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American Journal of Software Engineering and Applications
http://www.sciencepublishinggroup.com/j/ajsea
doi: 10.11648/j.ajsea.20170602.
ISSN: 2327-2473 (Print); ISSN: 2327-249X (Online)
Determination of Rounded Edge Diffraction Loss for a
Plateau Using Hacking Method
Victor Akpaiya Udom, Kalu Constance, Asuquo Ifiok Okon
Department of Electrical/Electronic and Computer Engineering, University of Uyo, Uyo, Nigeria
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To cite this article:
Victor Akpaiya Udom, Kalu Constance, Asuquo Ifiok Okon. Determination of Rounded Edge Diffraction Loss for a Plateau Using Hacking
Method. American Journal of Software Engineering and Applications. Vol. 6, No. 2, 2017, pp. 35-39. doi: 10.11648/j.ajsea.20170602.
Received : January 3, 2017; Accepted : January 18, 2017; Published : June 12, 2017
Abstract: In this paper, Hacking rounded edge diffraction loss method is used to determine the diffraction loss over a plateau
in the path of microwave signal in the GSM frequency band, 800 MHz to 2100 MHz. The computation is based on the path
profile with path length of 4996.243 m and a plateau in the signal path. The plateau has maximum elevation of 268.9 m and it
occurred at a distance of 3557.8 m from the transmitter. The line of sight clearance height is 45.747499 m and occultation
distance is 1538.759 m. At 800 MHz, the diffraction loss is 55.25 dB whereas at 2100 MHz the diffraction loss is 71.713 dB. The
result is useful for GSM network planning.
Keywords: Rounded Edge Diffraction, Diffraction Loss, Elevation Profile, Diffraction Parameter, Knife Edge Diffraction,
Hacking Rounded Edge Diffraction Method
1. Introduction
A plateau is an area of fairly level high ground. When an
isolated plateau is located in the path of microwave signal it
constitutes an obstruction. As an obstruction, the plateau will
cause diffraction loss [1-5]. Like other obstructions such as
hill and building, the plateau can be approximated as knife
edge obstruction. However, approximation will
under-estimate the diffraction loss that can be caused by the
plateau [6, 7]. In that case, a rounded edge obstruction
approximation is preferable [8-14].
In this paper, determination of rounded edge diffraction loss for
a plateau using Hacking method [15-19] is presented for 800 MHz
to 2100 MHz GSM (Global System for Mobile communication)
frequency band. The study utilizes the path profile of a microwave
link with a plateau in the signal path to construct the rounded edge
geometry which is then used to determine the rounded edge
diffraction loss expected from the plateau.
2. Theoretical Background
2.1. The Rounded Plateau Obstruction Geometry and
Parameters
Figure 1 shows the elevation profile of a plateau obstruction
between the transmitter (T) and the receiver (R).
Figure 1. The Elevation Profile Of A Plateau As The Obstruction In The Signal Path.
In order to determine the diffraction loss that the plateau will present using the rounded edge approach, a tangent (denoted in this paper as tangent line t) must be drawn from the transmitter to the elevation profile at the vicinity of the plateau vertex, as shown in figure 2. Similar tangent line (denoted in this paper as tangent line r) is also drawn from the receiver to the elevation profile at the vicinity of the plateau vertex. Then, a circle is fitted to the plateau at the vicinity of the plateau vertex in such a
36 Victor Akpaiya Udom et al. : Determination of Rounded Edge Diffraction Loss for a Plateau Using Hacking Method
way that the circle is tangential to the two tangential lines to the
elevation profile. In this paper, the tangent line t, the tangent
line r, their tangent points and their lengths denoted as S1 and
S2 are determined by drawing the tangent line t and tangent line
r on the graphical plot of the path profile. Also, the length of the
line of sight (LOS) denoted as S3 is measured out from the
graph plot of the path profile.
Figure 2. The Elevation Profile Of The Plateau Obstruction With Tangential Lines And Fitted Circle At The Vicinity Of The Plateau Vertex.
Figure 2 shows the essential parameters required for the
rounded plateau top diffraction loss computation. The key
dimensions include:
i. S1: the length of (tangent line t) the tangent from the transmitter to the intersection point of tangent line t and tangent line r. ii. S2: the length of (tangent line r) the tangent from the receiver to the intersection point of tangent line t and tangent line r. iii. S3: the length of the line of sight (LOS) which is the line from the transmitter to the receiver. iv. β: The LOS is inclined at angle β to the horizontal. The angle which the LOS makes with the horizontal is denoted as β where;
β ^
(^) (1)
where
H is the elevation of the transmitter and^ H is the elevation of the receiver. (^) H and (^) H are obtained from
the path profile data.
v. d1: the horizontal distance from the transmitter to the intersection point of the two tangents vi. d2: the horizontal distance from the receiver to the intersection point of the two tangents vii. d is the path length, that is the distance between the transmitter and the receiver, and d is given as;
d = (^) d d (2)
d and d are^ measured^ from^ the^ graph^ plot^ and^ the intersection point of tangent line t and tangent line r
viii. D: the occultation distance, which is the distance
between the tangent point before and the tangent point after the intersection point of tangent line t and tangent line t. D is the distance between the tangent point of tangent line t with the path profile and the tangent point of tangent line r with the path profile. In this paper, the tangent points are determined by drawing the tangent line t and tangent line r on the graphical plot of the path profile. Then, D is measured from the graph plot as the distance between the tangent points of tangent line t and tangent line r. ix. αt: the angle between the LOS and (tangent line t) the tangent line drawn from the transmitter to the elevation profile. x. αr: the angle between the LOS and (tangent line r) the tangent line drawn from the receiver to the elevation profile. The angles αt and αr are obtain by cosine rule as follows;
Cos αt
! "# !$ " !% " % & &$
(3)
αt Cos^
! "# !$ " !% " % & &$ (4)
Similarly,
αr Cos^
! %"# !$ " ! " % &% &$ (5)
The angle α is given as;
α αt αr (6)
xi. ( is the height of the intersection point of tangent line t and tangent line r above the LOS. ( is the height of the intersection point of tangent line t and tangent line r above the LOS. h is given as;
h
!*!+, -. !+, /0 (7)
xii. v is he diffraction parameter which is given as;
v (
% 4#4% 5 %
(8)
xiii. R is the radius of the circle fitted to the plateau in the vicinity of the plateau vertex. The radius of the circle fitted in the vicinity of the hill vertex. The circle fitted in the vicinity of the hill vertex is tangential to the tangent line t and tangent line r. The approximate value of R is estimated from the path profile using the formula [20, 21];
6 % 7 % - * "^ # %"^. (9)
2.2. Hacking Method for Computing Diffraction Loss over Rounded Edge
According to Hacking method for diffraction loss on rounded edge, the total diffraction loss, (^) A 49 : is given as;
A 49 : A;< =<> (10)
38 Victor Akpaiya Udom et al. : Determination of Rounded Edge Diffraction Loss for a Plateau Using Hacking Method
Table 2. Rounded Edge Parameters For The Plateau Obstruction.
f (GHz) Frequency 1000 λ (m) Wavelength 0. S1 (m) The length of the tangent from the transmitter to the intersection point of the two tangent 3283. S2 (m) the length of the tangent from the receiver to the intersection point of the two tangents 1714. S3 (m) the length of the tangent from the receiver from the transmitter 4996. dt (m) the distance from the transmitter to the intersection point of the two tangents, that is point 3282. dr (m) the distance from the receiver to the intersection point of the two tangents 1713. d (m) the distance from the transmitter to the receiver 4996. αt (radian) The angle the tangent line from the transmitter makes with the LOS 0. αr (radian) The angle the tangent line from the receiver makes with the LOS 0. α (radian) Sum of angles αt and αr 0. β (radian) The angle the LOS makes with the horizontal 0. h (m) The LOS clearance height 45. D (m) The occultation distance 1538. R (m) = The radius of the circle fitted in the vicinity of the hill vertex 31071.
Table 2 shows the key rounded edge parameters obtained
for the plateau obstruction. From Table 2, the path length (d) is
4996.243 m. Also, the tangent from the transmitter and the
tangent from the receiver intersected at a distance of
3282.9428 m from the transmitter and a distance of
1713.3002m from the receiver. The line of sight makes an
angle of 0.0044209 radians with the horizontal. The LOS
clearance height is 45.747499 m. The occultation distance is
1538.759 m.
Table 3 and figure 3 show the diffraction parameter and the
diffraction loss for the rounded edge plateau as computed by
the Hacking method. The diffraction parameter and also the
diffraction loss increases with frequency. At 800 MHz, the plateau will cause diffraction loss of 55.25 dB whereas at 2100 MHz the plateau will cause diffraction loss of 71.713 dB.
Table 3. The Diffraction Parameter and The Diffraction Loss For The Rounded Edge Plateau Computed by The Hacking Method.
Frequency (MHz) Diffraction Parameter, V Diffraction Loss (dB) 800 3.148764 55. 900 3.339769 57. 1800 4.723146 68. 1900 4.852571 69. 2100 5.101581 71.
Figure 3. The Diffraction Parameter and The Diffraction Loss For The Rounded Edge Plateau Computed by The Hacking Method.
4. Conclusions
Hacking rounded edge diffraction loss method is presented.
The method is used to determine the diffraction loss over a
plateau in the path of microwave signal in the GSM frequency
band, 800 MHz to 2100 MHz. The computation is based on
the path profile of a plateau. The results show how the
diffraction parameter and the diffraction loss vary with
frequencies within the given 800 MHz to 2100 MHz
frequency band.
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