning of city coverage of wireless signals. In the urban environment and inside buildings, the absorption of EM energy caused by building materials needs to be properly characterized. The operation frequencies of the 5G networks have not yet been defined. However, referring to preliminary studies on mm wave propagation [1,2], a systematic analysis of materials in the broad range from 50 GHz to 68 GHz is believed to be valuable.
Several experimental setups are currently employed to characterize materials at mm wavelength. The main methods of measurement are based on waveguide, free space or res onant cavity systems, in a variety of configurations [3][4][5][6][7][8]. Nevertheless, such methods are not the most appropriate for a reliable characterization of building materials, which typically The reverberation chamber (RC) method is used to estimate the average absorption cross section of building materials at mm wave frequencies. Analysed samples include concrete, travertine and bricks of different types. The investigation is carried out in the frequency range between 50 GHz and 68 GHz, which is of interest in the next generation of mobile telecommunication system. A cylindrical cavity is transformed into a RC through the use of a mechanical model stirrer. The chamber field is statistically homogeneous and depolarized; therefore it can be used to probe the average response of the sample under test. In particular, through a differential measure of the average quality factor (average insertion loss) it is possible estimate the fraction of power absorbed by the sample under test. Several cubeshape samples have been characterized and compared. Obtained results show that analysed samples have remarkably different levels of the electromagnetic wave absorption, depending on both material density and chemical composition. The absorption of pure water is used as a baseline to determine the dynamic range of the measurement. present irregular shape, random porosity and lack of homo geneity. In fact, waveguide methods have sample dimension strict constraints that may cause EM leakage problems, while free space measurements often suffer with unwanted edge effects; on the other hand, resonant cavity systems investigate materials behavior at isolate frequencies or in restricted range mainly. Moreover, the proposed task requires an analysis of realistic EM propagation environments. Although permittivity and permeability are intrinsic properties of the materials, the absorption capability of relatively large objects depends also on shape, volume, material type, and on the incoming wave polarization and direction of incidence. In the real environ ment the excitation of any structure exhibits random char acteristics: hence, evaluating the absorption capability for a particular condition could be meaningless. Therefore, a full characterization of EM absorption properties requires the measurement repetition using several angles of incidence and polarization. In particular, indoor propagation channels are characterized by multipath. Although most related research has dealt with path loss and temporal characteristics (such as time of arrival and delay spread), less attention has been paid to the angle of arrival of multipath, which is crucial for predicting the performance of adaptive array systems. For these reasons, a reverberation chamber (RC) setup [9][10][11][12] is believed to be the most suitable system to perform realistic testing of building materials. Such instrumentation, in fact, allows one to excite the material under test in a completely random way over a relatively broad frequency range, thus overcoming the limitation of other measurement methods based on transmission line models.
In this work, we perform an experimental evaluation of the average absorption cross section (ACS) of several building materials in a RC. A wellestablished RC method [13][14][15][16] is used to investigate the absorption of material samples made of travertine, concrete, Roman brick and refractory brick. The average absorption is of fundamental importance to predict the statistical field behavior, often showing field/power fluc tuations and fading in indoor and outdoor electro magnetic environments (EME). It is a crucial input parameter for example in the statistical analysis of an RC [17,18], and in the random coupling model (RCM) [19]. The paper is organ ized as follows: in section 2 the materials analyzed and the methods employed are reported, in section 3 the experimental results are presented and discussed, section 4 is then devoted to conclusions and highlights of research activity future developments.

Materials under test
The materials under test are of common use in the con struction of buildings. In particular, the following samples have been considered: a common brick made with ancient roman techniques (Roman Brick), which has been sub jected to sandblasting (then called S); a Roman Brick not subjected to sandblasting (then called NS), which presents a different aspect, less smooth than the former; two kind of refractory bricks, called as Refractory Red (more smooth) and Refractory White (less smooth); a sample of ultralight concrete, called as White Concrete; a Travertine sample, very commonly used in both ancient and modern architecture. The sample geometry is cubic with sides of about 5 cm. An additional absorption measurement has been performed on a cylindrical polystyrene sample holder, with approximately the same volume of the cubic samples, filled up with 125 ml of demineralized water. Table 1 reports the density of the materials under test. Material density, as sample geometry, is believed to have a significant impact on the average quality factor (Q) [20,21], and therefore on the average ACS. Also the chemical composition of the materials is relevant in the absorption of EM waves, hence an appropriate analysis of the chemical characteristics of the materials under test has been performed. Specifically, White concrete is porous and pres ents no aggregate larger than Quartz sand, which is typically used as binding agent (Aluminum powder is also inserted at a rate of 0.05%-0.08% by volume); it has lightweight and great resistance to fire. Roman Brick is a ceramic material made with purified clay, which is then pressed and cured in ovens. Both the Roman Bricks specimens present the same chemical composition, whereas the different density values are the result of different pressing manufacturing and curing. The refractory bricks are made of clay, calcium, with pres ence of alumina (Al 2 O 3 ) and silica (SiO 2 ), and present a great resistance to fire; as for the Roman Bricks, the samples present same chemical composition and different density due to different manufacturing process. Finally, Travertine, that is a sedimentary rock, is made of CaCO 3 with the pres ence of various oxides depending on the zone where it was formed.

Average ACS
The RC used to perform the materials characterization has a volume of 0.08 m 3 and consists of a cylindrical shape. Figures 1 and 2 show the experimental setup. The resonance frequency of the fundamental mode is f 0 = 833.7 MHz, giving a lowest usable frequency (LUF) of about 5f 0 = 4168 MHz. A vertical stirrer is placed inside the chamber. The stirrer has Zfolded shape with copper paddles: the bottom part has a height of 17 cm and a width of 13 cm, while the upper part has a height of 17 cm and a width of 6 cm. The stirrer is moved in a stepped (tuned) mode [22] by a stepper motor, which assures a 0.5° resolution. The transmitting and receiving antennas are two (AInfo) working between 50 GHz and 70 GHz. A vector network analyzer (VNA-Anritsu Model MS4647B) is used to measure the transmission coefficient between the two antennas, while they operate inside the chamber, both in presence and in absence of the sample. As VNA settings, the measurement registration has step of 20 MHz, a 1000 Hz IF bandwidth has been selected for noise reduction and a 5 s sweep time has been set for each range. By this way, a sufficient frequency resolution (1.25 MHz) can be reached to allow for a good electronic stirring/moving fre quency averaging [23]. The measurements are first performed at 180 uncorrelated stirrer positions (2° steps) and then used to obtain the empty RC average quality factor. Then, the absorbing material sample is placed over a polystyrene foam support inside the RC, and the mechanical stirring procedure repeated over 180 stirring positions to obtain the Q of the loaded RC. The RC is an overmoded cavity where wave mixing occurs and is accompanied by strong field fluctuations driven by the movement of the mechanical stirrer. Therefore, besides Q, also the ACS has to be averaged over the 180 stirrer positions. In particular, the average ACS is defined as [24] = P S ACS s i (1) where P s is the power dissipated by the sample and S i = E T 2 /η 0 is the incident scalar power density, whereas the bracket symbol • means either an ensemble average over the stirrer rotation and frequency stirring, η 0 is the free space wave impedance, and E T is the total field magnitude. In (1), idealized field unifor mity, anisotropy, and uncorrelation are assumed: consequently, the statistical distribution of the transmission coefficient S 21 approaches the asymptotic distribution χ 2 (chidistribution with 2° of freedom) [25][26][27][28]. The spectral characteristics of a mode stirred cavity are sensible to energy perturbations, e.g. a lowloss dielectric inclusion, because of the strong modal overlapping occurring in the overmoded regime. The total losses inside an RC are due to different loss mechanisms through walls, antennas and material samples. Indicated as Q u the quality factor mea sured without the material sample, and as Q l the one after the sample allocation inside the RC, the contribution Q s due to the material dissipation only can be easily evaluated by the differ ential measurement [13] = In terms of stored energy and dissipated power: where ω is the angular frequency of excitation, W the energy stored by the chamber, V the chamber volume, and c the speed of light in vacuum. By substituting (1) into (3) and unfolding, yields where λ is the wavelength at the operation frequency of the RC. The indirect ACS estimation can be achieved by S 21 (with and without the material sample) through the wellknown relation where S 21 2 is the average insertion loss-i.e. the rate P r / P t , where P r is the power captured by the receiving antenna R x with total radiation efficiency η Rx = − S 1 22 2 and P t is the power injected by the transmitting antenna T x with total radiation efficiency η Tx = − S 1 11 2 -and S 21 is the transmission scattering parameter between VNA port 1, connected to T x , and port 2, connected to R x . As shown in (5), the calibration has been performed by taking into account all the impedance mismatch effects due to cable, antennas, con nectors, and proximity. In particular, the reflection coefficient of the antennas has been taken into account in Q and ACS computation [11].

Results and discussion
Before testing the building samples, we made sure that the 180 stirrer positions are statistically uncorrelated-meaning that they are able to effectively change the cavity boundary  conditions, thus creating new sets of modes to foster wave field mixing. In a conventional RC operated at microwave regimes (~up to 10 GHz), a 1° angular step size is typically used in ACS experiments. However, there is a limited sci entific literature on the operation of an RC at mmWave fre quencies [29,30]. We calculate the correlation coefficient between stir traces in a range of angles between 0.5 and 2°. In particular, n a n a bn b n a n a n b n b where N is the number of field samples used to calculate the coefficient between position a and b.
Calculating the correlation between stir traces is impor tant in RC to assess the field mixing and the effectiveness of the stirrer. The correlation is calculated between original and shifted stir traces. In figure 3 the time lag (TL) is plotted in frequency for three different stirrer angular steps. Such a factor represents the shift between stir traces, i.e. fields sampled collected at a specific point for a specific frequency are shifted of TL data samples: 'a' and 'b' in (6) are the data sets which the correlation is calculated from, so they are statistical variables [9,31]. In this case 'a' and 'b' are the data sets given by the chosen TL, TL1 or TL2, i.e. for the generic lag k, they represent data set with the latest Qk observations versus the first Qk observations, considering Q the total amount of data. For instance, considering 180 stirring positions, if k = 1 the first Q1 values are correlated to the latest Q1 ones, i.e. Q 1 ... Q 179 versus Q 2 ... Q 180 . For k = 2, the first Q2 values are correlated to the latest Q2, i.e. Q 1 ... Q 178 versus Q 3 .... Q 180 , and so on. In (6) the summa tion limit N is so given by Qk.
If the correlation values are close to 1 then the angular step size could be relaxed without loss of chamber sensitivity. On the contrary, if the correlation values are close to zero then a small step size is required to increase the RC sensitivity at these frequencies. Results in figure 3 show that the correla tion coefficient becomes lower than the empirical threshold 1/e when the angular step is between 1° and 2°, so a stirrer step of 2° (180 positions) turns out to be a safe choice. In our measurements we observed an oscillating behavior of the cor relation function in frequency that is much evident with the increase of angular positions. This behavior is currently under investigation.
In figures 4 and 5 the results obtained for the Q factor and ACS are plotted. The thick lines are obtained as an ensemble average of the thin (shaded) lines: this is a usual procedure to mitigate the large spectral variability of RC measurements [10]. Figure 4 shows the average quality factors of the RC both when loaded and unloaded with material samples, as well as with and without the polystyrene sample holder inside the RC working volume. Also, the quality factor in presence of a sample with water is shown. The dynamic range of the measurement is set between unloaded RC and loaded RC with water. In the presence of water, the Q values are lower than in presence of the test samples (around 3200), the empty RC has much higher Q values (around 17 000): this is a clear indica tion that the measurement setup offers enough dynamic range to properly quantify the ACS of the building material samples under test.
The Q of the investigated material samples is highlighted in figure 4(b) as compared against water, which shows a con sistent trend over the investigated frequency range. In par ticular, the Q values increase at frequencies between 50 GHz and 53 GHz, and then are almost flat until 63 GHz. At higher frequencies, the quality factor decreases until 66.5 GHz and increases again until 68 GHz. All the Q values fall within the range from 4000 to 5750. Figure 5 shows the ACS values for all the investigated material samples. Interestingly, the samples show an almost flat ACS between 53 and 63 GHz, as anticipated by the Q measurements. The large scale frequency behavior of the ACS of cubic samples has a Uprofile: whether this effect can be ascribed to the sample shape-the cylindrical sample with water has a different profile-or to the specific characteris tics of the RC facility [32,33], needs to be further investi gated and clarified. Fine scale frequency fluctuations encode the mat erial behavior, and their dependence on the chemical composition is also an interesting issue to be investigated. The material density values in table 1 have a clear correlation with the quality factor and ACS measurements: the higher the density, the higher the Q and the lower the ACS, since more compact materials increase the material reflectivity, while less dense materials have greater absorption. Such qualitative explanation is confirmed both for Refractory Red and Refractory White, as materials with the same chemical composition present different values because of their den sity; the same findings are obtained for Roman Brick S and NS. Travertino presents the lowest values of ACS and has the highest density. The sample made of White Concrete, instead, presents a special behavior: it has the lower density, thus a very low Q factor should be expected. Conversely, the Q values measured suggest that the chemical components play a more important role than the density do for such material at mmWave: the presence of aluminum powder, in fact, can improve the reflectiveness of the material and delimit the effect of the low density. Moreover, considering the chemical composition, Refractory bricks, which includes alumina and silica, presents ACS values higher than or equal to those of Roman Bricks: such a result is due to the presence of metallic  components, which improve the reflectiveness. Finally, the surface roughness also plays an important role: from the plots in figure 4 it can be appreciated that the Refractory White, that is less smooth than the Roman Brick S, presents quite the same properties of the Roman Brick S, even if it has higher density and metallic inclusions in its chemical composition.

Conclusions
RC measurements of an average ACS have been performed at mm Wave regime for selected building materials. Both the quality factor and the absorption crosssection of cubic mat erial samples have been obtained through the RC method. The observed frequency behavior is almost flat over a wide fre quency band from 53 to 63 GHz. Further investigations are necessary to relate large and finescale frequency fluctua tions to both the sample shape and the chemical composition of materials. Ongoing research is devoted to the investigation of the effects of the surface roughness and shape, as well as of the RC test fixture, on the ACS, in order to better characterize arbitrary materials at very high frequencies.