ENRI Int. Workshop on ATM/CNS. Tokyo, Japan (EIWAC2010)[EN-027] Aeronautical satellite propagation channel
characteristics using multiple antennas+

T. A. Myrvoll ∗ J. E. Håkegård ∗ B. Holter ∗∗Communication Systems, SINTEF ICT,
Trondheim, Norway.
[Tor.Andre.Myrvoll | Jan.E.Hakegard | Bengt.Holter ]@sintef.noAbstract In this work we have investigated the use of multiple antennas for satellite-aircraft communications. In particular, wehave looked at how signals received by antennas attached to the aircraft are correlated as a function of their separation distance.
The signal correlation is an important factor when determining how effective a multiple antenna scheme will be. We have
limited ourselves to reflections from sea surfaces due to the relatively simple analytical properties as opposed to land surfaces.
The aeronautical channel is well described in the literature and analytical results exist for communications parameters like delay
and Doppler spreads. There does not however, seem to be a simple analytical model to describe the correlation between signals
as observed at different points in space. We therefore used Monte Carlo methods combined with electromagnetic scattering
theory to obtain numerical estimates of the correlations. Due to the computational complexity we reduced the problem to a
two-dimensional representation. That is, the sea surface is a one dimensional function, and the aircraft is positioned at analtitude h above the surface. Although this is a simplification, we still believe that the insights we gain with respect to changes
aircraft altitude, elevation angles and sea surface roughness, are valid.
Keywords ATM, CNS, CARATS

1

INTRODUCTION

correlation coefficient is close to one, the signals areclose to correlated and no diversity gain is obtained. If
however the correlation coefficient is close to zero, thesignals are close to uncorrelated and diversity gains
can be obtained.
In this publication, the correlation coefficient of
the signal reflected by the earth surface is exploredfor low elevation angles and for flights over sea. Dueto the waves of the sea surface, the receiver antennas
will receive signals reflected by not only one point
but from a surface area. The size of the area depends
among others on the sea state and the flight altitude.

Systems providing communications between aircraft and ground play a vital role for the security, safety
and efficiency of air traffic. As most of the earth surface is covered by water or ice, flights over these areas
will often be out of reach of terrestrial communication
systems and must therefore rely on satellite communication.
Several satellite communication systems, such as
Inmarsat, provide aeronautical services in the so-called
ORP (ocean, remote, polar) domain. A drawback related to geostationary satellite systems such as Inmarsat
is that the polar coverage is poor, as the satellite will
be located below the horizon for latitudes above 82◦ .
Moreover, reliable communication is often difficult
above 65◦ - 70◦ due to low satellite elevation angles.
For polar routes, and some intercontinental routes, this
implies long time spans without reliable communication means.
A propagation channel with low satellite elevation
angle will generally be affected by multipath propagation, as the receiver antenna will receive signals reflected by the earth surface and the fuselage, as well as
the direct signal. An efficient strategy to combat multipath propagation is to use multiple antennas. By implementing diversity schemes such as maximum ratio
combining (MRC), the inherent diversity in multipath
propagation channels can be exploited to obtain significant performance gains. A condition for obtaining
diversity gain is however that the signals received by
the different antenna elements are uncorrelated. If the

2. SCATTERING THEORYThis section describes the use of Monte Carlo simulations of scattering from a one dimensional (1D)rough sea surface. The goal of the simulations is to investigate the correlation between points in the diffuse
component of the scattered electro-magnetic field. The
first subsection will give a brief overview of the underlying theory and the approximations that need tobe made to facilitate the numerical simulations. Later
subsections will present the simulation results as wellas interpretations and discussions.
2.1. The theory of scattering of electromagnetic
waves from rough surfaces
Research into the effect of scattering from roughsurfaces, be it e.g. acoustic or electro magnetic waves,
has been conducted for more than a century. Our work
will be based on [1] and [2].

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T. A. Myrvoll, J. E. Håkegård, B. Holter

Satellite

Antennassurface was a plane coinciding with the tangent plane.
This approximation is stated to be valid wheneverκ(2)where κ is the radius of curvature of the surface, λis the carrier wavelength and γ is the elevation angle,
that is, the angle between the horizon and the direction of observation. Clearly, care must be taken at low
elevation angles as not to violate this assumption.

Elevation

Figure 1: Geometry of satellite-aircraft communications. The elevation angle is measured between thesatellite and the horizon.

2.1.3. The scattered field E(p)The scattered field off a surface S as seen from apoint p in free space, is given by the Helmholtz integral:
!
"
∂E
∂ψ
−ψ
dS
(3)
E(p) =
E
∂n
∂n
S

20

15

where the constituents are as follows in the one-dimensional
case:

10

Surface height [meters]λ
4π sin γ

5• Under the Kirchhoff approximation the electricfield is equal to E = (1 + Γ)E1 . Here E1 =exp ik1 · r where k1 is the wave-number and r isa directional vector from the origin to the point(x, ζ(x)), ζ(x) being a realization of the Gaussian surface. Γ is the reflection coefficient of asmooth plane-wave on a flat surface.

0

−5

−10

−15

−20
−100

−80

−60

−40

−20
0
20
Surface x−axis [meters]

40

60

80

• ψ = exp(ikR)
is the reflected wave. R is the disRtance from the point of observation, p, and thepoint of reflection (x, ζ(x)). The scalar k is equal
to the wave number, k = 2π
λ .

100

Figure 2: Random surface example. Rms height is
1.25 m, rms slope 0.07 and the resulting correlation
length is 25 meters.

• ∂E∂n is shorthand for ∇E · n, n being the surface
normal. Under the Kirchhoff approximation it
can be shown that ∂E∂n = i(1 − Γ)E 1 k1 · r.

2.1.1. Modeling the sea surface
Before we can get into the scattering theory, weneed a model for a rough sea surface. Although there
is a rich theory of models for spectra of sea waves,it has been shown that a simple Gaussian process described by the root-mean-square (rms) height σ andthe spatial correlation distance L is a sufficient model
for many applications. There is a third parameter, α,that describes the rms slope of the waves. When the
waves have a Gaussian spectrum it can be shown that:
√ σ
α= 2
(1)
L
This relation is useful when one wants to chose reasonable values for σ and L, as α has been determined
empirically for various weather conditions.

• The same goes for ∂ψ
∂n . Computing the deriva∂ψ(ik2 R−1)∇Rtive yields ∂n = φ
R• dS is the infinitesimal length of a surface segment at some point x.

2.2. Numerical simulations
This section describes the Monte Carlo simulations. The geometry of the simulations is given in the
Figure 1.
Here the assumption is that the satellite is at infinity while the airplane antennas are at a much closer
distance. The non-flatness of the earth is not considered, as it will only be an issue at very low angles atwhich the Kirchhoff approximation is invalid anyway.
The Monte Carlo simulation is performed as follows:

2.1.2. Approximations and conditions
The Kirchhoff approximation states that the field
existing on a point of a surface is the same as if the296

ENRI Int. Workshop on ATM/CNS. Tokyo, Japan (EIWAC2010)

angles 20, 15, 10 and 5 degrees above the horizon,
as well as wave heights of 0.5 and 5.0 meters1 . The
immediate interpretation of these results is as follows:• The effective surface area contributing to the reflected power increases with decreasing elevation angles.
• The ratio between specular and diffuse powerincreases with decreasing elevation angles.
• The main contribution to the specular reflection
comes from the area around the glistening point– the surface point where the elevation angle isequal to the observation angle to the aircraft.

	
  Figure 3: Specular-to-diffuse power ration [dB]. Fromleft to right the bars represent the elevation angles 20,
15, 10 and 5 degrees.

• For an elevation angle equal to five degrees andwave height 0.5 meters, the surface seems tobe effectively flat and the specular component
dominates.

1. Filtering white Gaussian noise using a spatial
correlation filter having a Gaussian shape andcorrelation length L creates a series of surfaces.
An example of a surface is shown in Figure 2
for rms height 1.25 meters, and rms slope 0.07
– which corresponds to a wave correlation distance of 25 meters.

All of the above observations are consistent withtheory. Based on the above observations we can adjust our domain of integration. The parameters used
are summarized in Table 1.
Finally, the specular-to-diffuse power ratio is shownin Figure 3. Clearly, for the 0.5 meter wave heightscenario, the specular component becomes relatively
stronger when the elevation angle decreases. For the
5.0 meter wave height scenario this effect is not seen,
which indicates that the surface roughness is sufficient
to completely annihilate the specular component forelevations at least down to 5 degrees.

2. For each surface the Helmholtz integral is evalλ, anduated. We use a mesh size of dx = 10
assume that the aircraft is at height h and xposition zero. The antennas are placed at 0, a,
2a, 3a, and so on, where a typically is somemultiple of a wavelength.
3. For each antenna position a series of complex
channel gains are now available, and we cancompute their correlation.

3.2. Antenna correlations
The correlation between antennas on an aircraft
traveling at an altitude of 1000 meters is estimated forseveral elevation angles: 5, 10, 15 and 20 degrees.
The wave heights are 0.5 and 5.0 meters. For eachcombination of elevation angle and wave height, 1000
random surfaces were generated and the electric fieldat each of the antennas was computed.
All simulations are summarized in the graphicalrepresentations in Figure 5 and 6. We make the following conclusions from these figures:

3. EXPERIMENTAL RESULTS
3.1. Prelimenary simulations
The experiments are performed for a carrier frequency of 1.5 GHz, which corresponds to a wavelength of 0.2 meter. This means that the integration
resolution is 2 cm, or 50 points per meter. Clearly,
integration domains in the order of tens of kilometers make for very intensive simulations, motivating
the use of smaller domains. On the other hand, using
too small domains result in a less rich scattering environment and consequently more correlation between
antennas.
As an initial experiment we will focus on a low altitude aircraft scenario with h=1000 meter and a domain of integration equal to -30000 to 5000 meters.
Here x-coordinate equal to zero corresponds to thepoint right below the aircraft. The satellite is assumed
to be at minus infinity. We then compute the average
power of the specular and diffuse components per surface area for several elevation angles. The results areshown in Figure 4a through Figure 4h for elevation• The correlation between antennas increases as
the elevation angle decreases.
• Larger wave heights results in less correlation
between antennas for all elevations.
• The correlation is more dependent on the elevation angle than the wave height.
1 When wave heights are specified without the explicit use of theterm rms, it is assumed that the wave height corresponds to fourstandard deviations. This means that there is a 95% likelihood of
any wave to be below the wave height when measured from troughto crest.

297

T. A. Myrvoll, J. E. Håkegård, B. Holter

0,022

0,022

Diffuse power

Diffuse power

0,02

0,02

Specular power

Specular power
0,018
Power contribution for surface

Power contribution for surface

0,018
0,016
0,014
0,012
0,01
0,008
0,006

0,016
0,014
0,012
0,01
0,008
0,006

0,004

0,004

0,002

0,002

0
-30000-25000-20000-15000-10000

-5000

0

0
5000

-30000-25000-20000Surface location [m]-15000-10000-5000(a) Elevation 5 degrees, wave height 0.5 m
0,01Specular power

Specular power

Power contribution for surface

Power contribution for surface

0,008

0,007
0,006
0,005
0,004
0,003

0,007
0,006
0,005
0,004
0,003

0,002

0,002

0,001

0,001

0
-15000-10000

5000

0,009

0,008

-200000

0,01

Diffuse power

0,009-250005000(b) Elevation 5 degrees, wave height 0.5 m

Diffuse power-300000

Surface location [m]

-5000

0
0

5000

-30000-25000-20000Surface location [m]-15000-10000-5000

Surface location [m](c) Elevation 5 degrees, wave height 0.5 m(d) Elevation 5 degrees, wave height 0.5 m

0,0055
Diffuse power

0,004
Diffuse power

0,005

Specular power

0,0035Specular power
0,003

Power contribution for surface

Power contribution for surface

0,00450,004
0,00350,003
0,00250,002
0,00150,00250,002
0,00150,001

0,001
0,00050,00050-30000-25000-20000-15000-10000

-5000

0
0

5000

-30000-25000-20000Surface location [m]-15000-10000-5000(e) Elevation 5 degrees, wave height 0.5 m

5000(f) Elevation 5 degrees, wave height 0.5 m

0,00160,0009Diffuse power

Diffuse power
0,0014

Specular power

0,0007
Power contribution for surface

Power contribution for surface

0,0008Specular power

0,00120,001
0,00080,00060,00040,00060,00050,00040,00030,00020,00020,00010-300000

Surface location [m]-25000-20000-15000-10000-5000

00-30000

5000

Surface location [m]-25000-20000-15000-10000-5000

0Surface location [m](g) Elevation 5 degrees, wave height 0.5 m(h) Elevation 5 degrees, wave height 0.5 m

Figure 4: Specular (solid green) and diffuse (dashed red) power contributions from surface.

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ENRI Int. Workshop on ATM/CNS. Tokyo, Japan (EIWAC2010)

Table 1: Simulation parameters for the various scenarios
Physical parameters
Elevation Waveheight RMSSlope
5
0.5
0.07
5
5.0
0.07
10
0.5
0.07
10
5.0
0.07
15
0.5
0.07
15
5.0
0.07
20
0.5
0.07
20
5.0
0.07
1

It may seem counter-intuitive that the correlation
increases with the surface area contributing to the reflection. A larger surface implies a richer scattering
environment, which should result in less, not morecorrelation. The explanation for this observation may
be found by considering the effective wavelength of
the incoming signal at low elevations (see Figure 7).
For a wave height of 0.5 meters and a wavelengthof 0.2 meters, the effective wavelength will be larger
than the wave height when the elevation angle is lessthat arcsin(0.2/0.5) = 23.6 degrees. For low angles thephase variations will no longer be uniformly random
over 0 to 2π, but rather narrowly distributed.
Why the larger wave height is showing more correlation than the small wave height is less clear. Sinceboth scenarios use the same rms slope, the correlation
lengths are different and makes them difficult to compare. Using the same rms slope as in the 0.5 metermodel will lead to very choppy waves, which in turnleads to blocking at low elevations.

● Elevation 20 degrees▲Elevation 15 degrees■Elevation 10 degrees★Elevation 5 degrees

0,9
0,8

Correlation

0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
0

1

2

3

4

5

6

7

8

9

10

Antenna distance [m]Figure 5: Correlation between antennas as a functionof distance. Wave height 0.5 meters.
1● Elevation 20 degrees▲Elevation 15 degrees■Elevation 10 degrees★Elevation 5 degrees

0,9
0,8

Correlation

0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
0

1

2

3

4

5

6

7

8

9

Integration range
Lower bound Upper bound-300000-300000-150000-150000-100000-10000
0
-7500
0
-7500
0

10

Antenna distance [m]Figure 6: Correlation between antennas as a functionof distance. Wave height 5.0 meters.

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T. A. Myrvoll, J. E. Håkegård, B. HolterA•sin(γ)γ

1D vs. 2D: A 2D model will on one hand have aricher scattering environment, but on the other hand,the scattered field will attenuate as r−2 as opposedto r−1 . As the fastest decorrelation occurs for highelevation angles with smaller effective reflective surface areas, the attenuation may not be very important
given that a “sufficiently” large area of the surface
contributes. In that respect, the richer scattering environment should imply that the 1D simulations are
an upper bound on the decorrelation.
Backscattering and shadowing: These effects havenot been considered in this work. The backscattering
effect is believed to be of little importance as it mostly
affects the overall attenuation of the reflected signal.
The shadowing or blocking effect may impact our results in theory, at least for large wave heights and low
elevation angles. See Figure 9 where part of the surface is blocked by waves. The figure indicates that theeffective surface wave height may be reduced, which
in turn could increase correlation.
Polarization: Polarization has only been considered in the sense that a horizontally polarized EM
wave is reflected perfectly from the surface. This isaccording to theory when considering plane waves
and surfaces. A vertically polarized wave would see
an elevation angle dependent attenuation. For a 1D
surface this is sufficiently accurate, but for a 2D surface the full modeling of polarization effects should
be undergone.

A

Figure 7: The effective wavelength of an incoming
EM wave. Given a surface with a total variation A,
the observed variation at an angle γ is A sin γ. Equivalently, the effective wave length of the EM wave is
λsin γ .

5. COPYRIGHTThe authors confirm that they, and/or their company or institution, hold copyright of all original material included in their paper. They also confirm they
have obtained permission, from the copyright holder
of any third party material included in their paper, topublish it as part of their paper. The authors grantfull permission for the publication and distribution of
their paper as part of the EIWAC2010 proceedings or
as individual off-prints from the proceedings.

	
  Figure 8: Shadowing/blocking of EM wave by sea
surface. The figure shows the blocking of incoming
waves from the satellite.

4. CONCLUSIONS

6. REFERENCES

Using a simple one-dimensional representation ofa rough sea surface we have investigated the antenna
diversity corresponding to the signal reflected fromthe surface. Depending on the elevation angle andsurface roughness, the channel gain correlation is lessthan 0.2 when the antennas are 3-10 meters apart. Finally, we want to discuss some of the shortcomings ofthis model and how they may impact the results:[1] P. Beckmann and A. Spizzichino, The scatteringof electromagnetic waves from rough surfaces.
Norwood, Mass.: Artech House, c1987.
[2] P. Bello, “Aeronautical channel characterization,”
Communications, IEEE Transactions on, vol. 21,
no. 5, pp. 548–563, 1973.

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