Propagation Modeling Dependent on Frequency and Distance for Mobile Communications via High

Altitude Platforms (HAPs) Zeynep Hasirci and 1. Hakki Cavdar

Abstract-In this paper, propagation modeling and performance analysis on the HAPs are obtained. Elevation angle is the dominant parameter on the model. All possible propagation environments are divided into four groups: suburban (SU), urban (U), dense urban (DU) and urban high rise (UHR). These groups are modeled using well-known statistical models with a dependence on elevation angle. The main parameters are the elevation angle, Rayleigh and Ricean propagation factors, and percentage of time a given fade depth is exceeded. To observe the effects of the parameters on the model, the correlation coefficients between model parameters and the fade depth are calculated. This new HAP model contains two cases-line of sight (LOS) and non-line of sight (NLOS) between a HAP and a user. In a conclusion, obtained models are combined with free space path loss and full formulations of total path loss for the four possible HAPs propagation environments at three different frequencies (2, 3.5, and 5.5 GHz) are given.

Keywords-HAPs, Propagation Model, Elevation Angle, Path Loss, Performance, HAPs Link Design, Correlation.

I. INTRODUCTION

PROVIDING wireless communications via High Altitude Platform Station (HAPs) is a new opinion to overcome the shortcomings of both the terrestrial tower-based and

satellite systems [1]. HAPs is defined as "a station located on an object at an altitude of 20 to 50 Ian and at a specified, nominal, fixed point relative to the earth" [2].

HAPs may provide the new possibilities for wireless communications such as large coverage areas, less hardware, and high data rate and short propagation delay with combining advantages both the terrestrial-based ground and satellite systems. Although there are many advantages explained above, its design needs to solve some critical problems. The problems on the design of the system may be summarized below: the spacecraft stability in the orbit, overcome the required energy in the orbit, the propagation characteristics and modeling, coverage planning, and transceiver design etc. The propagation phenomenon on the HAPs systems is a critical point in the system design. In the large coverage area, the mobile user can move at the different propagation environments, thus signal strength which is received by mobile user is affected. In order to the realization of the system, the estimation and modeling of propagation

Manuscript received February 12, 2012. Z. Hasirci is with Karadeniz Technical University, Dep. of Electrical and

Electronics Engineering, 61080 Trabzon, Turkey (corresponding author phone: +90-462-377 4204; e-mail: zhasirci@ktu.edu.tr).

l.H. Cavdar is with Karadeniz Technical University, Dep. of Electrical and Electronics Engineering, 61080 Trabzon, Turkey.

characteristics for all different coverage areas is necessary. It is well known that free-space path loss (FSL) will not be sufficient and suitable alone for HAPs.

The previous investigations in literature may be given briefly. Empirical Roadside Shadowing Model (ERS) or empirical models for satellite communication can be used to estimate a more useful approach for HAPs propagation [3, 4]. Statistical modeling approaches can be used for coverage planning and estimating total path loss via HAPs communication systems [5, 6]. Deterministic wideband modeling of satellite propagation channel with buildings blockage and system strategies in mobile-satellite urban scenarios is obtained [7- 9]. In terrestrial and satellite mobile systems, propagation model for vegetation effects is obtained [10]. The effects of model for mobile communications via HAPs in built-up areas are introduced with taking into account buildings blockage [12]. An overview is given about channel modeling for satellite and HAPS system design [13].

The aim of this paper is to introduce propagation modeling and performance analysis on the HAPs. Section II presents the propagation modeling and fading analysis for four different environments. Obtained models are combined with free space path loss, and full formulations of total path loss are given in section III. Here, the link performance is described using by fading probability (P). P is defined as 1 % that describes the link performance is 99%. It means received signal is greater than the given fade level at the abscissa. Because the link performance is important for transceiver design, fading distribution estimation is necessary. Finally, the numerical results are given in section IV.

II. PROPAGATION MODELING ApPROACH

A. Statistical Model with a Dependence on Elevation Angle The elevation angle and propagation environments are the

most effective parameters to determine the propagation characteristics on the HAPs. Firstly, the statistical ITU-R Rec. P . 14lO model [14] is used for modeling of propagation environments. With the help of this, LOS (line of sight - PLOS) and NLOS (non-line of sight PNLOS = 1 - PLOS) probabilities corresponding to the each angle of elevation is calculated [12] and used in the proposed model. PLOS and PNLOS probabilities in the streets are function of the elevation angle [12].

By using the calculations, fade distributions are examined for four different propagation environments. The statistical model for land mobile satellite system (LMSS) which was developed by Barts and Stutzman [15] is used to obtain the proposed model. The model developed by Barts and Stutzman may be given in Eqs. (1), (2) and (3) [15].

978-1-4673-1118-2/12/$3 1.00 ©20 12 IEEE 287 TSP 20 12

For the fading distribution of LOS propagation depends on the Ricean parameter (K1) where C1 (F) is the fraction of time or distance traveled by the mobile that the signal will fade greater than F dB when LOS.

- (HU1) C1 (F) = e-u-z -

Vi = 0.01(Kl)2 - 0.378(Kl) + 3.98

V2 = 331 .35(Klr2.29

K1 = Ricean unfaded carrier-to-multipath ratio (dB)

(1)

The simple model for NLOS propagation depends on the Rayleigh parameter (K2) where C2 (F) is the fraction of time or distance traveled by the mobile that the signal will fade greater than F dB when NLOS.

(2)

K2 = Rayleigh unfaded carrier-to-multipath ratio (dB)

By combining C1 (F) and C2 (F) with using PLOS andPNLOs, the total distribution C(F) is obtained as an elevation (8) dependent model.

(3)

The final equation is given in Eq. (3) and with the help of Eq. (3), fading distribution that depends on angle of elevation, K1 and K2 for four different propagation environments are obtained as shown in Fig.1,Fig.2 and Fig.3.

All possible propagation environments are divided into four groups which are shown below:

SU = Suburban U = Urban DU = Dense Urban UHR = Urban High Rise

The effects of the parameters (8, K1 and K2) over the fade depth dependent on the environment type are summarized in the figures given above. Firstly, all possible fade depths corresponding to the all parameters (8, K1 and K2) for four different propagation environments are calculated. As it is mentioned before, all calculations are obtained in case the link performance is 99% (P= 1 %).

In order to determine the effects of the parameters on propagation scenario, the correlations between fade depth (F) and 8, K1 and K2 are calculated, respectively. The Ricean (K1) and Rayleigh (K2) propagation parameters are between 10-20 dB and the range of elevation angle is taken from 5° to 90°. The results are shown in Table I.

The correlation coefficient's size is always between 0 and 1. The sign of the correlation coefficient depends on the slope of the regression line. A perfect correlation of ± 1 occurs only when the data points all lie exactly on a straight

K1= 10 dB, K2= 10 dB,Ele\08tion Angle= 4So

= = �:� = = = I �� I UHR -- -------- �

- - _1

- ________ _ I

'J I 1\ 10 15 20 25 30 35 40

Fade De pth, (dB)

Fig.l. Fading distribution for four propagation environments (SU, U, DU, UHR) using 8 = 45° , KI� K2 � 10 dB.

10' ��_K

�'�_

'0_d

_B . �

K2_�

1_0 d

�B,_

Ele_�

t_'oo�

A�",'_e ��8 0 0_��

-==�===========:==== l-�� I -� -----------I---- -UHR _ L ___________ L _____ _ _

=======c===== I ------ 1------

Fade Depth, (dB)

Fig.2. Fading distribution for four propagation environments (SU, U, DU, UHR) using 8 = 80°, KI� K2 � 10 dB

K1= 20 dB, K2= 20 dB,Elevation Angle = 45° 10' -�-�-�-'------r----'---'---------'

= = = = = =�� - - = =

J = =

J = =

�-------- - 1-- 1---1--1--

- ---, --

=BJU - - U - DU

UHR - - -1- --

10" _� ____ �"-------'_--".L�--"------1 o 10 15 40

Fade De pth, (dB)

Fig.3. Fading distribution for four propagation environments (SU, U, DU, UHR) using 8 = 45°, Kl � K2 � 20 dB

TABLE l CORRELATIONS BETWEEN FADE DEPTH (F) AND 8, Kl, K2. (FOR THE LINK

PERFORMANCE 99%)

OF-B OF-Kl OF-K2 SU 0,963 -0569 0,999 U -0,956 -0539 0,999

DU -0,830 -0,502 1 UHR -0,715 -0,487 1

line. A correlation greater than 0.8 would be described as strong, whereas a correlation less than 0.5 would be described as weak. As seen in Table I, the correlation between fade depth (F) and elevation angle (8) is strong, the correlation between fade depth (F) and Rayleigh parameter

288

TABLE ll VALUE OF PARAMETERS IN EQ. (4) FOR THE LINK PERFORMANCE 99%

8 a 5° < 8 < 50" 12.475

SU 51°<8<61° 28.096 62° < 8 < 90° 15.792 5° < 8 < 70° 17.313

U 71°<8<85° 46.808 86° < 8 < 90° 51.423 5° < 8 < 80" 18.732

DU 81° < 8 < 88° 96.917 89° < 8 < 90° 106.002 5° < 8 < 70" 17.772

UHR 71° < 8 < 88° 56.462 89° < 8 < 90° 1040.697

R

'Y

Fig. 4. HAPs geometry

b c 0.304 0.004 0.525 0.129 0.053 0.567 0.178 5.788E-05 0.588 0.016 0.449 0.581 0.132 1.24E-05 1.119 0.007 1.053 0.567 0.05 1.92E-07 0.589 0 11.57 0.254

Transmitter

R. Earth surface

C>

d 0.997 0.887 0.019

1 0.988 0.033

1 0.995 0.019

1 1

0.497

(K2) is strong, the correlation between fade depth (F) and Ricean parameter (Kl) is not strong but not also weak. As a result, the model of fade depth should contain the all parameters together which are mentioned above. Multiple regression analysis should be used for the fade depth model. The general purpose of multiple regression (the term was first used by Pearson, 1908) is to learn more about the relationship between several independent or predictor parameters and a dependent or criterion parameter. Thus, for the obtained model, fade depth (F) is taken as a dependent parameter and the other parameters (8, Kl, K2) are taken as independent parameters. The Eq. (4) is created with multiple regression analysis and parameters (a, b, c, d) which are used in Eq. (4) presented in Table II. With the help of Table II, fade depth corresponding to a certain elevation angle (8) and propagation environment can be calculated.

F = la - h.B - c.Kl + d.K21 (4)

III. PATH Loss MODELING FOR HAPs

Determination of propagation characteristics is very important for the link and system design. So, path loss calculation is a necessity for HAPs like as the other systems. The HAPs geometry is shown in FigA and with the help of FigA, Eq. (5 ), Eq. (6), Eq. (7) and Eq. (8) can be calculated in a simple way. For all calculations, height of the platform, h, is taken as 22 km.

R+h R sin(90+ 8) sin(180-(90+8+y)

R y = cos-1(-cos e) - e R+h rkm = �R [cos-1( �cos e) - e]

180 R+h

(5 )

(6)

(7)

rkm is the projection distance between the projection point of transmitter (B) and the receiver (A) and R is earth radius,

- - - - - - - - - - - -I == �� 1- ----

- - - - - - - - - - - - -�-- UHR - ----I -----1-

1200L --�------C=-------C�---;;;20;;CO ----;;;2 50 dian)

Fig. 5. Path loss dependent on rkm for four environments

6371 km.

dkm = .JR2 + (R + h)2 - 2R(R + h) cosy (8)

dkm is the distance between the transmitter (C) and the receiver (A). Finally, the path loss can be expressed in dB as

where is the free space loss LFSL which can be calculated as

(9)

LFSL = 92.4 + 20l0g (dkm) + 20log (fGHz) (10)

where dkm is the distance between the transmitter and the receiver in km and fGHz frequency in OHz. Moreover, Lex which is shown in Eq. (11) represents fade depth or extra loss in dB as a function of 8, Kl and K2.

Lex = F = la - h.B - c.Kl + d.K21 (11)

If we look at the curves of path loss which depends on projection distance (rkm ) in Fig. 5 , it is clear that the most complex curve for modeling belongs to the suburban (SU) environment. By modeling this curve, all the other curves can be easily represented. So, a curve fitting process was applied to the path loss data for SUo

Due to the complexity in the high curvature area, the data was analyzed and modeled in two parts. Both a power

function k = P11x - P21p3 and a sigmoid function S = � l+e-were used. The power function was used to model the overall variation. On the other hand, the model was divided into two parts with the help of sigmoid function. For an improved representation capability, a linear component l = P4x was added to the model. For a detailed description of modeling steps, one should refer to the authors' study [16]. The model function is given Eq. (12).

PL = s[3k + l] - (k + l) + d ( 12)

This model is depends on only the projection distance. However, the model also needs a frequency parameter. The frequencies are selected from the 2 to 60Hz frequency band considered for 30 and 40 mobile systems. In this range, the effect of change in frequency was modeled with a 2nd degree polynomial. Finally, obtained path loss model in terms ofrkm

289

190

180

170 ____ � _ �.;.: __ � :_ : ___ L---�: __ -::-___ .--�-----O-O--�--� - --

... •. e· .. 160 I •••.•••

• calculation 2.0 GHz model 2.0 GHz

• calculation 3.5 GHz - ------ model 3.5 GHz

• calculation 5.5 GHz -- model 5.5 GHz

120 0L ------!:5o------;c1oCC o ----:1cc:SO---2=oc:-o ---:::250 Projection distance, r(km)

Fig. 6. Path loss calculation and model for a suburban (SU) environment at frequencies of 2.0, 3.5 and 5.5 GHz.

190.---�--�--�---�-----e--- --

180 - - - - 1- - - - - - - T .... -'----•• � -:�:�-.---�-�.- - --

I •••

170 ' ::::::: :, _

_ :_" _._----____ --,

• calculation 2.0 GHz -- model 2.0 GHz

� calctjation 3.5 GHz model 3.5 GHz calculation 5.5 GHz mooel 5.5 GHz

140

130

1200 L ------;':50;-------;,= 00C--�,5CC O ----::2"' OOC--.-250 Projection distance, r (km)

Fig. 7. Path loss calculation and model for an urban (U) environment at frequencies of 2.0, 3.5 and 5.5 GHz.

and fGHZ for four propagation environments are given below in Eq.(13), Eq.(14), Eq.(15) and Eq.(16).

A. Path Loss Model for Suburban (SU) with a Dependence on rkm and fGHZ

k = 1.45401rkm - 12.14121°6220 - 0.0962rkm

1

5 = 1 +e 100(rkm 12.1412)

l = 0.3520rkm

PLsu(dB) = s[3k + l] - (k + l) + 0.3651fGH/ +5.2486fGHZ + 125.5279

(13)

B. Path Loss Model for U with a Dependence on rkm and fGHZ

k = 3.04101rkm - 1.56601°4499 - 0.0546rkm 1

5 = -----::-=-;---:-:-= 1 +e-100(rkm-1.5660)

l = 0.9557rkm

PLu(dB) = s[3k + l] - (k + l) + 0.3651fcHZ 2 (14)

+5.2487fGHz + 122.6696

C. Path Loss Model for DU with a Dependence on rkm and fGHZ

k = 3.8236hm - 0.71371°·3692 - 0.0309rkm

190.---�--�--�---�-----,

180 - --- - -.�.:.-.-: � -:---� __ �-:--=---=.--�-=--�--=-: - --

••••• .-

• __ .----e 170 •••••

• ,----,--c,'-" c-", c-;oo --c2-:-.0 ccGHc-lz mooel 2.0 GHz calculation 3.5 GHz

-- mooel 3.5 GHz • calculation 5.5 GHz -

-- mooel 5.5 GHz 140 - --------------------

1W ---------------------

1200L -----O;50C------c,OO;::;c---CO,5c:- 0 ---;;20;; 00-----;;;260 Projection distance, r (km)

Fig. 8. Path loss calculation and model for a dense urban (DU) environment at frequencies of 2.0, 3.5 and 5.5 GHz.

190

180 - - - - - - - - - - � __ �-�. -- -:._-_�-::---�--�--�-� - -- -.--

.- I ___ -----.----. J---.

170

150

.... . · r ·

.. ... .. . .

•••• -.--.

calculation 2.0 GHz -- model 2.0 GHz

• calculation 3.5 GHz model 3.5 GHz

• calculation 5.5 GHz -- model 5.5 GHz

, I ��--------- �----------r ---- �

'W�0----�60;--------;,�OO;----�15�0-----2�O�0----�250 Projection distance, r (km)

Fig. 9. Path loss calculation and model for an urban high rise (UHR) environment at frequencies of 2.0, 3.5 and 5.5 GHz.

1

5=

-----:--::-:7--::-;:-=

1 +e-100(Tkm 0.7137)

l = 8.6021rkm

PLDU(dB) = s[3k + l] - (k + l) + 0.3693fcHZ 2 +5.2716fcHZ + 125.5443

(15)

D. Path Loss Model for UHR with a Dependence on rkm and fGHZ

k = 3.9181Irkm - 0.67201°3075 - O.0072rkm

1

5 = 1 +e 100(rkm 0.6720)

l = 7.7722rkm

PLUHR(dB) = s[3k + l]- (k + l) + 0.3650fGH/ +5.2480f GHz + 130.5403

IV. NUMERICAL RESULTS

(16)

In this study, a propagation model is obtained using well­known statistical models with a dependence on elevation angle. Moreover, total path loss model is also obtained for four propagation environments from the 2 to 6 GHz frequency band, namely at 2.0, 3.5, and 5.5 GHz for the link performance 99%.

290

TABLE III MEAN SQUARE ERROR (tlw ) AND STANDARD DEVIATION (CTw ) OF PATH

Loss MODEL FOR HAPs AT 2-6 GHz FREQUENCY BAND

SU U DU UHR fierr O-err f1.err O-err f1.err O-err f1.err (Jeff

2.0 GHz 0.0005 0.0707 0.0007 0.1464 -0.0019 0.0960 0.0034 0.1232 3.5 GHz 0.0788 0.1262 0.0382 0.1503 0.0221 0.0998 0.0223 0.1081 5.5 GHz 0.0783 0.1262 0.0375 0.1503 0.0220 0.0998 0.0420 0.1081

Although all results explained above are shown in the figures and equations, some results may be summarized as follows: fading depth (F) are 10 dB, 19.5 dB, 23.5 dB, 26 dB for SU, U, DU and UHR, respectively using e = 45°, Kl= K2 = 10 dB. It can be well shown from these results, the fade depth decreases with the increasing the elevation at the same conditions. The light fade values occur for all environments at high elevation angle with small Kl and K2, at the range of 7-10 dB. For all regions at the heavy fading, the fading depth is observed at the range of 33 dB - 38 dB.

U sing the developed path loss model, the path loss at the HAPs: for example at 50 km projection distance (rkrn), for SU, the total path loss is obtained 153 dB, 158 dB, 16 1 dB; for U, the total path loss is obtained 16 1 dB, 166 dB, 170 dB; for DU, the total path loss is obtained 164 dB, 169 dB, 173 dB; for UHR, the total path loss is obtained 165 dB, 170 dB, 174 dB at 2.0, 3.5 and 5.5 GHz, respectively. It is well seen from the findings, UHR has the worst propagation conditions, so the path loss is bigger than the other regions. The HAPs should be located at the top of the UHR region in order to decrease the path loss and provide more efficient service. When the HAPs is at the top of the one big city, the neighbor cities may be served with the same HAPs. The equations (13), (14), (15), (16) and the figures 6, 7, 8, 9 which were developed here may be used the calculation of the path loss for other different regions. Because while a HAP is serving for an UHR area, the other regions which is located at hundred kilometers away may be served via the same HAPs. So, all possible conditions were considered in this research.

Table III summarizes mean square error (;terr [dB]) and standard deviation (O'err [dB]) of path loss models at 2-6 GHz frequency band. The verification of proposed model may be shown at this table, the range of differences between 0.0005 dB and 0.0788 dB for all frequencies and environments. The error has too small and acceptable value.

V. CONCLUSION

High altitude platforms (HAPs) are considered as a new alternative to terrestrial and satellite systems. With some of their outstanding features, as well as their capability to provide a wide spectrum of compelling services, it is supposed that HAPs will play an important role in next­generation networks. Thus, there are many studies about it. One of the most important problems to be solved is estimation of the propagation characteristics and path loss. A statistical propagation model for fading distributions is determined in this research. Using these obtained fade distributions and geometrical structure of HAPs, the path loss formulas are developed with combining well-known

291

propagation theory, free space loss. Obtained fade distributions and path loss models may be used on the determination for the link design of HAPs. Observed results for path loss values show that the option of HAPs on the requirements of mobile communication is suitable and applicable.

In future work, new propagation models can be developed with experimental studies depend on geographical conditions. Considering the system requirements, the selecting of modulation/demodulation, the increasing of data rate, determining the most suitable multiplexing techniques, and the design suggestions about hardware and software of the system are the major works on HAPs. With these studies, the most optimal system design and planning can be developed.

REFERENCES

[1] G. M. Djuknic, J. Freidenfelds, and Y. Okunev, "Establishing wireless communications services via high-altitude aeronautical platforms: a concept whose time has come?" IEEE Communications Magazine, vol. 35, no. 9, pp. 128-135, 1997.

[2] "Revised technical and operational parameters for typical IMT -2000 terrestrial systems using high altitude platform stations and CDMA radio transmission technologies", LTU Document, 8-1I307-E, 1999, ITU.

[3] "Propagation data required for the design of earth-space land mobile telecommunication systems," Recommendation lTU-R P.681-6, 2003, ITU.

[4] M. A. N. Parks, B. G. Evans and G. Butt, "High elevation angle propagation results applied to a statistical model and an enhanced empirical model, " IEE Electron. Lett., vol. 29, no. 19, pp. 1723-1725, 1993.

[5] C. Oestges, "A stochastic geometrical vector model of macro- and megacellular communication channels, " IEEE Trans. Veh. Technol., vol. 51, no. 6, pp. 1352-1360, 2002.

[6] C. Oestges and D. Vanhoenacker-Janvier, "Coverage modeling of highaltitude platforms communication systems, " IEE Electron. Lett., vol. 37, no. 2, pp. 119-121, 2001.

[7] P. A. Tirkas, C. M. Wangsvick and C. A. Balanis, "Propagation model for building blockage in satellite mobile communication systems, " IEEE Trans. Antennas Propag., vol. 46, no. 7, pp. 991-997, 1998.

[8] Z. Blazevic, L Zanchi and L Marinovic, "Deterministic wideband modeling of satellite propagation channel with buildings blockage, " IEEE Trans. Veh. Technol., vol. 54, no. 4, pp. 1225-1234, 2006.

[9] C. Oestges and D. Vanhoenacker-Janvier, "Propagation modeling and system strategies in mobile-satellite urban scenarios, " IEEE Trans. Veh. Technol., vol. 50, no. 2, pp. 422-429, 2001.

[10] T. Sofos and P. Constantinou, "Propagation model for vegetation effects in terrestrial and satellite mobile systems, " IEEE Trans. Antennas Propag., vol. 52, no. 7, pp. 1917-1920, 2004.

[11] S. R. Saunders and A. Argo-Zavala, "Antennas and Propagation for Wireless Communication Systems, " 2nd ed. New York: Wiley, 2007.

[12] J. Holis and P. Pechac, "Elevation Dependent Shadowing Model for Mobile Communications via High Altitude Platforms in Built-Up Areas, "IEEE Trans. Antennas Propag., vol. 56, no. 4, 2008.

[13] M. Vazquez-Castro, F. Perez-Fontan and B. Arbesser-Rastburg, "Channel modeling for satellite and HAPS system design, " Wireless Commun. Mobile Comput., vol. 2, no. 3, pp. 285-300, 2002.

[14] "Propagation data and prediction methods required for design of terrestrial broadband millimetric radio access system operating in a frequency range about 20-50 CHz," Recommendation lTU-R P.141 0-2, 2005, ITU.

[15] R. M. Barts and W. L. Stutzman, "Modeling and simulation of mobile satellite propagation, " IEEE Trans. Antennas Propag., vol. 40, no. 4, pp. 375-382, 1992.

[16] Z. Hasirci, "Propagation Modeling and Performance Analysis on the High Altitude Platform Stations (HAPs), " MSc Dissertation, Dep. of Electrical and Electronics Eng., Karadeniz Technical Univ., Trabzon, Turkey, 20 I 1.