Propagation Path Loss Models for Mobile Communication

Lukáš KLOZAR1, Jan PROKOPEC1

1 Dept. of Radio Electronics, Brno University of Technology, Purky ova 118, 612 00 Brno, Czech Republic

xkloza00@stud.feec.vutbr.cz, prokopec@feec.vutbr.cz

Abstract. Signal propagation and path losses are the key elements of wireless network design. This paper describes tuning process of empirical propagation path loss models for typical environments (urban, suburban, open areas). The Hata based models were compared with data measured in Brno. Model corrections were suggested and tested for GSM frequency band. The correction is aimed on the short range propagation in cellular networks. For model fitting to the measured data and for a deviation error estimation was used the mean square error (MSE). The tuned propagation model was used for localization in cellular network using particle swarm optimization (PSO) technique and geometrical technique.

Keywords Propagation model, path loss, Okumura-Hata, mean square error, corrections, fitting, localization, particle swarm optimization.

1. Introduction Mobile communications have become a mass

necessity in every day life. Mobile communication networks also provide a connection to the IP networks (Internet...), thanks to good accessibility of signal, makes the mobile networks easy and perspective way to access high speed data connection. The networks for the mobile communication uses for cover an area with signal a cellular structure [1]. In the center of each cell is a base transceiver station (BTS), also called the base station (BS). The BS is a main radio communication element of the cellular network. It often serves several spatially divided sectors. Every sector has its own cell ID (CID), which uniquely identify it. Density of the BS depends on traffic and vary from place to place. Propagation environment is divided into three types: urban - with high BS density and cell size of few hundred meters, suburban – with lower building heights a medium sized cell, open areas – with cell size up to 30 km. The cellular topology solves spectral congestion by reusing the same frequency channels in spatially enough distant cells. So with limited spectrum is possible to cover

unlimited area [2]. Neighboring BSs uses different absolute radio frequency channel number (ARFCN) channels to minimize the interferences. Cell information like CID, local area code (LAC), ARFCN, received signal level (RxLev), etc., are common part of system communication between BTS and mobile station (MS) [2]. The broadcast control channel (BCCH) carries these system informations.

Signal attenuation on way from a transmitter to a mobile receiver is described as path losses (PL). The PL depends on actual connection conditions between BTS and MS [2]. Main formula (2) for signal's free-space path loss [2] describes line of sight (LOS) propagation case with no environmental distortion. For non-line of sight (NLOS) cases the propagation path loss is described by using a adequate propagation model [3].

2. Path Loss Modeling Propagation loss (1) [2], [4], [5], [6] is a difference

value between the radiated power PT and the received power PR

RTP )( PPdBL . (1)

2.1 Free-space Path Loss The free-space path loss [2] (see Fig. 1) expresses

reduction of power dependent on distance between transmit and receive antenna, see formula (2). Where f is frequency in MHz and d is BTS-MS distance in meters.

dfdBL 1010FS log20log2044.32)( . (2)

2.2 Path Loss Models Determination of free space path loss LFS from

formula (2) does not consider effects of propagation in real environment, therefore propagation models are used to determinate path loss.

978-1-61284-324-7/11/$26.00 ©2011 IEEE

2.2.1 Okumura-Hata Model

The Okumura-Hata (OH) model [5] uses empirical data to determinate path loss LOH (see formula (3)) for typical environment according to the value of environmental correction factor CA [5].

CAdBAdBLOH 10log)( (3)

where

)(log82.13)(log16.2655.69 1010 mb hahfA ,(4)

bhB 10log55.69.44 . (5)

The hb is BTS antenna height in meters and f is frequency in MHz. The correction factor a(hm) is for the MS antenna height hm in meters and d is BTS-MS distance in meters.

Urban areas [5] CA = 0. For medium-small city

)8.0log56.1(

)7.0log1.1()(

10

m10m

fhfha (6)

and for large city [5] (f 400MHz)

1.1)54.1(log29.8)( 2m10m hha (7)

Suburban areas [5]

4.5)28/(log2 210 fCA (8)

Open areas [5]

94.40log33.18)(log78.4 102

10 ffCA (9)

The limitations of Okumura-Hata model [5]: MHzf 1500,150 , mhb 200,30 , mhm 10,1 ,

kmR 20,1 .

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 104

80

90

100

110

120

130

140

150

160

170

180

Distance [m]

Pat

h lo

ss [d

B]

Free space and Okumura Hata model

FS 900MHzFS 1500MHzOH URBANOH SUB-URBANOH OPEN

Fig. 1. The free space propagation path loss and the Okumura

Hata model (f = 900 MHz, hb = 30 m, hm = 1.5 m).

2.2.2 COST 231 Extension for Hata Model

The COST 231 [8] [9] extension expands frequency limit of OH model (see section 2.2.1) up to 2 GHz. The COST path loss is described as follows:

CH

bm

b

CHCHCH

Cdhha

hfCdBAdBL

1010

1010

10

log]log55.69.44[)(log82.13log9.333.46

log)( (10)

where the correction factor a(hm) is same as for the OH model (see section 2.2.1, formula (6)(7)(8)). The correction coefficient CCH for metropolitan cities is used [8]. The CCH = 0 for medium sized cities and suburban areas, and CCH = 3 dB for metropolitan areas. Frequency limitation of the COST 231 Hata model [9]: MHzf 2000,1500 .

2.2.3 Two Slope Model Extension

Tha Hata model is valid for distances over 1 km [5]. For the short distances less than 1 km is signal level significantly influenced by combination of the LOS and the NLOS signal path [7]. Two slope models with the different path loss exponent for each part are used. To extend the OH model, the join distance of both slopes (see formula (11)) is set to 1 km [7].

)(log)(log)( 1010OH BPLBPNEAR ddslopedLL (11)

where dBP = 1km is break point distance (1 km) in kilometers [5], d is BTS-MS distance in kilometers, LOH(dBP) is the OH path loss equation (3) for distance dBP. SlopeL is near area path loss slope [7] and LFS(dBP) is free space path loss equation (2) for distance dBP.

)(log)(log)(log)()(log)(

201010

201020FS10OH

ddddLddLslope

BP

BPBPL (12)

where distance d20 = 0.02 km. The LFS(d20) is free space path loss equation (2) for distance d20. For the distance over 1 km is used the OH model [5] (see equation (3)).

2.2.4 Multiple Slope Model

Extended multiple slope Hata model [10] describes path loss at near site (distance < 1km). The path loss of this model [10] is given by different equations (13), (14), (15) for different separations d between BTS and MS. The two slope model and the extended multiple slope Hata model are showed in figure (Fig. 3).

For d < 0.04km

622

10

10

10/)(log10

log2044.32)(

mb

CH

hhd

fdBL (13)

For d < 0.1km and d > 0.04km

)()(loglog

loglog)()(

40100401010010

401010

403

dLdLdd

dddLdL S

(14)

For d < 0.1 km and d < 20 km

)}10/(log20.0max{)8.0log56.1(

},10min{)7.0log1.1()(log

},30max{log82.132000/log10

2000log9.333.46)(

10

10

10

10

10

10

103

b

b

m

b

S

hf

hfhadB

hf

dL

(15)

where B is same as in equation (5).

0 200 400 600 800 1000 1200 1400 160050

60

70

80

90

100

110

120

130

140

150

Distance [m]

Pat

h lo

ss [d

B]

3-slope and 2-slope model

2-slope URBAN2-slope SUB-URBAN2-slope OPEN AREA3-slope URBAN3-slope SUBURBAN3-slope OPEN

Fig. 2. The 2-slope extension compared with the 3-slope

extension of path loss model for Urban, Suburban and Open areas for near site (f = 1500 MHz, hb = 30 m, hm = 1.5 m).

3. Measurement Results Measured data was collected around Brno using the

GSM 900/1800 modem. The collected data shows minimal difference among measured types of environment for near site. The figure (Fig. 3) shows comparison between the measured data and the multiple slope model described in section 2.2.4.

0 200 400 600 800 1000 1200 1400 160080

90

100

110

120

130

140

150

Distance [m]

Pat

h lo

ss [d

B]

3-slope COST 231 Hata model

URBANSUB-URBANOPEN AREA3-slope URBAN3-slope SUBURBAN3-slope OPEN

Fig. 3. Comparison of the measured data and the multiple slope

model (see section 2.2.4), f = 1500 MHz, hb = 30 m, hm = 1.5 m.

The figure (Fig. 4) shows comparison between the measured data and the two slope model described in section 2.2.3.

0 200 400 600 800 1000 1200 1400 160080

90

100

110

120

130

140

150

Distance [m]

Pat

h lo

ss [d

B]

2-slope Okumura Hata model

URBANSUB-URBANOPEN AREA2-slope URBAN2-slope SUBURBAN2-slope OPEN

Fig. 4. The measured data and the two slope Hata model

(section 2.2.3) for f = 1500 MHz, hb = 30 m, hm = 1.5 m.

4. Model Tuning The measured data are used for tuning process of the

multiple slope Hata model [10] (see section 2.2.4). Proposed model enhancement has break points at distance d = 0.04 and d = 0.25 km. Up to the first break point (0.04 km) the propagation path loss is determined according to the formula (13). For the path loss estimation for the distance between 0.04 km and 0.25 km the formula (14) is used and for distance over 0.25 km is used formula (2) for the free space path loss [2].

4.1 Model Fitting to Measured Data To achieve the best fit to the measured data the mean

square error (MSE) (see equation (16)) was calculated between the measured path loss value and the predicted values by propagation models [6]. The following path loss models have been fitted using the MSE [6]: Two slope model [7] (section 2.2.3), multiple slope model [10] (section 2.2.4) and tuned multiple slope path loss model (section 4).

1

2

N

SfLLMSE

PM (16)

where LM is measured path loss and LP is predicted path loss. The coefficient Sf = 100 shifts the model to clearly estimate the MSE value form the equation (16), it also has to be included in formula (17). Values of the MSE (15) are used to modify adequate propagation model Lmodel

LMSE = Lmodel + Sf – MSE. (17)

The path loss model fitting results, based on the MSE (see equation (16)), are showed in the figure (Fig. 5).

0 200 400 600 800 1000 1200 1400 160080

90

100

110

120

130

140

150

Distance [m]

Pat

h lo

ss [d

B]

MSE path loss model fitting

Measured data3-slope Tunned model2-slope model3-slope COST model

Fig. 5. The measured data and fitted models for f = 1500 MHz,

hb = 30 m, hm = 1.5 m.

The MSE is also used to deviation error estimation (see Tab. 1) for each fitted model (see Fig. 5). The tuned model has the lowest error for sub urban area.

Area type Path loss model

2-slope 3-slope 3-slope tuned

Urban 17.31 12.8 11.27

Sub-urban 15.19 10.24 8.74

Open 13.73 13.73 10.11

Tab. 1. The deviation error between the measured data and the fitted models.

5. A Localization Test of the Propagation Models Using PSO Propagation models fitted in section 4.1 have been

tested for localization of the MS in a cellular network. Based on the measurement a received signal level (RXLEV) is used to determinate the distance BTS-MS.

The PSO uses 25 agents with personal scaling factor Sp = 1.5, global scaling factor Sg = 2.49. Main loop has 20 iterations with good convergence in 10th iteration. Main criteria function computes Euclidean distance between BTS and MS in universal transverse mercator geographic coordinate system.

6. Conclusion Aim of this work was short range test of the Hata

based propagation path loss models [2], [5]. Propagation models were fitted, to the measured data collected around Brno, according to value of the MSE. New modification of the 3 slope propagation model [10] was created and fitted to measured data. The lowest MSE was, according to the

table (Tab. 1), for suburban environment. This is because in Brno is low average building heights and lot of parks and free places, therefore the signal attenuation is lower.

The 3 slope path loss model [10], 2 slope path loss model and tuned 3 slope model was fitted to the measured data and the MSE was set, see table Tab. 1. The tuning process of 3 slope model reduces the deviation error by 1.5 dB.

Tested models were used for localization of the MS in cellular network. The PSO was used to set the best location. Average error in location was in hundreds of meters for each model. Tuned 3 slope model error is 565 m and 2 slope model error is 478 m.

Acknowledgements The paper is supported by the research program of

Brno University of Technology, “Electronic Communication Systems and New Generation Technology (ELKOM)” MSM0021630513.

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