Investigation of a Radio Propagation Model for Vegetation Scatter

Dynamic Channels at BFWA Frequencies

Sérgio Morgadinho

1,3

, Juergen Richter

Rafael F. S. Caldeirinha

1,2,3

and Telmo R. Fernandes

1,2

Instituto de Telecomunicações, Leiria, Portugal

Polytechnic Institute of Leiria, Departament of Electrical and Electronic Engineering, Leiria, Portugal

University of Glamorgan, Faculty of Advanced Technology, Pontypridd, U.K.

Keywords: Radio Propagation Model, Radiative Energy Transfer (RET), Time-variant Channel, Vegetation Scatter,

Dynamic Effects, BWA Frequency.

Abstract: The successful deployment of wireless technologies in the micro- and millimetre frequencies relies on the

understanding of radio channel propagation and accurate radio propagation models. To this extent, the

dynamic effects of vegetation on radio signals are investigated, as a function of wind direction, receiver

location and vegetation depth. Furthermore, a radio propagation model, based on the RET, is investigated as

an approach to predict the channel dynamic effects of vegetation scatter at 20 GHz. The model is evaluated

for a structured forest medium, and its performance is assessed through the use of primary, secondary and

error quantification statistics.

1 INTRODUCTION

Growing demand for bit stream access to provide

multimedia services, at fixed and mobile locations,

have led the industry to continue to develop new

technological solutions capable of surmounting the

technical hurdles involved. Broadband Wireless

Access (BWA) systems envisage the use of the

frequency band from 2 to 60 GHz (IEEE 802.16,

2011); (Mehmet et al., 2006). The IEEE Standards

Association has standardized a suite of 802.16

standards to cover LOS and non-LOS connectivity

covering the 2 to 10 GHz and 10 to 60 GHz

frequency bands, respectively (IEEE 802.16, 2011).

The 20 to 40 GHz frequency band is to be used for

BFWA (Broadband Fixed Wireless Access) systems.

The successful deployment of technologies in the

micro- and millimetre frequency bands relies,

amongst other factors, on the precise planning,

design and successful implementation of the

communication systems. In order to achieve this, in

depth understanding of the radio channel

propagation phenomena and consequent accurate

radio propagation models are essential.

Within the many obstacles, that may be present

in the propagation path in rural, sub-urban and urban

scenarios, several studies have shown that vegetation

can critically affect the received radio signal (Meng

et al., 2009); (Violette et al., 1985); (Schwering et

al., 1988); (Caldeirinha, 2011); (Al-Nuaimi and

Hammoudeh, 1993). The effects of absorption and

scattering of static vegetation have been considered,

while relatively few studies have considered the

effects of wind induced vegetation movement. These

studies show that wind causes the foliage medium to

move to an extent that results in significant temporal

variations of the received signal (Naz and Falconer,

2000); (Kajiwara, 2000); (Perras and Bouchard,

2002); (Hashim and Stavrou, 2006); Crosby et al.,

2005). The recommended model for vegetation

attenuation is the ITU-R P833 (ITU), of which the

latest version has been updated to include results of

measurements made in the UK and Norway for both

attenuations and to include the dynamic effects

caused by wind induced foliage movement.

The work presented in this paper aims to

contribute to the modelling of the dynamic effects

covering the micro- and millimetre frequency bands.

A model is proposed as a reasonable approach to

predict the time-variant scattered signal from

vegetation. The proposed model is based on the

Radiative Energy Transfer (RET) theory.

This paper is structured as follows. In section 2

the results from an investigation on the dynamic

effects of vegetation on radio signals, are presented.

Two sets of measurements were performed at 20

329

Morgadinho S., Richter J., F. S. Caldeirinha R. and R. Fernandes T..

Investigation of a Radio Propagation Model for Vegetation Scatter Dynamic Channels at BFWA Frequencies.

DOI: 10.5220/0004069203290339

In Proceedings of the International Conference on Signal Processing and Multimedia Applications and Wireless Information Networks and Systems

(WINSYS-2012), pages 329-339

ISBN: 978-989-8565-25-9

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

GHz. One set of measurement on single trees, and

the other on a structured formation of trees. The

results are analysed as to the impact of wind

incidence on single trees, and the interrelated impact

of wind direction, vegetation depth and location of

radio receiver on received signals inside a forest

medium. Section 3 describes the proposed model

rationale and formulation. A brief description of the

RET and dRET theories is provided as well as the

reasons leading to consider the dRET model to

predict time-varying estimates of received radio

signals inside forest media. The proposed modelling

methodology makes use of the dRET input

parameters to extend the dRET to consider channel

dynamics. Both the model input parameters and

intensity equations, used to calculate the received

scatter signal, are expressed in equations. Section 4

presents the model assessment results. A simulation

structured tree formation scenario is used to validate

the proposed modelling approach against measured

data. The model is assessed against various receiver

positions and wind directions. Primary and

secondary statistics are used to evaluate the model

performance. In addition, ERMS errors are

calculated for a number of scenarios to quantify the

performance of the model. The model is shown to be

a reasonable approach to model the dynamic effects

in foliage channels. Section 5 concludes the paper. A

summary of the findings is presented as well as

suggestions for further model improvements and

validation processes.

2 STATISTICAL

CHARACTERISATION OF THE

DYNAMIC EFFECTS IN

FOLIAGE MEDIA

The investigation of the dynamic effects of

vegetation on propagating radio signals in single

trees and groups of trees is essential to understand

the behaviour of scattered signals from foliage under

wind induced movement. The propagation of radio

signals through and scattered from foliage is

expected to vary according to the change of wind

speed, wind incidence in reference to the point of

illumination of the air-to-vegetation interface and

position of the receiver inside a forest medium, i.e.

vegetation depth.

Specific measurements were performed to

investigate these matters, and to enable the

assessment of the proposed model performance.

2.1 Measurement Geometry

Radio measurements were performed on two distinct

scenarios, inside an anechoic chamber. The

measurements were executed using a Continuous

Wave (CW) measurement system operating at a

fixed frequency of 20 GHz.

The single tree scenario measurements were

performed on one downscaled tree, of the Ficus

species, where the time-varying re-radiation pattern

of the tree was recorded. The experiment geometry

is depicted in Figure 1 a). The re-radiation pattern

was recorded over an angular range of 240º, with an

angular resolution of 2º. Both the transmitter and

receiver were placed in far field region of the

antennas, illuminating around 90% of the centre

canopy. This guarantees the received signal

originates either from scattered signals from the

foliage or signals propagating through the foliage

medium. In these experiments a horn antenna of 10

dBi gain was used on the transmitter side, and a 20

dBi Gaussian antenna, with a 4º beam width, was

used at the receiver. The dynamic signal envelope

was recorded over a period of 10s at a sampling rate

of 1 kHz, per scatter angle. The wind induced effects

were simulated with a household fan, placed in four

distinct locations around the tree, as depicted in

Figure 1 a). The fan produced wind at a constant

speed of 4.7 m/s, and illuminated the full extent of

the canopy.

(a)

(b)

Figure 1: Measurement geometry of the: a) single tree and

b) tree formation scenarios.

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The tree formation measurements were

performed on trees of the Ficus species, where the

directional spectrum was recorded at four specific

positions inside the forest medium. The experiment

geometry is depicted in Figure 1 b). The directional

spectrum was recorded by rotating the receiver

around its own axis, in the azimuth plane, over a

range of 360º with an angular resolution of 2º. The

transmitter was placed conveniently to guarantee the

illumination of 90º of the air-to-vegetation interface.

The 10 and 20 dBi antennas used in the single trees

measurements, were also used in these

measurements, on the transmitter and receiver side,

respectively. The received time-series were recorded

over a period of 10s, per angle, with a sampling rate

of 1 kHz. Once again the wind induced effects were

simulated with a household fan, placed in four

distinct locations around the tree, as seen in Figure 1

b). The fan produces a wind front at the air-to-

vegetation interface with relative narrow width

illumination (around 2 trees), in comparison to wide

uniform wind illumination observed in outdoor

forest geometries. However, given the small

dimensions of the indoor measurement geometries,

the employed method to generate artificial wind is

found to be suitable.

2.2 Statistical Analysis

A statistical analysis was performed on the single

tree and tree formation measurements. The ensuing

results are presented. The single tree results focus on

the effects of different wind incidences on the

scattered radio signals. The tree formation results

aim to investigate the effect of vegetation depth on

the received signal, as wind induced vegetation

movement causes channel dynamics across the

foliage medium, from different incidences.

The analysis of the single tree results is done

through the appreciation of the re-radiation pattern

through a skewed box plot based on a Lognormal

distribution, and second order statistics Average

Fade Duration (AFD) and Level Crossing Rate

(LCR). Concerning the box plot depictions, on each

blue box the central mark is the median, the edges of

the box are the 25

and 75

percentiles, the whiskers

(dotted line) extend to the most extreme data points,

and the outliers (red dots) are plotted individually.

The box plot enables the analysis of the following

information about the data: position, spread,

skewness and tails. The measured radio signal

scattered from the vegetation volume is shown to be

influenced by the direction of the artificially

generated wind. As wind is blown on to a single tree

from a specific direction, two areas of vegetation

motion need to be considered. One area of the tree,

where the wind incises directly on the foliage (active

area), and another area opposite to the first (quiet

area). The foliage dynamics in the quiet area are

observed to be reduced in comparison to the active

area, as a result of wind speed decay through the

vegetation media. A comparison between measured

re-radiation patterns obtained with opposite wind

directions is depicted in Figure 2. The active area is

considered to be from Φ=-120º to Φ=-50º and

Φ=50º to Φ=120º, for wind directions B and F,

respectively. The quiet area may be defined as the

opposite, in reference to the wind direction. For both

wind incidences in analysis, the received signal in

the active area presents an increased standard

deviation in comparison to the quiet area. This is

indicated by the lack of outliers in the active area

below the mean level. The increased number of

outliers in the quiet area below the mean level shows

that the received signal seldom falls into signal

levels as low as the ones observed in the active area.

In addition, analysis of the AFD and LCR statistics,

depicted in Figure 3 and Figure 4, show that the

deep fades in the active area as well as the fast-

fading signal variation are greater compared to the

quiet area results. Furthermore, analysis of the

results in Figure 5, show that a distinct

differentiation can be made on whether the wind

incidence is on the transmitter or receiver side. The

depicted results relate to AFD and LCR statistics,

obtained at Φ=-90º and Φ=90º, for wind incidences

of B and C. These show lower signal fades and

signal crossing rates observed in results from wind

direction B, against wind direction C. When the

direction of wind illuminates the tree canopy in the

same direction of the propagating radio wave, the

received signal presents smaller signal fades and

lower signal variation compared to wind

illumination from the receiver (opposite) side.

The investigation of the tree formation results is

done through the analysis of the re-radiation pattern

and its corresponding boxplot. The measured

directional spectrum inside a forest medium is

shown to be influenced not only by the direction of

wind illumination, but also the amount of vegetation

between the source of wind and position of the

receiver. Analysis of the results depicted in Figure 6,

show that the origin of measured scatter dynamics

varies according to the wind source of illumination.

For instance, Figure 6 a) shows the re-radiation

pattern relative to wind direction B. In this case the

measured dynamics observed from Φ=-100º to

Φ=50º (except in the main lobe region where the

InvestigationofaRadioPropagationModelforVegetationScatterDynamicChannelsatBFWAFrequencies

331

(a) (b)

Figure 2: Measured re-radiation boxplot patterns for wind incidences from: a) B and b) F.

(a) (b)

Figure 3: Measured AFD statistics at Φ=-90º and Φ=90º, for wind incidences from: a) B and b) F.

(a) (b)

Figure 4: Measured LCR statistics at Φ=-90º and Φ=90º, for wind incidences from: a) B and b) F.

(a) (b)

Figure 5: Measured statistics at Φ=-90º and Φ=90º, for wind incidences from B and C, concerning: a) AFD and b) LCR.

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(a) (b)

Figure 6: Measured directional spectrum from position Rx2, with wind incidence from: a) B and b) F.

(a) (b)

Figure 7: Measured directional spectrum from position Rx3, with wind incidence from: a) B and b) C.

received signal is coherent and presents little or no

variation at all) are relative to the time-varying

scatter originating from trees 1, 2 and 3 (as signalled

in Figure 1 b)). Given this geometry, these are the

trees most affected by the incidence of wind, and

more prone to generate dynamic scattering of

propagating signals. On the other hand, through

analysis of Figure 6b), the change of wind source

from B to F, results in increased dynamic scatter

from trees 2, 3 and 4, indicated by the standard

deviation observed around -125º≤Φ≤50º. These

results show that the change of wind direction does

not have a significant impact on the averaged

directional spectra. However change of wind

incidence does account for a change in measured

dynamics in specific angular regions, depending on

the wind direction.

Vegetation depth is expected to play a significant

role on the effect of wind on foliage and its effect on

propagating radio signals. As wind propagates

through vegetation its force decreases as a result of

wind decay and dispersion. As a consequence, wind

induced vegetation movement will decrease

resulting in lower channel dynamics. Results shown

in Figure 7 allow the observation of this. The

standard deviation observed in the measured

directional spectrum at Rx3 with wind from position

B, is close to neglectible. The depth of 2 to 3 trees is

too great for wind to have a noteworthy impact on

trees 3 and 4, and cause significant channel

dynamics. The change of wind direction from B to

C, results in high scatter dynamics from tree number

5 (region 50º≤Φ≤90º) and mild effects from trees 3

and 4 (region -50º≤Φ≤-10º). These results show that

the wind point of source, forest geometry and

position of radio receiver are all intrinsically

interrelated. These variables need to be considered

collectively when investigating the modelling

methodology and developing the propagation model

rationale.

3 MODEL RATIONALE AND

FORMULATION

The channel characterisation discussed in the

previous section, has shown that the propagation

phenomena of radiowaves in forest media, under

time-varying conditions, depends extensively on the

geometry of forest, location of receiver and source

of wind variation in reference to the receiver

position. The considered modelling approach must

take into account these deciding factors and provide

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333

not only insight into radio propagation physical

phenomena in forested scenarios but also enable

geometrical consideration of the scenario variables.

To this extent the model is based on the RET theory,

more specifically one of its derivatives, the dRET.

The RET theory, or energy transport theory,

models vegetation as a random homogeneous

medium comprised of small discrete scatterers. The

RET has been shown to be a good solution to predict

the complex phenomena of radio propagation

through vegetation, as it provides accurate

evaluation of the through vegetation attenuation with

both horizontal and slant foliage paths (Johnson and

Schwering, 1985); (Meng and Lee, 2010); Rogers et

al., 2002). In spite of this, the RET has a crucial

shortcoming. It assumes the forest as a

homogeneous medium, and that it extends to

infinity. In order to overcome these limitations, an

improved version named the discrete RET (dRET)

was proposed by Didascalou (Didascalou et al.,

2000) and further enhanced by Fernandes

(Fernandes et al., 2007).

In the dRET the vegetation volume is divided

into non-overlapping cubic cells. This is particularly

beneficial in dealing with inhomogeneous media.

The process of splitting a forest formation into

discrete elementary volumes allows the assignment

of different scattering parameters to each cell. Each

cell may be represented by four input parameters

(Didascalou et al., 2000); (Fernandes et al., 2007):

the absorption coefficient (σ

, in Np/m), the

scattering cross section per unit volume (σ

, in m

-1

and the phase function parameters α and β. The

phase function may be understood as the cell

radiation pattern, with a pronounced forward lobe in

the direction of signal propagation, and an isotropic

background (Johnson and Schwering, 1985). The

input parameters of each cell are used to calculate

the incident intensity (the RET uses intensity as a

fundamental quantity). An iterative algorithm is used

to gather all the interactions between the cells, to

perform the computation of intensity across the

forest formation. The total specific incident

intensity, in each cell, can be decomposed into the

reduced intensity I

and diffuse intensity I

. While

both the input and output coherent intensities I

exhibit the same definite direction, each input

diffuse intensity component

generates several

output components due to the scattering process

(Johnson and Schwering, 1985); (Fernandes et al.,

2007), as depicted in Figure 8.

The reduced and diffuse intensity were originally

expressed in (Johnson and Schwering, 1985), and

further discretised by (Didascalou et al., 2000);

(Fernandes et al., 2007), to allow discrete

formulations for losses due to absorption, scattering ,

increase of intensity resulting from scattering

contributions from surrounding cells.

Figure 8: Representation of a single cell with size ∆s.

The dRET enables insight into the complex

propagation phenomena in scatter media, based on

physical attributes of the vegetation (e.g. phase

function). Furthermore, due to its discretised

formulation it allows the enhanced resolving of the

various directional intensities originating from

individual vegetation cells. For these reasons, the

proposed modelling methodology will be based on

the dRET to provide time-varying estimates of

received signal inside forest medium.

Since the dRET, in its current rationale, is only

applicable to static conditions, the extension of the

dRET to consider channel dynamics will be done

through the time-variation of its input parameters.

Analysis of the dRET input parameters time-varying

properties, and its impact on the dRET predicted

directional spectra, has been conducted (Morgadinho

et al., 2011); (Sergio et al., 2011). The published

results have shown that the dRET parameters vary

over time with wind induced foliage movement, as

the branches, twigs and leaves move and sway to the

wind (Sergio et al., 2011). In addition, variations of

the dRET input parameters are directly correlated to

variations observed on the directional spectrum

(Sergio et al., 2011). The extraction of the dRET

input parameters for a single tree is done from its

measured re-radiation pattern. The re-radiation

pattern is the convolution of the tree scatter profile

(phase function) and the receiver antenna pattern.

Although the measured re-radiation pattern differs

from the tree real radiation pattern, due to the

receiver antenna distortion effect, it is considered a

valid approximation of the tree scatter pattern. For

time-invariant conditions, a single averaged re-

radiation pattern is obtained, and an optimum

Gaussian function is fitted against it (Johnson and

Schwering, 1985). However, to ensure the

parameters may be retrieved as a function of time,

OUT

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334

multiple re-radiation patterns are recorded over a

period of time, each one corresponding to a specific

time instant. Single Gaussian curves are estimated

for each instant, from which the input parameters are

retrieved, Figure 9. dRET parameters α and σ

are

estimated according to the backscatter level; β is

calculated from the Gaussian function HPBW; σ

estimated from the difference between the phase

function main lobe signal level and the

corresponding line-of-sight level. These parameters

may be expressed as:

)()()( ttt

SAE

σσσ

(1)

()

)(1

)(

)(),(

)(

ttP

αψ

−+

⎟

⎠

⎞

⎜

⎝

⎛

⎟

⎠

⎞

⎜

⎝

⎛

−

(2)

where Ψ is the angle subtended by the input and

output directions, and σ

is the extinction

coefficient.

Figure 9: Gaussian phase function.

These parameters may be extracted under

different wind conditions, i.e. wind speeds and

incidences, to be later used in tree formation

simulations under corresponding wind conditions.

Parameters α and σ

are particularly sensitive to

any changes in the side scatter level as they are

estimated accordingly from the backscatter level.

Under time-static conditions these parameters are

extracted from an averaged backscatter level.

However, under time-varying conditions, averaging

the backscatter level will decrease both angular and

time variations. Therefore, both parameters are

extracted from a backscatter level estimated for a

single angle of Φ=|90º|, where the recorded signal is

expected to originate from tree scattering alone

(Sergio et al., 2011).

In addition, the discretised intensities, depicted in

Figure 8, expressed in (Didascalou et al., 2000),

used to estimate the output radiation of each cell

may be re-written as a function of time:

00 0

(, ) (, ) () (, )

OUT IN IN

ri ri E ri

It It tIt s

γγσγ

−Δ

(3)

(, ) (, ) () (, )

() (,,')(,') (,,)(,)

OUT IN IN

dd Ed

IN IN

SdSri

It It tIt s

tPt It Pt It s

γγσγ

σγγγσγγγ

=+− Δ+

⎡⎤

⎣⎦

⎡

⎤

⎢

⎥

⎣

⎦

∑

(4)

where

and

OUT

are the input, and output

reduced intensities,

and

OUT

are the input and

output diffuse intensities, and P represents a discrete

version of the phase function. Thus, the total output

intensity is defined as:

),()(),(),(

γγγδγγ

tItItI

OUT

+−=

(5)

4 ASSESSMENT OF THE

DYNAMIC MODEL

PERFORMANCE

The tree formation measurement scenario, depicted

in Figure 1 b), was used as a reference for the

assessment of the proposed modelling approach

performance. To this extent, the simulation scenario,

depicted in Figure 10

, enabled a comparison

between resulting modelled data and acquired data,

for different wind incidences. This assessment aims

to investigate the model performance as a function

of: wind incidence and receiver position inside the

forest media.

Figure 10: Simulation geometry of the tree formation

depicted in Figure 1 b).

The evaluation between modelled and measured

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335

data is done through the consideration of the

averaged directional spectra and its corresponding

standard deviation. The averaged directional

spectrum depicts the standard deviation information

through the use of an errorbar. Furthermore,

secondary statistic AFD is used to evaluate the

ability of the model to predict deep fades throughout

the bi-static scatter angle. The performance of the

proposed model is quantified by the calculation of

the ERMS (Root-Mean-Square) error, between

simulated and measured data. The ERMS errors are

provided in two ways: ERMS D-S is the averaged

error from directional spectra through time, and

ERMS T-S is the averaged error from time series as

a function of the receiver scatter angle Φ.

The time-varying model input parameters, for the

Ficus tree, were extracted from the measurement set

depicted in Figure 1 a). The parameters were

extracted for a period of 10 seconds, consequently

resulting in a simulation time frame of 10 seconds.

Table 1: Averaged ERMS error statistics.

Rx1

Wind incidence ERMS D-S (dB) ERMS T-S (dB)

B 1.3 4.3

C 2.6 5.3

E 1.6 4.4

F 1.1 4.2

Rx2

B 6.5 8.8

C 4.0 7.3

E 5.7 8.0

F 5.5 8.9

Rx3

B 3.1 7

C 2.9 6.1

E 2.3 6.8

F 2.5 4.8

Rx4

B 7.0 16

C 1.2 8.4

E 1.8 9.1

F 2.8 9.9

The presented results indicate that the model is

able to predict the directional spectra envelope and

its variation with time, with relative agreement. The

simulation results obtained from receiver positions

Rx1 and Rx2 are assessed with more detail. A

comparison between measured and simulated

directional spectra and AFD statistic from Rx1 is

provided in Figure 11 and Figure 12. These results

show that the model is able to provide estimates of

the signal averaged directional spectra standard

deviation, where the envelopes of the measured and

simulated fit accordingly, as observed in Figure 11

a) and b), respectively. In addition, given the wind

incidence from C, the model accurately estimates the

resulting signal variation from trees 2, 3 and 4,

although it tends to underestimate the occurring

magnitude of signal variation (see Figure 11 b)). The

AFD statistics, depicted in Figure 12, show that the

model underestimates the duration of fades in the

order of 1 to 2 seconds, but is able to predict the fade

level magnitude with satisfactory agreement. Similar

behaviour is observed in simulated results obtained

from Rx3, with wind incidence from E, depicted in

Figure 13 and Figure 14. The model estimates the

signal variation originating from trees 3 and 4 with

relative accuracy, in both envelope and magnitude.

Although the duration of simulated fades

underestimate the deep fades observed in measured

data, a comparison between measured and simulated

time series (Figure 13 b)) shows the model is able to

predict, with relative accuracy, time series with

significant variation through time (in the order of

15-20 dB).

A set of averaged ERMS are presented in Table

1, for all wind directions and receiver positions.

Relatively low ERMS D-S and ERMS T-S errors are

observed for all wind incidences and receiver

positions. These results suggest the model performs

with relative agreement when estimating both the

envelope of the directional spectra as well as its time

variation due to wind induced vegetation scatter.

5 CONCLUSIONS

A radio propagation model for dynamic channel

vegetation scatter effects has been investigated as to

its feasibility. In order to understand the foliage

channel behaviour under wind induced effects, a

study has been conducted on single trees and

structured forest medium measurements. Results for

single tree measurements showed that as wind is

blown on to a single tree from a specific direction,

two areas of vegetation motion need to be

considered. One area of the tree, where the wind

incises directly on the foliage (active area), and

another area opposite to the first (quiet area). The

foliage dynamics in the quiet area are observed to be

reduced in comparison to the active area, as a result

of wind speed decay through the vegetation media.

Additionally, when the direction of wind illuminates

the tree canopy in the same direction of the

propagating radio wave, the received signal presents

smaller signal fades and lower signal variation

compared to wind illumination from the receiver

(opposite) side. Furthermore, tree formation results

indicate that change of wind incidence results in a

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336

change in measured dynamics in specific angular

regions, depending on the wind direction. The wind

point of source, forest geometry and position of

radio receiver are all intrinsically interrelated and

need to be considered collectively when considering

the modelling methodology.

For this reason the investigated modelling

approach must provide not only insight into radio

propagation physical phenomena in forested

scenarios but also enable geometrical consideration

of the scenario variables. To this extent, modelling

of the dynamic effects in vegetation is done through

the use of the dRET theory because of its ability to

resolve various directional intensities originating

from different directions. The proposed dynamic

model makes use of the dRET time-variant input

parameters properties to predict time-varying scatter

from wind induced vegetation movement. Model

assessment results show that the model tends to

underestimate the time-variation and duration of

signal fades. In spite of this, the presented model is

able to perform with relative agreement when

estimating the directional spectra and time-variation

envelopes, as well as the fade level magnitude.

Further work is expected to encompass the

validation of the investigated model against

measurement data collected in outdoor environment.

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APPENDIX

(a) (b)

Figure 11: Comparison between measured and simulated data from position Rx1, with wind incidence C, considering: a)

directional spectra errorbar and b) directional spectra standard deviation.

(a) (b)

Figure 12: Comparison of data from position Rx1, with wind incidence C, between: a) simulated and b) measured data sets.

(a) (b)

Figure 13: Comparison between measured and simulated data from position Rx2, with wind incidence E, considering: a)

directional spectra errorbar and b) time series at Φ=.

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(a) (b)

Figure 14: Comparison of data from position Rx2, with wind incidence E, between: a) simulated and b) measured data sets.

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