第 509 回 URSI-F 資料
2006 年 11 月 17 日（金）マイクロ波帯ワイヤレスアクセスにおけるハイトゲインモデルの検討
New Method for Evaluating Height Gain at Subscriber Station for Wireless Access Systems
in Microwave Band
直樹†

北

山田

Naoki KITA

渉†

Wataru YAMADA

佐藤 明雄††
Akio SATO

日本電信電話株式会社
NTT アクセスサービスシステム研究所
NTT Access Network Service Systems Laboratories, NTT Corporation†

東京工科大学
コンピュータサイエンス学部
School of Computer Science, Tokyo University of Technology††

1. INTRODUCTION
Broadband wireless access (BWA) systems have been drawing a great deal of attention concerning broadband
wireless access services such as wireless Internet access that provide tens of megabits per second or higher transmission
speeds to users [e.g., 1]. There is a wide spectrum for BWA systems at millimeter-wave frequencies, but the technology is
not sufficiently mature to make these systems cost-effective for mass users, and a reliable non-line-of-sight (NLOS)
operation is desired to extend the applicable area of fixed wireless access (FWA) systems. Therefore, research on the
microwave band BWA system and its propagation channel characteristics is a topic of great interest (e.g., [2]-[4]).
The propagation models for FWA or nomadic wireless access (NWA) systems must be more accurate in regard to
the dependency on local conditions around subscriber stations (SSs) than models for mobile communication systems. The
reason for this is that the propagation conditions between a base station (BS) and a SS are strongly influenced by the local
conditions of the SS because the SS is stationary (or at least has very limited mobility) in the FWA or NWA scenarios.
There is of course the ray-tracing propagation model, which represents the best site-specific modeling method [e.g., 5],
but this model generally requires a very long calculation time and huge digital terrain and building databases. Therefore, amodel is required that is simpler and that can take into consideration the local conditions of the SS.
Modeling of the variation in height of the SS antenna with respect to the path loss (simply referred to as “heightvariation of the path loss at a SS” hereafter) is an important issue in the design of wireless access systems. The model musttake into consideration the local conditions around the SS. Here, the local conditions around a SS mean the buildingheight, road width around the SS, and the distance between the BS and SS. There have been studies such as [6], [7] on thisheight variation of the path loss at a SS for radio communication system design. However, most of these studies deal with
the UHF band up to 2 GHz and focus on mobile communication systems (not FWA or NWA systems). So, the SS antennaheight is limited to approximately 3 m (in [6]), and the range of the BS-SS separation is limited to more than 1 km (in [7])in these models. The height variation of the path loss at a SS for locations higher than 3 m is important for FWA scenarios
in which the SS antenna is established on a rooftop or on a wall of a building. In addition, predicting the path loss andheight variation of the path loss at a SS in the near region (BS-SS separation of less than 1 km) is important. The path loss
prediction in not only the far region in order to estimate the limit of the radio zone, but also that in the near region in orderto estimate the achievable transmission speed within the radio zone are necessary because the transmission speed varies
depending on the received signal strength according to an adaptive modulating function in modern wirelesscommunication systems such as IEEE802.11 wireless LAN (Local Area Network) systems [8] or IEEE802.16 wireless
MAN (Metropolitan Area Network) systems [9] used in wireless access systems.
Although some publications reported some measurement examples for the height variation of the path loss at a SS for
microwave band BWA systems [10], [11], these did not propose a model for estimating the height variation of the pathloss at a SS.
This paper proposes a height variation model of the path loss for evaluating height gain at a SS in the microwave
band. The model takes into consideration the local conditions around a SS and the horizontal distance between the BS and
SS. The target area of the model is a fairly homogeneous propagation environment such as a residential area, which is an
important service area for wireless access services.
Section 2 describes the characteristics of the height variation of the path loss and height gain at a SS based on
measurement results in real environments. Section 3 presents the analysis of the mechanism for the dependency of heightvariation of the path loss at a SS on the location based on geometrical optics (GO) and the uniform geometrical theory of-1-

第 509 回 URSI-F 資料
2006 年 11 月 17 日（金）diffraction (UTD) [12]. In Section 4, the modeling of the height variation of the path loss at a SS taking into consideration
the local conditions around the SS will be presented, and validation of the model in terms of height gain with measured
height variation of the path loss at the SS in the microwave band carried out in a residential area in Tokyo and in Ibaraki
prefecture in Japan will be presented. Finally, we present our conclusions in Section 5.

2. HEIGHT VARIATION CHARACTERISTICS OF PATH LOSS AT SS IN REAL ENVIRONMENT
The measurements for the height variation of the path loss at a SS were carried out in the Suginami area in Tokyo.
The SS antenna height (hSS) was changed from 4.5 m to 10.5 m continuously during measurement at each measurement
point using a flexible pole set on top of the van as shown in Fig. 1 and Picture 1. The area is flat. The average height of thebuildings in the area is approximately 7.5 m, but some apartment buildings are higher than 10 m.
Typical examples of the acquired height variation characteristics of the received level are shown in Figs. 2(a) and2(b). Figures 2(a) and 2(b) correspond to the measured results when the BS-SS separation distance is relatively short (330m) and relatively long (1360 m), respectively. The plots in both figures represent 1-m high section mean values of theacquired data at 5.2 GHz / CW. The BS antenna height is 32 m. The propagation path between the BS and SS isline-of-sight (LOS) and Non-LOS (NLOS) when the SS antenna height is 10 m and 5 m in both figures. The difference inthe height variation characteristics of the received level between Figs. 2(a) and 2(b) is clear. The slope of the level
attenuation due to a decrease in the SS antenna height is small in Fig. 2(a) compared to that in Fig. 2(b). The difference inthe received level between the SS antenna height of 10 m (LOS) and 5 m (NLOS) is 11 dB and 19 dB in Figs. 2(a) and 2(b),respectively. It seems that the slope of the level attenuation due to a decrease in the SS antenna height becomes relatively
small in the near region (BS-SS separation is relatively short) compared to that in the far region (BS-SS separation isrelatively long).
The term, ‘height gain’ is introduced. Height gain, Gh_b, a, is defined as the relative received level when the SS
antenna height is b (m) based on a (m). Here, b > a, the received level represents a 1-m high section mean value of theacquired data shown as plots in Fig. 2. Figure 3 shows the dependency on the BS-SS horizontal distance of the height gain
at hSS = 10 m based on hSS = 5 m at hBS = 32 m in the Suginami area, which includes the measured results shown in Figs.
2(a) and 2(b). The SS antenna height of 5 m corresponds to just above the rooftop of a one-story building, and 10 m
corresponds to just above the rooftop of a second-story building. Figure 3 indicates that the height gain, Gh_10m, 5m,
depends on the BS-SS horizontal distance, and the height gain tends to be large in the relatively far region rather thanthose in the relatively near region.

3. PROPAGATION MECHANISMS CAUSING HEIGHT VARIATION DEPENDENCY ON LOCALSS CONDISIONS
3.1 Calculation of Height Variation of Path Loss at SS
The variation in the path loss according to the SS antenna height and multipath wave components arriving at the SS
antenna were calculated based on GO and UTD to reveal the propagation mechanisms that cause the height variation
dependency on the local SS conditions.
The assumed propagation model is shown in Fig. 4. Here, w is the building spacing, and h1 and h2 are the buildingheights. The calculated arrival waves at the SS antenna are the direct wave (only in the LOS region), one-time toeight-time regular reflected waves from the building walls, one-time diffracted waves due to the corners of the rooftops ofbuildings, and one-time diffracted and reflected waves from the corners of the rooftops and walls of the buildings. For
simplicity, only two neighboring buildings are considered and each building is approximated as rectangular bodies. For
calculations of the diffracted waves, the UTD for metal edges is used. For calculations of the reflection coefficients on thewalls of buildings, a complex permittivity of 6.95 – j0.74 (that of concrete at 5 GHz) [13] is used.

3.2 Calculation Results and Discussion
The calculated results using the model employing GO and UTD mentioned above for different local conditions(especially, incidence angle θ) of a SS are shown in Figs. 5(a) and 5(b) with the measured results shown in Figs. 2(a) and2(b). Both the calculated and measured results shown in Figs. 5 are normalized by letting the average level of the received
power in the LOS region on the building roofs above approximately 2 m be 0 dB. Figure 5(a) shows the results in which
the BS-SS horizontal distance is 330 m and θ = 4.06°, and Fig. 5(b) shows those for 1360 m of BS-SS horizontal distanceand θ = 0.94°. The measured values are the averages of the power over a 1-m section in height.

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第 509 回 URSI-F 資料
2006 年 11 月 17 日（金）The calculated results in Figs. 5(a) and 5(b) also indicate the contents of the arriving multipath waves. In thesefigures, (0) denotes the direct wave, (1)–(3) the 1 to 3-time reflected waves and (D) the once-diffracted wave. Although
the once-diffracted waves arrive at any height of the SS antenna, there are restrictions on the height for the direct wave andthe reflected waves. The lengths of the straight lines for (0)–(3) indicate the height ranges in which the respective wave
can be received at the SS antenna. The calculated total level (power derived from the vector sum of the direct, reflected,
and diffracted waves) agrees with the measured results in both Figs. 5(a) and 5(b).
Figure 5(a) shows that the one-time, two-time, and three-time reflected wave components represented by indexes (1)– (3) are dominant compared to the one-time diffracted wave component represented by index (D). In Fig. 5(a), themeasured level agrees with the calculated level of the direct, one- and two-time reflected wave components at theminimum height where the direct, one- and two-time reflected waves arrive at the SS antenna, respectively. On the other
hand, Fig. 5(b) shows that the arrival region of the regular reflected waves represented by indexes (1) – (3) is very shortand the one-time diffracted wave component represented by index (D) is dominant compared to these regular reflected
waves. In addition, the height variation of the total level is nearly equal to that of the one-time diffracted wave.
These results show that a change in the height variation characteristics is caused by the difference in composition of
the arriving waves at the SS antenna. In other words, whether or not the regular reflected waves have a level higher thanthe one-time diffracted wave when arriving at the SS strongly influences the height variation characteristics of the pathloss.
Figure 6 shows the mechanism of the propagation over the rooftops based on a geometrical propagation model. We
can divide the height variation of the path loss due to the BS-SS horizontal distance into the following three regions
depending on the arriving wave dominant to the entire level.
(a) The direct wave dominant region where the BS-SS horizontal distance is very short.
In this region, the direct wave can arrive at any height of the SS antenna. The path loss and the height variation of
the path loss at the SS are dominated by the propagation loss of the direct wave.
(b) The reflected wave dominant region where the BS-SS distance is relatively short.
In this region, a strong reflected wave as a one- or two-time reflected wave and diffracted wave can arrive at any
height of the SS antenna in the NLOS region. The propagation loss of the minimum-time-reflected wave arriving at
any height of the SS antenna is smaller than that of the diffracted waves in the NLOS region. The path loss and heightvariation of the path loss at the SS in this region are dominated by the reflected waves. The path loss in the relatively
near region corresponds to the direct, one-, and two-time reflected wave components at the minimum height where
the direct, one- and two-time reflected waves arrive at the SS, respectively.
(c) The diffracted wave dominant region where the BS-SS distance is relatively long.
In this region, a strong reflected wave as a one- or two-time reflected wave can only just arrive at the SS antenna
in NLOS region where the SS antenna height is lower than that of the surrounding buildings, and only weak
many-time-reflected waves and diffracted waves can arrive at the SS antenna. The propagation loss of theminimum-time-reflected wave arriving at the SS becomes larger than that of the diffracted wave. The path loss andheight variation of the path loss at the SS in the far region are dominated by the diffracted waves from the edge of thebuilding roof. The path loss and height variation of the path loss at the SS nearly correspond to that of the diffracted
wave.
In the next section, we describe a new simple model for the height variation of the path loss reflecting the local
conditions around the SS in terms of the arrival conditions of regular reflected and one-time diffracted wave
components.

4. MODELING OF HEIGHT VARIATION IN PATH LOSS REFLECTING LOCAL SS
CONDITIONS
4.1 Height Variation Model for Path Loss Reflecting Local SS Conditions
The height variation of the path loss due to the local SS conditions, especially the BS-SS horizontal distance, can bedivided into three parts in terms of the dominant wave as mentioned in the previous section. The height variation of thepath loss in each part is expressed as follows.

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第 509 回 URSI-F 資料
2006 年 11 月 17 日（金）(a) When the BS-SS horizontal distance is very short (LOS region)
The direct wave is a dominant influence on the height variation of the path loss at a SS, Lh(hSS). Figure 7(a) shows
the geometry for the calculation of the height variation of the path loss at a SS, and Lh(hSS) is expressed as Eq. (1).
⎧⎪ 4π d 2 + (h − h ) 2 ⎫⎪BSSS
Lh (hSS ) ≈ 20 ⋅ log ⎨
⎬
λ
⎪⎩
⎪⎭

(1)

Here, λ is the wavelength.
(b) When the BS-SS horizontal distance is relatively short
The reflected waves are a dominant influence on the height variation of the path loss at a SS. Figure 7(b) shows thegeometry for the calculation of the height variation of the path loss at the SS. Point A represents the boundary between the
LOS and NLOS regions, and the path loss at Point A is defined as the reference level for the height variation of the pathloss. Term LR(ΔhSS) is expressed as the excess loss based on the path loss at Point A. Here, ΔhSS is the depth to the NLOS
region from Point A of the SS antenna. As mentioned in the previous section (Fig. 5(a)), LR(ΔhSS) corresponds to theexcess loss of the direct, one-, and two-time reflected wave components at the minimum height where each wave
component can arrive at the SS antenna. The depth to the NLOS region from Point A of the SS antenna, ΔhSS,k, and theexcess loss of the k-time reflected wave, LR(ΔhSS,k), at the minimum height of the SS antenna where the n-time reflectedwave can arrive at the SS antenna are expressed as Eqs. (2a) and (2b).
kw ⋅ (hBS − hb )⎧⎪d sin ϕ − w1⎪
ΔhSS , k = ⎨⎪ (kw − w1 + w2 ) ⋅ (hBS − hb )⎪d sin ϕ − w1⎩

(k : Even)(k = 0,1,2,3,⋅ ⋅ ⋅)(2a)(k : Odd )⎛ d kp ⎞⎟LR (ΔhSS , k ) ≈ 20 log⎜
⎜ d ⋅ Rk ⎟
p
0
⎝
⎠

(2b)

Here, ϕ is the angle between the building row and the line of visibility/LOS, R is the reflection coefficient of the wall
surface of the building in the microwave band and is specified as -8 dB as indicated in Ref. [14], and hb is the averagebuilding height. In addition, in terms of the variables in Fig. 7(b), dkp, which is the path length of k-time reflected waves,is geometrically given by Eq. (2c).
d kp =⎧w ⋅ (h − hb ) ⎫1
2⋅ Ak + ⎨hBS + ΔhSS , k − hb + 1 BS⎬
sin ϕ kd sin ϕ − w1 ⎭
⎩

2

(2c)

⎛ d sin ϕ⎞⋅ tan ϕ ⎟⎟⎝ Ak⎠

ϕ k = tan −1 ⎜⎜d sin ϕ + kw⎧
Ak = ⎨⎩d sin ϕ + (k − 1)w + 2w2(k : Even)(k : Odd )The path loss between the limiting height of the k-time reflected wave and that of the k+1-time reflected wave is found tobe subject to linear interpolation by Fig. 5(a). Hence, the path loss in the reflected wave region can be given by thefollowing, obtained from linear interpolation using Eq. (2).
When ΔhSS , k ≤ ΔhSS < ΔhSS , k +1
LR (ΔhSS ) = LR (ΔhSS , k ) +LR (ΔhSS , k +1 ) − LR (ΔhSS , k )ΔhSS , k +1 − ΔhSS , k-4-⋅ (ΔhSS − ΔhSS , k )(k = 0,1,2,3,⋅ ⋅ ⋅)(3)

第 509 回 URSI-F 資料
2006 年 11 月 17 日（金）Figure 8 shows an example of the calculated results using Eq. (3) as the ratio of w1 to w2 is varied at several values ofϕ. Figure 8 indicates that the height pattern of the path loss variation at any ϕ fluctuates except for when the ratio of w1 to
w2 equals one. The center of the fluctuations corresponds fairly well to the height pattern of the path loss variation when
the ratio of w1 to w2 equals one. In this paper, we attempt to construct the height variation model of the path loss at the SS
as simple as possible. Hence, for simplicity, both distance w1 between the SS and the building on the BS side, and distance
w2 between the SS and the building on the BS side, and distance w2 between the SS and the building on the other side of the
BS are set to 1/2w.
w1 = w2 ≅

1
w
2

(4)

(c) When the BS-SS horizontal distance is relatively large
The diffracted waves are a dominant influence on the height variation of the path loss at a SS. Figure 7(c) shows thegeometry for the calculation of the height variation of the path loss at the SS. The once-diffracted wave from the buildingedge is dominant-arriving wave in this region. As the once-diffracted wave, let us consider the diffracted wave from thediffraction points α and βin Fig. 7(c). Hence, the excess loss in the NLOS region based on the path loss at Point A,
LD(ΔhSS) is expressed as follows.
As the once-diffracted wave, let us consider the diffracted wave from diffraction points α and βin Fig. 7(c). Hence,the excess loss in the NLOS region based on the path loss at Point A, LD(ΔhSS) is expressed as follows.
22⎧⎛ D ⋅ d⎞ ⎛ Dβ ⋅ d 0 p ⎞ ⎫⎪
⎪⎜
α
0p
⎜
⎟
⎟
+
LD (ΔhSS ) ≈ −10 ⋅ log ⎨
⎟ ⎬
⎜
⎟ ⎜
⎪⎩⎝ d α ,a ⋅ d α ,b ⎠ ⎝ d β ,a ⋅ d β ,b ⎠ ⎪⎭(5)Here, ΔhSS is the depth to the NLOS region from Point A of the SS antenna, and Dα and Dβ are the UTD diffraction
coefficients. Although the UTD diffraction coefficient has polarization dependence, the diffraction coefficients used here
are the averages of the results for vertical and horizontal polarizations. Terms dα,a and dβ,a are the distances from the BS
antenna to diffraction points α and β, while dα,b and dβ,b are the distances from diffraction points α and β to the SS. These
are given by
2

2
⎫
⎧
⎫
⎧ d sin ϕ ⋅ (hBS − hb )w ⎪⎪2dα , a = ⎨ d 2 − ⎨− ΔhSS ⎬ − 1 ⎬ + (hBS − hb )
d
w
sin
ϕ
sin
ϕ
−
1
⎭
⎩
⎪⎭
⎪⎩

⎫
⎛ w ⎞ ⎧ w ⋅ (h − hb )d α ,b = ⎜⎜ 1 ⎟⎟ + ⎨ 1 BS
+ ΔhSS ⎬⎝ sin ϕ ⎠ ⎩ d sin ϕ − w1
⎭
2

2

(6a)

(6b)
2

2
⎧
⎫
⎫
⎧ d sin ϕ ⋅ (hBS − hb )w ⎪⎪2dβ ,a = ⎨ d 2 − ⎨− ΔhSS ⎬ − 2 ⎬ + (hBS − hb )
d
w
sin
ϕ
sin
ϕ
−
1
1⎪
⎭
⎩
⎪⎩
⎭

⎛ w ⎞ ⎧ w ⋅ (h − hb )⎫d β ,b = ⎜⎜ 2 ⎟⎟ + ⎨ 1 BS
+ ΔhSS ⎬
d
w
sin
ϕ
sin
ϕ
−
⎝
⎩
⎭
1
1 ⎠
2

2

(6c)

(6d)

Distance w1 between the SS and the building on the BS side, and distance w2 between the SS and the building on the otherside of the BS are set to 1/2w as well as when the BS-SS horizontal distance is relatively short.
Term LD(ΔhSS) is the function of the variables, w, ϕ, θ, and f. The dependency of LD(ΔhSS) on these variables is shown in
Figs. 9(a), 9(b), 9(c), and 9(d), respectively. The figures indicate that the characteristics of LD(ΔhSS) are logarithmic versus
the depth to the NLOS region when ΔhSS is greater than 1 m, and the dependencies of LD(ΔhSS) on w, ϕ, and θ are not sostrong. The difference in LD(ΔhSS) within the parameter range of 10m ≤ w ≤ 30m , 20° ≤ ϕ ≤ 90° , and 0° ≤ θ ≤ 5° is less thanapproximately 6 dB as shown in Figs. 9(a)-9(c). On the other hand, the dependency of LD(ΔhSS) on the frequency is not
negligible as shown in Fig. 9(d). Therefore, for simplicity, an approximate equation, which represents the calculation
values of LD(ΔhSS) using Eq. (5) and contains only variable f, can be derived as Eq. (7).

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第 509 回 URSI-F 資料
2006 年 11 月 17 日（金）⎧{5.8947 ⋅ log( f ) + 0.31519}⋅ ΔhSS (− 0.003559 f + 0.65122 )⎪⎪⎪LD (ΔhSS ) ≈ ⎨{3.7432 ⋅ log( f ) + 19.245}⋅ log(ΔhSS ) + 5.8947 ⋅ log( f ) + 0.31519⎪⎪⎪⎩
24.5 ⋅ log(ΔhSS ) + 9.6379 ⋅ log( f ) − 4.93981(0 ≤ ΔhSS < 1)
(1 ≤ ΔhSS < 10)(7)(10 ≤ ΔhSS )Equation (7) is derived as follows. First, the central values in each parameter range mentioned above are chosen withregard to street angle ϕ, distance w between the buildings, and angle θ. In other words, w = 20 m, ϕ = 45 deg., andθ = 2 deg. Next, the calculation results of LD(ΔhSS) using Eq. (5) using w = 20 m, ϕ = 45 deg., and θ = 2 deg. at somefrequencies within the range of 2 to 30 GHz are approximated as a power function of ΔhSS at 0 ≤ ΔhSS < 1 and alogarithmic function of ΔhSS at 1 ≤ ΔhSS as follows.
⎧ A ⋅ (ΔhSS )B⎪
LD (ΔhSS ) ≈ ⎨⎪C ⋅ log(Δh ) + D
SS⎩(0 ≤ ΔhSS < 1)(8)

(1 ≤ ΔhSS )Here, A, B, C, and D are coefficients for approximated formulas. These coefficients are derived from the calculated values
by the least squares method at each frequency. The coefficients depend on the frequency, and can be approximated as afunction of f. The calculated results of Coefficients A and B are shown in Fig. 10(a), and that for Coefficients C and D are
shown in Fig. 10(b). Coefficients C and D are considered to be divided into two parts, i.e., when 1m ≤ ΔhSS < 10m
and 10m ≤ ΔhSS . The solid circles and squares in Figs. 10(a) and 10(b) represent the values of the coefficients at eachfrequency derived from the calculated results. The solid and dashed lines in the figures represent a least squares regression
line and are expressed as follows.
A = 5.847 ⋅ log( f ) + 0.31519(9a)

B = −0.003559 ⋅ f + 0.65122(9b)⎧3.7432 ⋅ log( f ) + 19.245
C=⎨
24.5
⎩

(1 ≤ ΔhSS < 10)(10 ≤ ΔhSS )(9c)⎧5.8947 ⋅ log( f ) + 0.31519
D=⎨⎩9.6379 ⋅ log( f ) − 4.93981(1 ≤ ΔhSS < 10)(10 ≤ ΔhSS )(9d)

The Eq. (7) can be derived from Eqs. (8) and (9).
Some calculation examples of Eq. (7) are shown in Fig. 11 with the calculation values obtained using the original Eq.
(5).
The height variation in the excess loss to the total received level at the SS, L(ΔhSS), depends on the dominant (strong)waves (reflected waves or diffracted waves) as mentioned before. In addition, the excess loss due to the arriving reflected
waves and the arriving diffracted waves in the NLOS region can be derived as LR(ΔhSS) and LD(ΔhSS), respectively.
Therefore, L(ΔhSS) can be expressed as Eq. (10).
L(ΔhSS ) ≈ min{LR (ΔhSS ), LD (ΔhSS )}(10)

Examples of the calculation results are shown in Fig. 12(a), 12(b), and 12(c). The solid lines in these figures represent
L(ΔhSS). The figures indicate that the relationship of the amount between LR(ΔhSS) and LD(ΔhSS) changes as the horizontal
distance between the BS and SS, d, increases. In the near region, d = 50 m, LR(ΔhSS) is less than LD(ΔhSS), and LR(ΔhSS)
becomes L(ΔhSS). In addition, the dependency of L(ΔhSS) on the frequency corresponds to that of the reflected waves. So
the frequency dependency is negligible in this region. On the other hand, in the far region, d = 1000 m, LR(ΔhSS) is greater-6-

第 509 回 URSI-F 資料
2006 年 11 月 17 日（金）than LD(ΔhSS), and LD(ΔhSS) becomes L(ΔhSS). The dependency of L(ΔhSS) on the frequency corresponds to that of thediffracted wave.

4.2 Expression of Height Variation Model for Path Loss Reflecting Local SS Conditions
The discussion is now summarized by model representations as follows.

When ΔhSS , k ≤ ΔhSS < ΔhSS , k +1
LR (ΔhSS ) = LR (ΔhSS , k ) +L(ΔhSS ) ≈ min{LR (ΔhSS ), LD (ΔhSS )}(11)

LR (ΔhSS , k +1 ) − LR (ΔhSS , k )(12a)ΔhSS , k +1 − ΔhSS , k

ΔhSS ,k =⋅ (ΔhSS − ΔhSS , k ) (k = 0,1,2,3,⋅ ⋅ ⋅)2kw ⋅ (hBS − hb )2d ⋅ sin ϕ − w(12b)⎛ d kp ⎞⎟LR (ΔhSS , k ) ≈ 20 log⎜
⎜ d ⋅ Rk ⎟
⎠
⎝ 0p

1
d kp =⋅
sin ϕ k(12c)(d ⋅ sin ϕ + kw)2⎧w ⋅ (hBS − hb ) ⎫+ ⎨hBS + ΔhSS , k − hb +⎬2d ⋅ sin ϕ − w ⎭
⎩

(12d)

2

⎞
d sin ϕ⋅ tan ϕ ⎟⎟
d
kw
ϕ
sin
+
⎠
⎝
⎛

(12e)

ϕk = tan −1⎜⎜⎧ {5.8947 ⋅ log( f ) + 0.31519}× Δh SS (−0.003559⋅ f + 0.65122 )⎪⎪⎪{3.7432 ⋅ log( f ) + 19.245}× 5.8947 ⋅ log( f ) + 0.31519
LD (ΔhSS ) ≈ ⎨⎪24.5 ⋅ log(ΔhSS ) + 9.6379 ⋅ log( f ) − 4.93981⎪⎪⎩(0 ≤ ΔhSS < 1)
(1 ≤ ΔhSS < 10)(10 ≤ ΔhSS )(13)

4.3 Comparison with Measured Data in Terms of Height Gain at hss = 10 m Based on hSS = 5 m, Gh_10m, 5m
4.3.1 Measurement
The measurements for height variation of the path loss at the SS were carried out in the Suginami area in Tokyo andthe Tsukuba area in Ibaraki prefecture in Japan. The measurement scenarios and features are shown in Table I. The areas
are flat. It should be noted that these areas include many two-story houses. The subscriber station antenna height (hSS) ischanged from 4 m to 10 m continuously at each measurement point. The frequency is 2.2, 5.2, or 25.15 GHz (CW). Boththe BS and SS antennas are omni-directional in the horizontal plane and the polarization is vertical. The measured heightgain at hSS = 10 m based on hSS = 5 m, Gh_10m, 5m, is acquired from the 1-m section median value of the measured heightvariation of the received level.
Here, the height gain, Gh_10m, 5m, is used as an evaluation parameter for the height variation with respect to the received
level.

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第 509 回 URSI-F 資料
2006 年 11 月 17 日（金）4.3.2 Validation
Regardless of the SS location, the average value of hBS, ϕ, w, and hb for all measurement points in each scenario are
given as calculation parameters. The calculation results of the height gain, Gh_10m, 5m, are acquired as follows. Term ΔhSS
can be expressed using hSS as shown in Eq. (14).
ΔhSS = hb − hSS −w(hBS − hb )2d − w(14)

Therefore, we can acquire the calculated value of L(ΔhSS) when hSS = 5 m and 10 m using Eqs. (11)-(14). If ΔhSS becomes
negative, that is, a LOS condition arises between the BS and SS antennas, -6 dB is given as the L(ΔhSS) regardless of the
SS antenna height because L(ΔhSS) is normalized by the path loss at the boundary between the LOS and NLOS regions.
The difference in L(ΔhSS) between when hSS = 5 m and 10 m is defined as the height gain, Gh_10m, 5m. The measured resultsin the scenarios in Table I and calculation results using Eqs. (11) and (14) are shown in Figs. 13(a)-13(e).
The tendency for the BS-SS horizontal distance of the calculation results agrees with that of the measured results inall measurement scenarios. Figure 13(a) shows the height gain at both 2.2 and 5.2 GHz. Although the calculation results
indicate that the height gain has a frequency dependency on the BS-SS horizontal distance, no clear difference in themeasured results between 2.2 and 5.2 GHz is observed. It appears that the frequency dependency of the measured heightgain between 2.2 and 5.2 GHz is negligible in comparison to the location dependency or measurement error. However,Fig. 13(b) shows the results at 5.2 and 25.15 GHz, and indicates a clear frequency dependency of the measured results aswell as for the calculated results. These results in Figs. 13(a) and 13(b) indicate that there is a frequency dependency forthe height gain on the BS-SS horizontal distance, and it becomes remarkable as the frequency difference becomes large.
Figures 13(c), 13(d), and 13(e) show the results at 5.2, 2.2, and 25.15 GHz, respectively. Parameters such as hBS, hb,
ϕ, and w in Figs. 13(c)-13(e) are different from those in Figs. 13(a) and 13(b). The results in all the figures show good
agreement with the measured and calculated height gain.
Based on the above discussion, it can be said that this height gain model can represent the characteristics of the heightgain reflecting the local conditions of the SS. In other words, the height gain depends on the frequency, local conditions
around the SS, and the horizontal distance between the BS and SS in the microwave band.

5. Conclusion
A height variation model of the path loss for evaluating the height gain at a SS taking into consideration the local SS
conditions, the horizontal distance between the BS and SS, and operating frequency in the microwave band was presented.
The model assumes fairly homogeneous propagation environments in terms of the building conditions such as aresidential area as an applicable area.
The propagation mechanism causing the dependency of the height variation characteristics of the received level at a
SS on the SS location are clarified in terms of the GO using UTD. The difference in the composition of the arriving wave
at the SS causes a change in the height variation characteristics of the path loss at a SS. The height variation characteristics
strongly depend on whether or not regular reflected waves have a higher level than that of the one-time diffracted wave
arrive at the SS.
There is no frequency dependency of the height variation of the path loss at the SS where the regular reflected wave
components are dominant (relatively near region). On the other hand, the frequency dependency of the height variation of
the path loss at the SS where the one-time diffracted wave component is dominant (relatively far region) is the same asthat of the diffracted waves.
A representation of the model was shown, and the model was validated using measured data and the validity of themodel was indicated.
This model is useful for the radio zone design of microwave band BWA systems operating under NLOS conditions,and for height gain estimation at mobile station antennas in mobile communications.

References[1] H. Bolcskei, A.J. Paulraj, K.V.S. Hari, R.U. Nabar, and W.W. Lu, “Fixed Broadband Wireless Access: State of the Art,
Challenges, and Future Directions,” IEEE Commn. Mag., vol. 39, Issue 1, pp. 100-108, Jan. 2001.
[2] M. Danesh, J.-C. Zuniga, and F. Concilio, “Fixed Low-Frequency Broadband Wireless Access Radio Systems,” IEEE Commn.
Mag., vol. 39, Issue 9, pp. 134-138, Sept. 2001.
[3] H. Sari, “Technical Challenges and Trends in Broadband Wireless Access at Frequencies between 2 and 11 GHz,” IEEE ICTTA
2004, pp. LVII- LVIII, April 2004.

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第 509 回 URSI-F 資料
2006 年 11 月 17 日（金）[4] P. Soma, D.S. Baum, V. Erceg, R. Krishnamoorthy, and A.J. Paulraj, “Analysis and Modeling of Multiple-Input Multiple-Output(MIMO) Radio Channel Based on Outdoor Measurements Conducted at 2.5 GHz for Fixed BWA Applications,” IEEE ICC 2002,
vol. 1, pp. 272-276, April 2002.
[5] S.Y. Tan, et al., “Microcellular communications propagation model based on the uniform theory of diffraction and multiple image
theory,” IEEE Trans. Antennas. Propag. Vol. 44, pp. 1317-1325, Oct. 1996.
[6] European Cooperation in the Field of Scientific and Technical Research EURO-COST 231, “Urban Transmission Loss Models for
Mobile Radio in the 900 and 1800 MHz bands,” Rev.2, The Hague, Netherlands, 1991.
[7] Rec. ITU-R P.1546-2: “Method for point-to-area predictions for terrestrial services in the frequency range 30 MHz to 3000 MHz,”
Volume 2005 P series, ITU, Geneva, Aug. 2005.
[8] ANSI/IEEE Std 802.11, 1999 Edition (R2003), “Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY)
Specifications,” IEEE, June 2003.
[9] IEEE Std 802.16e-2005 and IEEE Std 802.16-2004/Cor1-2005, “Physical and Medium Access Control Layers for Combined
Fixed and Mobile Operation in Licensed Bands,” IEEE, Feb. 2006.
[10] N. Kita, A. Sato, and M. Umehira, “A Path Loss Model with Height Variation in Residential Area Based on Experimental andTheoretical Studies Using a 5G/2G Dual Band Antenna,” IEEE VTC 2000-Fall, vol. 2, pp. 840-844, Sept. 2000.
[11] C.L. Hong, I.J. Wassell, G. Athanasiadou, S. Greaves, and M. Sellars, “Wideband channel measurements and characterization forbroadband wireless access,” IEE ICAP 2003, vol. 1, pp. 429-432, March 2003.
[12] D.A. McNamara, C.W.I. Pistorius, and J.A.G. Malherbe, Introduction to The Uniform Geometrical Theory of Diffraction,
AETECH HOUSE, 1990.
[13] M. Lott, Y. Fifield, D. Evans, and S. Hulyalkar, “Radio Channel Characteristics for Typical Environments at 5.2 GHz,” in ACTS
Mobile Communication Summit, pp. 252-257, Aalborg, Denmark, Oct. 1997.
[14] E.N. Bramley, and S.M. Cherry, “Investigation of microwave scattering by tall buildings,” Proc. of IEE, Vol. 120, No. 8, pp.
833-842, Aug. 1973.

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第 509 回 URSI-F 資料
2006 年 11 月 17 日（金）SS antennaBS

4.5 to 10.5 m

Flexiblepole

Building

Van

Fig. 1

Measurement method.

BS - SS separation distance: 330 m

11

11

Measured
Mean valueof each 1 m

9
8
7
6

5.2 GHzh = 32 m

5

11 dB

4
-150

-140

-130

Measured
Mean valueof each 1 m

9
8
7
6

5.2 GHzh = 32 m

5

BS

-120

-110

-100

BS

19 dB

4
-160

-90

-150

Relative level (dB)

Fig. 2(a)Example of height variation characteristics.
(In near region)

Measurement campaign.

BS - SS separation distance: 1360 m

10
SS antenna height [m]10
SS antenna height (m)Picture 1-140 -130 -120
Relative level [dB]

-110

-100

Fig. 2(b) Example of height variation characteristics.
(In far region)

30

Height gain, G

h_10m, 5m(dB)

Suginami area
25

5.2 GHzh = 32 m

Direct wave
Diffracted, Diffracted + Reflected wave
Multiple reflected wave

BS

20
15

SS

Fig. 2(b)

θ

10

h2

Fig. 2(a)

5
0

BS

hSS

h1

w
0

500
1000
1500
BS-SS horizontal distance (m)2000

Fig. 3
Dependency on BS-SS horizontal distance ofheight gain at hSS = 10 m (LOS) based on hSS = 5 m(NLOS).

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Fig. 4

Considered propagation model.

hBS第 509 回 URSI-F 資料
2006 年 11 月 17 日（金）9(2)

w = 25 m(0)θ = 4.06 (deg.)

8

(D)

7

(1)

(3)

6
5

f = 5.2 GHz

4
-40

-30

Measured

10

SS

SS

SS antenna height, h (m)hBS = 32 m

Calculated

SS antenna height, h (m)Measured

10

-20
-10
0
Relative level (dB)9(0)

hBS = 32 m

(2)

(3)

(1)
8
7

(D)

6

w = 10 m

θ = 0.94 (deg.)

5
4

10

Calculated

f = 5.2 GHz
-40

-30

-20
-10
0
Relative level (dB)10

Fig. 5(b) Typical examples of comparison between
calculated and measured results (θ = 0.94 deg).
(BS-SS horizontal distance = 1360 m).

Fig. 5(a) Typical examples of comparison between
calculated and measured results (θ = 4.06 deg).
(BS-SS horizontal distance = 330 m).
BS

Dominant wave
Non-dominant wave
BuildinghBS

Height variationof SS antenna, hss

SS
w1 w2

d

w
Dominant
wave

Directwave

Propagation Direct
loss
wave

1 - time

2 - timek - time

Diffracted wave

Reflected wave

Minimum time-reflected wave
> diffracted wave

Minimum time-reflected wave
< diffracted wave

Fig. 6 Mechanism of propagation over rooftops based on geometrical propagation model.

Building

Cross
section

θ

hBS

hBS
hSS

dsinϕ

Plan
BS

BS

ϕ

A
hb

dsinϕ

d
d

Building

ϕk
ϕ

Cross
section

hSS
w
Plan

w1 w2
A
SS

SS

Fig. 7(a) Propagation model based on dominant waves
that influence height variation of path loss.
- Geometry when the BS-SS distance is very short (LOS).

Fig. 7(b) Propagation model based on dominant waves
that influence height variation of path loss.
- Geometry when the BS-SS distance is relatively short.

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第 509 回 URSI-F 資料
2006 年 11 月 17 日（金）

θ
hSS

hb
dsinϕ

Plan

w1 w2

BS

ϕ
d

α

θ = 5 Deg., w = 15 m
Depth to NLOS region (m)Building

hBS

0

Cross
section

α A β

β
SS

0 deg.

ϕ = 40 deg.

8

0

10

20

30

40

50

60

Calculation examples of Eq. (3).

Fig. 8w

Depth to NLOS region, ΔhSS (m)Depth to NLOS region, ΔhSS (m)ϕ=80 deg.

0.01
10 m
15 m
20 m
25 m
30 m

0.1

1
f = 5 GHzϕ = 45 deg.
θ = 2 deg.

100Fig. 9(a)

10
20
30
40
Excess loss, LD(ΔhSS) (dB)ϕ

Calculation examples of Eq. (5).
- Dependency on w

20 deg.
30 deg.
40 deg.
45 deg.
50 deg.
60 deg.
70 deg.
80 deg.
90 deg.

0.1

1

f = 5 GHz
θ = 2 deg.
w = 20 m

10
30

50

0

10
20
30
40
Excess loss, LD(ΔhSS) (dB)50

Fig. 9(b) Calculation examples of Eq. (5).
- Dependency on ϕ

0.01

0.01
θ

Depth to NLOS region, ΔhSS (m)Depth to NLOS region, ΔhSS (m)ϕ=6Excess loss, LR (ΔhSS) (dB)

0.01

0.1 deg.
0.3 deg.
0.5 deg.
1.0 deg.
2.0 deg.
3.0 deg.
4.0 deg.
5.0 deg.

0.1

1

f = 5 GHzϕ = 45 deg.

w = 20 m

10
30

w1/w2
1
9
1/9

4

10

Fig. 7(c) Propagation model based on dominant waves
that influence height variation of path loss.
- Geometry when the BS-SS distance is relatively long.

30

2

0

Fig. 9(c)

10
20
30
40
Excess loss, LD(ΔhSS) (dB)

0.1

1

ϕ = 45 deg.
θ = 2 deg.
w = 20 m

10
30

50

f
2 GHz
3 GHz
4 GHz
5 GHz
10 GHz15 GHz20 GHz25 GHz30 GHz

0

10

20

30

40

Excess loss, LD(ΔhSS) (dB)Calculation examples of Eq. (5).
- Dependency on θ

Fig. 9(d) Calculation examples of Eq. (5).
- Dependency on f

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50

10

第 509 回 URSI-F 資料
2006 年 11 月 17 日（金）40

1m ≤ ΔhSS < 10m w = 20 m
ϕ = 45 deg.
10m ≤ ΔhSS
θ = 2 deg.

0m ≤ ΔhSS < 1m
w = 20 m
ϕ = 45 deg.
θ = 2 deg.

6

30

4

A

2
0

Coefficient

Coefficient

8

Values derived from
calculated result

B

1

20

C
D

10
0
-10

50

10
Frequency, f (GHz)

Values derived from
calculated result
1Fig. 10(b) Calculation results of coefficients.
- Dependency of coefficient C and D on frequency.

Fig. 10(a) Calculation results of coefficients.
- Dependency of coefficient A and B on frequency.

2 GHz
2 GHz cal. using Eq. (7)2 GHz cal. using Eq. (5)5 GHz cal. using Eq. (7)5 GHz cal. using Eq. (5)20 GHz cal. using Eq. (7)20 GHz cal. using Eq. (5)1
ϕ = 45 deg.
θ = 2 deg.
w = 20 m

10

Table 1

4

6

6

Suginami
20

21

32

15

38

56

45

44

28

17

13

16

19

48

7.5

9.0

7.8

7.5

2.2
5.2

5.2
25.15

5.2

11

6

22

7

7

(a)

(b)

(c)

(d)

(e)

D

(b) d = 100 m

Meas. 2.2 GHz
Meas. 5.2 GHzSS(c) d = 1000 m

Cal. 2.2 GHz
Cal. 5.2 GHz

30
25
20
15
10
hBS = 18 m

5

hb = 7.5 m

0

7.5

ϕ = 38 deg.

-5

2.2

8 L (Δh )Fig. 12Calculation examples for height variation ofpath loss at SS.

G

18

4

10
10
0 10 20 30 40 0 10 20 30 40
Excess loss (dB)(a) d = 50 m

Tsukuba

L R (ΔhSS )2

6

L D (Δh SS )L R (Δh SS )0 10 20 30 40

Measurement scenarios and features

L R (ΔhSS )

8

8
10

50

h BS = 20 m
h b = 7.5 m
w = 13 m

2

4

Calculation example of Eq. (7).

Area
BS antennaheight, hBS(m)
Average roadangle, ϕ(deg.)
Averagebuilding
separation, w(m)
Averagebuildingheight, hb(m)Frequency(GHz)
Number ofmeasurement
ponts
ID, Fig. 13

2

(dB)

Fig. 11

10
20
30
40
Excess loss, LD(ΔhSS) (dB)0
ϕ = 45 deg.

L D (Δh SS )h_10m, 5m

025 GHz5 GHz

00Depth to NLOS region, ΔhSS (dB)

Depth to NLOS region, ΔhSS (m)

0.01

0.1

50

10
Frequency, f (GHz)25.15

Suginami area

w = 17 m

-10
0

500

1000

1500

2000

BS-SS horizontal separation, d (m)Fig. 13(a) Comparison between measured andcalculated results.
- Suginami area (hBS = 18 m, f = 2.2 and 5.2 GHz).

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第 509 回 URSI-F 資料
2006 年 11 月 17 日（金）Meas. 5.2 GHz
Meas. 25.15 GHz

Cal. 5.2 GHz
Cal. 25.15 GHz

Meas. 5.2 GHz
Cal. 5.2 GHz

20

20

10

10

5

hBS = 20 m

0

hb = 9.0 m

G

15

G

15

(dB)

25

h_10m, 5m

25

(dB)

30

h_10m, 5m

30

ϕ = 56 deg.

-5

Suginami area

-10
0

200

5

hBS = 21 m

0

hb = 7.8 m

ϕ = 45 deg.

-5

w = 13 m

-10

400

600

800

0

1000 1200

500

Fig. 13(b) Comparison between measured andcalculated results.
- Suginami area (hBS = 20 m, f = 5.2 and 25.15 GHz).

Cal. 2.2 GHz

(dB)

15

10

10

0

hb = 7.5 m

G15

h_10m, 5m

20

(dB)

20

h 10m, 5m

25hBS = 32 m

Suginami areahBS = 15 m

5

hb = 7.5 m

0

ϕ = 44 deg.

-5

2000

Meas. 25.15 GHz
Cal. 25.15 GHz

30

25

5

1500

Fig. 13(c) Comparison between measured andcalculated results.
- Suginami area (hBS = 21 m, f = 5.2 GHz).

Meas. 2.2 GHz
30

1000

BS-SS horizaontal separation, d(m)BS-SS horizontal separation, d (m)G_w = 16 m

Suginami area

ϕ = 28 deg.

-5

w = 19 m

Tsukuba area

w = 48 m

-10

-10
0

500

1000

1500

0

2000

400

600

800

1000

BS-SS horizontal separation, d (m)BS-SS horizaontal separation, d(m)Fig. 13(d) Comparison between measured andcalculated results.
- Suginami area (hBS = 32 m, f = 2.2 GHz).

200

Fig. 13(e) Comparison between measured andcalculated results.
- Tsukuba area (hBS = 15 m, f = 25.15 GHz).

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