DIRECTIONAL SPECTRUM MODELLING IN INHOMOGENEOUS

FORESTS AT 20 AND 62.4 GHZ

Telmo R. Fernandes, Rafael F. S. Caldeirinha

ESTG-Leiria/Institute of Telecommunications-DL

Alto do Vieiro - Morro do Lena, 2411-911 Leiria, Portugal

Miqdad O. Al-Nuaimi, J

urgen Richter

Radiowave Propagation and System Design Research Unit, School of Electronics, University of Glamorgan

Treforest, CF37 1DL, United Kingdom

Keywords:

Radiative Energy Transfer, Micro and Millimetre Wave Propagation, Vegetation, Foliage Attenuation.

Abstract:

This paper presents a radiowave propagation model for inhomogeneous forests based on the Radiative Energy

Transfer theory (RET) model. This model, which is a discretised version of the RET, is able to simulate

the behaviour of radiowaves inside a forest which contains various types of vegetation and free space gaps.

The forest is divided into non-overlapping square cells, each one with different propagation characteristics.

The propagation properties of each cell rely on speciﬁc propagation parameters, which are extracted from

vegetation using an appropriate measurement method which is also described. The model performance is

assessed through comparison between predicted values and directional spectrum measurements carried out in

an isolated inhomogeneous forest at 20 and 62.4 GHz. This forest, located in South Wales, is formed by 6

different species of trees of various sizes and leaf types. The measurements were performed with the trees

in-leaf.

1 INTRODUCTION

The growth of ﬁxed and mobile radio networks ex-

perienced in the last decades, has led to an increased

need for cost effective, and enhanced utilisation of the

available bandwidth and system coverage. This en-

hancement can be accomplished through a more ef-

ﬁcient use of the available radio spectrum. A more

efﬁcient use of the radio spectrum relies on accurate

radio planning tools which allow system planners to

effectively predict the behaviour of their radio com-

munication systems in terms of coverage and interfer-

ence on existing systems.

The radiowaves interact with the obstacles and sur-

rounding environment present in the radio path cre-

ating undesirable effects which need to be accurately

modelled. From these obstacles, vegetation is very

likely to be present in sub-urban and rural environ-

ments, causing degradation in the performance of the

radio systems. To this extent, the understanding of the

interaction between radiowaves and vegetation media

is very important.

Various propagation models have been applied to

vegetation with different degrees of success (Rogers

et al., 2002). From these, the Radiative Energy Trans-

fer theory (RET) has yielded good results for micro-

and millimeter wave frequencies (Rogers et al., 2002;

ITU-R, 2005). In (Rogers et al., 2002), results from

an extensive measurement campaign are used to com-

pare the predictions of the RET with actual measure-

ment data in the 1 to 60 GHz frequency band. This

work has established a generic model for radiowave

propagation in vegetated areas which was recently ap-

pended to the ITU-R recommendation in force (ITU-

R, 2005). Although this model is based on three

different propagation mechanisms, it is reported that

the scattered component, which is modelled with the

RET, is dominant in terms of the received signal level.

The ﬁrst known application of the RET theory to

model the radiowave propagation in vegetation me-

dia was reported in (Johnson and Schwering, 1985)

which is based on the RET modelling presented in

(Ishimaru, 1997). Both of these RET formulations

present some approximations which limit the applica-

bility of the model, e.g. the model considers a ho-

mogeneous medium; the medium is not physically

limited and special geometry conditions must be met.

The vegetation media is normally inhomogeneous in

nature as leafs tend to grow more in the periphery of

the forest due to the increased sunlight exposure. An-

other limitation is that vegetation normally appears in

limited or isolated groups, and forest volumes are nor-

164

R. Fernandes T., F. S. Caldeirinha R., O. Al-Nuaimi M. and Richter J. (2006).

DIRECTIONAL SPECTRUM MODELLING IN INHOMOGENEOUS FORESTS AT 20 AND 62.4 GHZ.

In Proceedings of the International Conference on Wireless Information Networks and Systems, pages 164-170

 SciTePress

mally limited by the ground and the top of the vege-

tation.

To overcome the issues presented above, a discre-

tised version of the RET (dRET) was presented in

(Didascalou et al., 2000). A development of this

model as well as a complete assessment was per-

formed in (Fernandes et al., 2005) using an idealised

scaled-down version of a forest formed by 16 Ficus

Benjamina plants inside an anechoic chamber at 20

and 62.4 GHz.

In order to apply the dRET, the vegetation volume

is divided into non overlapping square cells each one

presenting distinct propagation characteristics. The

signal ﬂow in each of the cells is subsequently calcu-

lated using an iterative algorithm which evaluates the

interactions between the different cells.

In this paper, the dRET formulation is used to sim-

ulated the behaviour of a full scale outdoor forest

formed by 6 different species of trees. The assess-

ment of the model is performed by comparing the pre-

dicted values with the actual measurement data ob-

tained from outdoor measurements at 10 locations in-

side the test forest.

In section 2, the RET based scattering propagation

models which are used during this paper as well as the

differences between the original RET and its discre-

tised version are presented. The model input propaga-

tion parameters are also described. The site speciﬁcs,

including both the geometry and the tree characteris-

tics, used to validate the proposed model is also pre-

sented. The experimental procedures used to extract

the vegetation parameters as well as the overall model

validity in terms of excess attenuation caused by tree

is also outlined. Section 4 presents and discusses the

measurement results. Finally in section 5 the conclu-

sions of the paper are presented.

2 THE SCATTERING

PROPAGATION MODELS

2.1 The Radiative Energy Transfer

(RET)

The RET models vegetation as a homogeneous

medium randomly ﬁlled with similar scatterers,

which are characterised by the following set of pa-

rameters:

• The Extinction Coefﬁcient or k

. This parameter

speciﬁes the amount of energy which is lost due to

absorption and scattering;

• The Scattering Coefﬁcient, k

, which speciﬁes the

scattered energy;

• The scatter directional proﬁle p (ˆs, ˆs

′

), known as

Phase Function (Ishimaru, 1997), with ˆs

′

and ˆs

representing the directions of the energy entering

and emanating from each scatterer, respectively.

The phase function is normally modelled according to

Eq. 1 (Johnson and Schwering, 1985; Ishimaru, 1997)

which represents a Gaussian function superimposed

to an isotropic background level:

p (γ) = α





−

(

)

+ (1 − α ) , (1)

where α is the ratio between the forward lobe power

and the total power of the phase function, β represents

the half power beamwidth of the forward lobe and γ

is the angle subtended by ˆs and ˆs

′

The RET equation is normally expressed in its dif-

ferential form, presented in Eq. 2.

= −k

I + k

4π

p (ˆs, ˆs

′

)Idw, (2)

where the left hand side (LHS) describes the spa-

tial variability (i.e. derivative) of intensity over one

scatterer, while the ﬁrst term on the right hand side

(RHS) accounts for the reduction in intensity due to

the absorption and scattering. The second term on

the RHS represents the increase of intensity resulting

from the scattering contributions of surrounding scat-

terers (Johnson and Schwering, 1985). In (Johnson

and Schwering, 1985), the overall intensity I is di-

vided into two different intensities: the reduced inten-

sity, I

and the diffuse intensity I

. I

is the atten-

uated incident intensity whereas I

accounts for the

contributions from incoherent scattered components

inside the vegetation medium.

2.2 The Dret Formulation

The discrete RET (dRET) was originally proposed by

(Didascalou et al., 2000), as a method to overcome the

RET limitations in terms of applicability to isolated

vegetation volumes. In the dRET modelling, the veg-

etation volume is divided in non-overlapping square

cells and an iterative algorithm is used to gather all

the interactions between these primary cells, allowing

for the computation of the intensity across the entire

tree formation. This approach of splitting the vege-

tation in discrete elementary volumes, allows one to

assign different scattering parameters to every cell,

consequently enabling an inhomogeneous vegetation

volume to be more accurately represented. This is de-

picted in Fig. 1.

The dRET approach presented in (Fernandes et al.,

2005) and used here, comprises 4 major improve-

ments compared to the algorithm given in (Di-

dascalou et al., 2000). These are summarised as fol-

lows: (i) the improved dRET version yields results

for angles other than those which are integer multi-

ples of 45

◦

; (ii) it accounts for the effect of the receiv-

ing antenna radiation pattern; (iii) the dRET differen-

tial equation is more readily solved, which means that

piecewise linear approximation is no longer needed,

so that the algorithm can cover larger cell sizes; and

(iv) the cell parameters can be deﬁned individually,

thus allowing one to deﬁne inhomogeneous scenarios.

3 EXPERIMENTAL PROCEDURE

An experimental program was designed to evaluate

the performance of the dRET model in a real outdoor

environment. This program involved two main tasks:

the dRET parameter extraction and the evaluation of

the excess attenuation caused by trees at several loca-

tions inside the test forest.

3.1 Description of the Measurement

Site

The measurement site is located in the North-East of

Cardiff in South Wales. The test forest is an isolated

group of trees formed by 6 different species. To com-

pletely characterise the test forest, precise locations of

each tree and the mean canopy diameters were mea-

sured using a theodolite. Using this data, a 2D rep-

resentation of the forest is presented in Fig. 2. The

transmitter location (TX) and the direction where it

was pointed in the measurements are also presented.

The red dots which are labeled Mpx, represent the re-

ceived signal measurement locations. The tree species

present in the test forest as well as the dimensions of

the trees are presented in Table 1.

For each of the species, the leaf size parameters

were measured. These mean sizes are presented in

Table 2.

Figure 1: 2D cell structure.

Table 1: Tree species of Wyevale Garden Center site.

Canopy Tree

Tree Label Common Name Diameter (m) Height (m)

T1 Oak 11.4 10.9

T2 Oleaster 12.1 16.5

T3 Ornamental Cherry 6.1 3.5

T4 Oleaster 14.0 17.7

T5 Ornamental Cherry 5.2 3.5

T6 Ornamental Cherry 6.0 3.5

T7 Ornamental Cherry 6.0 3.5

T8 Ornamental Cherry 3.0 3.0

T9 Silver Birch 4.5 8.4

T10 Silver Birch 6.5 6.4

T11 Silver Birch 10.0 10.0

T12 Oleaster 12.5 15.6

T13 Silver Birch 5.6 5.5

T14 Oleaster 12.0 15.0

T15 Oak 5.6 2.5

T16 Oak 10.1 7.2

T17 Gean 9.6 7.3

T19 Pecan 3.9 8.9

T20 Oak 8.0 9.6

T21 Pecan 8.3 5.2

T22 Pecan 7.0 7.0

T23 Oak 6.1 7.8

T24 Oak 7.2 6.8

T25 Pecan 6.8 13.0

T26 Pecan 6.2 14.3

T27 Pecan 3.9 4.3

3.2 Directional Spectrum

Measurements

To evaluate the excess attenuation caused by the vege-

tation, the RX antenna was placed at each of the loca-

tions shown in Fig. 2 and the directional proﬁle of the

received signal was evaluated. This evaluation was

performed positioning the receiver antenna at 5.5 m

high, which represent approximately one half of the

mean canopy height of the trees which form the test

forest. At each location, the RX antenna was rotated

clockwise 360

◦

around its vertical axes (θ

) in 1

◦

Figure 2: Scaled drawing of the Wyevale Garden Center test

site.

Table 2: Tree leaf sizes of Wyevale Garden Center site.

Leaf Size

Common Name Length (cm) Width (cm)

Oak 13 8

Oleaster 9 0.8

Ornamental Cherry 10 6

Silver Birch 4 2.5

Gean 15 6

Pecan 9 3

incremental steps.

The TX antenna was placed outside the forest in

the position shown in Fig. 2 at 13 m distance from

the air to vegetation interface. To achieve an almost

uniform illumination of the interface, very broad 50

◦

(10 dBi) half power beamwidth antennas were used at

both test frequencies. At the receiver side, high gain

directional antennas were used. At 20 GHz the RX

antenna was of the lens horn type with 33 dBi and 4

◦

of HPBW, while at 62.4 GHz a lens horn antenna with

36 dBi and 2.8

◦

of HPBW was used.

3.3 Parameter Extraction and

Scaling

The dRET input parameters must be extracted from

speciﬁc measurement data. This data is obtained

from received signal measurements in speciﬁc loca-

tions around the tree as explained in Fig. 3. The dis-

tances d

1,2,3

were chosen so that 100% of the canopy

width could be illuminated within the HPBW of the

TX antenna, and at the same time, the RX antenna

was placed as close as possible to the tree canopy.

At each of the 3 measurement locations presented in

Fig. 3 (labeled M

) the receiver antenna was rotated

around the vertical axes in a ±45

◦

range in 1

◦

steps.

The extraction of k

was based on the measurement

of the insertion loss caused by the tree, and conse-

quently relied on measurements M

and M

. The ra-

Figure 3: Parameter extraction measurement setup.

Figure 4: Approximated method to measure parameter β.

tio between the maximum received powers at these

locations was used to calculate k

using Eq. 3.

3 max

1 max

= e

−k

−d

)





, (3)

where P

1 max

and P

3 max

are the maximum receiver

powers at positions M

and M

, respectively, and d

is the distance between the TX and the n

measure-

ment location in meters.

To extract the phase function parameters α and β, a

modiﬁed version of the re-radiation indoor measure-

ment procedure (Fernandes et al., 2005) was used.

This modiﬁed version overcomes some of the inac-

curacies reported in (Richter et al., 2002) and is sim-

pler to carry out. The β optimisation is based in mea-

surement M

, where the ideal measurement position

is replaced by a more convenient approximated po-

sition, as explained in Fig. 4. The optimisation of

α uses the side scatter level of the tree obtained from

measurement M

, which is subsequently used to opti-

mise α in Eq. 1. Finally, k

is extracted by modelling

the tree as a single dRET cell. As there are no in-

teractions involved between cells a simple version of

the dRET diffuse intensity equation (Fernandes et al.,

2005) is used to optimise k

, providing the measured

side scatter level.

The parameter extraction was performed for 5 of

the 6 species present in the test forest. The trees cho-

sen to carry out the parameter extraction were: T

, T

and T

. These were chosen due to their

location at the border of the forest, thus avoiding the

possible contamination of measured results caused by

interference from the other species. The extracted pa-

rameters are presented in Tables 3 and 4 for 20 and

62.4 GHz respectively. Some parameters were im-

possible to calculate, specially for the larger trees, due

to the high attenuation of the coherent signal compo-

nent. In these cases average parameter values were

assigned to the corresponding trees.

To limit the stair case error due to the discretisation

of the forest, while maintaining a reasonable compu-

tational time, a 2.5 m vegetation cells division was

used, as depicted in Fig. 1. In order for the phase

0 50 100 150 200 250 300 350

−60

−50

−40

−30

−20

−10

RX antenna rotation angle (deg)

Excess attenuation (dB)

RMS

= 10.8 dB

Measured Signal

Predicted Signal

Figure 5: Measured and predicted signals in M P

at 20

GHz.

function parameters to remain valid, these have to be

adapted to the new vegetation volumes by performing

an appropriate scaling. The scaling method used here

is explained in (Fernandes et al., 2006), which sug-

gests a linear behaviour of α and β with the variation

of the vegetation volume.

4 MEASUREMENT RESULTS

The assessment of the dRET propagation model re-

sults was performed comparing the predicted results

with directional spectrum measurements were carried

out at 10 locations inside the forest according to the

procedure explained before. The measured excess at-

tenuation can subsequently be compared with the pre-

dictions calculated by the dRET algorithm for the test

forest depicted in Fig. 2 when modelled with the cell

structure presented in Fig. 1.

A comparison between the measured received sig-

nal and the predicted signal values obtained at M P

is presented in Figs. 5 and 6, at 20 and 62.4 GHz,

Table 3: Input parameter values extracted from selected

vegetation blocks at 20 GHz.

Tree 20 GHz

Label k

α β

0.38 0.28 0.36 10.7

◦

0.99 0.25 0.13 7.0

◦

0.75 NA 0.05 13.7

◦

0.68 NA NA 15.9

◦

0.45 NA 0.13 19.5

◦

Mean 0.65 0.26 0.17 13.4

◦

Table 4: Input parameter values extracted from selected

vegetation blocks at 62.4 GHz.

Tree 62.4 GHz

Label k

α β

0.31 0.13 0.08 4.7

◦

1.26 1.02 0.07 15.5

◦

0.81 NA NA 12.1

◦

0.51 0.10 0.15 14.9

◦

0.50 0.38 0.04 11.1

◦

Mean 0.68 0.41 0.09 11.7

◦

0 50 100 150 200 250 300 350

−70

−60

−50

−40

−30

−20

−10

RX antenna rotation angle (deg)

Excess attenuation (dB)

RMS

= 9.16 dB

Measured Signal

Predicted Signal

Figure 6: Measured and predicted signals in MP

at 62.4

GHz.

respectively. In these measurements, which were per-

formed at the air to vegetation interface, the RX sig-

nal level is strongly inﬂuenced by the direct path be-

tween the TX and the RX antennas. Hence, the plots

present a signal shape which is very close to the radi-

ation pattern of the receiver antennas, particularly in

the angular region around 0

◦

where the RX antenna

is pointing to the TX. Although a good overall agree-

ment between predicted and measured curves can be

observed, specially when the RX and TX antennas

are aligned, a slightly increased error is present in the

prediction of the signal which is scattered from the

forest. This may be explained due to some inaccu-

racy in the estimation of k

parameter corresponding

to the surrounding trees during the parameters extrac-

tion phase.

Figs. 7 and 8, present the results for M P

, which

is located behind tree number 1. The results for 20

GHz (Fig. 7) also present a good agreement between

the measured and the predicted received signal values.

Nevertheless, there is a tendency to underestimate the

scattered signal from tree number 1. This effect is

present in the 220 to 330

◦

angular range and might

be due to the incorrect estimation of the beamwidth

0 50 100 150 200 250 300 350

−80

−70

−60

−50

−40

−30

−20

−10

RX antenna rotation angle (deg)

Excess attenuation (dB))

RMS

= 8.91 dB

Measured Signal

Predicted Signal

Figure 7: Measured and predicted signals in M P

at 20

GHz.

0 50 100 150 200 250 300 350

−65

−60

−55

−50

−45

−40

−35

−30

−25

−20

−15

RX antenna rotation angle (deg)

Excess attenuation (dB)

RMS

= 7.58 dB

Measured Signal

Predicted Signal

Figure 8: Measured and predicted signals in MP

at 62.4

GHz.

of the scattering proﬁle of tree number 1. The un-

derestimation of this parameter will concentrate the

scattered radiation in the forward scattering region

(θ

= 340

◦

) leading to the mentioned inaccuracy.

Around θ

= 200

◦

the dRET model predicts a peak

in the received signal which corresponds to the sig-

nal scattered from tree number 9. The misalignment

between this peak and the correspondent peak in the

measured signal is likely to be due to the approxima-

tion in discretisation of the tree position inherent to

the cell division process.

The 62.4 GHz plot (Fig. 8) presents an absolute er-

ror of 10 to 13 dB in the forward scattering region

(around 340

◦

). This can be due to some blockage

which was taken into account in the k

extraction. In

fact, k

is extracted by measuring the excess atten-

0 50 100 150 200 250 300 350

−80

−70

−60

−50

−40

−30

−20

RX antenna rotation angle (deg)

Excess attenuation (dB)

RMS

= 9.02 dB

Measured Signal

Predicted Signal

Figure 9: Measured and predicted signals in M P

at 20

GHz.

0 50 100 150 200 250 300 350

−70

−65

−60

−55

−50

−45

−40

−35

−30

−25

−20

RX antenna rotation angle (deg)

Excess attenuation (dB)

RMS

= 14.5 dB

Measured Signal

Predicted Signal

Figure 10: Measured and predicted signals in M P

at 62.4

GHz.

uation caused by the tree, using a radial path which

is different from the line used to measure the atten-

uation. Attenuation differences between different ra-

dial paths of 20 dB have been published in literature

(Caldeirinha, 2001). This may help to explain this

discrepancy.

Figure 9 presents the measured and predicted re-

ceived signal values in position MP

at 20 GHz.

A good correspondence between the two values

is present in the forward scattering region around

= 330

◦

± 70

◦

. In the angular region where the

RX antenna is pointing away from the test forest, i.e.

◦

≤ θ

≤ 110

◦

the measured signal shows an in-

creased received signal level which appears to be due

to scattering in the vegetation structures surrounding

the test forest. These structures, lying outside the

Table 5: Model performance assessment using the RMS er-

ror criterion.

Measurement RMS error (dB)

Position 20 GHz 62.4 GHz

11.8 9.0

10.8 9.2

13.9 7.8

8.9 7.6

12.5 16.5

13.5 13.5

9.6 6.7

18.7 11.8

9.0 14.5

13.2 NA

Mean 12.2 10.7

test forest were not modeled and consequently are not

taken into account by the dRET modelling thus ex-

plaining why the model seems to be unable to predict

accurately the signal level within this angular region.

At 62.4 GHz the signal level in position M P

was

relatively low and could only be measured for a nar-

row angular region. Outside this region the received

signal was too close to the receiver noise level, which

is around -70 dBm, to be measured. The measured

and predicted values seem to exhibit a level offset

which seems to be due to a vertical misalignment of

the RX antenna. This offset generates a larger RMS

error when compered with the remaining measure-

ment positions.

The overall RMS error for the complete set of mea-

surement performed at 20 and 62.4 GHz is shown in

Table 5. The RMS error is consistently below 15 dB

except at a few locations in the forest. The mean over-

all RMS error is 12.2 and 10.7 dB at 20 and 62.4

GHz, respectively. Although the RMS error values

are slightly above ﬁgures found in other published re-

sults, these can be considered reasonably low. They

also demonstrate the beneﬁts of dRET modelling, par-

ticularly when considering inhomogeneous media.

5 CONCLUSIONS

This paper presents a model for radiowave propaga-

tion in inhomogeneous vegetation media for micro

and millimeter waves, which is based on the RET. The

model relies on 4 vegetation dependent propagation

parameters and a method to extract and scale these

parameters is also presented. The input parameters

are extracted from the different vegetation volumes

forming the test forest using the proposed method at

20 and 62.4 GHz. Subsequently these parameters are

used in the model to generate excess attenuation pre-

dictions at several locations inside the test forest. Fi-

nally, the predicted and measured results are com-

pared using the RMS error criterion. This is shown

to be consistently below 15 dB. Although this RMS

error value is within the range of other published re-

sults, in some measurement locations the error was

found to be as high as 18.7 dB. This is thought to

be due to localised blockages, inaccuracies in the pa-

rameter extraction method and also misalignment of

the RX antenna during the attenuation measurement

phase. An improved parameter extraction method is

thus being investigated to eliminate higher error dis-

crepancies.

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