Microwave Propagation Modeling and Measurement of ... - IEEE Xplore

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 63, NO. 1, JANUARY 2015

Microwave Propagation Modeling and Measurement of Scattering and Absorption Inside a Canopy Using the FDTD Technique Rafael F. S. Caldeirinha, Member, IEEE, and Miqdad O. Al-Nuaimi

Abstract—This paper proposes a novel method aimed at modeling microwave scattering and absorption inside a canopy, arising from the interaction with the individual components of the vegetation specimen, starting from primary models for leaves, trunk and branches. The method is based on the finite-difference time-domain (FDTD) technique to predict the 3-dimensional re-radiation fields of the entire tree, by combining the effects of the single elements forming the tree. Appropriate measurements performed in an anechoic chamber environment at microwave frequencies, i.e. 20 GHz, and in the forward scattering region, provided both model validation and a deeper insight into the problem. The model is shown to be capable of predicting the near-field radiated signal and the radar cross section (RCS). The predictions yielded good agreement with measurements and provides a good basis for a planning model capable of accounting for single trees in the radio path. Index Terms—Absorbing media, dielectric measurements, finite difference methods, microwave radio propagation, scattering, vegetation.

I. INTRODUCTION

P

ROPAGATION effects on terrestrial communications systems in the microwave and millimeter-wave frequency bands have been the subject of considerable study in the last few years [1]. The modeling of absorption and scatter due to the presence of vegetation represents a significant problem in macro- and micro-cellular geometries, in which errors yielded by prediction models amount to several decibels [2], [3]. Most of the vegetation models found in the literature have been formulated for military purposes for the development of new numerical communication techniques and radar systems. Despite the lack of models capable of ascertaining the propagation effects of single trees, a single-tree scattering model is presented in [4], in which the canopy is modeled as a cylindrical volume containing randomly distributed and oriented branches

Manuscript received June 03, 2014; revised September 22, 2014; accepted October 18, 2014. Date of publication October 28, 2014; date of current version December 31, 2014. This work was supported by the University of South Wales (formerly the University of Glamorgan), Pontypridd, U.K. R. F. S. Caldeirinha is with the Instituto de Telecomunicaçóes, Leiria, Portugal, the Polytechnic Institute of Leiria, School of Technology and Management, Leiria 2411–901, Portugal and also with the University of South Wales, School of Engineering, CF 37 1DL, Pontypridd, U.K. (e-mail: rafael. [email protected]). M. O. Al-Nuaimi is with University of South Wales, School of Engineering, CF 37 1DL, Pontypridd, U.K. Digital Object Identifier 10.1109/TAP.2014.2365571

and leaves. On the other hand, the statistical models available in the literature do not account for the interaction of the incident radio wave with the individual constituent elements of the tree [5]. This paper addresses this interaction and seeks to characterize the influence of the tree elements on the various propagation modes caused by it.

II. METHOD OUTLINE In this paper, a novel method aimed at studying the propagation modes arising from the interaction between radiowaves and single trees at 20 GHz, particularly in the forward scattering region, is presented. The method using the finite-difference time-domain (FDTD) technique [6], [7], is shown to provide a more detailed insight into the propagation process. A. Complexity of Vegetation Modeling Accurate modeling of the propagation of radiowaves at microwave and millimeter-wave frequencies through tree foliage is generally difficult. This is due to the complexity of the tree electromagnetic geometry and its constituent elements, e.g. trunk, branches, and leaves, where dimensions can be comparable to the radio signal wavelength over a wide range of frequencies. Modeling of the propagation modes arising from vegetation media depends primarily on the physical parameters specific to the tree, such as size, shape, and orientation, and also on the electromagnetic properties of the tree materials, which, in turn, are influenced by the moisture content of leaves, branches, and trunk. Furthermore, parameters of the radio link associated with the operational frequency, directivity of transmit and receive antennas, and their heights and polarization, add further complexity to the characterization of scattering modes from and in the vicinity of the tree. Despite its complex nature, the canopy volume has been treated in the literature [5], [8], as a homogeneous mixture of discrete, randomly distributed and oriented dielectric disks and cylinders representing leaves and branches, respectively. Statistical models are usually used to compute the path loss due to trees, based on the physical and statistical properties of the trees, e.g., the probability density functions of leaves and branches, as well as their electrical characteristics and dimensions. In particular, Jong et al. [9] have proposed a theoretical model for azimuthally bistatic scattering from deciduous trees, as shown in Fig. 1. An interesting particularity in this model is that of the , which treats the

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CALDEIRINHA AND AL-NUAIMI: MICROWAVE PROPAGATION MODELING

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Fig. 1. Bistatic scattering model geometry showing the direction of the incident field and scatter from the tree canopy.

bistatic scattering (radar) cross sections of leaves and branches separately, as follows:

(1) and are the number densities and In the model, the bistatic scattering cross sections of branches and leaves, respectively, and are the effective propagation constants in the canopy for the direction and , whose derivation based on scattering amplitude tensor elements of branches and leaves is extensively detailed in [10]. and are the path lengths to and from the volume defined by through the canopy. Research aimed at single-tree characterization and modeling attempts to build such models starting from those applicable to single components, i.e., leaves and branches [5]–[8]. However, analytical solutions of such complex electromagnetic problems are difficult to obtain. This paper considers models for single leaves and trees, based on the radar cross section (RCS), arising from their interaction with an incident plane wave. Predicted results of the RCS for a ficus plant are compared with measurement results. B. Numerical Implementation The proposed method provides a means of accurately computing electromagnetic scattering by arbitrarily shaped relatively complex metal or dielectric objects excited by an external plane wave. The method analyzes the entire geometry provided as input and computes a solution to the problem based on a full wave analysis. The FDTD method is a direct solution of Maxwell’s time dependent Curl equations. It uses simple difference approximations to evaluate the space and time derivatives [6]. The required computer storage and running time is proportional to the electrical size of the volume being modeled and the grid resolution. A finite volume of space is subdivided into cells of size by by (representing unit cubic cells). The FDTD space consisting of , and cells should contain both the scattering object and a sufficient thick layer of

Fig. 2. Geometry of a FDTD space grid showing a general scatterer in freespace medium.

free space, i.e., at least 15 cells spacing, separating the boundaries of the object on all sides from boundaries of the cell space [6]. Fig. 2 illustrates a tree structure embedded in a FDTD space grid. Special numerical absorbers are used at the outer boundary of the grid in order to prevent unwanted reflection of the signals that reach this boundary. The method estimates the electric fields just outside the limits of the FDTD mesh and, subsequently, uses them in the FDTD equations inside the computational space. The major advantage of being an estimation method is that the size of the FDTD mesh is not increased by using it, although some storage is needed for saving fields at previous time steps. The latter is, however, minimal and can be negligible in a typical FDTD storage calculation. Values of permeability , permittivity , and conductivity assigned to each field component in each cell define the position and the electrical properties of the scatterer. The method was implemented by using a comprehensive FDTD algorithm, which runs on a powerful computer. Although discussion of the fundamentals of the FDTD method is beyond the scope of this paper, the full 3-dimensional computer algorithm can be found in [6]. The individual components of the vegetation specimen were modeled using simple geometrical shapes and characterized by their material complex permittivities, effective volume occupied, and the statistical distribution and orientation of branches, twigs and leaves, as described next. The scattering problem is analyzed in two stages by treating the complex near-field region and the far-field region separately. The latter is obtained by a near-to-far field transformation based on electromagnetic equivalents of the scattered near fields [6]. III. CASE STUDY I: A SIMPLE LEAF MODEL Leaves are an important feature of any vegetation canopy. In order to model the scattering of a tree effectively, it is essential to develop an efficient and effective technique for predicting the RCS of a single leaf to form an input to the model proposed in (1). Based on this, an individual leaf of the vegetation specimen was modeled in the FDTD space using a simple geometrical shape and characterized by its complex material permittivity and effective volume occupied. The tree under investi-

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gation was a Ficus Benjamina Daniel of the type used mostly indoors. Considering that at microwave frequencies, the leaf is electrically thin with lateral dimensions of a fraction of the wavelength , it would appear that the FDTD technique can handle this accurately. A. Evaluation of Complex Dielectric Properties of Single Leafs The dielectric constant, or relative permittivity , of a material is a measure of the manner in which that material interacts with an incident electromagnetic wave [15]. and are the medium and free-space permittivities, respectively. The permittivity is complex in nature, as shown in (2). The real part determines the propagation characteristics of a wave in a material, i.e., its velocity and wavelength and the imaginary part determines the absorption or loss of energy during the propagation through the material.

TABLE I LINEAR REGRESSION COEFFICIENTS FOR THE MEASURED COMPLEX RELATIVE PERMITTIVITY

process. He then proposed a relative macroscopic static permittivity model of a leaf given by (4), under the assumption that , , and and . (4) Having established in the leaf, the complex relative permittivity at microwave frequencies can be evaluated from (5) and (6), as given in [19]–[21], for both real and imaginary parts of the leaf relative permittivity.

(2)

(5)

In the past, models for the calculation of the dielectric permittivity of vegetation have treated them as a simple mixture of bulk vegetation material and water [15], [16], with the water divided up into bound and free components. These models are, however, unrealistic in their assumption that the water within the vegetation comprises discrete water particles dispersed in the bulk vegetation material, as concluded by Fung [16]. However, the model proposed by Fung considered that the water distribution within the vegetation was spatially continuous. Based on this model and other related published measurements found in the literature for the complex permittivity of leaves from different plants, Mätzler [17] has proposed a semi-empirical dielectric formula, which covers the 1–100 GHz frequency range. This model is thought to give a good estimate of the dielectric properties of fresh single leaves over the frequency range. The complex relative permittivity of the single leaf was first evaluated from appropriate measurements to determine the mass of water in the leaf. This parameter, together with the volume occupied by the leaf, provides the basis for the models proposed by Fung and Mätzler, as described in the next subsections.

(6)

B. Fung’s Volumetric Water Content Method The model developed by Fung provides an estimate for the static permittivity of a single leaf as a function of volumetric water content fraction . The model was proposed initially by Loor [18], [19], in the form of (3). A leaf was modeled to be a mixture of some solid material, characterized by permittivity , with water particles distributed continuously within the leaf, represented by permittivity , and with being the effective internal dielectric constant, which is an unknown. The model also considers the depolarization factors of the particles expressed by , as follows:

(3) Direct estimation of the permittivity of the mixtures, represented by , was investigated by Fung to be a rather difficult

In both equations, is the operational frequency, and is the relaxation time of the water, which depends very much on the temperature. At ambient temperature (i.e., 20 C) with the wavelength expressed in centimeters. C. Mätzler’s Dry-Matter Fraction Method The model developed by Mätzler showed that the complex dielectric (relative) permittivity of a fresh leaf was linearly related to the water content in the leaf. The model was applied to various fresh leaves of different types having a gravimetric water content with salinity of 1.0% and with a rather constant density of 0.95 g/cm . The resulting expression for the dielectric permittivity was based on the regression lines fitted to the measured dielectric data, which suggested to be a linear function of . Equations (7) and (8) show the linear regression functions, respectively, for the real and imaginary parts of the complex dielectric permittivity, where is the dry matter fraction of the leaf, which is directly related to by (9). The regression coefficients in the formulas are presented in Table I at 20 GHz. (7) (8) (9) D. Experimental Work The complex relative permittivity of the single leaf was first evaluated from appropriate measurements to determine the mass of water in the leaf. This parameter, together with the volume occupied by the leaf, provides the basis for both models. The measurements consisted of separating the actual water contents from the rest of the leaf constituent, as suggested by [17]. For a single leaf, the (gravimetric) water content fraction, , is usually measured on a wet weight basis given by (10), where and are, respectively, the total fresh (wet)


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TABLE II ESTIMATION OF COMPLEX RELATIVE PERMITTIVITY USING FUNG’S AND MÄTZLER’S METHODS AND ESTIMATION OF THE CONDUCTIVITY IN A SINGLE LEAF

to vary between 3 and 5. Based on this assumption, results were therefore obtained for both limits in the range using (13), leading to an estimation as to the average volume fraction of water in the leaf, i.e., . Thus, the value of can be calculated and, subsequently, the complex relative permittivity of the leaf at 20 GHz, using the model proposed by Fung, as shown in Table II. Fig. 3. Relation between leaf area and the amount of moisture in fresh ficus leaves.

and after drying (dried) weights of the leaf. Consequently, the weight of moisture in the leaf may be expressed by (10) (11) A total number of 19 fresh leaves were placed inside a specialized oven kept at a constant temperature of 100 C, and their weights monitored every 24 hours, until a constant weight value for each leaf was to be obtained. The leaves chosen for the measurements were of different sizes and, hence, volumes so that a direct relation between water content and area of the leaf could be evaluated. Prior to measurements, each leaf was scanned on millimeter paper so that an accurate estimate of its area could be determined. In addition, their thicknesses were measured using an extremely accurate digital micrometer to enable precise FDTD space modeling. Most leaves yielded an average thickness of 0.25 mm. Subsequently, leaves were weighted individually, using a high-precision scale of 10 mg, together with the tray on which each leaf was placed to go into the oven for drying. Fig. 3 shows the results from the measurement campaigns performed on the various leaves, which relates the mass of water in a single leaf with its effective area occupied. A piecewise linear curve fit to the measured data suggests a linear trend between leaf area and contents of water in the leaf. The water content fraction can be computed from the slope of this line. The dry-matter fraction was evaluated to be , which indicates that 74.1% of the leaf mass is water. The complex relative permittivity and subsequently, the conductivity, were evaluated at 20 GHz, respectively, to be and Sm . To find the relation between and , let be the density of the solid material and be the density of water. Then, (10) can be written in the form of [17] (12) in the formulation above is an unknown. Fung However, has solved the equation by using the ratio as a parameter

(13)

On the other hand, similar results for the complex relative permittivity of the leaf may be obtained using Mätzler’s approach. In this case, only the dry-matter fraction needs to be calculated using (9) (i.e., ), which is well within the specified range) and then to estimate the permittivities by solving (7)–(9). Results are presented in Table II. Significant discrepancies may be observed between the two methods in the prediction of the complex relative permittivity. Although the dry-matter method provides an error of 10%–15% in its predictions [17], the volumetric method provides the average dielectric properties, averaged over several leaves of different plants. For this reason and because the first method has used best fit to measured data obtained at frequencies close to the ones used in the study, it would appear justifiable to use Mätzler’s estimates in the FDTD computation. In addition, the conductivity of the leaf, , may be evaluated from the complex relative permittivity by rearranging (2) to include the conductivity of the leaf and angular frequency , as shown in (14). Results are presented in Table II based on Mätzler’s results. (14)

E. Problem Space and Leaf Geometry The computational space for the FDTD simulations was calculated based on the physical dimensions of the leaf under investigation. The leaf was 10.5 cm long and 4.5 cm wide, with a thickness of 0.25 mm. At least a cell size of 0.25 mm (i.e., , assuming a highest frequency of 20 GHz) is required to model the thickness of the leaf. The FDTD program can accommodate a maximum of 7 million cells, thus allowing the problem space to be split into two grids to obtain the spatial resolution required, as shown in Fig. 4. These can be defined as the main grid containing all the problem space with a cell size of , and a subgrid circumscribing only the leaf. The latter must have a spatial resolution to accommodate

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Fig. 4. Problem space of the leaf model in the agation out of the paper.

plane, with direction of prop-

TABLE III LINEAR REGRESSION COEFFICIENTS FOR THE MEASURED COMPLEX RELATIVE PERMITTIVITY

Fig. 5. Normalized near-electric-field distribution cuts in the plane at of the metallic leaf (top) and dielectric leaf (bottom) illuminated by a 0 and 90 ) for (a) , (b) , normal incidence plane wave ( , and (d) . (c)

the thickness of the leaf. Except for the cells used in the geometry of the leaf, all other cells were of free space. The problem space can therefore be expressed in terms of number of cells for both grids, as shown in Table III. A total number of 5 975 300 cells was used to model the leaf, which is within the physical limitations of the computer. F. Near Electric Field Distribution Results at 20 GHz Simulation results obtained from a single-leaf model with different dielectric properties in the near-regions of the object are presented. The method was applied to a dielectric leaf, with dielectric properties as detailed in Table II and compared with results obtained from an idealized leaf made of a high conductivity material—the “metallic leaf.” Simulations were performed for various angles of the incident -polarized plane wave to the surface of the leaf. These are outlined as follows: i) normal incidence with the plane wave traveling in the positive -direction defined by 0 and 90 ; ii) parallel incidence with the plane wave traveling in the positive -direction defined by 0 and 180 ; and oblique incidence with the plane wave traveling in the plane defined by 0 and 240 . and are the angles subtended from - to - or -axis and the angle subtended from - to -axis, respectively. Figs. 5 and 6 present near-field results for the normalized electric-field distribution (in V/m) transverse sections (cuts) of the dielectric leaf, which are compared with results obtained from an idealized leaf. These are expressed in terms of total electric-field distribution and its components in the - - and -directions, respectively, , , and , for normal incident plane wave. The electric field, or simply

Fig. 6. Normalized near-electric-field distribution cuts in the plane at of the metallic leaf (top) and dielectric leaf (bottom) illuminated by a 0 and 90 ) for (a) , (b) , normal incidence plane wave ( , and (d) . (c)

E-field, cuts are presented in the and planes, which are respectively, the plane normal to the surface of the leaf and the plane in which the leaf is located. The plane wave incident


on the leaf is subsequently scattered in all directions. A color scale was used to display the intensity of the fields in the computational space. The cuts in the plane are transverse cuts of the leaf plane at . Fig. 5 shows the cross-sectional image of the leaf, which in the graphs are represented by a vertical thin line. The cuts in the plane were rotated counterclockwise by 90 for display convenience. This is the case of Fig. 6, where it can be observed that the plane of the leaf is, in fact, the plane. The direction of propagation of the incident angle is out of the paper for the case of normal incidence. 1) Near-Field Discussion: The distribution of the E-field intensity in and around the leaf has been observed to be highly dependent on the angle of the incident plane wave, in addition to the properties of material making up the leaf. Referring to Fig. 5, one can see the behavior of the E-field intensity in the plane transverse to the leaf surface for a normal incidence. High E-field intensity has been computed in the shadow region of the dielectric leaf [see Fig. 5(d) (bottom)], indicating that a significant amount of energy penetrates the leaf, which is consistent with the presence of dielectric material. This results in a much reduced E-field intensity being scattered backwards, contrary to the case of the metallic leaf. Of special note in Fig. 6 is the E-field intensity inside and on the faces of the dielectric leaf, which suggests high energy concentration and consequently high absorption due to its relatively high content of water. This can be clearly observed in the -direction, with E-field intensity as high as 30–50 dB above the intensity observed in the case of the metallic leaf. The black color observed in the area occupied by the metallic leaf [see Fig. 6 (top)] indicates E-field intensity well below 40 dB relative to the amplitude of the incident plane wave. This behavior clearly suggests no signal penetrating the metallic leaf, as expected due to its high conductivity value. Significant signs of diffraction and depolarization were observed specifically on the contours of the leaf (Fig. 6), thus giving rise to relatively high intensity values of the E-fields in the - and -directions. In the -direction, the depolarization effect was enhanced by the error produced by the staircasing effect of the geometry, as shown in Fig. 6. From the computed near-field results of a leaf model, it can be concluded that high energy is concentrated inside the dielectric leaf when this is illuminated by a plane wave. Such behavior has shown to be dependent of the angle of the incident plane wave. The high energy absorption in the dielectric leaf is consistent with results obtained in early publications [21], where leaves were observed to attenuate the re-radiated signals from branches and twigs of the general model. This is also consistent with the distribution of the scattered signals observed in the near field of the leaf, which are significantly reduced in amplitude when compared with the results obtained for the idealized metallic leaf. The scattering modes emerging from a single leaf in the radio path are, however, highly dependent on the incident angle of the plane wave. In this approach, the 3-D re-radiation E-fields of the entire leaf were predicted by combining the various propagation modes setup on the leaf. Thus, the interactions of the plane wave with the leaf in the near field will assist in interpreting the results obtained in the far-field region.

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G. Prediction of Bistatic RCS of Single Leaves Normalized far-field RCS predictions of the single-leaf model were obtained for steady-state analysis of the scatter problem. Steady-state calculations were performed at 20 GHz, as shown in Fig. 7(a). RCS was computed in the plane as a function of the azimuthal angle . Only -fields were considered in the analysis of both metallic and dielectric leaves when illuminated at different angles of the incident plane wave, presented in the next subsections. 1) Far-Field—Steady-State Discussion: The bistatic RCS predictions obtained at a single frequency suggest a strong forward scattering, especially in the case of a normal incidence plane wave, as shown in Fig. 7. A common local maximum in the forward direction 0 was obtained for both leaf types, which is expected since the wave is propagating in this direction. The maximum value at 0 was about 4.04 dBsm (decibel relative to one square meter) for the metallic leaf, in contrast to the 7.62 dBsm found for the dielectric leaf. The main first value corresponds to an equivalent area of grid FDTD cells at this frequency, which can be compared with the cells of the dielectric leaf . In the region characterized by the side and backscatter of the leaf 60 90 , the RCS was observed to exhibit a rather constant value below 39 dBsm, corresponding to a maximum area of 15 15 main grid cells. This behavior is supported by the relatively small thickness of the leaf, although in the region defined by 90 60 , the RCS of the metal leaf was observed to be about 5 dB (and 1 dB for the dielectric leaf) higher that its symmetric region, which is explained by the relatively thinner right end of the leaf, as shown in Fig. 4. Comparison between the two leaf models yielded an average of 10 dBsm difference in these regions. The orientation of the leaf with respect to the angle of the incidence plane has been shown to play an important role in the prediction of the bistatic RCS. Fig. 7(b) and (c) clearly indicates this effect on the calculated RCS, respectively, for parallel and oblique incident angles. However, in the oblique incident case, results demonstrated that mostly the forward scatter region is affected by a reduction of 15–16 dB of the RCS value. For parallel incidence [see Fig. 7(b)], a maximum of 51.9 dBsm (or about an area of 11.5 main grid FDTD cells) was predicted in the case of the metallic leaf, and 71.87 dBsm (equivalent to an area of 1 subgrid cell) for the dielectric leaf. The relatively small values of the RCS indicate virtually little or no scattering signal in this plane, which is expected when considering the thickness of the leaf, with it being much smaller than the wavelength. Furthermore, since the E-field was horizontally polarized (in the -direction) for this particular incident angle, the in interaction appeared to be insignificant for the received the plane. From the results obtained, and especially where a strong coherent component predominates in the received signal level, the behavior of the RCS is shown to have a similar trend between the metallic and dielectric leaves, over the azimuthal angle range. This clearly suggests that a simple metallic geometry is capable of predicting the scaled scattered fields of a real leaf at 20 GHz. In the general model, the effects of leaves can be observed to attenuate the re-radiated signals from the branches

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Fig. 8. Physical dimensions of the metallic treelike structure and its orientation.

Fig. 9. Photographs of the metallic structure used in the experiments at interim stages of its construction: (a) metal trunk; (b) metal trunk+1 branch; (c) metal trunk+2 branches; and (d) metal trunk+6 branches.

IV. CASE STUDY II: IDEALIZED METALLIC STRUCTURE MODEL An idealized metallic treelike structured has contributed a great deal to the understanding of the propagation modes arising from single trees in the radio path. A first step into the direction of the desired model to assist in the prediction of bistatic RCS of leaves and trees was to model the metallic treelike structure, whose electromagnetic and geometric properties were easier to define. The structure was modeled using the FDTD technique, which enabled a more accurate modeling of the interaction of the incident plane wave with the elements comprising the structure and thus providing a way forward to validate the proposed model. Results expressing the predicted bistatic RCS in the far-field region were obtained and compared with the results obtained in [22] and [23]. Fig. 7. Normalized computed RCS in the plane for metallic and dielec0 and tric leaves illuminated by (a) by a normal-incidence plane wave ( 90 ), (b) a parallel incidence plane wave ( 0 and 180 ), 0 and 240 ). and (c) an oblique incidence plane wave (

and twigs, thus reducing the multiple internal scattering between elements in the tree canopy. This provides further confirmation to results reported in [21].

A. Computational Space and Idealized Structure Geometries The structure used in the study had physical dimensions and orientations of its elements similar to those identified in Figs. 8 and 9. The structure comprising several metallic rods to mimic a trunk and branches were modeled from a perfect electric conductor material. For simplicity and considering the physical orientation of the individual constituents of natural ficus trees, 45


TABLE IV PHYSICAL PARAMETERS OF THE INDIVIDUAL COMPONENTS METALLIC STRUCTURE

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OF THE

Fig. 10. Normalized near-electric-field (V/m) distribution cuts in the plane at of the metallic tree at some interim stages when illuminated 0 and 90 ). by a normal incidence plane wave (

angles were used in the tree simulations so that currents induced on tilted branches/twigs would generate equal co-polar and cross-polar signals. By adjusting the angles of branches and twigs, it will affect the multiple internal scattering phenomena and, hence, the results in the far field. Considering the FDTD computational space required to model the complete structure and constrained by the computational limitations of the procedure, a minimum spatial resolution of was achieved with a time step of 4.81 ps. Indeed, such a large resolution might introduce some errors in the speed of propagation within the FDTD cell space. However, these errors were estimated by [24] to be smaller than 5.7% for a resolution of . The errors were considered during the assessment of the proposed model. The problem space was defined by cells, corresponding to a total of 6 460 320 cells, which also includes the 15 cells of free space required around the contour of the structure. The number of cells used to model individual components comprising the structure are outlined in Table IV. The structure in the main grid was orientated in such a way that the main trunk was oriented in the -directions with branches located in the plane.

Fig. 11. Normalized near-electric-field (V/m) distribution cuts in the plane of the metallic tree with main trunk and two branches when at 0 and 90 ) for illuminated by a normal incidence plane wave ( , (b) , (c) , and (d) . (a)

B. Near-Electric-Field Distribution Results at 20 GHz at All Interim Stages The normalized E-field distribution in the near field was computed for a constant normal incidence with the -polarized plane wave traveling in the -direction, defined by 0 and 90 . Computed E-field intensities were obtained at each interim stage of construction of the idealized structure. Fig. 10 presents the component of the electric-field distribution. In order to assess the depolarization effects, illustrations of the electric-field components are given in Fig. 11. The elements of the structure are depicted in white color in all graphs. C. Prediction of Bistatic RCS for all Interim Stages Similarly to Case Study I, the normalized far-field RCS predictions at each interim stage of construction of the metallic tree were obtained for the steady-state analysis at 20 GHz, as shown in Fig. 12. RCS was computed in the plane as a function of the azimuthal angle , by considering only -fields of the RCS. Results are plotted in a polar format over the entire azimuthal scan of . Normal incidence plane wave ( 0 and 90 ) in the positive -direction was assumed in all simulations of the metallic structure. Analysis and discussion of results are presented in the next subsection.

Fig. 12. Normalized computed RCS in the plane for the metallic treelike structure at interim stages of its construction, illuminated by an normal in0 and 90 ): Metallic tree with (a) main cidence plane wave ( metallic trunk only and (b) main metallic trunk, and one branch (c) main metallic trunk and two branches and (d) main metallic trunk and six branches.

D. Discussion of Results 1) Near-Field Discussion: The interaction of the incident plane wave with the individual components making up the structure can easily be observed in the results obtained in the near field. The E-field distribution in the FDTD computational space

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clearly gives an indication as to the propagation mode setup on the structure. The interaction strongly depends on the number of metallic branches added to the main metallic trunk, which can clearly be seen from visual inspection of Fig. 10. Fig. 10(a) shows the interaction of the plane wave with one branch attached to the main metallic trunk. This has revealed significant scattering occurring from the surface of the trunk in the plane of the polarization wave ( plane). The reflecting waves will interfere with the wave traveling around the object in the direction of propagation, producing short-term multipath fading, which results in corrugated waves (interference patterns) in the very near field of the trunk. The interaction becomes stronger near the branch. Its oblique orientation with respect to the direction of propagation and thus to the polarization orientation causes re-radiated signals traveling in the direction of the branch as currents are set up on its surface. This also contributes to significant enhancement of the cross-polarized signals, confirming results reported in [25] and [26], as depicted by the and electric-field components, in addition to (the co-polarized component) of Fig. 11. As more branches are added to the metallic trunk, such effects become even stronger, leading eventually to overall degradation of the incident plane wave. The predicted 3D near E-field distribution of the various interim stages of the idealized metallic structure is very useful in understanding and establishing the multiple internal scattering occurring between elements within the canopy, confirming earlier results reported in [21] and [23]. 2) Far-Field—Steady-State Discussion: Far-field calculations of the near-field interactions were obtained for each interim stage of construction of the metallic structure. Fig. 12 shows the full bistatic scattering pattern of each structure, which suggests a common strong forward scattering in the direction of propagation 0 . Similarly, the peak observed at about 180 is due to the back scattering from the structure. In the back scatter region, the amplitudes of the RCS are lower than in the forward scatter region. Large variability of RCS amplitudes occur at scattering angles around 90 and 270 , which corresponds to the direction in the plane of the structure. The impact of the number of branches added to the main metallic trunk on the RCS is mostly visible in the forward and back scatter regions. The largest difference observed between interim stages occurs for the main metallic tree with six branches [see Fig. 12(d)], whose simulations revealed an increase of about 5 dB of the RCS (equivalent to an area of about 506 000 FDTD grid cells), relative to its predecessor structure of Fig. 12(c). On the other hand, the backscatter region is observed to increase with the number of branches by a similar amount as in the forward direction, except for the case of the complete structure, where a reduction was observed. In the scattering regions around 90 and 270 , there is little change observed in RCS, which, except for the case of only one branch attached to the main trunk [Fig. 12(b)] is explained by the symmetry of the structure around its vertical axis ( -direction). It should also be noted that the orientation of the elements comprising the structure lies in the plane perpendicular to the direction of propagation, and therefore relatively small interactions are observed in these directions when compared with the forward direction. The asymmetry in the case of only one

TABLE V PEAK RCS IN THE FORWARD, SIDE, AND BACKSCATTERING REGIONS OF EACH METALLIC TREE INTERIM STAGE

branch results in a 0.87-dB reduction of the RCS in the direction of the branch (i.e., 270 ). Such a decrease is equivalent to a detectable area of 195 500 FDTD main grid cells, which is approximately the number of cells occupied by the trunk. In the regions around 0 , the RCS amplitudes are observed to change rather progressively with the exception of the complete structure. Here, it is evident that more interactions are caused by the branches. Table V presents a summary of the peak bistatic RCS computed in the forward, side, and backscatter directions for each tree structure investigated. The computed results presented in this case study revealed that significant multiple internal scattering occurs between the elements of the structure, giving rise to constructive and destructive interference patterns. The interference pattern can explain the deep fades observed at specific angles of the scattering pattern reported in [23] and [26] for the same metallic structure. More conclusive results will be obtained from a dielectric model, including twigs and leaves, presented in case study III. V. CASE STUDY III: DIELECTRIC TREE MODEL STRUCTURE The FDTD-based model was finally applied to a dielectric tree model aimed at obtaining a reasonable prediction of the bistatic RCS of real trees. The model examined factors arising from moisture content in leaves, branches, and seasonal variations, density of scatterers, and trunk/branch relative sizes, and modeled these with sufficient accuracy for use in the design and performance evaluation of radio systems. In Section VI, the verification of the model was obtained by comparing the results expressing the predicted bistatic RCS in the far-field region with the results obtained in [26]. A. Computational Space and Dielectric Tree Geometries The idealized dielectric tree has identical physical dimensions and orientations of its elements similar to those of the metallic tree model of the previous section. In addition, smaller dielectric rods are added to each branch in the model, representing secondary branches and twigs to which are attached several dielectric leaf blocks, as shown in Fig. 13. Secondary branches were either vertically or horizontally oriented along each branch. Twigs are tilted at 45 on each side of the secondary branches. Leaves in the model are represented by blocks of ten leaves each, attached to the twigs in a preferred horizontal orientation. The leaves in the canopy are distributed symmetrically around the main trunk. The number of cells used to model the secondary branches, twigs, and leaf blocks are outlined in


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Fig. 14. Normalized near-electric-field (V/m) distribution cuts in the plane at of the dielectric tree at all interim stages when illuminated 0 and 90 ). by a normal incidence plane wave (

Fig. 13. Physical representation of the dielectric tree model in the (a) in 2-dimensional and (b) in 3-dimensional.

TABLE VI PHYSICAL PARAMETERS OF THE INDIVIDUAL COMPONENTS DIELECTRIC STRUCTURE

plane:

OF THE

Fig. 15. Normalized near-electric-field (V/m) distribution cuts in the plane of the dielectric tree with six branches, primary and secondary at 0 and twigs, and leaves, illuminated by a normal incidence plane wave ( 90 ) for (a) , (b) , (c) , and (d) .

Table VI. The physical parameters of the dielectric structure have already been defined in Table IV. The dielectric properties of leaves used in the model are defined in Table II. In the case of the trunk, branches, and twigs, these are assumed to have identical dielectric properties. It was, however, not possible to evaluate their dielectric properties from measurements due to lack of resources available. These are assumed to have a dielectric constant for a conductivity of 7.78 S/m at 20 GHz [16]. The problem space is also defined by cells, corresponding to a total of 6 460 320 cells. A minimal spatial resolution of is achieved. B. Near-Electric-Field Distribution Results at 20 GHz at All Interim Stages Computed E-field intensities were obtained at each interim stage of construction of the dielectric structure, as shown in . The first interim stage comprised the main Fig. 14 for dielectric trunk to which are attached six primary dielectric branches [see Fig. 14(a)]. In the second stage, all secondary branches were added to the structure [see Fig. 14(b)], followed by twigs in the third stage [see Fig. 14(c)]. Finally, the leaf blocks were attached to the twigs, representing therefore the complete dielectric tree [see Fig. 14(d)]. The leaf blocks are depicted in shades of green material, where as the trunk, branches, and twigs are depicted in shades of brown material, as indicated in the figures. Fig. 15 presents the electric-field decomposition for the complete dielectric tree.

Fig. 16. Normalized computed RCS in the plane for the dielectric treelike structure at interim stages of its construction, illuminated by an normal in0 and 90 ): dielectric tree with (a) six cidence plane wave ( primary branches, (b) plus secondary branches, (c) plus twigs, and (d) finally with leaf blocks.

C. Prediction of Bistatic RCS at all Interim Stages In this subsection, the normalized far-field RCS predictions are presented for the dielectric tree structure at each interim stage of its construction, as shown in Fig. 16.

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D. Discussion of Results 1) Near-Field Discussion: Similarly to the previous two case studies, the first simulation was aimed at demonstrating the near-field interaction with the various elements making up the dielectric tree. Fig. 14 shows the E-field distribution intensity of the structure comprising a dielectric trunk with primary branches. Since all primary branches are aligned in the direction defined by 45 in the plane, the interaction is shown to be quite significant for cross-polarized planes, thus representing the worst case scenario corresponding to the normal incidence case relative to the idealized (flat) structure. This is the case of E-field distribution in the - and -directions, which have yielded peak values as high as 10 dB below the maximum co-polarized E-field level [Fig. 15(a)]. Such cross-polarized enhancement is observed mostly in the regions surrounding the branches. Similar behavior was also observed in the case of the complete metallic structure, which has been reported in early sections. It can be clearly observed that the intensity of the interactions is relatively small in the case of the dielectric tree, which is explained by absorption due to the water content and presence of dielectric material in its elements. In Fig. 14(b), the secondary dielectric branches are added to the structure, which have resulted in a significant reduction of both co-polarized and cross-polarized E-field intensities. Multiple internal interactions may be responsible for such behavior when considering the next interim stage of the tree [see Fig. 14(c)], which shows a relative enhancement of the intensities in all polarized directions. The cross-polarized interactions are quite visible in the regions surrounding the twigs [Fig. 15(c)]. This confirms the fact that electromagnetic currents are set up on their surfaces, re-radiating the incident signals according to their orientations. The multiple internal scattering between the elements clearly gives rise to complex interference patterns. In a real tree, these elements are distributed randomly in the canopy, contributing therefore to an overall change of polarization or even almost total depolarization of the incident plane wave, confirming the results obtained in [25]. In Figs. 14(d) and Fig. 15, the near-field interactions of the complete structure, including the leaf blocks, are shown. One may observe the effects of these blocks, which attenuate the signal re-radiated by the branches and twigs, reducing therefore the multiple internal interactions observed in the previous stage. The interference patterns can explain the deep fades observed at specific angles of the scattering pattern reported in [26]. Nevertheless, should the computational resources become available in the near future, it would be possible to consider extending the present model to 3D with more branches introduced. This would allow further results to which a correlation analysis between angle of incidence, polarization, and re-radiation patterns can be established. This forms useful further work, as stated in Section VII. 2) Far-Field—Steady-State Discussion: Fig. 15 illustrates the simulation results of the full bistatic scattering pattern for each structure investigated. The multiple internal interactions observed within the dielectric canopy dictates the behavior of the bistatic RCS in the far field. A common local maximum is found in the forward scattering direction, which tends to increase with the number of elements added to the structure. The

TABLE VII PEAK RCS IN

THE FORWARD, SIDE AND BACKSCATTERING EACH DIELECTRIC TREE INTERIM STAGE

REGIONS

OF

scattering intensity is obtained by summing up the intensities of the many re-radiated signals with different phases, giving rise to either constructive or destructive interference. This explains the deep fades observed at specific angles of the scattering pattern, which has been the main subject of previous work [21], [23]. Table VII presents a summary of the peak bistatic RCS computed in the forward, side, and backscatter directions for each tree investigated. Of particular interest are the results obtained for the tree with leaf blocks, whose RCS results suggest high absorption caused by the leaves in most directions of the scattering pattern, as shown in Fig. 16(d). The behavior of the bistatic RCS can be summarized as follows. In the forward scatter region, the predicted results reveal a well-defined forward lobe of the scattered signal, with a relatively isotropic background [see Fig. 16(a)], as postulated by the radiative energy transfer (RET) theory [1]. The beam tends to broaden as the elements are added to the structure. The broadening of the forward lobe is a result of the currents induced on the various elements comprising the structure, re-radiating the incident signal governed by their own orientation. This is accompanied by the multiple contributions arising from the internal interactions between the elements of the canopy, indicated by the near-field analysis of the problem space. The insertion of secondary branches to the structure has caused a rather interesting scatter pattern, as shown in Fig. 16(b). It is observed that most of the elements of the structure were orientated in the vertical direction, giving rise to strong scatter signal components in the -polarization. This can clearly be seen in Fig. 16(b), particularly at 45 and in the side and back scatter regions. By adding the twigs to the structure, the multiple internal scattering is observed to increase (as shown in Fig. 14), producing a strong forward lobe with deep nulls at specific angular positions and a well-defined isotropic background in the regions away from the forward scatter (Fig. 16). This is in good agreement with the RET theory, which postulates such behavior for a random medium of scatterers. Finally, the leaf blocks are observed to attenuate the multiple internal interactions, as shown in Fig. 13, resulting in a relatively smoother scatter pattern, when compared with the case without leaves [Fig. 16(d)]. This is consistent with results obtained in [27] at 2 GHz for the out-ofleaf case, where a greater number of multipath components were observed to reach the receiver, giving rise to severe multipath effects. Despite the relative simplicity of the 2D dielectric model presented in this case study, compared with a natural tree which


has many more scatterers in 3D space, the model is shown to be very useful. The model gives a more detailed insight and well-supported fairly accurate predictions of the scattering processes arising in a natural canopy interacting with an incident radiowave. Verification of the model is presented in Section VI for both idealized and natural trees.

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TABLE VIII ASSESSMENT OF THE RMS PREDICTION ERROR FOR VARIOUS TREE SPECIMENS

VI. VERIFICATION OF THE BISTATIC RCS MODEL BASED ON A FAR-FIELD APPROXIMATION Experimental verification of the model could only be undertaken with measurement data obtained in the near-field region of the tree. A near-field to far-field approximation was therefore utilized in the subsequent analysis. Assuming first-order multiple scattering approximation within the canopy [22], the radar equation gives the reflected signal received back at the input of the receiver terminal at distance from the volume element in the canopy, as shown in (15). In the latter, is the transmitted power, , and are the gains of the transmitting and receiving antenna in the direction of and , respectively (see Fig. 1). (15) Bistatic scattering results reported in [22] and [23] were used to assess the model proposed in this paper. The verification was done first on the metallic treelike structure at all interim stages of its construction and then on a natural ficus tree. Measurement results were, however, converted into RCS values by solving (15). Such manipulation of the equation demanded an accurate knowledge of each experiment link budget. Contributions from the direct coupling between antennas and the scattered signals from the canopy were not possible to resolve accurately for the system used in the measurements. To minimize the problem, a directional antenna was used at the receiver, ensuring that only the scattered signals from the tree were received. In the transitional scatter regions, defined by 20 60 , this was not entirely achieved, because the received signal experienced direct contribution from the antennas in addition to those scattered from the tree, and the RCS could not be estimated accurately. Under these conditions, the predicted bistatic RCS in the farfield region are compared with the near-field measured results conducted inside the anechoic chamber, over the angular range defined by 90 35 . 0 represents the direction of propagation signal. Table VIII gives the comparison between the predicted and the measured RCS results for the various stages of the metallic structure. In general, it is clear from the results that predicted values are relatively higher than the measured ones. On the one hand, this is explained by the effective capture area of the receiving antenna, which is collecting and averaging the power in an area composed of free space and sample material. On the other hand, this clearly shows the influence of near-field effects on the calculation of the Bistatic RCS. As the number of elements in the structure increases, the difference between the measured and predicted RCS should become smaller. This is the case for the complete dielectric tree, whose predicted RCS results agree reasonably well with those measured using a ficus tree comparable in size. This is shown

Fig. 17. Predicted RCS (using the FDTD dielectric model) and measured 0 results of ficus tree, illuminated by a normal incidence plane wave ( and 90 ) at 20 GHz.

in Fig. 17, where reasonable agreement can be seen in the forward scatter region, with nulls in the measured results being located at similar positions to those predicted by the model. In contrast, differences with the rms error of about 10 dB can be seen in Fig. 17 in the side scatter region. The impact of leaves in the dielectric structure presented a relatively small rms error reduction of about 0.24 dB when compared with the case without leaves, as given in Table VIII. Nevertheless, the differences can be explained by the difference in leaf thickness between the modeled structures and the ficus tree, and the 3D nature of the tree. The thicker natural structure contains more leaves, which tend to absorb the re-radiated signal. This causes the measured scatter signal to be significantly lower compared with the flatter (2D) dielectric structure. The relatively small rms error obtained between the predicted and measured results presented in Table VIII reveals that the FDTD-based model is effective in characterizing the bistatic RCS of single natural trees. VII. CONCLUSION A model has been developed and applied for two idealized structures consisting of metallic and dielectric leaves using the FDTD technique. This has enabled a more accurate modeling of the interaction between the incident plane wave and single leaves, providing a useful insight into the propagation modes. The dielectric properties of the leaf model were first evaluated

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from appropriate measurements to measure the water content in a leaf, and subsequently used in the FDTD-based model. The interaction of the leaf with the incident plane wave is observed to be highly dependent on the angle of the incident plane wave. A high concentration of energy inside the leaf is revealed, explaining the absorption processes occurring in the leaf as a result of its relatively high moisture content. This effect is noted to be independent of the angle of the incident signal. Far-field results of the leaf model has shown that a leaf produces a strong forward scatter in the direction of propagation when illuminated by a normal or even an oblique incidence plane wave. In such cases, the behavior of the RCS is shown to exhibit a similar trend for both the metallic and dielectric leaf types, suggesting that a simple metallic geometry appropriately scaled is capable of predicting the re-radiation performance of a natural leaf. The leaf model can be used as part of a larger physical model comprising a main trunk, a number of main branches, twigs, and leaves, which simulate a dielectric tree. A preliminary test of the desired model was performed by modeling the metallic treelike structure used in Section II, whose results revealed interference patterns strongly dependent on the number of elements making up the tree. This has revealed significant multiple internal scatterings, giving rise to constructive and destructive interference patterns. A deeper understanding of the scattering process is presented, which explains the depolarization results of [25] and the reasons for the strong fades in the re-radiated signal at specific tree orientations. Application of FDTD to the dielectric tree model has yielded predicted re-radiation fields and RCS results, which are found to be in good agreement with measured results using a comparable size natural tree. The scattering process is obtained by summing up the intensities of the interactions with the various elements of the tree, producing a strong scattering in the forward direction. Good agreement is particularly obtained in the forward scatter region. The emerging model is capable of predicting the re-radiation performance of natural trees with sufficient accuracy, especially in the forward regions, enabling results to be used in the design and performance evaluation of radio systems affected by vegetation. The model, in its 2D form, is capable of further development aimed at extending the model to larger vegetation structures, excluding the ground reflection effects. The scatter prediction model represents a very useful aid in the planning and design of broadband wireless communication systems. ACKNOWLEDGMENT The authors are grateful to the University of South Wales (formerly the University of Glamorgan), U.K., for making available its facilities used in this research project. REFERENCES [1] R. Johnson and F. Schwering, “Transport theory of millimeter wave propagation in woods and forest,” Fort Monmouth, NJ, USA, Tech. Rep. CECOM-TR-85-1, 1985. [2] “Radiowave propagation effects on next generation fixed services terrestrial telecommunications systems,” COST 235, Final Rep., ISBN 92-827-8023, 1996. [3] F. K. Schwering, “Millimeter-wave propagation in vegetation: Experiments and theory,” IEEE Trans. Geosci. Remote Sens., vol. 26, no. 3, pp. 355–367, May 1988.

[4] Y. L. Jong and M. Herben, “Tree-scattering model for improved propagation prediction in urban microcells,” IEEE Trans. Veh. Technol., vol. 53, no. 2, pp. 503–513, Mar. 2004. [5] S. A. Torrico, H. L. Bertoni, and R. H. Lung, “Modelling tree effects on path loss in a residential environment,” IEEE Trans. Antennas Propag,, vol. 46, no. 6, pp. 872–880, 1998. [6] K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics. Boca Raton, FL, USA: CRC Press, 1993. [7] K. Umashankar and A. Taflove, “Novel method to analyze electromagnetic scattering of complex objects,” IEEE Trans. Electromagn. Compat., vol. EMC-24, no. 4, pp. 397–405, Nov. 1982. [8] F. Ulaby and K. Sarabandi et al., “Michigan microwave canopy scattering model,” Int. J. Remote Sens., vol. 11, no. 7, pp. 1223–1253, 1990. [9] Y. L. Jong and M. Herben, “Modelling the scattering from trees for propagation prediction in urban microcells,” presented at the Millennium Conf. Antennas Propag., Davos, Switzerland, Apr. 2000. [10] M. Torleif, “An improved near- to far-zone transformation for the finite-difference time-domain method,” IEEE Trans. Antennas Propag., vol. 46, no. 9, pp. 1263–1271, Sep. 1998. [11] P. A. Tirkas and C. A. Balanis, “Finite-difference time-domain method for electromagnetic radiation, interference, interaction with complex structures,” IEEE Trans. Electromagn. Compat., vol. 35, no. 2, pp. 192–203, May 1993. [12] L. A. Vielva, J. A. Pereda, A. Vegas, and A. Prieto, “Simulating 3D waveguide discontinuities using a combination of Prony’s method and FDTD with improved absorbing boundary conditions,” Proc. Inst. Electr. Eng.—Microw., Antennas, Propag., vol. 141, no. 2, pp. 127–132, Apr. 1994, doi: 10.1049/ip-map:19941026. [13] K. Umashankar and A. Taflove, “Novel method to analyze electromagnetic scattering of complex objects,” presented at the Millennium Conf. Antennas Propag., Davos, Switzerland, Apr. 11–15, 2000. [14] J. D. Kraus, Antennas, 2nd ed. New York, NY, USA: McGraw-Hill, 1988. [15] A. K. Fung and H. S. Fung, “Application of first-order renormalisation method to scattering from a vegetation-like half-space,” IEEE Trans. Geosci. Electron., vol. GE-15, no. 4, pp. 189–195, Oct. 1977. [16] A. K. Fung and H. S. Fung, “Scatter model for leafy vegetation,” IEEE Trans. Geosci. Electron., vol. GE-16, no. 4, pp. 281–286, Oct. 1978. [17] C. Mätzler, “Microwave (1–100 GHz) dielectric model of leaves,” IEEE Trans. Geosci. Remote Sens., vol. 32, no. 4, pp. 947–949, Sep. 1994. [18] G. P. Loor, “Dielectric properties of heterogeneous mixtures containing water,” J. Microw. Power, pp. 67–73, 1968. [19] G. P. Loor and F. W. Meijboom, “The dielectric constant of foods and other material with high water contents at microwave frequencies,” J. Food Technol., vol. 1, pp. 313–322, 1966. [20] F. T. Ulaby and M. A. E. Raynes, “Microwave dielectric spectrum of vegetation—Part II: Dual-dispersion model,” IEEE Trans. Geoscience Remote Sens., vol. GE-25, no. 5, pp. 550–557, 1987. [21] N. C. Rogers et al., “Generic model of 1–60 GHz radio propagation through vegetation,” Radiocommunications Agency, Contract Number AY3880/510005719, Final Rep., May 2002. [22] R. F. S. Caldeirinha and M. AL-Nuaimi, “Analysis of the re-radiation functions of single trees and idealised structures at 20 GHz,” in Proc. Millennium Conf. Antennas Propag., Davos, Switzerland, Apr. 2000, vol. 1, p. 460. [23] R. F. S. Caldeirinha, “Radio charaterisation of single trees at micro- and millimetre wave frequencies,” Ph.D. dissertation, Univ. of Glamorgan, Glamorgan, U.K., Apr. 2001. [24] C. W. Trueman and R. J. Luebbers, “RCS of cubes, strips, rods and cylinders by FDTD,” presented at the Ann. Symp. Appl. Comput. Electromagn. Soc., Monterrey, CA, USA, Mar. 1992. [25] R. B. L. Stephens, M. O. AL-Nuaimi, and R. Caldeirinha, “Characterisation of depolarisation of Radio Signals by single trees at 20 GHz,” presented at the IEEE15th Nat. Radio Sci. Conf., Cairo, Egypt, Feb. 1998, B12. [26] R. Caldeirinha and M. Al-Nuaimi, “Co-polar and cross-polar measurements of the re-radiation signal at 20 GHz from a tree and their analysis in the region around the nulls,” presented at the IEEE 16th Nat. Radio Sci. Conf., Ain Shams Univ., Egypt, INV4, Cairo, Egypt, Feb. 1999. [27] R. F. S. Caldeirinha and M. AL-Nuaimi, “Wideband characterisation of the dispersive effects on isolated mature trees for 2-GHz band urban microcells,” presented at the URSI General Assembly, Maastricht, The Netherlands, Aug. 2002.


Rafael F. S. Caldeirinha (M’00) was born in Leiria, Portugal, in 1974. He received the B.Eng. (Hons) degree in electronic and communication engineering and the Ph.D. degree in radiowave propagation from the University of Glamorgan, U.K., in 1997 and 2001, respectively. His Ph.D. research work focused on vegetation studies at frequencies from 1 to 62.4 GHz. He is currently Head of the Antennas & Propagation (A&P-Lr) Research Group at Instituto de Telecomunicaçóes, Leiria, Portugal, and a Coordinator Professor in mobile communications at the School of Technology and Management (ESTG), Polytechnic Institute of Leiria (IPL), Portugal. His research interests include studies of radiowave propagation through vegetation media, radio channel sounding and modeling and frequency-selective surfaces, for applications at microwave and millimeter-wave frequencies. He has authored or coauthored more than 80 papers in conferences and international journals, one book chapter, and four contributions to ITU-R Study Group, which formed the basis of the ITU-R P.833-5 (2005) recommendation. Prof. Caldeirinha is a member of the editorial board of the International Journal of Communication Systems, Program Chair of WINSYS International Conference between 2006 and 2012, Appointed Officer for Awards and Recognitions of the IEEE Portugal section since 2014, and a Member of IET.

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Miqdad O. Al-Nuaimi received the B.Sc. (Hons) degree in electronic and electrical engineering from the University of Birmingham, Birmingham, U.K., in 1967, and was awarded the Ph.D. degree in electronic and communication engineering for his research work in RADAR detection theory in 1972 and the Doctor of Science (D.Sc.) degree for his contribution to advanced knowledge to radiowave propagation and system design in 2006, both from the University of Loughborough, Loughborough, U.K. For more than 30 years, he has worked in the communication industry and higher education, specializing in radio communication system and radiowave propagation. He is currently a Professor Emeritus with the University of Glamorgan. He has authored (coauthored) more than 130 scientific papers. Prof. Al-Nuaimi is a Fellow of the Institution of Electrical Engineers and has contributed actively to its Professional Groups. He is also a member of UK Study Group 3 of the ITU-R.