December 2012 - URSI

surface, and the way light propagates in Figure 10 is what
we should expect as a propagation mechanism in a cellular
system. In other words, the transmitting antennas (usually
tilted down toward the ground) excite a radiating field in the
cell. In the intermediate region, this behaves as a radiating
field from a line source, and in the far-field region, it behaves
as a Norton surface wave. This wave then represents one of
the main dominant means by which the base-station antenna
communicates with the mobile device. This mechanism of
propagation is shown in Figures 8-10. The stretching of the
lights in Figures 9 and 10 hence essentially represents the
image of the primary source. Again, it is important to note
that what we are observing in Figure 10 is not a surface
wave as in the true classical sense of Schelkunoff, but the
radiated fields associated with a surface wave.
Figures 9 and 10 give us physical insight into how
waves propagate in mobile communications. They thus
illustrate why smart antennas and beamforming have not
been very successful in cellular communications until now,
despite all of the research efforts done in those fields. If the
real scenario of propagation is something similar to what
we see in Figures 8-10, then we should change our outlook
of the implementation of multiple antennas and adaptive
arrays in cellular systems. The important point is that the
effect of the ground plays a dominant role. This equivalent
line source, formed from the images, generates a field in
the air that decays as 30 dB per decade. As observed in [1],
this decay of the fields at 30 dB per decade with distance is
generated in the intermediate region, approximately where
the slow-fading region ends. This is approximately at a
distance of about 4 HTX HRX
[69] from the base-station
antenna. Here, H
TX
and H RX
represent the heights of the
transmitting and the receiving antennas over the ground,
and is the wavelength of operation.
Conventionally, in wireless communications textbooks
(such as [70]), this problem of propagation modeling is
tackled first by explaining the two-ray model over a flat
perfectly conducting Earth. In the two-ray model – the
incident and the reflected ray – the reflection coefficient is
taken to be 1 , and (the angle of incidence) is always
2 (i.e., a perfectly reflecting Earth is considered).
However, the two-ray model illustrates that the intermediate
path loss is 20 dB per decade instead of 30 dB per decade,
as we have presented. After explaining the two-ray model,
empirical models are usually presented, such as the wellknown
Okumura-Hata model [60]. Although empirical
models have been extensively applied with good results,
they suffer from some disadvantages. The main disadvantage
is that empirical models provide no physical insight into
the mechanism by which propagation occurs. In addition,
these models are limited to the specific environments
and parameters used in the measurements. To find more
satisfactory models, researchers usually follow one of
two paths: They either choose more sophisticated physical
models – which encounter other propagation mechanisms,
such as diffraction, scattering, and ray tracing [60] – or
they delve into statistical modeling [70]. We quote a very
interesting conclusion from [60]:
Although the plane Earth model has a path loss exponent
close to that observed in actual measurements (i.e., 4), the
simple physical situation it describes is rarely applicable
in practice. The mobile is always almost operated (at
least in macrocells) in situations where it does not have
a line-of-sight path to either the base station or to the
ground reflection point, so the two-ray situation on which
the plane Earth model relies is hardly ever applicable.
To find a more satisfactory physical propagation model,
we examine diffraction as a potential mechanism.
Instead of examining diffraction as a potential
mechanism or going to statistical modeling, the work
presented in this paper gives a rigorous mathematical
solution based on the exact Sommerfeld formulation of the
two-ray model, but with an imperfectly reflecting Earth taken
into consideration. This approach directly implies that the
physical model of propagation in the cellular environment
described above is the radiation field associated with a line
source. Namely, the power decreases with the distance
from the transmitter tower by 30 dB per decade for most
of the practical area of a typical cell. The multipath fading
and shadowing due to buildings and large obstacles then
appear as small variations around the main 30 dB-perdecade
slope line, as seen in the measured data. Almost
none of the physical models – such as the dielectric canyon
model, the flat edge model, and sophisticated ray-tracing
models [60] – take fields produced by a line source into
consideration. Actually, it is easy to illustrate the difference
between the “two-ray perfectly refl ecting Earth” model
(used conventionally) and the “imperfectly reflecting Earth”
model. In the companion paper [1], the mechanism of
propagation was illustrated using a diffraction model, and,
alternately, using an infinite line of sources, generated by
the imperfectly conducting ground, representing the image
due to the original source, as illustrated here.
In summary, the ray theory can never predict a decay
1.5
of the fields as 1 R . The analysis of Van der Pol presented
here provides a physical picture of how the wave, which is
not a surface wave, propagates over an imperfect ground
from the base-station antenna to the mobile device. In short,
besides the direct ray from the source, there are the fields
from a line source, generated by the image of the original
source over the imperfectly conducting ground, which can
be easily visualized in Figures 9 and 10.
8. Conclusion
The objective of this paper was to illustrate that the
propagation path loss in the intermediate region of a cell in
a cellular communication system is three, which leads to a
path loss of 30 dB per decade. This type of field resembles
that of a radiation field associated with a two-dimensional
source. These statements can be derived from the classical
18 The Radio Science Bulletin No 343 (December 2012)