design_values_ed02[1].pdf

Design Values and Coverage Probability

White Paper

Design Values and

Coverage Probability

Alcatel File Reference Date Edition Page design_values_ed02.doc 10/2001 02 1

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CONTENTS

1. SCOPE .....................................................................................................................4

2. RECEIVE BUDGET ..................................................................................................4

3. SIGNAL STATISTICS AND COVERAGE PROBABILITY AT ONE AREA ELEMENT.................................................................................................................6

3.1 Signal Statistics Within One Area Element...................................................................................... 6

3.2 Coverage Probability For One Area Element................................................................................... 7

4. CELL BORDER AND CELL AREA ........................................................................10 4.1 Decrease of Power Level Within a Cell .......................................................................................... 10

4.2 Cell Area Coverage In a Cell (Ideal Model)..................................................................................... 10

4.3 Necessary Margins for Real World Conditions ............................................................................. 12

5. SUMMARY .............................................................................................................13

6. REFERENCES........................................................................................................13

FIGURES Figure 1: Signal Distribution Probability .................................................................................................. 6

Figure 2: Coverage Probability as Function of Power Level .................................................................. 7

TABLES Table 1: First Receive Budget .................................................................................................................. 4

Table 2: Receive Budget (referenced to street level)............................................................................. 5

Table 3: Coverage Probability as Function of Power Difference (Area Element)............................... 8

Table 4: Fade Margins and Power Values as Function of Required Coverage Probability............... 8

Table 5: Relation of Cell Area Coverage and Border Coverage ......................................................... 11




SYMBOLS AND ABBREVIATIONS

Symbol Meaning Unit

F power level dBm

F(R) power level at the cell border dBm

Fmed median power level dBm

Fthr power threshold level dBm

F95% power value that needs to be achieved at 95% of the locations

dBm

attenuation exponent hBS base station antenna height m

Mfad fade margin dB

pcell cell area coverage probability %

pcov coverage probability at an area element %

R cell range m or km

Standard deviation of signal level dB




1. SCOPE

This document describes Alcatel's concept of design values and coverage probabilities for the design of GSM networks.

Starting from an exemplary receive budget, it explains the influence of margins in order to achieve a certain coverage probability on the cell area, and relates this to a coverage probability and power level at the cell border, which helps the network planner during the design phase of a network.

2. RECEIVE BUDGET

In this chapter, we will elaborate the required receive level that is necessary to provide a good communication link to the subscriber.

In [1] (GSM 05.05) the reference sensitivity level for GSM mobile stations is defined as -102 dBm for both GSM 900 and GSM 1800. For GSM 1800 mobile stations, approved before 1st December 1999, this level was set to 100 dBm, but the following calculations shall be valid for new mobile stations only. So from the level point of view, there is no difference between GSM 900 and GSM 1800.

In [2] (GSM 03.30) an interference degregation margin of 3 dB is recommended. Additionally, a body loss of 4 dB is considered in order to take into account the fact, that the MS antenna may be shadowed by the body of the subscriber.

These figures are no fixed values, but follow statistical variation. In simple modelling this variation is ignored. However, it shall be kept in mind as reality.

Thus, a first receive budget may look as follows: Value Error / Variation

Simple Realistic

Mobile phone sensitivity 102 dBm 0 dB 2 dB Reduction of sensitivity by interference 3 dB 0 dB 0...+3 dB Body loss 4 dB 0 dB 4 dBRequired level at subscriber 95 dBm

Table 1: First Receive Budget

As a conclusion, we can say that a good communication link can be provided to the user, when a receive level of 95 dBm is achieved. Most of the GSM traffic today is generated inside of buildings, while radio network planning tools usually predict the receive level at street level, and measurements usually are performed on streets as well. In order to consider this difference, an indoor penetration margin is introduced. The exact value depends on the building structure, but 20 dB of indoor penetration margin can be assumed as a reasonable approach.




Therefore we can convert the required level at the subscriber to a required level on street level:

Value Error / Variation

Simple Realistic

Required level at subscriber 95 dBm Indoor penetration loss 20 dB 0 dB 5 ... +15 dBRequired level on street level 75 dBm

Table 2: Receive Budget (referenced to street level)

Therefore, a good network design would try to achieve a receive level at street level of 75 dBm. Because of the statistical nature of the radio signal, it is not possible to provide this level at every place and at every instance of time. In order to consider this, the coverage probability must be introduced.




3. SIGNAL STATISTICS AND COVERAGE PROBABILITY AT ONE AREA ELEMENT

3.1 Signal Statistics Within One Area Element

The field strength prediction will calculate a median value Fmed for a given location. In reality, the received level will not be constant, but will vary with time and with position within the predicted area element. The variation can be modelled with a log-normal distribution (see [2], [3] and [5]), which means that the logarithm of the field strength (so the field strength level in dBV/m or the power level in dBm) are normally distributed around the median value.

The formula of the normal distribution is

( )

= 2

2

2exp

21)(

medxxxp

where x is the measured value, xmed is the median value and is the standard deviation. The following picture shows the probability distribution of the received power level (Gaussian curve). The maximum of the curve is located at the median value.1

Signal Distribution

Power Level

Prob

abili

ty

Figure 1: Signal Distribution Probability

The standard deviation of this distribution depends on the propagation environment. In [2] (GSM 03.30), a value of =7 dB is used for flat urban environment, in dense urban environment higher

1 This graph of a normal distribution around a mean value of 0 with a standard deviation of 1 can be generated e.g. with the Excel function NORMDIST(X,0,1,FALSE), where X is the x-value. It is also described in standard text books about statistics.




values and in rural environment lower values can be observed. Hilly terrain further increases the value of . In the following, we will assume a standard deviation of =8 dB. It is clear that there is a finite probability for very high and very low power levels. It is also clear, that with a predicted level of 75 dBm only in 50% of the cases the subscriber will experience a level of F=75 dBm or better (outdoor), which was assumed to be required for a good communication link (indoor).

It is therefore necessary to design the network for a higher median value, so that the outdoor target value of 75 dBm can be observed with a higher probability.

3.2 Coverage Probability For One Area Element

In a normal distribution with a median value of xmed and a standard distribution of , the probability pcov that x exceeds the threshold x0 is (see [3]):

[ ]

===0

00cov 22

121)(

x

medxxerfdxxpxxpp

with erf(x) as the error function, the integral of the Gauss function.

The following figure shows this distribution2, where on the x-axis we find the field strength level

above the median level in units of the standard deviation.

Coverage Probability

0%

25%

50%

75%

100%

-3 -2 -1 0 1 2 3

(Fmed-Fthr) / sigma

Pro

babi

lity

(%)

Figure 2: Coverage Probability as Function of Power Level

2 This graph of a cumulative normal distribution with a mean value of 0 and a standard deviation of 1 has been generated with the Excel function NORMDIST(X,0,1,TRUE), where X is the x-value




It is obvious that if the median value is equal to the threshold value, a coverage probability of exactly pcov=50% is achieved. If the median value Fmed is 1 higher than the threshold value Fthr, the coverage is pcov=84%. For a required coverage probability of pcov=95% (which is a common value), the median has to be 1.64 higher than the threshold. This difference FmedFthr is called the fading margin Mfad.

thrmedfad FFM = The following table summarises a few values:

Fade margin Mfad in units of

Coverage Probability pcov

1 15.9% 0 50.0%

1 84.1%

1.28 90%

1.64 95%

2 97.7%

3 99.87%

Table 3: Coverage Probability as Function of Power Difference (Area Element)

Coming back to the required level of Fthr=75 dBm in the street (equivalent to 95 dBm indoor), the required median value Fmed will depend on the required coverage probability pcov. The following table is valid for a standard deviation of =8 dB.

Required Coverage Probability pcov

Fade Margin Mfad []

Fade Margin Mfad [dB]

Median Power value Fmed [dBm]

50.0% 0.003 0.00 75.0 84.1% 1.00 8.00 67.0 90.0% 1.28 10.3 64.7 95.0% 1.64 13.2 61.8 98.0% 2.05 16.4 58.6 99.0% 2.33 18.6 56.4

Table 4: Fade Margins and Power Values as Function of Required Coverage Probability

3 The three columns of this table have been generated with the Excel functions NORMINV(X,0,1), NORMINV(X,0,8) and NORMINV(X,-75,8) where X is the probability.




This shows that radio networks have to be designed for a higher median value, so that the threshold value can be achieved with a certain probability.

Certainly, it is not possible to design radio networks with exactly 100% coverage probability, as this would require an infinite fading margin.

Common target values for local coverage probabilities are pcov=90% and pcov=95%.




4. CELL BORDER AND CELL AREA

Requirement: The required field strength level F95% shall be exceeded at 95% of locations within the cell area.

Question: What field strength level F(R) needs to be predicted at the cell border R, taking into account the statistical variation?

4.1 Decrease of Power Level Within a Cell

Up to now, we have only spoken about the power level and the coverage probability on a given area element, neglecting the fact, that a radio network is built by many cells.

Towards the border of a cell, the power level, and therefore also the coverage probability will decrease, because the path loss will increase with increasing distance to the base station.

In ideal free space conditions, the power level would decrease by 20 dB per decade of distance, however in urban areas, higher decrease factors are found. According to the Hata formula given in [4], the path loss increases with

( ) dhBS lglg55.690.44 so for a typical BS antenna height of hBS=25 m, a decrease of 35 dB per decade of distance is experienced. This corresponds to an attenuation exponent of =3.5 (35/10=3.5).

4.2 Cell Area Coverage In a Cell (Ideal Model)

Designing a radio network for a defined power level and a defined coverage probability at cell borders will mean that closer to the base station, you will experience a higher power level and a higher coverage probability.

The goal, however, is not a figure to be reached at the cell border, but an average over all the cell area, which makes sense, as the subscribers are arbitrarily distributed over the area and do not know about cells and cell borders.

The cell area coverage probability pcell is the average of all local coverage probability values pcov on the cell area, and can therefore be computed as:4

= dApRpcell cov21

4 This formula assumes an ideal circular cell, which is not the case in reality.




In [3], this integral is solved under the assumption of flat terrain, homogenous morpho structure and circular cell shape, so that the formula can be rewritten as:

( )

++=

+

baberfeaerfp b

ab

cell111

21 2 12

with

=2

)(RFFa thr and

=2lg10 eb

As a result of this formula, one can relate the cell border coverage probability pcov to the cell area coverage probability pcell. Parameters are the standard deviation (e.g. =8 dB) and the attenuation exponent (e.g. =3.5). The following table lists a few results, assuming =3.5 and a threshold Fthr=75 dBm:

Clutter type Stand. Dev. [dB]

Pcell (area) Pcov (edge) Fad.Marg. Mfad [dB]

F(R) [dBm]

urban, flat 8 75.8% 50.0% 0 -75

urban, flat 8 95.0% 85.9% 9 -66

urban, hilly 13 95.0% 89.2% 16.1 -59

rural, flat 5 95.0% 81.6% 4.5 -70.5

suburban, flat 6 95.0% 83.3% 5.8 -69

Table 5: Relation of Cell Area Coverage and Border Coverage

In the first line of the table we see a coverage probability at the cell border of pcov=50%, which represents a power level of Fmed=75 dBm. Averaged over the cell area, the coverage probability will be pcell=75.8%.

We now assume that the level Fthr=75 dBm shall be measurable at 95% of all locations over the cell area, i.e. F95%=75 dBm. In the second line of the table, we assume an average cell area coverage probability of pcell=95% (design target). Using a standard deviation =8 dB and an attenuation exponent =3.5, the coverage probability at the cell border will drop to pcov=85.9%. This is equal to a fade margin of Mfad=1.125 = 9 dB. So the design value F95%=75 dBm requires a median power level F(R)=66 dBm at the cell border. In other environments, the fade margin Mfad can range from 4 to 16 dB and more, depending on the standard deviation and the attenuation exponent , which itself depends on the base station antenna height hBS.




4.3 Necessary Margins for Real World Conditions

Under ideal conditions, in order to achieve the requirement of Pcell=95% with a measured field strength level Fthr=75 dBm on street level, the design must be done accordingly for 75 dBm at 95% of the area elements (design value F95%=75 dBm), as seen in chapter 4.2. However, some systematic errors, which are not covered by the planning tool calibration process, must be taken into account:

non-accuracy of morpho structure and terrain elevation data bases, hillyness of the terrain, which impacts the applicability of the ideal statistical model from Jakes

[3],

planning of real sites will always leave some white spots due to final correction of real site locations vs. designed sites

non-circular cell shapes (clover like for three-sector configurations) which increase the cell border area compared to the total cell area. This impacts as well the results from the ideal statistical model from Jakes [3].

As these errors are not lognormal distributed, the sum of the errors are not lognormal distributed either, so the effects cannot be modelled with an increased standard deviation.

To care for these cases, the design value is typically taken more conservative than the actual required value. A margin of 4 dB is a minimum value for any area leading to design value F95%=71 dBm, if we want to measure 75 dBm in 95% of the cases. With a lognormal standard deviation of =8 dB, a design value F95%=71 dBm is equivalent to a predicted field strength value F(R)=62 dBm at the cell border, after application of a Mfad=9 dB margin to compensate the lognormal fading over the area (see Table 5) above.

So the median value at the cell border that the planner needs to design the network for is F(R)=62 dBm.

The following real world conditions may be considered as well by introducing additional small margin:

signal variation from indoor penetration and body loss, sensitivity variation from mobile phones and interference handover margins are leading to delayed use of the best serving cell within cell border areas If they are considered, the required field strength level Fthr and the design value F95% have to be incremented by the same amount.




5. SUMMARY

For a good communication link in GSM, a received power level of 95 dBm is required. If the typical subscriber is located within a building, the design must care for 75 dBm in the streets. If a certain reference level must be achieved in the planned area with a given probability (e.g. 75 dBm in 95% of the area), the design value for the cell border will be much lower (e.g. 9 dB less for flat, dense urban area).

Considering the real world, an additional margin of 4...5 dB has to be applied to care for inaccuracies and implementation tolerances.

This document explained how a given coverage requirement can be converted to a design value that must be achieved at the cell border.

6. REFERENCES

[1] ETSI EN 300 910 (GSM 05.05 version 8.5.1 Release 1999): Radio transmission and reception

[2] ETSI TR 101 362 (GSM 03.30 version 8.3.0 Release 1999) Radio network planning aspects

[3] Jakes, W.C. Jr. (Ed.) (1974): Microwave Mobile Communications, John Wiley, New York, NY, USA

[4] Hata, M. (1980) Empirical Formula for Propagation Loss in Land Mobile Radio Services, IEEE Trans. on Vehicular Technology, VT-29

[5] Lee, W.C.Y (1989) Mobile Cellular Telecommunication Systems, McGraw-Hill, New York, NY, USA



SCOPERECEIVE BUDGETSIGNAL STATISTICS AND COVERAGE PROBABILITY AT ONE AREA ELEMENTSignal Statistics Within One Area ElementCoverage Probability For One Area Element

CELL BORDER AND CELL AREADecrease of Power Level Within a CellCell Area Coverage In a Cell (Ideal Model)Necessary Margins for Real World Conditions

SUMMARYREFERENCES

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