Cost and Performance Tradeoff Analysis of Cell Planning Levels

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Master of Science Thesis Stockholm, Sweden 2013 TRITA-ICT-EX-2013:2013:51

J U N G A O

Cost and Performance Tradeoff Analysis of Cell Planning Levels

K T H I n f o r m a t i o n a n d C o m m u n i c a t i o n T e c h n o l o g y

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Master Thesis

Cost and Performance Tradeoff Analysis of Cell Planning Levels

by

JUN GAO

Supervisor: Ki Won Sung Examiner: Jens Zander

School of Information and Communication Technology (ICT) KTH Royal Institute of Technology

Stockholm, Sweden

Feb 2013

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Abstract

In wireless communication systems, optimal placement of base station locations, i.e., cell planning, has been considered one of major tools for performance improvement.

However, the cell planning requires significant effort for acquiring suitable sites as well as expensive computer software for finding out optimal locations. While the price of equipment has dropped rapidly, the cost of cell planing remains similar or becomes even more costly with increasing complexity of wireless systems. Therefore, the cell planning cost has become a burden to network operators. There is a need to examine cost benefit of sophisticated cell planning.

In this thesis, we investigate the tradeoff between cost and performance of different cell planning levels. We assume that the regular hexagonal cell strucuture represents the optimal cell planning, and model cell planning levels by means of randomness in two-dimensional point processes. We also introduce a simple cost model which takes into account non-linear increase in total cost with different cell planning levels.

Numerical results are obtained from Monte Carlo simulations. It is observed that the cost benefit of cell planning depends on the pace of the cost increase. When fast increase in the cost against better cell planning is assumed, we can find a region where lower level of cell planning is more cost-effective. This thesis provides a tool for decision making that operators can utilize. More realistic simulations and cost models remain as further study.

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Acknowledgements

First of all, I would like to express my sincere gratitude to my thesis supervisor Researcher Ki Won Sung. He always gave me enlightening suggestions guided me out of confusion during the thesis. Without his patience and encouragement I cannot go this far. In addition, I have to thank my examiner Professor Jens Zander, who gave me very important suggestions during the proposal, which makes my thesis more meaningful, reasonable, practical and accurate.

Furthermore, I want to thank Zhihao Zheng, who provided me lots of useful docu- ments and good suggestions. Moreover, I would like to thank my parents, my wife, friends and other classmates who gave me supports and encouragements through all my life.

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List of Figures

3.1 Self-deployed Model . . . 12

3.2 Optimal planning Model . . . 13

4.1 SINR Performance with cell edge SNR equals to 25dB . . . 19

4.2 SINR percentile performance under interference-dominated situation with uncorrelated fading . . . 21

4.3 SINR performance under noise-dominated situation . . . 21

4.4 Throughput performance under noise-dominated situation . . . 22

4.5 CPR under interference-dominated situation with C_p= 1, n = 1 . . . 23

4.6 CPR under noise-dominated situation with Cp = 1, n = 1 . . . 24

4.7 CPR under interference-dominated situation with fading case n = 1 . . 25

4.8 CPR under interference-dominated situation with fading case C_p = 1 . . 25

vii

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List of Tables

2.1 Point Processes Examples . . . 10 3.1 System Parameters . . . 16

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Abbreviations

BS Base Station

BPP Binomial Point Process CPR Cost to Performance Ratio PPP Poison Point Process

SINR Signal to Interference and Noise Ratio SNR Signal to Noise Ratio

TPP Thomas Point Process UE User Equipment

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Chapter 1

Introduction

Nowadays, mobile equipment is an indispensable gadget for most of us. Such as smartphones, tablet computers and laptops let us obtain latest information and communicate with each other anytime anywhere. This is not only because of the rapid evolution of the technology in wireless system but also the effective cost control of the system, which let people can enjoy the convenience with low price.

In order to control the cost while achieving certain performance requirement, operators need to do radio network planning or cell planning. A reasonable cell planning is based on geographic data (including data characterizing the service area), radio system data (indicated the characteristics of the radio transmission scheme to be implemented) and quality requirements (normally including degree of coverage, quality of service and interference levels etc.) [1]. Many other aspects need to be taken into account as well, such as implementation cost and resource utilization [2]. Because of the importance as well as the complexity of cell planning, there are lots of studies focused on this topic. In [3], it studied how the radio network planning can improve the network capacity and quality of service in WCDMA network.

According to its conclusions, simple radio network planning already can lower the interference and improve network capacity.

However, since the fast evolution of wireless technology and the intensive competi- tion between equipment venders, equipment cost has dropped dramatically. There- fore cost of cell planning became one of the major costs [4]. Lots of recent studies turned their focuses on self-deployed networks. This kind of networks does not need

1

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2 CHAPTER 1. INTRODUCTION

careful pre-planning and most of times are just randomly placed by unskilled users.

So it requires less or even no effort of cell planning and can significantly reduce the cost on cell planning. In practice, to achieve optimal planning network scheme is also not possible. First reason is the high cost of cell planning itself. Optimizing scheme needs both experienced technicians and expensive computer software. More- over, optimal planning network scheme also has many difficulties in implementing.

Such as the unavailability of some BSs site places. For example, a planned BS site is in the middle of a road. Such situations will cause implemented deployment to fall in between self-deployment and planned deployment.

1.1 Related Work

[5] studied and compared self-deployment and optimal planning from both performance and cost perspectives. It tried to find out when the self-deployed network is feasible as well as economical compared with planned network. Three distinct regions, in the paper, have been noticed. Self-deployed networks could be economical under a certain required throughput and coverage. Also it noticed that under shadowing environment, self-deployed network is more useful. But the scenarios in between have not been studied yet. [6] studied the system coverage and capacity performance in a very detailed way. it divided the deployment into three different types which are self-deployed, grid installation and optimal planning. Each of them requires more planning efforts. It implemented these three different deployment methods into different environment. Self-deployment is proved as a viable alterna- tive to more complex network planning especially for very dense networks. Although cell planning cost such as site acquisition and sophisticate software cost has been noticed in the paper, only device and installation manpower cost are considered.

Moreover, the cost performance of different deployment has not been studied in a quantitative way.

1.2 Motivation and Problem Formulation

Under the situation of demand on high traffic but low pricing scheme, the tradeoff between cost and performance became essential and critical for decision making.

Several questions need to be answered:

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1.3. AIM AND CONTRIBUTIONS 3

• From performance perspective, how much it can gain from better planned network?

• From cost perspective, how much it will cost for the gain?

In this thesis, we will study the relationships between the performance improvement and cell planning levels as well as the tradeoff between performance gain and cost.

The problems are analyzed and studied by system simulation. Self-deployed network scheme is simulated through binomial point process (BPP). We consider the geographic information as a kind of randomness introduced into the system. Then because of the popularity and special properties of hexagonal model, we chose it as the optimal planning scheme. In order to measure the performance and cost trends of different planning extents, cell planning levels is defined. Self-deployed networks can approach to optimal planning networks continuously by control cell planning levels. Moreover, simple cost model is introduced and the trend of tradeoff between cost and performance is analyzed.

1.3 Aim and Contributions

The aim of the thesis work is to answer two questions:

• What is the relationship between cell planning levels and performance gain?

If planning efforts cannot gain much then planning could be meaningless.

• How much it will cost for the performance gain under different planning levels.

Since cell planning and implementation all require extra costs, the efficiency of the cost needs to be considered.

This thesis is supposed to be a very good reference for decision makers, e.g. operators, to decide whether an improvement is possible and cost efficient.

In this thesis, through system simulation and data analysis, the relationships between basic performance metrics and cell planning levels have been obtained. We model the levels of cell planning in terms of randomness of base station locations in two-dimensional point processes. Moreover a simple cost metric has been introduced

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4 CHAPTER 1. INTRODUCTION

into the simulation in order to analyze the tradeoff between cost and performance.

This thesis considered cell planning levels as a parameter of wireless systems. This is a novel way to analyze wireless system performance and cost problems. More careful and detailed studies could be led by this thesis.

1.4 Scope

For system performance, because of the similarity in calculation between throughput and SINR, in this thesis, we mainly focused on the system SINR performance, which is the most basic metric for most of wireless systems. In the simulation system, system outage has not been considered and it could be part of the future works of more detailed studies. There is no actual UE in the simulation system but test points to collect the SINR information. This situation leads to no more resources allocation mechanism in the system as well. The geometry shapes of whole coverage area are different between ideal planned network and self-deployed network. They are hexagon and square respectively. This difference is mainly because of the difficulty of fitting arbitrary number of hexagons into square. But, because of the symmetry of these two shapes and the introducing of interesting area, there will be no big difference between the properties of these two systems.

Finally, snapshot-based Monte Carlo simulation is adopted. Simulation results are based on thousand times of static snapshots.

1.5 Outline

The rest of chapters are organized as following:

In Chapter 2, it is the literature review about point processes. Since the system is based on random processes. Basic knowledge about point processes is necessary.

It introduced the basic concept of point processes as well as some famous and popular models. Chapter 3 describes the system model adopted in this thesis as well as basic assumptions, considered scenarios, performance metrices and network parameters. Simulation results are presented and analyzed in detail in Chapter 4.

The results are divided into two parts, which are system performance part and cost and performance tradeoff part. Finally, in Chapter 5, conclusions are made based

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1.5. OUTLINE 5

on the results in previous chapters and possible utilization of the results and future works are proposed.

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Chapter 2

Review of Point Processes

Point processes are the basic mathematical tools to generate random processes in space. Because of the unpredictability of UEs, points with uniform distribution are mostly used to simulate their position. However, in recent studies, some other point processes are introduced, such as PPP, TPP etc. Since it found that the distribution of UEs has obvious effects on the performance of wireless systems [7]. On the other hand, BSs are normally simulated by deterministic models, such as hexagonal model. But the randomness of BS has been noticed recently. A tractable approach to coverage and rate has been mentioned by using PPP in [8]. [9] emphasized the necessity of random spatial models and provided a basic tutorial about them. PPP, Matern hard core and other models have been mentioned. [10] even advocated a so-called Geyer saturation model, which could accurately reproduce the spatial structure of wireless networks.

In this thesis, all the performance and cost analysis are based on cell planning levels. In order to define cell planning levels in a quantitative way, basic concepts of point processes are reviewed, features of some specified models are studied and compared with deterministic models. In this chapter, we are going to lead readers go through these important concepts on point processes. Furthermore, some widely- used and/or important models are talked briefly.

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8 CHAPTER 2. REVIEW OF POINT PROCESSES

2.1 Fundamental of Point Processes

Point processes, in statistic and probability theory, indicate random processes, which are consisted of a set of points, and these points are isolated in time and space. Isolation here means an occurrence of one point will have no effect to the occurrences of other points. Also, the space here can be applied to more general space defined by mathematics. Normally, the problem will not be that complex and abstract and space is limited within time and 2 or 3 dimensions. Under this specified situation, it can be called spatial point processes [9]. In general, point processes are to study the distribution of random points. And the points here could stand for events, which are consisted of the time and locations of the occurrences. For example, it could be the impulses of neurons within a human brain. It is not only useful in telecommunication field, but also lots of other fields such as epidemiology, material science, economics, neuroscience etc.

Every point process ξ can be represented by equation 2.1:

ξ =

N

X

i=1

1_A(ω_i) (2.1)

Where N is an integer, ω is a realization set of countable points within a space Ω and ω_i ∈ ω. 1_A(•) indicates the Dirac measure which has the expression in equation 2.2:

1A(x) =

( 0 x /∈ A

1 x ∈ A (2.2)

Where A is a subset of Ω.

2.2 Poisson Point Processes

The most common space used when considering point processes problems within telecommunication field is the Euclidean space, which is denoted as R^d. And normally d is equal to 2 or 3. So R²means the 2-dimension plane space and R³indicates the 3-dimension space.

The ubiquitous example of point processes in R^d is the Poisson point processes, which is the expression of Poisson process in space. Since Poisson process has two

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2.3. OTHER POINT PROCESSES 9

properties. First is the number of events is independent in each interval and the second is that the probability for different number of events occur in one interval is Poisson distribution which is shown in equation 2.3:

P_r(X = k) = λ^ke^−λ

k! (2.3)

Where k means number of events happened in the same interval and λ is the ex- pectation of the random variable K. A Poisson point processes can be described as following, with the intensity µ is a collection of random variables N (A, ω), and A ∈ R^d and ω ∈ Ω and Ω is the sample space.

1. If A₁, A₂, . . . are disjoint sets then N (A₁, •), N (A₂, •), . . . are independent.

2. N (A, •) is Poisson with mean µ(A): P_r(N (A) = k) = ^e^−µ(A)_k!^µ(A)^k.

To generate Poisson point processes to simulate BSs’ deployment, Poisson distribution is used to generate the number of points for each occurrence and uniform distribution is used to allocate BSs within one simulation.

2.3 Other Point Processes

Except PPP, there are lots of other types of point process. Some of them are listed in Table 2.1 [9]. Matern hard core point processes form a generic class of point processes whose points are never closer to each other than some pre-defined distance while Poisson point processes has no such constrain [11]. Hard core models can be constructed from Poisson point processes by removing certain points in order to achieve the distance control. A so-called Geyer saturation model is mentioned in [10], which can accurately reproduce the spatial structure of a wireless network.

This model is based on Geyer saturation process, which has been specified in [12].

It is a generalization of the Strauss process [13] and the advantage of Geyer process is that it can be both clustered and regular processes. Also, both of Strauss and Geyer process can be reduced to Poisson point processes.

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10 CHAPTER 2. REVIEW OF POINT PROCESSES

Point

Process Key Properties Practical Example

BPP Total number of nodes within given area is fixed. Each node is i.i.d. (independent and identically distributed) and uniformly distributed.

A known number of BS with specified area.

Poisson

cluster Clustered nodes, and cluster locations are independent.

Sensor networks, networks with hotspots.

Poisson plus Poisson

cluster Independence between the PCP and the PPP. Attraction between nodes.

PPP represents the mobile users in a macrocell and the PCP represents femtocells or hotspots.

Matern

hardcore Begin with PPP. Have minimum inter-node distance limitation.

CSMA/CD networks.

Table 2.1: Point Processes Examples

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Chapter 3

System Model

3.1 Assumptions

It is difficult to decide which planning scheme is the best for system performance for a wireless system. But regular deployment provides better performance than random deployment is observed in [8]. In this thesis, hexagonal models are assumed as optimal planning scheme. Meanwhile, self-deployed scheme is generated through BPP. Moreover, we assume that by increasing the minimum inter-site distance in self-deployed scheme, the final deployment can approach to optimal planning scheme. This assumption is based on that hexagonal tiling is the dentist way to arrange circles in a 2-dimension plane. When area and number of BSs are decided.

Without transmission power control scheme, we can treat each BS and its coverage area together as identical circle. So the dentist and fairest way to deploy all BSs into the area is according to hexagonal model.

3.2 Cell Planning Levels

Cell planning levels are the parameter to indicate how well a wireless system is planned. According to our assumption, minimum inter-site distance is used to control the system deployment changing from self-deployed scheme to optimal planning scheme. And the ultimate value for minimum inter-site distance should be equal to the inter-site distance of hexagonal model. So we define the cell planning levels as

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12 CHAPTER 3. SYSTEM MODEL

equation 3.1:

P L := d

D d ≤ D (3.1)

Where d is the minimum inter-site distance and D is the inter-site distance of hexagonal model. According to the definition, cell planning levels should between 0 and 1.

3.3 Network Model

0 5 10 15 20 25 30 35 40

Figure 3.1: Self-deployed Model

Since self-deployed scheme is simulated through BPP. It is simpler to allocate all BSs within a square area and use Voronoi tessellation to divide the boundary of each cell like shown in Figure 3.1. However, dividing a square area with hexagonal pattern has some constrains. First is that the number of hexagons cannot be arbitrary and second is that the edge of the division is not smooth. So, to avoid these constrains, square coverage area is dropped in hexagonal model. Instead, to generate the coverage shape, the first hexagon is arranged in the center and rest of hexagons

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3.3. NETWORK MODEL 13

are circling around the center hexagon tire by tire until all hexagons are arranged.

We tried to keep the symmetry of the whole pattern, which means on the outmost tire, rest of the hexagons are not continuously arranged on one edge but one by one on the opposite edge. The total number of hexagons is equal to the number of BSs and the whole area covered by hexagons is equal to the square area in self-deployed scheme. The pattern is shown in Figure 3.2.

−25 −20 −15 −10 −5 0 5 10 15 20 25

−25

−20

−15

−10

−5 0 5 10 15 20 25

Figure 3.2: Optimal planning Model

Because the area covered in these two models are not the same. It is not fair to compare these two models directly. In order to solve this problem, interesting area is introduced into the system. An interesting area is a circle area around the center of the coverage area. It is shown as the red circle in both Figure 3.1 and Figure 3.2.

An interesting area is designed to cover a certain portion of the whole area. And its radius is decided by the portion. Since the sampling and analysis works are focused on this area. The results are comparable for these two models. Moreover, border effects can be partially avoided since no sampling point will be on the edge of the area. Border effects happen when users are allocated on the edge of the covered

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area. Such users get much less interference compared with users around the center.

This kind of unfairness is normally undesirable during system analysis.

Testing points are uniformly distributed within the interesting area to collect system information. Each of the testing point will not only receive the power from the BSs within the interesting area but also these outside of the interesting area. In both Figure 3.1 and Figure 3.2, the red points indicate the testing points.

3.4 Path Loss Model

Path loss model used in this thesis work is COST-Hata-Model referred from [14]

and shown in equation 3.2:

L_b = 46.3 + 33.9 log f − 13.82 log h_Base− a(h_Mobile) + (44.9 − 6.55 log hBase) log d + Cm

(3.2)

And a(h_Mobile) is defined by equation 3.3:

a(hMobile) = (1.1 log f − 0.7)hMobile− (1.56 log f − 0.8) (3.3) In these two equations, f stands for frequency in MHz, d stands for distance in km, hBase stands for base station antenna height in meter and h_Mobile stands for mobile antenna height. Also, the constant C_m is defined by equation 3.4:

Cm =

( 0dB, for medium sized city and suburban centres with medium tree density

3dB, for metropolitan centres (3.4)

3.5 Fading Model

Lognormal fast fading is used to judge the system performance under fading cases.

Lognormal calculation is in linear scale, which means in decibel scale, it is a normal distribution. It can be noted by 3.5:

ℵ(µ, σ²) (3.5)

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3.6. COST MODEL 15

Where µ is the mean and σ² is the variance. The PDF of the normal distribution is shown in equation 3.6:

1 σ√

2πe⁻

(x−µ)2

2σ2 (3.6)

3.6 Cost Model

According to [5, 15], the total cost of a network deployment can be divided into two parts. They are radio equipment cost and site-related cost. And they are the linear function to the number of BSs N . In this thesis, we assume that same equipment is used in different deployment schemes. So the radio equipment cost C_r is the same.

One of the main parts in site-related cost is the cell planning cost. If we assume that cell planning cost is proportional to cell planning levels. Then we can calculate the planning cost as P L × C_p, where C_pis the cell planning cost of optimal planning networks. And for self-deployed networks, cell planning cost should be 0.

However, Linear relationship between cell planning levels and cell planning cost is very ideal. Since cell planning cost does not only include cost for planning but also cost of implementation, such as site-acquisition cost. While cell planning levels increasing, the difficulty of generating the final scheme is increasing. It will be more time consuming. The calculation will require higher accuracy. More experienced technicians and experts will be needed. Sophisticated computer and software will be indispensable. In addition, the flexibility of choosing site position during implementation could be decreased dramatically. Based on all of these facts, that the relationship between cell planning cost and cell planning levels is nonlinear is very possible. In the thesis, we assume it is an exponential relationship. And it is defined by equation 3.7:

C_tot:= N [C_r+ P Lⁿ× C_p] n ≥ 1 (3.7) Where n is the exponential index. And linear relationship can be reduced from this equation by setting n to 1.

3.7 System Parameters

The parameters of the simulation system is made according to [16] and [17]. They are shown in Table 3.1.

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Parameters Values Note

P_t 46dBm BS transmission power for no power control situation.

f 1.8GHz Carrier Frequency.

hb 32m Effective BS height.

hm 1.5m Effective mobile height.

σ 8dB The standard deviation of

shadow fading.

tn -174dBm/Hz Thermal noise density level.

noise figure 5dB

bandwidth 10MHz Bandwidth of downlink signal.

gm 0dB Antenna gain of mobile sta-

tion.

g_b 14dB Antenna gain of BS.

test point 10 number of test point for each simulation.

d_min 35m The minimum distance be-

tween test point and BS.

percent 50% The portion of the interesting area.

density 0.5 per km² The BS density.

area 1600km² The whole simulation area.

Table 3.1: System Parameters

3.8 Performance Metrics

We considered SINR, throughput and cost to performance ratio (CPR) as the performance metrics. SINR is the most basic parameter of a wireless system. Its calculation is defined according to 3.8:

SIN R = P_i

P

n6=iPn+ N (3.8)

Where P_i is the received signal power, P

n6=iP_n is the total received interference and N is the noise power.

System throughput is calculated according to 3.9:

T = log₂(1 + SIN R) (3.9)

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3.8. PERFORMANCE METRICS 17

Where SINR is in linear scale.

Since the average throughput under different deployment could be different, in order to compare the cost under different deployment, CPR is introduced. And it is defined by equation 3.10:

Cu := Ctot

T (3.10)

According to the definition, it is easy to see that CPR is the cost on unit throughput.

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Chapter 4

Analysis

4.1 Performance Analysis

Figure 4.1 shows the average SINR performance under interference-dominated situation.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

−2.5

−2

−1.5

−1

−0.5 0 0.5 1 1.5 2

Average SINR Performance (dB Scale)

Cell Planning Levels

SINR (dB)

Average SINR without fading Average SINR with fading

flat area

Figure 4.1: SINR Performance with cell edge SNR equals to 25dB

In the figure, red line with stars and purple line with crosses stand for without and 19

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20 CHAPTER 4. ANALYSIS

with un-correlated shadow fading cases respectively. The x-axis is the cell planning levels. 0 indicates totally self-deployed scheme without minimum inter-site distance limitation. And 1 indicates the optimal planning scheme, which is simulated by hexagonal model. The simulations after 0.73 are skipped since they are too time- consuming to generate the pattern by using self-deployed way.

According to the figure, nearly linear trend can be observed for both curves. This means, for average SINR performance, higher planning levels lead to better performance. Moreover, a flat area has been marked out. This area at the beginning of both curves indicates that for very low planning level situation, limited planning effort will not improve the performance. However, since the width of this area is very limited and it is at the very beginning of the planning levels. The effects of this area are very limited. The effects of fading are obvious from the figure. Although the two curves start from almost the same point. Without fading case has much larger slope than the case with fading. It means that fading can degenerate the improvement of planning levels on SINR performance gain.

Average performance gives us a common sense about the whole system performance.

In order to investigate it in more detail, the SINR performances of different percentiles has been checked as well. Figure 4.2 shows the performances of 2.5, 50 and 97.5 percentile respectively with uncorrelated fading attended.

As expected, all these three curves have linear performance, which is consistent with the average performance. The slope difference between the three curves is not obvious, but the 97.5 percentile curve has the largest slope. From the figure we can conclude that the performance gain distributed into different percentiles almost equally. Higher percentiles can gain more but it is very limited.

Besides the interference-dominated situation, the noise-dominated situation has been studied as well. The average SINR performance is similar to the performance under interference-dominated situation. The main difference is the cross point of the two curves. In Figure 4.3 shows the performance under noise-dominated situation (cell edge SNR equals to -3dB):

In Figure 4.2, the cross point is not obvious since the two curves merged into each other. And it is at the very beginning of the curves. in Figure 4.3, the cross point

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4.1. PERFORMANCE ANALYSIS 21

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

−15

−10

−5 0 5 10 15 20 25

Percentile SINR Performance under Unco−related Fading (dB Scale)

SINR (dB)

2.5 percentile 50 percentile 97.5 percentile

Figure 4.2: SINR percentile performance under interference-dominated situation with uncorrelated fading

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

−4

−3.5

−3

−2.5

−2

−1.5

−1

−0.5 0 0.5

Average SINR Performance (dB Scale)

SINR (dB)

Average SINR without fading Average SINR with fading

flat area

cross point

Figure 4.3: SINR performance under noise-dominated situation

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goes up obviously. This is mainly because the lower transmission power under noise-dominated situation. Lowered transmission power makes the fading effects more dominate to the average SINR performance. When cell planning levels are low, the deployment randomness can be compensated by the randomness caused by fading. So average SINR performance under fading case is much better than its under fading free case. Moreover, the flat area is still exist in both curves and performance decreasing can be observed in this area.

Also, system throughput has been investigated. Because the calculations of system throughput and SINR in decibel scale are similar. The figure is as expected, similar to SINR figure. In Figure 4.4, it shows the throughput performance under a noise- dominated situation.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.9 1 1.1 1.2 1.3 1.4 1.5 1.6

Average Throughput Performance

Throughput (bit/s/Hz)

Average Throughput without fading Average Throughput with fading

flat area

Figure 4.4: Throughput performance under noise-dominated situation

Moreover, the flat area has been noticed as well, which happened in SINR performance. But the decreasing in throughput is more obvious. The decreasing may indicate that planning not always gains in performance.

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4.2. TRADEOFF BETWEEN COST AND PERFORMANCE 23

4.2 Tradeoff between Cost and Performance

In previous section, we analyzed the system SINR and throughput performances under both noise and interference dominated situation. Linear trend has been observed. However, since the cost also rises while cell planning level increasing.

Tradeoff between cost and performance exists. In this section, the tradeoff is going to be investigated based on our cost model.

Figure 4.5 shows the CPR performance with different cell planning levels under interference situation. At the beginning of the curves, there is a rapid rise area.

Within this area, the CPR increases faster than the following area. And it is more obvious in fading free case. Also, the two curves merged into each other at the beginning. This is consistent with their SINR performance. In fading free case, after the rapid rise area, a turning point can be observed and the rest pattern is much flatter than the trend in fading case. The trend is simpler in fading attending case. The whole pattern is more like a straight line and the slope almost keeps the same as in rapid rise area. Small slope indicates the slow increasing in CPR. While large slope is just the opposite. It indicates the rapid rise in CPR. So flat pattern is preferred.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

70 75 80 85 90 95 100 105 110

Cost to Performance Ratio

Cell Planning levels

Cu

without fading with fading

rapid rise area

turing point

Figure 4.5: CPR under interference-dominated situation with Cp= 1, n = 1

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Under the noise-dominated case, the pattern is different. It is shown in Figure 4.6:

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

75 80 85 90 95 100 105 110 115 120

Cost to Performance Ratio

Cu

without fading with fading

rapid rise area turing points

flat area

Figure 4.6: CPR under noise-dominated situation with Cp= 1, n = 1

According to Figure 4.6, rapid rise area still exists and it is much steeper than under interference situation. Turing points are clearer for both with and without fading cases. There is an obvious flat area in the case without fading and even CPR decreasing happens in this area. The whole performance under fading attending case is also more straight line like. But the rapid rise area is more apparent under noise-dominated situation.

Different C_p values can lead to different performance patterns as well. In Figure 4.7, the curves with Cp = 1 and Cp = 0.5 are compared. It is apparent that value of Cp

has big effects on the slope of the curves. While C_p increasing, the slope increases rapidly.

In previous part, we investigated the cost performance only based on n = 1. n = 1 indicates the linear cost model. And as we mentioned before, linear case is a very ideal case. So nonlinear models should be considered. Figure 4.8 shows different trend with three different n values.

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4.2. TRADEOFF BETWEEN COST AND PERFORMANCE 25

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

70 75 80 85 90 95 100 105 110

Unit Rate Cost(with fading case)

Cu

Cp=1 Cp=0.5

trend while Cp increasing

Figure 4.7: CPR under interference-dominated situation with fading case n = 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

70 75 80 85 90 95 100 105 110

Cu

n = 1 n = 1.5 n = 2

trend while n increase flat area

first turing point second turing point

Figure 4.8: CPR under interference-dominated situation with fading case C^p= 1

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The effect is obvious. As value of n increase, the curve becomes flatter at beginning but much steeper on the tail. Whole trend changes from linearity to exponential.

Especially in case of n = 2, there is an obvious flat area. This area supposes to be the most cost efficient area. A turning point can be observed on this curve as well.

Part after the turning point is the most uneconomical area.

The effect is obvious. As value of n increases, the curve becomes flatter at beginning but much steeper on the tail. Whole trend changes from linear to exponential.

Especially when n = 2, there is an obvious flat area at the beginning. And according to the pattern, the width of this area should be extended while n increasing. Two turning points can be observed. The first one is immediately after the flat area.

Curve begins to go upward starting from the first turning point. After the second turning point, the curve goes up much steeper.

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Chapter 5

Conclusion and Future Works

5.1 Conclusion

In this thesis, first we analyzed the relationship between system SINR performance and cell planning levels. Cell planning levels are the parameters used to indicate planning efforts in this thesis. And it is defined as the ratio between minimum inter-site distance limitation of self-deployed scheme and the inter-site distance of optimal planning scheme. Linear patterns have been obtained, which indicates that planning efforts can get relevant performance improvement and the improvement is distributed into different percentile almost evenly. Moreover, with and without fading cases under interference and noise dominated situations have different features. For interference dominated situation, fading will degenerate the performance for most of the planning levels. But for noise dominated situation, fading however can improve the performance for about half of the planning levels. Also, fading makes the whole performance pattern flatter, which means the performance gains are more moderate and degraded.

In throughput performance analysis, a flat area has been noticed, which also happens in SINR performance. Within this area, performance keeps almost the same while cell planning levels increasing. This happens at the very beginning of the curve and the area is relatively narrow. It indicates that limited planning efforts will not gain in performance when cell planning levels are very low.

The tradeoff between cost and performance has been analyzed via CPR, which is 27

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28 CHAPTER 5. CONCLUSION AND FUTURE WORKS

the cost of unit throughput. When total cost is linearly increasing with cell planning levels. CPR is almost linear to cell planning levels as well. The increasing rate is mainly determined by the planning cost C_p. Large C_p values leads to large rates. Fading can enlarge the rate as well. Furthermore, two special areas have been noticed. First is the rapid rise area, within which the increasing rate is the largest comparing with other areas. It happens under both interference and noise dominated situations when cell planning levels is low. But it is more rapid under noise dominated situation. Secondly, a flat area has been observed under noise dominated situation. The increasing rate is small or even minus in this area. Large increasing rates indicate fast increasing in cost per throughput. Since the total throughput increases too, total cost can increase dramatically. Therefore, cost efficiency drops rapidly when the rate is large. And tradeoffs should be considered in such cases or areas, e.g. rapid rise area. On the opposite, small or even minus rate leads to moderate increasing in total cost while keeping or increasing cost efficiency. So, the flat area should be preferred by decision makers.

Moreover, when total cost is exponentially increasing with cell planning levels, very different patterns are obtained. While exponential power increases, low planning level area becomes flatter and the area extends. Rapid rise area happens when planning levels are high and increasing rate is larger when exponential power is large.

In a word, decision makers can predict their planning levels based on their budget and then adjust the budget to maximize their profit based on the whole pattern of the performance and cost trend of cell planning levels. But in order to use it into a practical situation, real cost value need to be used as well as the cost model need to be specified.

5.2 Future Works

Since the simulation system in this thesis only used very basic system parameters.

For further studies, more complex systems could be considered. Such as power control schemes and frequency reuse schemes could be implemented. Also, system outage threshold could be introduced into the system to decide the system feasibility before considering its performance and cost. Moreover, since we noticed that cost

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5.2. FUTURE WORKS 29

models have big effect on the results, detailed study on cost model could be another direction.

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www.kth.se TRITA-ICT-EX-2013:2013:51

Cost and Performance Tradeoff Analysis of Cell Planning Levels

J U N G A O

Cost and Performance Tradeoff Analysis of Cell Planning Levels

Cost and Performance Tradeoff Analysis of Cell Planning Levels

Abstract

Acknowledgements

Contents

List of Figures

List of Tables

Abbreviations

Chapter 1

Introduction

1.1 Related Work

1.2 Motivation and Problem Formulation

1.3 Aim and Contributions

1.4 Scope

1.5 Outline

Chapter 2

Review of Point Processes

2.1 Fundamental of Point Processes

2.2 Poisson Point Processes

2.3 Other Point Processes

Chapter 3

System Model

3.1 Assumptions

3.2 Cell Planning Levels

3.3 Network Model

3.4 Path Loss Model

3.5 Fading Model

3.6 Cost Model

3.7 System Parameters

3.8 Performance Metrics

Chapter 4

Analysis

4.1 Performance Analysis

4.2 Tradeoff between Cost and Performance

Chapter 5

Conclusion and Future Works

5.1 Conclusion

5.2 Future Works

References