2.5G Wimax Cell Planning

Journal of the Chinese Institute of Engineers, Vol. 32, No. 5, pp. 585-597 (2009) 585

*Corresponding author. (Tel: 886-3-4638800 ext. 7320; Fax:886-3-4554264; Email: [email protected])

The authors are with the Department of CommunicationsEngineering, Yuan-Ze University, 135 Yuan-Tung Road, Jungli,Taoyuan 320, Taiwan, R.O.C.

CELL PLANNING AND CHANNEL THROUGHPUT OF MOBILE

WiMAX AT 2.5 GHz

Jeich Mar*, Chin-Chung Ko, Chung-Haw Li, and Shao-En Chen

ABSTRACT

A combination of COST-231 Hata and SUI Erceg models is presented to predictthe propagation path loss of 2.5 GHz Mobile WiMAX in urban, suburban, flat-terrainwith light tree (rural A), flat-terrain with heavy tree (rural B) and hilly-terrain rural(rural C) environments. The cell sizes for five different terrain areas, three antennamodes and 90% service reliability are estimated through the downlink link budgetanalysis. Based on the radio coverage calculation results, the call holding time in agiven cell and channel throughput of the Mobile WiMAX are simulated to observe therelationship among mobile speed, antenna mode, operation environment and channelthroughput. The effect of user mobility on the handoff rate is considered in thesimulations. An example of cell planning for 2.5 GHz Mobile WiMAX is carried outfor a zone near Taipei city.

Key Words: cell planning, handoff rate, cell residence time, channel throughput.

I. INTRODUCTION

Mobile WiMAX is a broadband wireless solu-tion that enables the convergence of mobile and fixedbroadband networks through a common wide area broad-band radio access technology and flexible networkarchitecture. The Mobile WiMAX Air Interface adoptsOrthogonal Frequency Division Multiple Access(OFDMA) technology for improving multi-path per-formance and supporting non line-of-sight (NLOS)environments operation in the 2-11 GHz band. Thisyear, the 2.5 GHz frequency carrier band has been re-leased for the use of service providers in Taiwan. Cellplanning could aid service providers to optimize basestation (BS) configurations, antenna mode selections,and site locations, in order to meet quality of service,system capacity and service requirement standards atminimum cost. The Mobile WiMAX specificationproposes a 1024 orthogonal frequency division multi-plex (OFDM) approach to cope with expected chan-nel impairments (Liu and Li, 2005). Various

modulation schemes, namely BPSK, QPSK, 16-QAMand 64-QAM, can be selected for each user to guaran-tee the target BER. Mobile WiMAX supports a fullrange of smart antenna technologies to enhance bothcoverage and channel throughputs (WiMAX Forum,2007). The 1 × 2 SIMO is a typical Mobile WiMAXbaseline BS antenna mode. A single transmission an-tenna is used at each end of the link, in which the re-ceived signal is enhanced through the use of diversityin the dual receiver antennas at both the BS and themobile station (MS). The second base station antennamode provides a 2 × 2 multiple input multiple output(MIMO) configuration, which offers space-time cod-ing (STC) and spatial multiplexing (SM) modes. WithSTC antenna mode, identical downlink data streamsare sent from each transmission antenna providing spaceand time diversity. In an environment with rapidmultipath fading, STC enhances the signal-to-noise ratio(SNR) of the received signal at the mobile station toenable support of higher modulation efficiency bursts,and thus enhances the downlink capacity as well asdownlink range. With SM antenna mode, each of thebase station transmission antennas sends a differentdownlink data stream. This technique uses multiplepaths to distinguish between the different data streamsand has the theoretical potential to double the down-link capacity under favorable channel conditions.

586 Journal of the Chinese Institute of Engineers, Vol. 32, No. 5 (2009)

The coverage of WiMAX with 256 OFDM at 450MHz and 3.5 GHz are analyzed and compared (Javorniket al., 2006) using the Erceg path loss model for threedifferent environments. In this paper, the cell size of2.5 GHz Mobile WiMAX is estimated from the linkbudget using the COST-231 Hata propagation model(Javornik et al., 2006) and the Stanford UniversityInterim (SUI) Erceg model (Abhayawardhana et al.,2005) (Erceg and Greenstein, 1999). The channelthroughput of Mobile WiMAX has been simulated bypresenting multimedia call services and cell layoutscenarios to evaluate the channel throughput. Todetermine the channel throughput in terms of aver-age call holding time in a given cell, we need to com-pute the cell residence time and handoff rate for newgeneration and handoff calls at different MS speeds.The effect of 2 × 2 MIMO antenna modes and ve-hicle speed on cell size and channel throughput arealso analyzed and calculated.

The rest of the paper is organized as follows.In Section II a combination of the COST-231 Hatamodel and the SUI Erceg model is proposed for cellsize estimation in five different areas; Section IIIdetermines the fade margin and the coverage prob-ability under 90% service reliability conditions; theradio coverage calculation results and a cell planningexample are shown in Section IV; the simulations ofcell residence time and handoff rate at different MSspeeds in a given cell together with channel through-put of Mobile WiMAX are performed in Section V.Section VI concludes this paper.

II. CELL SIZE ESTIMATION IN FIVEDIFFERENT AREAS

The propagation model plays a significant rolein cell planning. The COST-231 Hata model wasdesigned at a frequency band range from 500 MHz to2 GHz to be widely used to estimate path loss in mo-bile wireless systems for urban, suburban and flatrural environments. The SUI Erceg model was ini-tially designed for suburban areas and for a frequencyband of 1.9 GHz. Refer to (WiMAX Forum, 2006),the COST 231- Hata model is applied for the propa-gation model of Mobile WiMAX in WiMAX Forum2006. The COST 231- Hata model is based on em-pirical results in the 2 GHz band and tends to makevery conservative prediction for 2.5 GHz. The SUIErceg model is another model commonly used for the2.5 GHz band and predicts cell sizes that are greaterthan those of real cells. Based on the predictionresults, the operator will need to perform model cali-bration through field tests for the final cell planning.Both models also can use correction factors to bewidely applied to other frequency bands (Javornik etal., 2006). The formulas for both models are taken

from (Abhayawardhana et al., 2005) (Erceg andGreenstein, 1999). The pass loss and shadow fadingare taken into account in the models.

1. COST-231 Hata Model

The basic pass loss equation in dB for the COST-231 Hata model is (Abhayawardhana et al., 2005)

PL = 46.3 + 33.9log10( f ) – 13.82log10(hb) – ahm

+ (44.9 – 6.55log10(hb))log10(d) + cm, (1)

where f is the frequency in MHz, d is the distancebetween receiver and transmitter in km, and hb is theBS antenna height above ground in meters. The pa-rameter cm is defined as 0 dB for suburban or ruralenvironments and 3 dB for urban environments. Theahm is defined for urban environment as

ahm = 3.20(log10(11.75hr)) – 4.97,

for f > 400 MHz (2)

and for suburban or flat rural environments,

ahm = (1.1log10 f – 0.7)hr – (1.56log10 f – 0.8),

(3)

where hr is the MS antenna height above ground inmeters.

2. Stanford University Interim (SUI) Erceg Model

The SUI Erceg model is divided into three typesof terrains, A, B and C. Type A is hilly terrain withmoderate to heavy tree density, representing ruralenvironments and is associated with the highest pathloss. Type B is characterized by either a mostly flatterrain with moderate to heavy tree density or a hillyterrain with light tree density. Type C is a flat ter-rain with light tree density and is associated with thelowest path loss for rural environments. The basicpath loss equation with correction factors is presentedas (Abhayawardhana et al., 2005),

PL = H + 10γlog10(dd0

) + X f + Xh + s for d > d0 ,

(4)

where d is the distance between the receiver and trans-mitter in meters, d0 = 100 m and H is defined as

H = 20log10(4πd0

λ ) , (5)

where λ is the wavelength. The parameter γ is aGaussian random variable over the population ofmacrocells within each terrain category. It can be

J. Mar et al.: Cell Planning and Channel Throughput of Mobile WiMAX at 2.5 GHz 587

Table 1 The parameters of the SUI Erceg model(Abhayawardhana et al., 2005)

Terrain Type Type Type parameter A B C

e 4.6 4.0 3.6g(m–1) 0.0075 0.0065 0.005k(m) 12.6 17.1 20.0

σγ 0.57 0.75 0.59µσ 10.6 9.6 8.2σσ 2.3 3.0 1.6

Fig. 1 Path loss curves of Mobile WiMAX using the COST-231Hata model and the SUI Erceg model

170

160

150

140

130

120

110

100

90

800 0.5 1 1.5 2 2.5

Cell size (km)

3 3.5 4 4.5 5

Path

Los

s (d

B)

Erceg CErceg BErceg ACOST-231 suburbanCOST-231 urban

written as (Erceg and Greenstein, 1999)

γ = (e – ghb + k/hb) + xσγ , (6)

where hb is the height of the base station antenna inmeters, σγ is the standard deviation of γ, x is a zero-mean Gaussian variable of unity standard deviationN[0, 1], and e, g, k and σγ are all data-derived con-stants for each terrain category. The shadow fadingcomponent s varies randomly from one terminal lo-cation to another within any given macro-cell. It is azero-mean Gaussian variable and can be expressedas (Erceg and Greenstein, 1999)

s = yσ, (7)

σ = µσ + zσσ , (8)

where y and z are the zero-mean Gaussian variablesof unit standard deviation N[0, 1], σ is the standarddeviation of s, µσ is the mean of σ, and σσ is the stan-dard deviation of σ. µσ and σσ are both data-derivedconstants for each terrain category. The numericalvalues of the above parameters are given in Table 1.

The correction factors of the model for the op-erating frequency and for the MS antenna height are(Abhayawardhana et al., 2005)

Xf = 6.0log10(f

2000 ),

Xh = –10.8log10( h r2

) for Terrain types A and B

= –20.0log10( h r2

) for Terrain type C, (9)

where f is the frequency in MHz and hr is the heightof the MS antenna above ground in meters.

3. Cell Size Estimation

The COST-231 Hata model and the SUI Ercegmodel are numerically calculated to obtain therelationship between cell size and path loss, as shownin Fig. 1, in which the parameters of the Mobile

WiMAX are (WiMAX Forum, 2006)

• Frequency = 2.5 GHz• MS height = 1.5 meter• BS height = 32 meter

Fig. 1 compares the propagation path loss (PL) cal-culated by the COST-231 Hata model and the SUImodel for urban, suburban and rural environments.It is interesting to reveal that the path loss obtainedby the COST-231 Hata model is higher than that ofthe SUI Erceg model, given the same cell size. Sowe may use the COST-231 Hata model to estimatethe cell size of Mobile WiMAX for urban and subur-ban environments, and use the SUI Erceg model forthree different terrain categories of rural environments.

III. LOGNORMAL FADE MARGIN ANDCOVERAGE PROBABILITY

In the link budget analysis, fade margin data forurban, suburban and rural environments are needed,together with the coverage probability and servicereliability. Coverage probability is the probability atlocation l in a cell with radius L, that the receivedsignal power is above threshold.

1. Coverage Probability

It is assumed that the local mean signal strengthin an area at a fixed radius from a particular basestation antenna is log-normally distributed. For log-normal fading environments, we define the receivedsignal strength W(dBm) with mean

–W and standard

deviation σW. The probability density of W is (Jakes,1993)


Table 2 Lognormal fade margin coverage prob-ability

σW α PW0(L) F.M

Urban 6 4 70% 3.2Suburban 8 3.4 76% 5.56

Rural 12 2.5 82% 11.2

p(W) = 12π σW

e– 12

(W – Wσ W

)2. (10)

The probability that W exceeds the threshold W0 is

PW0(l) = P[W ≥ W0] = p(W)dW

W0

∞

= 12 – 1

2erf (W0 – K + 10αlog( l

L)

2σ W

) , (11)

where the error function is erf(u) = 2π exp

0

u(–z2)dz,

K-W0 is defined as the fade margin in dB at l = L toassure reliable operation of the communication link,K is the mean received signal strength in dB at cellboundary l = L and W0 is the threshold of the receiver.We assume that the behavior of the mean value ofsignal strength follows an l–α law, thus

W = K – 10αlog( lL) , 2 ≤ α ≤ 4. (12)

2. Service Reliability

Service reliability Fu determines the proportionof useful service cell area within a circle of radius Lfor which the signal strength received by an MS ex-ceeds a given threshold W0. If PW0

is the probabilitythat the received signal W exceeds W0 in an incre-mental area dA (Jakes, 1993), then

Fu = 1πL2 PW0

dA . (13)

Letting

m =W0 – K + 10αlog( l

L)

2σ W,

n =10αloge

2σ W, (14)

we get

Fu = 12{1 – erf (m) + exp(1 – 2mn

n2 )[1 – erf (1 – mnn )} .

(15)

We use the above formulas to calculate lognormalfade margin and coverage probability at the cell edgefor a Mobile WiMAX system, as shown in Table 2(Parsons, 1992; Rappaport, 2002), where the servicereliability is set as 90%.

IV. RADIO COVERAGE CALCULATIONRESULTS

There are three basic types of downlinksub-channels including fully used sub-carrier (FUSC),partially used sub-carrier (PUSC), and adaptive

modulation and coding (AMC) and two basic typesof uplink sub-channels including PUSC, and AMC.In the PUSC mode, among all sub-carriers, only 720of them carry information. One hundred and twentysub-carriers transmit the pilot tones. In the FUSCmode, among all sub-carriers only 768 of them carryinformation. Eighty-three sub-carriers transmit thepilot tones (Liu and Li, 2005).

Six cases of downlink link budget analysis aresummarized in Table 3(a) for Mobile WiMAX in thesuburban environment (WIMAX Forum, 2006), case1 is a basic type of PUSC downlink sub-channel using2 × 2 MIMO STC antenna mode; case 1* is a basictype of PUSC downlink sub-channel using 2 × 2 MIMOSM antenna mode; case 2 is the PUSC downlink sub-channel using 1 × 2 SIMO antenna mode; case 3 is theFUSC downlink sub-channels using 2 × 2 MIMO STCantenna mode; case 3* is the FUSC downlink sub-chan-nels using 2 × 2 MIMO SM antenna mode; case 4 isthe FUSC downlink sub-channels using 1 × 2 SIMOantenna mode. The differences among the six casesare antenna modes and downlink sub-channel types.Finally the maximum allowable path loss results (indB) for the six cases in suburban areas are calculatedand listed in Table 3(a), where

• EIRP = Tx Power per Antenna Element + CyclicCombining Gain + Tx Antenna Gain + Pilot PowerBoosting Gain

• Rx Sensitivity = Rx Noise Figure + Thermal Noise+ SNR Required

• System Gain = EIRP + Rx Antenna Gain + Rx An-tenna Diversity Gain – Rx Sensitivity

• Maximum Allowable Path Loss = System Gain –Total Margin

Table 3(b) shows the cell sizes for the six cases infive environments, namely urban, suburban, flat-ter-rain with light trees (rural A), flat-terrain with heavytrees (rural B) and hilly-terrain rural (rural C)environments, respectively. Using lognormal fademargin and interference margin values specified in(Harri and Antti, 2000) for urban, suburban and ruralenvironments, the maximum allowable path losses forPUSC and FUSC types downlink sub-channels ofMobile WiMAX with 2 × 2 MIMO STC and SM an-tenna modes and 1 × 2 SIMO antenna mode are


Table 3 (a) Downlink link budget for Mobile WiMAX in suburban area. (b) Cell size of Mobile WiMAXfor different environments. ��( )* means the 2 ××××× 2 MIMO SM antenna mode

Base Station infrastructure

Mobile Unit (Handset Indoor)

Case 1(1*)

Tx Power per AntennaElement

Number of Tx AntennaElements

Number of Occupied Sub-Carriers

Rx Antenna Diversuty Gain(2 Antennas)

Power per Occupied Sub-Carrier

MIMO Gain (2 Antennas)

Tx Antenna GainPilot Power Boosting Gain

EIRP

Rx Antenna Gain

Rx Noise Figure

3.0(0)*

-1.0

7.0

3

-1.0

7.0

3.0(0)*

-1.0

7.0

3

-1.0

7.0

dB

dBi

dBMargins

Fast Fading Margin

Log Normal Fade Margin

Interference Margin

6.0

5.56

2.0

6.0

5.56

2.0

6.0

5.56

2.0

6.0

5.56

2.0

dB

dB

dB

Penetration Loss

Total Margin10.0

23.56

10.0

23.56

10.0

23.56

10.0

23.56

dB

dBMobile Rx Sensitivity

Sub-Carrier Spacing

Thermal Noise

Modulation (coding rate)

10.94

-174

QPSK(1/8)

10.94

-174

QPSK(1/8)

10.94

-174

QPSK(1/8)

10.94

-174

QPSK(1/8)

kHz

dBm/Hz

Rx Sensitivity (composite)

Rx Sensitivity (per sub-carrier)

-100.7

-129.9

-100.7

-129.9

-100.6

-129.9

-100.6

-129.9

dBm

dBm

SNR Required

Delta from Limiting cell rangedistance

-3.31

0.82

-3.31

0.82

-3.31

0.82

-3.31

0.82

dB

System Gain 160.0(154.0)*

157.0 159.9(153.9)*

156.9 dB

Maximum Allowable PathLoss

136.4(130.4)*

133.4 136.3(130.3)*

133.3 dB

Sub-channel type

10.0

2

840

28.1

3.0(0)*

15.0-0.7

57.3

PUSC

Case 2

10.0

1

840

25.1

0

15.0-0.7

54.3

PUSC

Case 3(3*)

10.0

2

851

28

3.0(0)*

15.0-0.7

57.3

FUSC

Case 4

10.0

1

851

25

0

15.0-0.7

54.3

FUSC

Units

Watts

dBm

dB

dBidB

dBm


Fast Fading Margin


Interference Margin

Penetration Loss

Total Margin

Log Normal Shadowing SD

3.2

6

137.8(131.8)*

3

10

22.2

6

3.2

6

134.8

3

10

22.2

6

3.2

6

137.7(131.7)*

3

10

22.2

6

3.2

6

134.7

3

10

22.2

6

dB

dB

dBdB

dB

dB

Cell size (COST 231 Urban) 0.6791(0.4578)*

0.5576 0.6746(0.4548)*

0.5539 km

dB

(b)(a)Urban Case 1 Case 2 Case 3 Case 4 Units


Fast Fading Margin


Interference Margin

Penetration Loss

Total Margin


5.56

6

136.4(130.4)*

2

10

23.56

8

5.56

6

133.4

2

10

23.56

8

5.56

6

136.3(130.3)*

2

10

23.56

8

5.56

6

133.3

2

10

23.56

8

dB

dB

dBdB

dB

dB

Cell size (COST 231 Suburban)

0.7572(0.5105)*

0.6217 0.7522(0.5071)*

0.6176 km

dB

Suburban


Fast Fading Margin


Interference Margin

Penetration Loss

Total Margin


11.2

6

131.8(125.8)*

1

10

28.2

12

11.2

6

128.8

1

10

28.2

12

11.2

6

131.7(125.7)*

1

10

28.2

12

11.2

6

128.7

1

10

28.2

12

dB

dB

dBdB

dB

dB

Cell size (Erceg model A) 1.095(0.827)*

0.952 1.09(0.823)*

0.948 km

Cell size (Erceg model B) 1.384(1.01)*

1.193 1.38(1.008)*

1.19 km

Cell size (Erceg model C) 1.53(1.097)*

1.393 1.52(1.094)*

1.39 km

dB

Rural

calculated. It is noted that case 1 generates the larg-est path loss, given the same environment, so its cellsize is larger than other cases. A base station installedin a rural C environment needs a plan incorporatingthe largest cell sizes for all cases. The maximum al-lowable path losses of PUSC 2 × 2 MIMO antennamodes are almost equal to those of FUSC 2 × 2 MIMOantenna modes. Because of having MIMO antennagain, the maximum allowable path losses of 2 × 2MIMO STC antenna modes of both PUSC and FUSCtype are 3 dB larger than the 1 × 2 SIMO antennamode and 6 dB larger than the single input single out-put (SISO) antenna so that the cell size of MobileWiMAX using 2 × 2 MIMO STC antenna mode islarger than when using 1 × 2 SIMO antenna mode.

Given 90% service reliability over the entire cellarea, the value of 3.2 dB used for the lognormal fademargin in the urban environment assures a 70% cov-erage probability at the cell edge; the value of 5.56dB used for the lognormal fade margin in the subur-ban environment assures a 76% coverage probabilityat the cell edge; the value of 11.2 dB used for the lognormal fade margin in the urban environment assuresa 82% coverage probability at the cell edge.

The cells planning for a zone near Taipei cityare shown in Figs. 2(a), (b) and (c) for FUSC 2.5 GHzMobile WiMAX with 2 × 2 MIMO STC antenna mode,1 × 2 SIMO antenna mode and 2 × 2 MIMO SM an-tenna mode, respectively. The circles a and b on theterrain map are the cell sizes in urban and suburbanareas, respectively, calculated by the COST-231 Hatamodel; the circles c, d and e in rural areas A, B and Care the cell sizes calculated by the SUI Erceg model,respectively.

The cell size in Fig. 2(c) is assumed to be identi-cal for all five operation environments. The ratios ofcell sizes in Figs. 2(a) and (b) to cell size in Fig. 2(c)are listed in Table 4, where circle a represents an ur-ban area, circle b represents a suburban area, and circlesc, d, and e represent rural areas A, B and C, respectively.It is noted that the sizes of all circles in Fig. 2(a) arelarger than those in Figs. 2(b) and 2(c). For this reason,the Mobile WiMAX using 1 × 2 SIMO antenna modeor 2 × 2 MIMO SM antenna mode needs more BSs tocover the same service area. Nevertheless, the cellsize of the Mobile WiMAX using a 2 × 2 MIMO SMantenna mode, which is identical to a SISO antenna,is the smallest but it can greatly improve the channel


Fig. 2 Cell planning for a zone near Taipei city for 2.5 GHz FUSC Mobile WiMAX: (a) with 2 × 2 MIMO STC antenna mode; (b) with 1× 2 SIMO antenna mode; (c) with 2 × 2 MIMO SM antenna mode

Table 4 Comparison of cell sizes in Fig. 2

ratio a b c d e

Fig 2a 2.2 2.2 1.75 1.87 1.93Fig 2b 1.483 1.483 1.33 1.39 1.61Fig 2c 1 1 1 1 1

throughput. So taking best advantage of STC and SMMobile WiMAX also supports adaptive MIMOswitching. This enables dynamic switching betweenSTC and SM depending on the existing channel con-ditions at any given time (WIMAX Forum, 2007).

V. CHANNEL THROUGHPUT

Based on the cell planning results, the channelthroughputs of the Mobile WiMAX are simulated toobserve the relationship among mobile speed, antennamode, operation environment and channel throughput.The digital simulation method in (Reilly, 1999) (Nelson,1995) is used to evaluate the channel throughput. Thecell layouts are given in Figs. 2(a), (b) and (c), whereeach antenna mode includes five different operationenvironments. Different shadowing fade margin valuesare considered in the link-budget calculation of do-ing cell planning. The Mobile WiMAX cluster iscomposed of concatenated segments where each seg-ment has installed a Mobile WiMAX system. Thesimulation parameters are listed in the following (Marand Huang, 2000; Mar et al., 2007):

• New call origination is modeled with Poisson dis-tribution function. Mean call arrival rate = 0.18calls/sec

• Average speed of users = 50, 100 and 120 km/hr• System traffic load ratio = 1

• Multi-data rate call ratio = DA,UGS : DA,BE : DA,nrtPS

: DA,rtPS = 1 : 1 : 1 : 1• System capacity = 40 equivalent slots (1 equivalent

slot = 64 Kbps)• Call completing ratio = 0.9• Minimum handoff to adjacent cell ratio (handoff

rate) for new generation call Rnr = 0.1

• Call management method: Complete sharing (CS)scheme without channel reservation (Mar andHuang, 2000)

DOCSIS 1.1 (Data Over Cable Service InterfaceSpecification) is adopted to define multimedia callservices: Unsolicited Grant Service (UGS), Best Ef-fort (BE), Non-Real-Time Polling Service (nrtPS) andReal-Time Polling Service (rtPS)(IEEE ComputerSociety and IEEE Microwave Theory and TechniquesSociety, 2006). UGS, BE, nrtPS, rtPS are assignedwith DA,UGS, DA,BE, DA,nrtPS, DA,rtPS equivalent slots,respectively. We assume that the data transmissionrate of one channel is equivalent to 64 Kbps per timeslot for Mobile WiMAX systems (VoIP applicationrequires 64 Kbps) (Mar et al., 2007). Therefore, oneequivalent slot is required for 1x data transmissionrate (64 Kbps) service (DA,UGS, DA,BE), two equiva-lent slots are required for 2x data transmission rate(128 Kbps) service (DA,nrtPS), and three equivalentslots are required for 3x data transmission rate (192Kbps) service (DA,rtPS). All types of calls have equal

(a) (b) (c)


priority to be serviced in a CS scheme. The call hold-ing time is defined as the time duration between theinstant that the slot is occupied by a call and the in-stant it is released by either call completion or callhandoff. The call holding time for a new call in sys-tem i, THn, i is the minimum of the unencumbered callduration Tu and the cell residence time for a new callin system i. Also the slot holding time THh, i for ahandoff call in system i is either the unencumberedcall duration Tu or the cell residence time Th, i for ahandoff call in system i, whichever is less. The ran-dom variables for THn, i and THh, i are given by

THn, i = min (Tu, Tn, i),

THh, i = min (Tu, Th, i). (16)

The unencumbered call duration Tu is the amount of

time that the call will remain in progress if it experi-ences no forced termination due to handoff failure.The unencumbered call duration is a random variablewith a negative exponential probability density func-tion (pdf). The mean unencumbered call duration is–Tu = u–1, in which u is the mean call unencumberedrate or call completion rate (Mar et al., 2007). Thecell residence time is defined as the time duration thatan MS resides in a cell. The distance between thepoint where a new call is originated and the point onthe cell boundary where an MS exits from cell is Zi.Then the cell residence time for a new call Tn, i isexpressed as Tn, i = Zi /Vi. This is a function of sys-tem parameters such as cell size, speed and directionof movement by the MS. The pdf of cell residencetime Tn, i for a new call in system i is derived in Ap-pendix A.

fTn, i(t)=

Vi max + Vi minπri

, for t = 0

8ri

3(Vi max – Vi min) πt2 1 –tVi min

2ri

2 3

– 1 –tVi max

2ri

2 3

, for 0 ≤ t ≤ 2riVi max

8ri

3(Vi max – Vi min) πt2 1 –tVi min

2ri

2 3

, for2ri

Vi max≤ t ≤ 2ri

Vi min

, (17)

where Vimax and Vimin are the maximum and minimumspeeds of the MSs in the system i, respectively. Thespeed of the MSs in the given cell is uniformly dis-tributed in [Vimin, Vimax]. Its mean speed is (Vimin +Vimax)/2 (Mar et al., 2007). The mean cell residence

time –T n

i for a new generation call in system i is deter-mined with the cell size and the mean speed of theMS. The pdf of the cell residence time Th, i for ahandoff call in system i is in Appendix A.

fTh(t)=

Vmax + Vmin2πri

, for t = 0

4ri

(Vmax – Vmin) πt2 1 –tVmin2ri

2

– 1 –tVmax

2ri

2

, for 0 ≤ t ≤ 2riVmax

4ri

(Vmax – Vmin) πt2 1 –tVmin2ri

2

, for2ri

Vmax≤ t ≤ 2ri

Vmin

. (18)


Fig. 3 Simulation flow chart for throughput

Set simulationinteral T, vehicle

speed anc cellsize

Set simulationinteral T, vehicle

speed anc cellsize

Handoff call toadjacent cell

Callcompletion

Computethroughput

Compute new callblocking and

handoff failureprobabilities

I(t) < Cx(t) ?

Call drop

RT

xj, Gj, N

The mean cell residence time –T h

i for a handoff call insystem i is determined with the cell size and meanspeed of the MS. The simulation flow chart for chan-nel throughput of Mobile WiMAX is shown in Fig.3, where G is system capacity, T is total simulationtime, and xj and Gj are the slot holding time and as-signed slots, respectively. The handoff rate is pro-portional to the reciprocal of mean cell residence time.Therefore, the handoff rate at cell size x and meanMS speed y for new generation call is determined by

Rx, yn = Rr

n T rn

T x, yn , (19)

where –T n

x, y is the mean cell residence time for newgeneration call under the conditions of cell size x andmean MS speed y. Rn

r and –T n

r are the reference handoffrate and reference mean cell residence time, respectively,for new generation call under the conditions of meanMS speed 50 km/h and maximum cell size 1.52 km.The handoff rate at cell size x and mean MS speed yfor handoff call is given by

Rx, yh = Rr

n T rh

T x, yh , (20)

where –T h

x, y is the mean cell residence time of handoffcall at cell size x and mean MS speed y.

–T h

r representsthe reference mean cell residence time for handoff callunder the conditions of mean MS speed 50 km/h andmaximum cell size 1.52 km. For each new generationcall and handoff call, which can be served in the givencell if I(t) ≥ Cx(t), where I(t) is the number of avail-able slots at time t, Cx(t) is the number of the requiredslots for new generation calls or handoff call at time t.The new generation calls or handoff calls will be droppedif I(t) < Cx(t). As soon as the call is generated in Mo-bile WiMAX (system i) successfully, the call may becompleted or handed off to an adjacent cell. N is the

total number of completion calls. The time subset inwhich blocking occurs is given by

B = {t : I(t) < CB(t)}, (21)

where CB(t) is the number of required slots for newgeneration calls at time t. The new call blocking prob-ability in the given cell is obtained by

PB =NBNg

, (22)

where the total number of blocked calls under the timesubset B is NB. The total number of new generationcalls is defined as Ng. The time subset in which handofffailure occurs in system i is written as follows:

H = {t : I(t) < CH(t)}, (23)

where CH(t) is the number of required slots forhandoff calls at time t. The handoff failure probabil-ity in a given cell is written as

PH =NHNh

, (24)

where the total number of handoff failure calls fortime subsets H is defined as NH. The total number ofhandoff calls is defined as Nh. The channel through-put of Mobile WiMAX is determined with

RT =xjG jΣ

j = 1

N

T . (25)

where xj and Gj are the call holding time and assignedslots, respectively, for each new generation call andhandoff call. In the preset simulation time T, the chan-nel throughput RT can be calculated.

The channel throughput of FUSC type downlinkMobile WiMAX system utilizing three antenna modes,


2500

2000

1500

1000

500

0

Case 3Case 4Case 3*

UrbanSuburbanRural type ARural type BRural type C

(a) (b)

0.18 0.19 0.2 0.21 0.22 0.23

New call origination rate (calls/sec)

0.24 0.25 0.26 0.27

Thr

ough

put (

kbps

)

2500

2000

1500

1000

500

00.18 0.19 0.2 0.21 0.22 0.23

New call origination rate (calls/sec)

0.24 0.25 0.26 0.27

Thr

ough

put (

kbps

)

Fig. 4. Channel throughput of multimedia call services with varied new call origination rates (a) for three cases in urban environment andat 50 Km/h MS speed; (b) for five environments in Fig. 2(a) and at 50 Km/h MS speed channel throughput in a given cell

Table 5 Channel throughput of multimedia call services in five environments for 50 Km/h, 100 Km/h and120 Km/h MS speeds

Antenna modes case 3 (Fig. 2(a)) case 4 (Fig. 2(b)) case 3* (Fig. 2(c))

Rural Rural Rural Rural Rural Rural Rural Rural RuralEnvironments Urban Suburban Urban Suburban Urban Suburban

A B C A B C A B C(cell size (km)) (0.6746) (0.7522) (0.5539) (0.6176) (0.4548) (0.5071)

(1.09) (1.38) (1.52) (0.948) (1.19) (1.39) (0.823) (1.008) (1.094)

For50 km/h 954.18 1052.69 1368.9 1818.12 1912.14 819.07 900.41 1300.74 1622.2 1864.4 1389.1 1533.1 2288.28 2832.61 2942.79

speed

For100 km/h 568.96 607.89 809.11 975.48 1079.2 503.15 543.68 718.8 879.9 980.7 918.3 957.6 1360.6 1521.44 1635.1

speed

For120 km/h 513.18 550.21 710.44 864.66 923.45 458.14 496.66 631.1 725.8 865.26 886.1 895.15 986.1 1340.2 1423.05

speed

Thr

ough

put (

kb/s

)

in five environments, at three vehicle speeds (50 km/h, 100 km/h and120 km/h) is shown in Table 5, wherethe call origination rate is set at 0.18 calls/sec; boththe new call blocking probability and handoff failureprobability are less than 0.05. The cell residence timeand handoff rate for new generation and handoff callsat different MS speeds are simulated and computedusing Eqs. (17), (18), (19) and (20), respectively. Theminimum handoff rates for new generation call areused as the reference handoff rate for the new gen-eration calls Rn

r. Rnr is set as 0.1 to satisfy the condi-

tions of both the new call blocking probability andhandoff failure probability less than 0.05. The chan-nel throughput for three cases with varied new callorigination rates in urban environment, at 50 Km/hspeed of MS is shown in Fig. 4(a) and the throughputfor five environments with varied new call origina-tion rates in case 3 and at 50 Km/h speed of MS isshown in Fig. 4(b). From Table 5, and from Figs. 4(a) and (b), it is noted that Fig. 2(c) using 2 × 2 MIMOSM antenna mode has the best channel throughputdue to different downlink data streams sent by eachtransmission antenna; Fig. 2(a) using 2 × 2 MIMOSTC antenna mode has a medium throughput due todiversity gain provided in both transmitter and receiver

antennas in all environments. Fig. 2(b) using 1 × 2SIMO antenna mode has the worst throughput due todiversity gain provided only in the receiver in allenvironments. Under the same antenna mode, ruraltype C has the better channel throughput than otherenvironments because it has the maximum cell size.Nevertheless, the channel throughput of MobileWiMAX for a vehicle speed 50 km/h is less than twicethat of vehicle speed 100 km/h, though the call hold-ing time doubles as the MS speed doubles because anincrease in handoff rate results in the increase of chan-nel throughput in a given cell. The channel through-put of multimedia call services in five environmentsfor 120 Km/h MS speed is simulated to observe thelimitations of mobile WiMAX for deployment inTaiwan. Fig. 4(a) shows that the channel throughputof the Mobile WiMAX increases with the call origi-nation rate when the vehicle is driving in an urbanarea at 50 km/hr. Fig. 4(b) compares the channelthroughput of Mobile WiMAX using 2 × 2 MIMOSTC antenna mode in five different areas at 50 km/hrvehicle speed. It is noted that within these five areas,the channel throughput of rural C is the best, followedby rural B, rural A, and suburban, and that in urbanarea is the worst.


VI. CONCLUSIONS

In this paper, the cell size in a zone near Taipeicity for the BS of 2.5 GHz Mobile WiMAX system isplanned. After the comparison of the propagation pathlosses evaluated from the COST-231 Hata model andthe SUI model, the COST-231 Hata model is proposedto estimate the cell size in urban and suburban areas,and the SUI Erceg model is proposed to estimate thecell size in rural A, rural B and rural C areas. Thecoverage probabilities for urban, suburban and ruralenvironments are 70%, 76% and 82%, respectively,where the service reliability is set as 90%. The linkbudget results validate that the cell size of the Mo-bile WiMAX using a 2 × 2 MIMO SM antenna modeis smaller than those using both 2 × 2 MIMO STCand 1 × 2 SIMO antenna modes. The cell size is de-termined with the link level performance of differentradio setups including antenna mode, modulation andcoding scheme, sub-channel type, fading margin, op-eration environments etc. Based on the estimated cellsize, the traffic performance including the new callblocking probability, handoff failure probability andchannel throughput are simulated and evaluated. Thechannel throughput simulation results show that us-ing a 2 × 2 MIMO SM antenna mode can significantlyimprove the channel throughput of the Mobile WiMAX.As soon as the vehicle speed increases from 50 km/hto 100 km/h, the channel throughput of Mobile WiMAXreduces more than half because the call holding timein a given cell decreases and the handoff rate increasesupon increasing MS speed.

ACKNOWLEDGEMENT

This work was supported by ITRI and FarEasTone Telecommunications Co., Ltd., Taiwan, R.O.C. The authors would like to thank the editors andreviewers for their valuable inputs.

NOMENCLATURE

B the time subset in which blocking occurscm the parameter defined as 0 dB for suburban

or rural environments and 3 dB for urban en-vironments

Cx(.) the number of the required slots for new gen-eration calls or handoff calls

CB(.) the number of the required slots for new gen-eration calls

CH(.) the number of required slots for handoff callsd the distance between receiver and transmit-

tere the all data-derived constants for each terrain

categoryerf (.) the error function

f the frequency in MHzFu Service reliabilityg the all data-derived constants for each terrain

categoryG the system capacityGj the assigned slotshb the BS antenna height above ground in metershr the MS antenna height above ground in metersH the time subset in which handoff failure oc-

curs in system iI(.) the number of available slotsk the all data-derived constants for each terrain

categoryK the mean received signal strength in dB at cell

boundaryl the location in a cellL the radius of the location in a cellN the total number of completion callsNB the total number of blocked calls under the

time subset BNg the total number of new generation callsNh the total number of handoff callsNH the total number of handoff failure calls for

time subsets Hp(.) the probability density functionPL basic pass lossPB the new call blocking probability in the given

cellPWo(.) the probability density function that the re-

ceived signal strength in dBm exceeds thethreshold of the received signal strength indBm

RT the channel throughput in the preset simula-tion time T

Rrn the minimum handoff to adjacent cell ratio

(handoff rate) for new generation calls the shadow fading componentT the total simulation timeTu the unencumbered call durationTh, i the cell residence time for a handoff call in

system iTn, i the cell residence time of for a new callTHn, i the minimum of the unencumbered call dura-

tion in system iTHh, i the slot holding time for a handoff call in sys-

tem i–Ti

h the mean cell residence time for a handoff callin system i

–Ti

n the mean cell residence time for a new gen-eration call in system i

–Tr

h the reference mean cell residence time forhandoff call under the conditions of mean MSspeed 50 km/h and maximum cell size 1.52km

–Tr

n the reference mean cell residence time for newgeneration call under the conditions of mean


MS speed 50 km/h and maximum cell size1.52 km

–T h

x, y the mean cell residence time of handoff callat cell size x and mean MS speed y

–T n

x, y the mean cell residence time for new genera-tion call under the conditions of cell size xand mean MS speed y

Vi the speed of the MSs in system iVi max the maximum speed of the MSs in the system

iVi min the minimum speed of the MSs in the system

iW the received signal strength in dBmWo the threshold of the received signal strength

of the receiver in dBm–

W the mean of the received signal strength indBm

x the zero-mean Gaussian variable of unitystandard deviation N[0, 1]

xj the slot holding timey the zero-mean Gaussian variables of unit stan-

dard deviation N[0, 1]z the zero-mean Gaussian variables of unit stan-

dard deviation N[0, 1]Zi the distance between the point where a new

call is originated and the point on the cellboundary where an MS exits from cell

α the parameter in the equation of mean valueof signal strength

γ the parameter of a Gaussian random variableover the population of macrocells within eachterrain category

λ the wavelengthµ the mean call unencumbered rate or call

completion rateµσ the mean of the standard deviation of the

shadow fading componentσ the standard deviation of the shadow fading

componentσw the standard deviation of the received signal

strength in dBmσγ the standard deviation of γσσ the standard deviation of the standard devia-

tion of the shadow fading component

REFERENCES

Abhayawardhana, V. S., Wassell, I. J., Crosby, D.,Sellars, M. P., and Brown, M. G., 2005, “Com-parison of Empirical Propagation Path Loss Modelsfor Fixed Wireless Access Systems,” 61st IEEEVehicular Technology Conference, Stockholm,Sweden, Vol. 1, pp. 73~77.

Erceg, V., and Greenstein, L. J., 1999, “An Empiri-cally Based Path Loss Model for Wireless Chan-nels in Suburban Environments,” IEEE Journal

on Selected Areas in Communications, Vol. 17,No. 7, pp. 1205-1211.

Harri Holma and Antti Toskala, 2000, WCDMA forUMTS – Radio Access for Third Generaion Mo-bile Communications, ISBN 0-471-72051-8, JohnWiley & Sons, NY, USA, pp.157~159.

Hong, D., and Rappaport, T. S., 1986, “Traffic Sys-tem and Performance Analysis for Cellular Mo-bile Radio Telephone Systems with Prioritizedand Non-prioritized Handoff Procedures,” IEEETransactions on Vehicular Technology, Vol. VT-35, No. 3, pp. 77-92.

IEEE Computer Society and IEEE Microwave Theoryand Techniques Society, 2006, IEEE Standard forLocal and Metropolitan Area Networks Part 16:Air Interface for Fixed and Mobile BroadbandWireless Access Systems Amendment 2: Physi-cal and Medium Access Control Layers for Com-bined Fixed and Mobile Operation in LicensedBands and Corrigendum 1, 3 Park Avenue, NY,USA, pp. 0_1-822.

Jakes, William C., 1993, Microwave Mobile Com-munications, ISBN 978-0-7803-1069-8, Wiley-IEEE Press, NY, USA, pp. 125-128.

Javornik, T., Kandus, G., Hrovat, A., and Ozimek, I.,2006, Comparison of WiMAX Coverage at 450MHz and 3.5 GHz, Department of Communica-tion systems, Jozef Stefan Institute, Jamova 39Ljubljana, Slovenia.

Liu, H., and Li, G., 2005, OFDM-Based BroadbandWireless Networks Design and Optimization, JohnWiley & Sons, NY, USA, pp. 219-221.

Mar, J., Chen, S. E., and Lin, Y. R., 2007, “The Ef-fect of the MS Speed on the Traffic Performanceof an Integrated Mobile WiMAX and DSRC Mul-timedia Networks on the Highway,” InternationalConference on Communications and Mobile Com-puting Proceedings of the 2007 international con-ference on Wireless communications and mobilecomputing (IWCMC2007), pp. 44-48

Mar, J., and Huang, J. P., 2000, “Traffic PerformanceAnalysis of the Integrated Dual Band Cellular RadioNetworks,” IEE Proceedings Communications, Vol.147, No. 3, pp. 180-186.

Nelson, R., Probability, 1995, Stochastic Process andQueueing Theory, Spriber-Verlay, NY, USA.

O’Reilly, P., 1999, Simulation with Visual SLAM andAweSim, Wiley, NY, USA.

Parsons, J. D., 1992, The Mobile Radio PropagationChannel, ISBN 0-471-96415-8, John Wiley &Sons, NY, USA, pp. 156-159.

Rappaport, Theodore S., 2002, Wireless Communi-cations – Principle and Practice, 2nd ed., PrenticeHall PTR, NJ, USA, pp. 138-141.

Varberg, D., and Purcell, E. J., 1997, Calculus,International 7th ed., Prentice-Hall Inc., NY,


USA, pp. 443.WiMAX Forum, 2007, A Comparative Analysis of

Mobile WiMAX Deployment Alternatives in theAccess Network, pp. 16-19, Available: http://www.wimaxforum.org/technology

WiMAX Forum, 2006, Mobile WiMAX – Part I: A Tech-nical Overview and Performance Evaluation, pp. 30-33, Available: http://www.wimaxforum.org/technology.

Manuscript Received: Oct. 30, 2007Revision Received: Oct. 23, 2008

and Accepted: Nov. 23, 2008

APPENDIX A DERIVATIONS OFEqs. (17) AND (18)

The pdfs of the cell residence time for a newcall and a handoff call were derived in (Hong andRappaport, 1986) where the minimum MS speed iszero. Here we derive the pdf of the cell residencetime for non-zero minimum MS speed, i.e., Vi is uni-formly distributed on the interval [Vi min, Vi max], whereVimin is positive and less then Vi max.

fVi(vi) =

1Vi max – Vi min

, for Vi min ≤ vi ≤ Vi max ,

i = A or B ,0 , elsewhere .

(A1)

It’s assumed that the angle between the direction ofthe MS and the direction from the MS to the centerof the cell is uniformly distributed in interval [0, π],and its direction remains constant during its travels

in the approximating circle cell of radius ri. The pdfof the distance between the point where a new call isoriginated and the point on the cell boundary wherethe MS leaves the cell was derived in (Hong andRappaport, 1986).

fZi(z) =

2πri

2 ri2 – z

22

, for 0 ≤ z ≤ 2ri ,


(A2)

Then the cell residence time for a new call is ex-pressed by Tn, i = Zi/Vi with pdf

fTn, i(t)

= w fzi(tw) fVi

(w)dw– ∞

∞

=

2(Vi max – Vi min)πri

2 wVi min

Vi max

ri2 – tw

22

dw ,

for 0 ≤ t ≤ 2riVi max

,

2(Vi max – Vi min)πri

2 wVi min

2ri/tri

2 – tw2

2dw ,

for2ri

Vi max≤ t ≤ 2ri

Vi min, i = A or B .

(A3)

Using L’Hô pital’s Rule (Varberg and Purcell, 1997),Eq. (A3) becomes

fTn, i(t) =

Vi max + Vi minπri

for t = 0 ,

8ri

3(Vi max – Vi min)πt2 1 –tVi min

2ri

2 3

– 1 –tVi max

2ri

2 3


,

8ri

3(Vi max – Vi min)πt2 1 –tVi min

2ri

2 3

, for2ri

Vi max≤ t ≤ 2ri

Vi min,

i = A or B .

(A4)

For the handoff call, the angle between the directionof the MS and the direction from the MS to the centerof the cell is assumed to be uniformly distributed in

interval [– π2 , π

2 ]. The pdf of the distance between the

point on the cell boundary where a handoff call is origi-nated and the point on the cell boundary where MS

leaves the cell was given in (Hong and Rappaport, 1986).

fZi(z) =

1π

1

ri2 – z

22

, for 0 ≤ z ≤ 2ri ,


(A5)


Then the cell residence time Th, i for handoff call is expressed by Th, i = Zi/Vi. The pdf of Th, i is derived as

fTh, i(t) =

Vi max + Vi min2πri

, for t = 0 ,

4ri

(Vi max – Vi min)πt2 1 –tVi min

2ri

2

– 1 –tVi max

2ri

2


,

4ri

(Vi max – Vi min)πt2 1 –tVi min

2ri

2

, for2ri

Vi max≤ t ≤ 2ri

Vi min,

i = A or B .

(A6)

If Vi min = 0 is substituted into Eqs. (A4) and (A6) theidentical formulas of f Tn, i

(t) and f Th, i(t) as shown in

(Hong and Rappaport, 1986) are obtained.

2.5G Wimax Cell Planning

Documents

Transcript of 2.5G Wimax Cell Planning