GSM network design for Stavanger and Sandnes

Jan Magne Tjensvold

November 6, 2007

Contents

1 Introduction 1

2 Background 22.1 Geography and population . . . . . . . . . . . . . . . . . . . . 22.2 Technology and equipment . . . . . . . . . . . . . . . . . . . . 4

3 Calculations 43.1 Omni directional antenna . . . . . . . . . . . . . . . . . . . . 43.2 Sectored antenna . . . . . . . . . . . . . . . . . . . . . . . . . 63.3 Voice channels . . . . . . . . . . . . . . . . . . . . . . . . . . 63.4 Traffic density . . . . . . . . . . . . . . . . . . . . . . . . . . . 63.5 Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.6 Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

4 Cost estimate 8

References 9

1 Introduction

This report investigates the design of a GSM network for the cities of Sta-vanger and Sandnes in Norway. It provides a cost estimate of the requiredinfrastructure in these two cities and for the highway connecting them. Theestimate only includes equipment costs and not maintenance costs or otheroperational costs which would be needed to keep the network fully func-tional during its lifetime. It only includes the cost for the base transceiverstations (BTS), base station controllers (BSC) and the mobile switchingcenter (MSC).

1

Figure 1: Map of Norway with thelocation of Stavanger and Sandnes.

Figure 2: Rogaland county withthe municipality of Stavanger inred and Sandnes in blue.

2 Background

2.1 Geography and population

Stavanger and Sandnes is located in the county of Rogaland, Norway as seenby Figure 1 and 2. Statistics Norway (SSB) [1] provides maps showing thepopulation density of an area. One such map of Stavanger and Sandnes hasbeen used as the basis for drawing an outline of the urban areas in Figure 3on the next page.

SSB provided some vital statistics for the two municipalities which isshown in Table 1 on the following page. The table also contains some otherstatistics in addition to SSB’s population and area statistics. Since we aredesigning a GSM network for the city areas we only use the urban areaand urban population statistics. We also make the assumption that thepopulation growth within each municipality is uniformly distributed overthe area it covers.

Using the distance calculation tool from Temakart Rogaland [2] thelength of highway E39, as shown in Figure 3, was found to be about 10.7km. We also assume that we will be able to get a market share of 35% .

2

Figure 3: Outline of the urban areas of Stavanger and Sandnes along withhighway E39.

Statistics Stavanger Sandnes HighwayArea 71.4 km2 304.5 km2 10.7 kmUrban area 43.4 km2 21.0 km2

Population 117 315 60 507Urban population 115 087 47 700Annual growth rate 1.22% 1.36%Market penetration 40% 45%Path loss slope, γ 3.6 3.6 2.7Bandwidth, BW 8.33 MHz 8.33 MHz 4.166 MHzTraffic/subscriber, E 0.040 Erlangs 0.035 Erlangs

Table 1: Area and population statistics for Stavanger and Sandnes.

3

2.2 Technology and equipment

LGC Wireless, Inc. [3] has been chosen as the supplier for the GSM networkequipment. In Table 2 you can see the specifications of their UltraWAVErange of BTSs, BSCs, MSCs and HLRs (Home Location Register is soldtogether with MSC). The equipment costs are estimated since none of thevendors was willing to provide their prices to this project.

Component Capacity Connections Cost (NOK)BTS 69.08 Erlangs 84 channels 400 000BSC 466 Erlangs 31 BTSs 1 800 000MSC 2 500 Erlangs 256 BSCs 4 500 000HLR 100 000 subscribers

Table 2: GSM network equipment specifications from LGC Wireless.

GSM requires a signal-to-interference ratio (SIR) of at least 14 dB. GSMchannel bandwidth is 200 kHz and by employing Time Division MultipleAccess (TDMA) each channel can carry 8 full-rate voice channels. We willuse a frequency reuse factor of N = 4. Roll out time (ROT ) is estimated to4 years, in which no additional equipment is expected to be installed. Thismeans that the capacity will remain constant during this time. We also aimfor a grade of service (GoS) of 1%. This means that in average 1 call isblocked for every 100 call attempts.

3 Calculations

3.1 Omni directional antenna

First we must find out if we should use omni directional or sectored antennas.For omni directional antennas the following formula for SIR applies

SIR = 10 log

(√

3N − 1)γ

j

(1)

where N is the frequency reuse factor, γ is the path loss slope and j is thenumber of surrounding cells. For a hexagonal cell layout, as seen in Figure 4on the following page, j is 6.

To simplify (1) we replace√

3N with q using the following equation

q =d

r=√

3N (2)

where d is the distance between the center of two cells using the same fre-quency and r is the radius of a cell. When inserting (2) into (1) we get the

4

1 2

3

45

6

Figure 4: Hexagonal cell layout.

following formula

SIR = 10 log[

(q − 1)γ

j

](3)

By applying our frequency reuse factor N = 4 to (2) we can calculate thevalue of q

q =√

3N =√

3× 4 = 3.464

We can now find the SIR in the two cities by using the specified path lossvalue of γ = 3.5 like this

SIRcity = 10 log[

(q − 1)γ

j

]= 10 log

[(3.464− 1)3.6

6

]= 6.318 dB

SIRcity is less than the 14 dB we require so we cannot use omni directionalantennas in the cities.

We use a similar formula to calculate the SIR for the highway. Since thehighway does not use a hexagonal cell layout, but rather a linear cell layout,we use the following formula

SIRhighway = 10 log [(2N + 1)γ + (2N − 1)γ ]

= 10 log[(2× 4 + 1)2.7 + (2× 4− 1)2.7

]= 27.55 dB

We find that SIRhighway is well above the required 14 dB. This means thatwe can safely use omni directional antennas for the highway.

5

3.2 Sectored antenna

Since we are unable to use omni directional antennas with N = 4 in thecities we must examine the possibility of using sectored antennas instead.In GSM a sectored antenna usually covers 120° and in a group of 3 sectoredantennas they cover a total of 360°. To find the SIR for GMS type of sectoredantennas we use

SIR = 10 log[

1q−γ + (q + 0.7)−γ

](4)

Using the previously discovered value of q and γ together with (4) we findthat the SIR for the cities is

SIRcity = 10 log[

1q−γ + (q + 0.7)−γ

]= 10 log

[1

3.464−3.6 + (3.464 + 0.7)−3.6

]= 17.62 dB

which is above the requirement of 14 dB. This allows us to use sectoredantennas in the city areas.

3.3 Voice channels

To find the number of voice channels m we use the following formula

m =⌊⌊

BW

Channels− 1⌋× SpeechPerRF

N × Sectors

⌋(5)

The −1 channel is the control channel which we have to make room for. Wefill (5) with our numbers for the two cities and the highway and get

mcity =⌊⌊

8.33 MHz200 kHz

− 1⌋× 8

4× 3

⌋= 26 channels

mhighway =⌊⌊

4.166 MHz200 kHz

− 1⌋× 8

4× 1

⌋= 38 channels

3.4 Traffic density

By assuming uniform distribution of the subscribers we can use this formulato determine the traffic density TD of each city

TD =E × Pop× Pene× (1 +Growth)ROT × Share

Area(6)

where E is the traffic per subscriber (call intensity) in Erlangs, Pop is thepopulation, Pene is the market penetration, Growth is the annual popu-lation growth, ROT is the roll out time in years and Share is the market

6

share. Using the values we have found together with (6) we find the trafficdensity of each city the following way

TDStavanger =0.040× 115 087× 0.40× (1 + 0.0122)4 × 0.35

43.4 km2

= 15.588 Erlangs/km2

TDSandnes =0.035× 47 700× 0.45× (1 + 0.0136)4 × 0.35

21.0 km2

= 13.216 Erlangs/km2

Next we need to determine how much traffic we can serve in each sector withthe number of voice channels and our target GoS. The Erlang-B functiongives us a starting point

GoS = B(E,m) =Em

m!∑mk=1

Ek

k!

(7)

where m is the number of voice channels and E is the call intensity inErlangs. Using (7) we determine experimentally that, to achieve a GoS of1% for the given number of voice channels, we will be able to serve thefollowing traffic per sector (TS)

TScity = 16.959 ErlangsTShighway = 27.253 Erlangs

3.5 Cells

To find out how many cells our network needs, and thus how many BTSs weneed to deploy, we first have to find out how much area a single cell covers.If we assume that the subscribers are distributed uniformly the followingformula will give us the answers we need

CellArea =TS × Sectors

TD(8)

Applying (8) to the TD and TS values we have found gives

CellAreaStavanger =16.959 Erlangs× 3

15.588 Erlangs/km2 = 3.264 km2

CellAreaSandnes =16.959 Erlangs× 3

13.216 Erlangs/km2 = 3.850 km2

To find the minimum number of cells we need to cover the given areas wedivide the total area on the cell area like this

Cells =⌈

Area

CellArea

⌉(9)

7

We use this formula to fine the number of cells required for Stavanger andSandnes

CellsStavanger =⌈

43.4 km2

3.264 km2

⌉= 14 cells

CellsSandnes =⌈

21.0 km2

3.850 km2

⌉= 6 cells

For the highway the cell radius can be much larger since it will not becompletely surrounded by other cells. Seeing as the longest distance theGSM specification supports in practical use is 35 km and our highway is10.7 km we can just use one single cell for the entire stretch of road.

Cellshighway = 1 cell

3.6 Equipment

The minimum number of BTSs needed is

TotalCells = 14 + 6 + 1 = 21 cells/BTSs

Each BTS can only handle 69.08 Erlangs and the total cell traffic is

CellTraffic = 3× TScity = 3× 16.959 = 50.877 Erlangs

so we do not need to increase the number of BTSs.The UltraWAVE BSC can connect 31 BTSs, which should be enough,

but it has a traffic limitation of only 466 Erlangs. The total traffic intensityis

TotalTraffic = TotalCells× CellTraffic = 21× 50.877 = 1068 Erlangs

which is more than a single BSC can handle. We find the number of BSCswe need by ⌈

TotalTraffic

TrafficLimit

⌉=⌈

1068466

⌉= 3 BSCs

One UltraWAVE X100 MSC can handle 256 BSCs and 2 500 Erlangs whichshould be more than enough for our purpose. Using the population numbers,annual growth, market penetration and market share we find that our totalnumber of subscribers will be about 25 000 at the end of year 4. This is wellwithin the limits of the UltraWAVE X100 HLR.

4 Cost estimate

Given the cost of each piece of equipment from Table 2 on page 4 we calculatethe total cost

TotalCost = 21×400 000+3×1 800 000+1×4 500 000 = 18 300 000 NOK

8

18.3 million NOK is the cost of the all the essential GMS network equipmentfor the cities of Stavanger and Sandnes pluss the highway. This number relieson some variables like expected market share and market penetration whichmight be hard to predict. The estimate is also very sensitive to the pathloss slope values and the estimated traffic per subscriber.

References

[1] Statistics Norway (SSB). URL http://www.ssb.no/.

[2] Temakart Rogaland. Detailed web map of Rogaland with distance andarea tools., URL http://www.temakart-rogaland.no.

[3] LGC Wireless, Inc. URL http://www.lgcwireless.com/.

9