Statistical Modelling of Time Variant Processes for Inter fer ence Analysis

in Mobile Radio Network Planning

Joachim Obeldobel, Holger Ruse, Florian Graf Mannesmann Mobilfunk GmbH, Am Seestern 1, D-40543 Diisseldorf, Germany

e-mail: jo@ tegate.mmo.de

T2 +49 211 533 2271 Fax: +49 211 533 2124

Abstract : In this paper d i f f erent methods for the s tat i s t ica l model l ing o f t ime variant processes for interference analysis in radio network planning tools are presented. These methods will be pointed out exemplarily for two network features, frequency hopping (FH) and base station power control (BTS power control). The methods are presently being implemented in a radio network planning t o o l used for p lanning the G S M network of Mannesmann Mobilfunk GmbH.

1 Introduction

All over the world mobile radio networks working with the GSM-standard are built up. These networks consist of several thousand base stations, as for example the German D2-Network. They are designed to offer a high quality service to several millions of subscribers. Networks with this dimension are designed and optimized with radio network planning tools running on workstations. Such radio network planning tools can be tools in time domain or statistical tools.[5] The radio network design process is generally subdivided into five steps: fieldstrength level prediction, cell calculation, interference analysis, channel demand calculation and channel assignment [2,3,5]. To support this design process mostly statistical tools are used because the design area includes several hundreds of base stations and the calculation time for such a design should allow several calculations per day [ l , 2, 51. Statistical tools contain algorithms which are modelling time variant processes like FH, BTS power control etc., in a statistical way. Statistical tools as well as tools in the time domain are used in the radio network optimization. Tools working in the time domain allow the simulation of time variant processes step by step to find optimal parameter settings for the radio network configuration. In comparison to time domain tools statistical tools will have less calculation time for the same radio network configuration.

In this paper two examples for modelling of time variant processes in statistical tools are described. In this two examples it is shown how the features FH and BTS power control can be modelled in the interference analysis . Chapter 2 gives a short overview about the basic steps and the used data in radio network planning and chapter 3 gives a detailed overview of the interference analysis in statistical radio network planning tools. In chapter 4 the modelling of FH in the interference analysis is described. Chapter 5 explains how BTS power control can be modelled in statistical radio network planning tools. The summary reflects the main aspects of this paper.

2 Basics

Radio network planning tools include different algorithms and different databases for each individual step in the network planning process [ 1,2,3]. For radio network planning one usually has a set of several hundred BTSs with attributes like location, antenna height, transmitter power, antenna type, lobe direction of each BTS. In the beginning of the network planning process, for every BTS a fieldstrength level prediction using database with altitude and morphostructure of the terrain, is made [4]. The fieldstrength level prediction for a certain BTS gives at each position of the planning area the median value of the fieldstrength level caused by this BTS [4]. The fieldstrength level is due to the long-term fading assumed to be normal distributed 14, 51. The standard deviation for normal fading depends on the morphology (urban, dense urban, forest, water, etc.). The short-term fading is mostly not modelled in statistical radio network planning tools [1,2,41. After the fieldstrength level prediction the cell calculation is done. The cell calculation is based on the fieldstrength level prediction and the handover algorithm, which is implemented in the hardware of the network. The cell calculation gives the assignment probability from each position to a certain BTS [3,5]. The next step in radio network planning is the interference analysis which is described more detailed in chapter 3. After the interference analysis the cell traffic and the channel demand calculation follows [3,5,6]. In this calculation step a traffic density database is used [2,5]. At least channels for each BTS will be assigned [1,3]

3 Interference analysis

The aim of the interference analysis is to determine the pairs of BTSs which are allowed to have a frequency reuse without having to much interference in their cell area and to calculate the interference of all assigned frequencies in the overall network. In this paper we only have a look at the interference caused by a BTS at a mobile receiver, the so called downlink interference, because this is the delimitative link lrection as the experiences with the existing network shows. Interference analysis is always done for a pair of two BTSs [ l , 2, 51. One BTS called 'interferer' interferes the cell area of the other BTS called 'carrier'. The cell area of a BTS is characterised through the fact that in the whole area the assignment probability Pa is > 0% to this BTS. In the next chapters it is shown that the interference analysis

0-7803-3692-5/96 0 1996 IEEE 823

is done in two steps. The first step is to calculate the local interference probability at each position. The second step is to calculate the global interference probability for the whole cell area.

3.1 Local interference probability The local interference probability is the probability that the carrier signal is a certain amount (C/I)~, , higher than the interferer signal. The envelope of the carrier signal and the envelope of the interferer signal both have time variant fieldstrength levels due to the time variant mobile radio channel [4,7]. The fieldstrength level is assumed to be normal distributed [4,7,8]. Carrier C and interferer I have different median values Fc50 and F150 at the mobile receiver location but they have identical standard deviations 0 due to the morphologic class at the mobile receiver location. Both long-term fading processes are assumed to be statistically independent. Based on the upper assumptions the local probability density P(FI~O,FC~O,G,FC,FI) is a two dimensional normal distribution of the carrier fieldstrength level Fc and the interferer fieldstrength level FI [71.

The local interference probability describes the probability that the current carrier to interferer ratio C/I is lower than the minimal (C/I)min recommended for a sufficient signal quality. This leads to the following equation for the local interference probability [ 1,7]

-cc --CO

(2) Figure 1 shows the two dimensional normal distribution of Fc and F,. The volume of the body over the interfered area is the local interference probability.

I fi

Figure 1 : Interference probability density

Equation (2) can be transformed by a substitution in the subsequent form where FT is the transformed integration variable.

For this one-dimensional integral the current local interference probability can be derived from a look up table P I .

3.2 Global interference probability The global interference probability is a quantity which' indicates for a pair of two cells if a frequency reuse is possible or not. The global interference probability Pg(cfl)" is the sum of the product of the local interference probability and the assignment probability over the whole cell area divided by the sum of the assignment probability over the whole cell area.

Cell area

(4) The numerator can be interpreted as the interfered cell area and the denominator can be interpreted as the average size of the whole cell area. The minimum carrier to interferer ratio (C/I)m,, is determined by the employed system technology. If the global interference probability Pg(~~)min is higher than a certain threshold Pgs then a channel reuse between carrier BTS and interferer BTS is not allowed. The threshold Pgs is determined by the network operator with regard to the network quality.

To calculate the interference of all assigned frequencies in the overall network the local interference probability and the global interference probability will be calculated in the same way as shown above after the frequency assignment. But the calculation will be done only for the assigned cochannels and adjacent channels and for each cell all interferences in the cell area are added together. The result then is the interference in each cell from all other cells.

4 Interference analysis considering FH

Frequency hopping is a GSM feature which is described in the technical specifications issued by the European Telecommunications Standards Institute [6, 101. FH leads to reduced interference probabilities on each frequency between carrier BTS and interferer BTS by changing the frequency 217 times per second and using different hopping sequences [ 1 1, 121. To model FH in radio network planning tools especially in the interference analysis it is necessary to identify the BTSs using FH for the analysis. In the interference analysis then different thresholds for BTSs with FH and without FH are used. For all FH BTSs the local and the global interference probability will be calculated as mentioned in equation (3) and (4). Then the global interference probability will be compared with a threshold P g s , ~ ~ . If the global interference

824 probability for the FH BTSs is higher than the threshold

P g s , ~ ~ a channel reuse between carrier BTS and interferer BTS is not allowed. The threshold P g s , ~ ~ is also determined by the network operator. This threshold is higher than the threshold Pgs for BTSs without FH. If P g s , ~ ~ = Pgs than the same frequency reuse but a higher signal quality in the network is achieved [ 1 1, 121. First experiences at Mannesmann Mobilfunk GmbH are showing that P g s , ~ ~ = [1,05 ... 1,15]*Pgs. To calculate the interference of all assigned frequencies in the overall network for BTSs using FH the same calculation can be used as described in chapter 3.2. But the result is an upper bound because the average probability of interference using FH is lower then calculated with equation (4).

5 Inter fer ence analysis cons id er ing BTS Power Control

The statistical behaviour of the mobile radio channel when the feature BTS power control is used is not as friendly as it is with frequency hopping. On one hand channels can remain interfered during a relatively long time period, and BTS power control can not change this situation. If the duration of interference i s to long it can cause a cut off call. On the other hand BTS power control transforms the long-term statistical behaviour of the received signal at the mobile station and at the BTS [7, 81. For this reasons BTS power control can not be modelled as simple as shown in chapter 4. Figure 2 shows two interfering BTSs under conditions of BTS power control. A mobile MSc is connected to the carrier BTSc. Depending on the pathloss LC and the received signal level RXPWRc at the mobile MSc, the BTSc controls the carrier power BTSPWRCcr,l. A second mobile MS1 is connected to the interferer BTSI. The BTSl controls the interferer power BTSPWRIct,l depending on the pathloss L ~ s l and the received signal level RXPWRM~I. The interferer BTSl interferes the mobile MSc with the signal level RXPWR1. The pathloss between BTS, and MSc is LI.

ETSPWR BTSPWR,

MS 1 - Radio Link -.-.-+ Interferer

Figure 2: Downlink interference with BTS power control

Normally the power control algorithm has an upper and a lower bound for the BTS power [8, 101 which means that the BTSl has the minimum power BSPWRI,~, and the maximum power BSPWRl,,,, which is equal to the uncontrolled BTS power of the interferer. BTSc has the minimum power BSPWRc,i, and the maximum power BSPWRc,,,, which is equal to the uncontrolled BTS power of the carrier. The mobiles in figure 2 are assigned to BTSI with the probability Pa, and assigned to BTSc with the probabilit]

5.1 A simple BTS power control algorithm The modelling of BTS power control is illustrated by the example of a simple control algorithm as shown in figure 3. While the signal level RXPWR is lower than the desired s igna l leve l R X P W R D ~ ~ the cont ro l led BTS power BSPWRct,l keeps constant at the level of the maximum power BSPWR,,,. If RXPWR intends to become higher than RXPWRD,,, BSPWRc,l will be reduced in that way that RXPWR gets equal to R X P W R D ~ ~ . BSPWRc,] can’t become lower than the minimum power BSPWR,i,. The desired signal level FSPWRD,~ is a parameter of the BTS power control algorithm.

RXPWR

t

I * L

BSPWR

I

Figure 3 : Mobile received signal level RXPWR and BTS-power BSPWR as a function of the pathloss L when using power control

5.2 Transformation of the fieldstrength level distribution For BTS power control the statistical behaviour of the mobile radio channel changes. The effect of long term fading is superposed by the power control algorithm. To calculate the local interference probability in equation (3) including BTS power control one has to solve a two dimensional integral. In general an analytic solution of this integral doesn’t exist. For practical use in a planning tool the parameters of the distributions of the received carrier signal and the received interferer signal have to be of a form which allows to transform the two dimensional integral in a one dimensional integral which can be provided in a look-up table. So one has to find parameters for the distribution functions so that the solution of the one dimensional integral can be provided in a look-up table. The received signal level distribution is the normal distribution. The parameters of this normal distribution have to be modified compared to the parameters of the received signal level distribution of a received signal without power control as shown in the following chapter. The parameter modification is different for carrier and interferer signal.

5.2.1 Carrier At first we are going to have a look at the median value of the carrier signal RXPWRc50. RXPWRc50 is the median value of the fieldstrength level caused by the uncontrolled BTS. The median value RXPWRcso is derived from the corresponding median value of the the fieldstrength level which is stored in the fieldstrength level database. It is assumed that the power control algorithm controls the median value.

j At the beginning of the modification the pathloss LC between the carrier BTS and its ass igned mobile is

825 calculated.

LC is the difference between the uncontrolled carrier power BSPWRc and the uncontrolled median value RXPWRc50.

c

If RXPWRcso is lower than RXPWRCD,,, the controlled carrier BTS power BSPWRcctrl will be set to BSPWRcmax. If RXPWRcso is higher than RXPWRcDes the BSPWRccWl will be evaluated so that RxPWRc5ocWl gets equal to RxPwRDe,. But

can't get lower than BSPWRc,,,. From BSPWRcCr,l the controlled median value Pc50crr~ is derived as follows

The standard deviation BC of the controlled carrier signal depends on the morphology at the mobile position and on the power control algorithm. In the interval in which the power control algorithm controls on the constant value RXPWRcDes the standard deviation is reduced because the power control algorithm tries to keep the received signal level stable. In the other intervals the standard deviation remains like it is derived by the morphology at the mobile position.

5.2.2 Interferer The controlled interferer BTS-power B S P W R I C ~ , ~ is determined by a mobile MSI connected to the interfering BTS. From this link the pathloss LMsl is calculated. L M ~ I is the difference between the uncontrolled interferer power BSPWRl and the uncontrolled median value RXPWRM~150 of the received interferer signal level at the location of MSI.

With the pathloss LMSI, the median value RXPWRMSISO and the power control algorithm the controlled BTS-power of the interferer BSPWRlc,l is calculated as follows

In addition the pathloss LI between the interfering BTSl and the interfered mobile MSc is calculated. LI is the difference between the uncontrolled interferer power BSPWRI and the uncontrolled median value RXF'WRI~O of the interferer level at the location of MSc.

With the pathloss LI and the controlled interferer power the median va lue of t h e con t ro l l ed in t e r f e r ing s igna l RXPWR~soctrl is computed.

The next step is to determine the standard deviation ~1 of the interferer signal RXPWR1cWl. It is assumed to be higher than the standard deviation of an uncontrolled interfering signal. This is for the following reason. The long-term fading process of the interfering signal is superposed by the time variant BTS-power of the interferer which is controlled by the mobile MSI. The long-term fading and the time variant BTS-power are statistically independent and therefore the standard deviation growth.

5.3 Local interference probability Since the median values and the standard deviations of the carrier signal and interferer signal are modified, the calculation of the local interference probability P has to be modified as follows.

1 P](C/I),,,.(RXPWRI~~C~~,, RXPWRC~OC+NI, "C) = ~no,ac *

2 RXPWRr+ C/I,,,, - A (RXPWRC - RXPWRC~OCtrl)

2 4 J

--w

dRXP WRcdRXP WRI

With a substitution the following one dimensional integral can be derived.

~ \ c p ~ ~ , , ~ ~ ~ ( R X P W R I ~ ~ C ~ ~ I , RXPWRc50ctri7 01 7 ac> =

.I Remember that the median value of the interferer level varies depending on the position of the mobile MS1 as shown in figure 2.

- 826

Q Pac>O 0 Pac=O

Figure 4 Interferer level depending on the mobile MS1

The average local interference probability IS determined by the following equation - P\C/I),>>,,, =

p[c/of,27, ( R X P W R 1 5 0 C t ~ l , R X P W R C 5 0 C t ~ l ) ffIi aC)'Pal Cell u i eu c Pal

Cell u ~ e u

(14)

5.4 Global interference probability The global interference probability is calculated as an average value of the local interference probability in a cell area.

Cell area (15)

The global interference probability will be compared with a threshold Pgs,ctr1. If the global interference probability is higher than the threshold PgS,Ctrl a channel reuse between carrier BTS and interferer BTS is not allowed. The threshold Pgs,ctrl is also determined by the network operator. This threshold is higher than the threshold Pgs. To calculate the interference of all assigned frequencies in the overall network the local and the global interference probability in equations (14) and (15) will be calculated for the assigned cochannels and adjacent channels and for each cell all interferences in the cell area are added together. The result is the interference in each cell from all other cells. The algorithm outlined above is presently being implemented in a network planning tool. The modified variances GC and 01 will be determined by field tests. The results of the interference analysis have to be validated by data gathered from the operating network. By evaluating the data a suitable value for the threshold PgS,Ctrl can be determined.

6 Summary

In this paper two examples for modelling time variant processes for interference analysis in radio network planning tools are presented. The first example 'is the modelling of FH and uses the same algorithms for the local and the global

for the interference analysis without FH. This method is implemented in a radio network planing tool at Mannesmann Mobilfunk GmbH. First experiences show that the threshold can be 5% ... 15% higher. In the second example an algorithm for BTS power control is given. This algorithm considers the controlled power of the carrier and the interferer signal. The local interference probability has to be averaged due to the fact that the interferer signal varies depending on the position of the mobile that is in contact with the interferer BTS. The global interference probability is an average value of the local interference probability in a cell area. This probability then has to be compared with a certain threshold which is also higher then the threshold for the analysis without BTS power control. The algorithm is presently being implemented in a radio network planing tool at Mannesmann Mobilhnk GmbH. Future work will concentrate on interference measurements to validate the thresholds for FH and BTS power control and to fix the threshold for the combination of FH and BTS power control in cells.

References [l] R. Simon, R. Beck, A. Gamst, G. Zimmerman, E.-G. Zinn,

"Rechnergestutzter integrierter Funknetzentwurf fur zellulare Funksysteme", NTG-Fachtagung "Bewegliche Funkdienste", Miinchen, November 1985

[2] A. Gamst, "Remarks on Radio Network Planning", 37th IEEE Vehicular Technology Conference, Florida, June 1987

[3] H. Ruse, "Cell Calculation in GSM Radio Communication Networks", 5th Nordic Deminar on Digital Mobile Radio Communications, Helsinki, December 1992

[4] M. Hata, "Empirical Formula for Propagation Loss in Land Mobile Radio Services", IEEE Transactions on Vehicular Technology, Vol. VT-29, No. 3, 1980

[5] A. Gamst, R. Beck, R. Simon, E.- G. Zinn, "An Integrated Ap- proach to Cellular Radio Network Planning", 35th IEEE Ve- hicular Technology Conference, Boulder, CO, 1985, pp 21 - 25

[6] "European Telecommunication Standard: European digital cellular telecommunications system (Phase 2); Physical layer on the radio path - General description (GSM 05.01)", Version 4.5.0, ETSI, May 1995

[7] William C.Y. Lee, "Estimate of Local Everage Power of a Mobile Radio Signal", IEEE Vol VT-34, February 1984

[8] J. G. Proakis, "Digital Communications", McGraw-Hill, New York 198

[9] I. N. Bronstein, K . A. Semendjajew, "Taschenbuch der Mathematik" 23. Aufl., Verlag Harri Deutsch; Thun, FrankfurtiMain

interference probabzity as for the interference analysis without FH. But the threshold for the comparison with the global interference probability is higher then the threshold

827

[lo] "European Telecommunication Standard: European digital cellular telecommunications system (Phase 2); Multiplexing and multiple access on the radio path (GSM 05.02)", Version 4.5.0, ETSI, August 1995

[ 11 ] A. Kuhn, W. Haggerty, U. Grage, M. Kerrler, C. Reyering, F. Arndt, W. Scholtholt, "Validation of the Feature Frequency Hopping in a live GSM Network" 44th IEEE Vehicular Technology Conference, Atlanta, April 1996

[ 121 W. Koch,J. Petersen,"Diversity und Frequenzsprungverfen im D-Netz", PKI Technische Mitteilungen 2/1990, February 1990

[13] F. Lambrecht, A. Baier, " Methodik der Funknetzplanung fur zel- lulare Mobilfunksysteme", ITG-Fachtagung 135, 26-27.9.995