微型基地台網路之佈局分析與效能估計

i

國

立

交

通

大

學

電子工程學系 電子研究所

博 士 論 文

微型基地台網路之佈局分析與效能估計

Femto Base Station Network Deployment & Performance

Analysis

研 究 生：曾勇嵐

指導教授：黃經堯 教授

微型基地台網路之佈局分析與效能估計

Femto Base Station Network Deployment & Performance

Analysis

研 究 生：曾勇嵐 Student：Yung-Lan Tseng

指導教授：黃經堯 Advisor：Ching Yao Huang

國 立 交 通 大 學

電子工程學系 電子研究所

博 士 論 文

A Dissertation

Submitted to Department of Electronics Engineering and Institute of Electronics

College of Electrical and Computer Engineering National Chiao Tung University

in Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy in

Electronics Engineering

May 2013

Hsinchu, Taiwan, Republic of China

iii

Femto Base Station Network Deployment & Performance

Analysis

Student：Tseng, Yung-Lan

Advisor：Dr. Huang, Ching-Yao

Department of Electronics Engineering and Institute of Electronics

National Chiao Tung University

ABSTRACT

In this dissertation, we will analyze how to improve the cellular

wireless communication system through the help of femto base station

(femto BS) networks. Femto BS is a base station which provides much

smaller coverage area and users can deploy femto BSs on locations where

they want to improve the Quallity of Service (QoS). To ensure a proper

downlink outage probability, design criterion based on a feasible femto

base station (BS) density is analyzed. Considering femto BS deployment,

a three-dimensional (3-D) Poisson model of random spatial distribution

and stochastic geometry are used. From the study, closed forms of

feasible femto BS density will be identified. Based on the frame structure

of 4G cellular communication system, we also provide a fast approach to

estimate the achievable throughput that user will obtain from femto BS

networks. The analysis results not only can be used to predict the

performance of various femto BS deployment scenarios but also can be

used as a design criterion for resource control mechanism designs. Our

research results about femto BS network can also be applied to other

research topics of wireless communications. In our study, we further

extend our study to the m-dimensional random networks and the fading

figure estimation of Nakagami fading channel.

微型基地台網路之佈局分析與效能估計

學生：曾勇嵐

指導教授：黃經堯 教授

國立交通大學電子工程學系暨電子研究所 博士班

摘

要

在這篇論文中，我們將討論如何利用微型基地台網路來增進蜂巢式

無線通訊系統的效能。微型基地台可以由一般使用者放置在任何地方

，以增加通訊系統覆蓋率或是提升使用者的網路頻寬。但是微型基地

台也為蜂巢式通訊系統帶來了新的問題。在我們的研究當中，我們提

出提供使用者完整的系統覆蓋率為目標，調整微型基地台在空間當中

的”密度”的想法。我們建立一個三維立體空間的隨機網路模型以及四

類干擾情況。在每一類干擾情況下，我們分析微型基地台網路所容許

的密度區間。在 4G 無線通訊系統的架構之下，我們也提供了一個

可以快速估計微型基地台網路傳輸頻寬的估計方法。因此，我們的研

究成果可直接應用於無線通訊系統對微型基地台網路的資源配置以

及使用者端的服務品質控制。除了微型基地台網路外，我們的研究成

果和數學分析還可以延伸應用在無線通訊的其他問題。在我們的論文

當中，我們也提出了 1) m 維的隨機網路, 和 2) Nakagami fading

channel 的 fading figure 估計方法, 兩項延伸應用。

v

致 謝

能夠完成這篇論文，真的要感謝出現在我生命周遭的許多人。首先，我要感謝 我的父親-曾建友先生以及母親-彭亞娜小姐。謝謝你們在我人生遭遇挫折時，能 夠一直持續地相信我，支持我，和幫我加油打氣。另外，還要感謝我的妹妹-映 嘉。你是全家的開心果，也祝福妳能順利完成妳的碩士班學業。 感謝我的指導教授-黃經堯教授這些年來的教導，讓我得以順利畢業。在研究 的過程中，老師一直給我很大的發揮空間，讓我得以解決難題，往前邁進。也謝 謝師母，師母的鼓勵常讓我銘記在心。感謝實驗室的夥伴們，從最初的慧源學長， 明原學長、阿坤學長、宜霖學長、文嶽學長、以及振哲學長，和我差不多同時進 入實驗室的彥翔、正達、建銘、裕隆、宜鍵、雲懷、大瑜、盟翔、宗奇、昌叡， 以及後期的傑堯學長、子宗、明憲、Ensya、烜立、智元、東佑、泓志、仲煒和 峻安。因為你們，我才有多采多姿的碩士班和博士班生活。希望即使在大家畢業 多年後，還是可以常常見面，聊聊近況。我也要在此感謝交通大學的許多教授， 包括王聖智教授、杭學鳴教授、蔣迪豪教授、林大衛教授、陳茂傑教授、等教授， 讓我得以一窺無線通訊之美，並了解什麼是做學問應有的態度。 我在資策會工作的同事們，羅耿介顧問，李永台組長、吉隆、志偉、誼學、俊 彥、均哲、舒慈、秋紋，以及和我一起在資策會工讀的智元、邵穎、佑賢、盈良， 謝謝大家在無線通訊標準活動上給我的協助。參與標準活動讓我收穫豐富。另外， 也謝謝宗諭常常討論和我討論數學和大台北美食餐廳情報。謝謝中央大學的許獻 聰教授和宜蘭大學的陳懷恩教授常常在標準提案上提供珍貴的建議。 除了感謝學校和工作上的夥伴之外，我也要謝謝 Toastmasters 國際英文演講 會的朋友們，包括 Legend Advance club、YZU club、和許多的 sister clubs。英文 演講雖然和學術研究沒有直接關係，但卻又是影響深遠。因為在這四年來持續參 與英文演講會，讓我不論是在學術會議還是日常生活，都可以有自信地在大眾場 合侃侃而談而且條理分明。這一點，是我在參加 Toastmasters 之前所欠缺的。 在這裡，我也遇到可以分享日常生活大小事情的好朋友們。未來的日子裡，我還 需要向 Toastmasters 的各位多多學習。 我也想要藉由這個機會感謝我在大學以及碩士班時期所參加的交通大學諮商 中心志工團。從西元 2000 年到西元 2006 年，我有七年的時間持續投入諮商中心 的活動當中。在諮商中心裡，我遇到了許多智慧和專業兼備的諮商老師，包括韶 玲老師、鶯珠老師、燦如老師、守謙老師、靜儀老師、景同老師、以及文昭姊等。 在交通大學這樣以理工為主的環境當中，諮商中心給我不同的視野來面對人生的 課題和選擇。而交通大學諮商中心志工團的好朋友們，十幾年的交情真的是很不 容易，有許多朋友已經為人父母了。希望當我們頭髮斑白時，大家還可以一起聚 首憶當年。 在這篇論文即將付梓之時，我在劉哲瑜先生的網路部落格上讀到下面這段話:

以前覺得很多夢想自己都達不到，但真的完成其中一項後，才會發現所謂的夢想

是「令你害怕的事」。當你願意給自己機會去正視害怕，才有機會達成夢想，如

果你不願去正視害怕，連眼前的敵人都不知道在哪，要怎麼擊倒它？要怎麼實現

夢想？

我想，這也正是我攻讀博士班的心情寫照。在這幾年的博士班生涯當中，除了專 業知識和求學態度的長進之外，也包含如何正視自己夢想，並全力以赴的心情轉 變。謝謝在這段期間協助我正視我的夢想的各位。篇幅有限，但要感謝的人真的 很多。另外，我還要謝謝郁心，在認識妳的這一年多的時間當中，我真的過得很 快樂。也謝謝妳在我心情不好時，能夠適時鼓勵我。 最後，謹以此論文獻給在天上的阿公、阿嬤和爺爺、婆婆 。 曾勇嵐 謹誌 2013 年五月,交通大學,新竹, 台灣

vii

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CONTENTS

FIGURES ... x

TABLES ... xi

Chapter 1 Dissertation Overview ... 1

1.1 Overview of Dissertation Background ... 1

1.2 Contribution and Outline ... 3

1.3 Definitions and Abbreviations ... 4

Chapter 2 Introduction of Femto BS ... 6

2.1 The Origin of Femto BS ... 6

2.2 Features of Femto BS Network ... 9

2.3 Benefits of Femto BS ... 12

2.4 Research Topics of Femto BS ... 13

2.4.1 Deployment Issue ... 13

2.4.2 Interference Analysis and Mitigation ... 14

2.4.3 Load Balancing ... 20

2.4.4 CSG/OSG Conflict ... 21

2.5 Conclusion ... 22

Chapter 3 3-D Femto BS Deployment models and Analysis ... 23

3.1 Analysis Model ... 23

3.1.1 Three-Dimensional Analysis ... 23

3.1.2 Homogeneous Poisson Point Process... 25

3.2 Femto BS Density Analysis ... 30

3.2.1 Scenario (a) Macro BS Is the Serving BS ... 32

3.2.2 Scenario (b) F1 Is the Serving BS ... 33

3.2.3 Scenario (c) CSG Femto BS Is the Dominant Interference Source to A Non-CSG User ... 36

3.2.4 Scenario (d) OSG Femto BS Network ... 42

3.3 Simulations ... 42

3.4 Discussion ... 49

3.5 Conclusion ... 49

Chapter 4 Extension of Log Value Estimation ... 51

4.1 Introduction ... 51

ix

4.3 Applications ... 56

4.4 Numerical Results ... 60

4.4 Conclusion ... 63

Chapter 5 Femto BS Netowrks Throughput Analysis ... 64

5.1 Analysis Model ... 64

5.1.1 Deployment Model ... 65

5.1.2 Transmission Protocol ... 65

5.2 Throughput Analysis... 67

5.2.1 Closed Form Expression ... 67

5.2.2 Approximation of Decoding Failure Probability ... 69

5.3 Simulations ... 70 5.4 Applications ... 74 5.5 Conclusion ... 75 Chapter 6 Conclusion ... 76 Reference ... 79 Publication List ... 86

FIGURES

Chap. 2

Fig. 2-1 Femto BS networks in the cellular System ... 9 Fig. 2-2 Functional overview of femto BS states and operation modes [16]

... 11 Fig. 2-3 Interference scenarios in the femto BS networks [15] ... 14 Fig. 2-4 Different cooperation levels of SON algorithms ... 17

Chap. 3

Fig. 3-1 Femto BS network analysis model ... 24 Fig. 3-2 Comparison of E[Un](Num)andE[Un](Est),δf1 =δf2...=40dB .. 44

Fig. 3-3 Outage probability estimated with the λa _{in Theorem I, where} dB 40 ... 2 1 = f = f δ δ . ... 45 Fig. 3-4 Feasible regions ofλa

andλb

. Here, we assume δ_f2 =δ_f3...=55dB and adjustδ_f1from 35 to 45 dB. ... 45 Fig. 3-5 Outage probability when λb

is located near the lower bound estimated from Theorem II, whereδ_f2 =δ_f3...=55dBandR_m =150m. 46 Fig. 3-6 Outage probability when C

C

λ is near the upper bound estimated from Theorem III. ... 47 Fig. 3-7 Outage probability of scenario (d). Here,δ_f1=40dB, δ_f3=...=65dB,

dB 50 ~ 1 4 2 = f δ .. ... 47 Fig. 3-8 Curves of R_mdunder differentδf2and

d λ . Here,δ_f1 =40dB, 65dB ... 3 = = f δ ,δ_f2 =41~50dB. ... 48 Chap. 4

Fig. 4-1 Decision rule to construct the lookup table of E[∆|M'] ... 60 Fig. 4-2 Evaluation of E(X,α,β,Ω)based on the closed form in (4.12)

and (4.17). ... 61 Fig. 4-3 Comparisions with differetent ML based estimators. N=100. ... 62 Fig. 4-4 Comparisions with differetent ML based estimators. N=30. ... 62

Chap. 5

Fig. 5-1 Resource blocks of OFDM system ... 66 Fig. 5-2 Comparisons of DNum and DApp curve when 10 (m )

-3 5

−

=

λ . ... 72 Fig. 5-3 Comparisons of DNum and DApp curve when 10 (m )

-3 2

−

=

λ .. ... 72 Fig. 5-4 Comparisons of D_Num and D_App by adjusting the value of λ ... 73 Fig. 5-5 Plot of CV(RMSE) by adjusting the value of λ ... 73

xi

TABLES

Chap. 1

Table 1-1 Definitions of corresponded vocabularies [1] ... 4

Table 1-2 Abbreviations of the corresponded vocabularies ... 5

Chap. 2 Table 2-1 Comparisons of femto BSs with other candidate technologies ... 12

Chap. 3 Table 3-1 Common spatial models [65] ... 26

Table 3-2 Closed forms utilized in the integral terms of E [ln(Rn)] [87] ... 29

Table 3-3 Closed forms of E[ln(Rn)] ... 30

Table 3-4 Notations and values of femto BS network parameters ... 43

Chap. 4 Table 4-1 Closed forms of E[ln(R_n|m)] ... 54

Chap. 5 Table 5-1 Parameters of simulations ... 71

C

HAPTER

1

D

ISSERTATION

O

VERVIEW

In this chapter, we will introduce the overview of our dissertation. In section 1.1, we introduce the background of our research. Then, we delineate the outline of our dissertation in section 1.2. In section 1.3, we summarize the definitions and abbreviations of vocabularies that often appear in this dissertation.

1.1 Overview of Dissertation Background

Cellular Wireless Communication network is now widely applied to serve a large part of the population in the world. In the era of first generation cellular network, the cellular network only supports voice service. Now, billions of users around the world require a wide range of data services from the real-time video streaming to the point to point packet transmission. It is expected the requirement towards the bandwidth will keep increasing in a dramatic speed. With the extention of cellular networks, it is already observed the increase of indoor data request. In 2008, more than 50% of voice call and more than 70% of data traffic are generated from the indoor environment[4]. However, because of the characters of signal propagation and complicated indoor surrounding, the cellular network still leaves indoor “coverage holes” in everywhere. To provide ubiquitous coverage, system providers need effective approaches to conquer the indoor coverage holes. Over the past few decades, many candidate technologies were proposed to improve the indoor bandwidth efficiency. Within these candidate approaches, Femto Base Station (Femto BS) is a promising technology which draws a lot of attention from

2 both the service providers and users.

The basic concept of femto BS is a base station which provides much smaller cell coverage in the cellular netowrks. In the history of cellular netowrks, devices such as micro BS and relay stations were proposed to enhance the signal quality and bandwidth efficiency. However, femto BSs obtain many features which are totally different with previous technologies. The features of femto BS include:

1) Femto BS can be deployed and installed by users. 2) Cell planning is absent in the femto BS networks.

3) Femto BS can provide different Quality of Service (QoS) to different users. 4) Femto BS needs to self-organize and self-optimize their operations.

5) Femto BS needs to cooperate with neighbor BSs automatically.

Because these innovative features and requirements of the femto BS network, femto BS leaves many problems to researchers. First, femto BSs bring flexibility to the cellular network by allowing users to deploy femto BSs by themselves. However, this flexibility makes the cell planning in the femto BS networks complicated. Furthermore, because users can install femto BSs in the location where the Singal to Interference plus Noise Ratio (SINR) needs to be enhanced, it can be expected there will be as many as thousands of femto BSs under the coverage of one macrocell. These femto BSs need to cooperate with each other to optimize the network performance. However, how to improve the efficiency of cellular network by optimizing the performance of femto BS networks is still a pending problem.

To improve the performance of femto BS networks, many studies concentrated on control mechanisms in Physical layer or Medium Access Control layer, such as the power control, resource allocation, or fractional frequency reuse. However, few researches took the random distributions of the femto BS networks, which will influence the system performance, into their consideration.

Besides the locations of femto BS networks, it is also difficult to analyze the throughput that femto BS networks contribute to the users. Most of the studies which analyzed the improvement of femto BS networks were achieved by field test or simulations. However, field test or computer simulations are not efficient in giving us the insight about how femto BS improves the system performance.

1.2 Contribution and Outline

In this dissertation, we will apply the concept of random network to analyze the femto BS networks. First, we use homogenous Poisson Point Process (HPPP) to describe the random distributions of femto BSs. Then, tools of stochastic geometry are applied to model the locations of femto BS networks. Our contributions include:

a) A novel 3-dimensional HPPP space model to analyze the femto BS networks.

In the previous studies about wireless communications, most of the scenarios were based on 2-dimensional (2-D) plane scenario. However, 2-D scenario cannot fulfill our requirement because femto BSs can be deployed by users in anywhere of the buildings. To address the feature of femto BS networks, we provide a novel 3-dimensional (3D) HPPP scenario to analyze the femto BS networks.

b) The range of feasible femto BS density of femto BS networks

Based on the stochastic features of femto BS networks, we will estimate the range of feasible femto BS density which provides fully coverage to the users. In our study, we will analyze the influence of the density of femto BS to the Signal to Interference Ratio (SIR). Then, we analyze how to control the femto BS density to decrease the probability of outage event. The conclusion of our analysis can be a reference of femto BS networks deployment and interference mitigation.

c) Extension to the log value estimation

Derived from our analysis, we also conduct a closed form to analyze the expected value of log value, E[ln(Rn|m)]. Here, m represents the dimension of HPPP and n represents the nth nearest node observed by the user. Rn|m represents the distance between the user and the nth nearest node in the m dimensional space. Both m and n can be any positive integer. In our study, we will show that our closed form expression of E[ln(Rn|m)] can be applied to many studies in wireless communications, such as the average signal strength estimation in random network (when m<3) and channel estimation of Nakagami fading channels.

d) Femto BS networks achievable throughput estimation

4

estimate the achievable throughput of femto BS networks. We will estimate the achievable throughput based on three assumptions: 1) OFDM (Orthogonal Frequency Division Multiplexing) system, 2) Non-cooperated packet transmission and 3) Hybrid Automatic Repeat Request.

The rest of the paper is arranged as follows: In Chap. 2, we will provide a broad introduction about the functions of femto BS and related research topics. In Chap. 3, we will estimate the range of feasible femto BS density under different scenarios. In Chap. 4, we extend our research result of E[ln(Rn|m)] to other studies of the wireless communications. In Chap. 5, we propose a closed form for the throughput estimation of femto BS networks. Finally, the conclusions and summaries of this dissertation are summarized in Chap. 6.

1.3 Definitions and Abbreviations

Table 1-1 Definitions of corresponded vocabularies [1]

Vocabulary Definition

Backhaul The intermediate links between the core network and base stations.

Base Station A network element in radio access network responsible for radio

transmission and reception in one or more cells to or from the user equipment.

Cell Radio network object that can be uniquely identified by a user

equipment from a (cell) identification that is broadcasted over a geographical area from base station.

Cellular Network A radio network distributed over land areas called cells, each served by

at least one fixed-location transceiver, known as a cell site or base station.

Connection A communication channel between two or more end-points (e.g. base

station, server etc.).

Core Network The central part of a telecommunication network that provides various

services to customers who are connected by the access network.

Coverage Area An area where services are provided by that cellular network to the

level required of that system.

Table 1-2 Abbreviations of the corresponded vocabularies

degree of satisfaction of a user of a service. It is characterized by the combined aspects of performance factors applicable to all services.

Service Provider A service provider is either a cellular network operator or another entity

that provides services to a user.

Throughput A parameter describing service speed. The number of data bits

successfully transferred in one direction between specified reference points per unit time.

User Equipment Equipment that allows a user to access the network services. For the

purpose of wireless communications the interface between the user equipment and the network is the radio interface.

Vocabulary Abbreviation

4G 4rd Generation

BS Base Station

CDF Cumulative Probability Function

CSG Closed Subscriber Group

DSL Digital Subscriber Line

DS-CDMA Direct Sequence-Code Division Multiple Access

ggd Generalized Gamma Distribution

HARQ Hybrid Automatic Repeat reQuest

HPPP Homogeneous Poisson Point Process

OFDM Orthogonal Frequency Division Multiplexing

OFDMA Orthogonal Frequency Division Multiple Access

OSG Open Subscriber Group

PDF Probability Density Function

QoS Quality of Service

SIR Signal to Interference Ratio

SINR Signal to Interference plus Noise Ratio

SON Self-Organization Network

6

C

HAPTER

2

I

NTRODUCTION OF

F

EMTO

BS

In this chapter, we will introduce the femto BS and research topics derived from femto BS. In section 2.1, we introduce the origin of femto BS. Then, the features & functionalities of femto BS are introduced in section 2.2. In Section 2.3, we list the benefits that femto BSs bring to the cellular network. Although femto BSs benefit the cellular network and users, femto BSs also create new problems. In Section 2.4, we explain the new research topics which are caused by femto BSs and the candidate solutions proposed by preliminary studies.

2.1 The Origin of Femto BS

With the progress of wireless access technology, users’ requirements to the cellular wireless communication systems also advance from voice service, short message, to the broadband data communications [2]. Therefore, the bandwidth requirement also grows in a dramatic speed [3]. Because of the popularity of wireless communication, now the users require wireless services in everywhere and so services providers of cellular communication systems need to provide ubiquitous coverage.

However, because of shadowing, multipath phenomenon, and wall penetration of buildings, the cellular network still leaves indoor coverage holes in anywhere. In the past, many candidate technologies were proposed to provide ubiquitous coverage. However, these candidate approaches also have their limits. In recent yeares, femto BS was

proposed to improve the inefficiency of celluar networks in the indoor environment [3]-[10].

The basic concept of femto BS is a base station which provides much smaller cell coverage in indoor areas. In the beginning, operators of cellular netowrks divided one large macro-cell, which is located in the metropolitan area, into many smaller cells. Small cells are applied in the metropolitan area because of two major reasons: First, comparing with suburb areas, areas with dense population have much heavier traffic loading. Under the condition that the backhaul bandwidth in each base station is the same, the cell size in metropolitan areas is shrunk from several kilometers to several hundred meters to guarantee the QoS that users obtains would not be affected by the population of their neighborhood. Second, users in metropolitan areas often suffer from serious signal degradation. Therefore, service providers generated the idea that deploying a base station closer to the end users to conquer the signal degradation. Now, because of more and more indoor traffic requests and strong signal degradation in the indoor areas, the size of base station shrinks further to serve the indoor users.

Before the proposal of femto BS, many candidate technologies were proposed to improve the radio access efficiency in the indoor condition. Here, we will introduce four of the most well known technologies: 1) micro BS, 2) relay station, 3) distributed antenna system, and 4) Wireless Local Area Network Access Point (WLAN AP).

Micro BS

Micro BS, which has been proposed nearly three decade ago [11], can be regarded as a base station with much smaller coverage. Similar to macro BS, micro cell is installed by system operators under careful frequency plan to prevent joint interference with neighbor base stations. The functionality of micro BS is the same with that of macro BS.

Relay Station

Relay station [12] is a signal repeater to receive and re-radiate radio signals from the poor coverage regions. However, their reuse of the licensed spectrum for backhaul limited the system throughput. Therefore, the benefit that relay station provides is limited and not simple to be deployed.

8

Distributed Antenna System

Distributed antenna (DAS) system [13] is also proposed to solve the signal degradation in the indoor environment. The basic idea of DAS is to install an indoor BS in the building and to deploy the antennas of the BS on different locations in the building. These antennas are connected with the BS through fiber or coaxial cable. DAS could largely improve the spectral efficiency of the network, if both the overlap between the coverage areas of the different antennas is reduced, and the coverage areas of the antennas fit as much as possible to the shape of the building. However, the backhaul connection of the BS is still limited. Furthermore, the deployment and wire connections between the BS and antennas are still complicated.

WLAN AP

Here, we use the IEEE 802.11 series standards [14] as the embodiment of WLAN AP. Comparing with the candidate technologies above, WLAN AP has the follow characters: i) It can be deployed by the users, and ii) Wireless LAN AP uses unlicensed bands to transmit/receive data. WLAN provides robust bandwidth connections in the indoor environment. However, WLAN AP provides service only in the indoor surrounding. Moreover, wireless LAN AP lacks handover and paging processes. So, it is difficult for WLAN AP to support user mobility. Furthermore, lack of joint cooperation between WLAN APs may enhance the mutual interference and so decrease the bandwidth efficiency of the network.

Because of more and more bandwidth requirement towards wireless communications and ubiquitous coverage for wireless broadband connection, these candidate technologies still cannot fulfill the users’ requirements. Therefore, femto BS was proposed during the last ten years. From 2007, femto forum, a not-for-profit membership organization, was founded to enable and promote femto BS and femto technology. Furthermore, to improve the system capacity, standard organizations of 4G cellular network, such as 4G LTE (Long Term Evolution) [15] and WiMAX (Worldwide Interoperability for Microwave Access) [16] system, already included femto BSs and the functionalities that femto BS needs in their standard documenets. In the next section, we will introduce the features and functions of femto BSs.

2.2 Features of Femto BS Network

Based on the requirement of 4G cellular network [15]-[16], femto BS is a short range, low cost and low power base station. Femto BS can be deployed and installed by users for better indoor signal quality and bandwidth. This user-installed base station communicates with the cellular network through broadband connection such as DSL, cable modem, or even air link. Femto BS has many features, such as:

(1) Flexibility of deployment

The topology of macro BS network and femto BS network in the cellular network can be expressed through Fig. 2-1. Here, macro BS network represents the company of macro BSs and femto BS network represents the company of femto BSs. In Fig. 2-1, it is clear that the coverage of the femto BS network can be overlapped by the macro BSs or isolates from the macro BS networks. In Fig. 2-1, we call the areas that out of the coverage areas of cellular network as the coverage holes. Femto BSs are deployed to co m p en s a t e t h o s e c o v e r a g e h o l e s . B es i d es c o m p en s at i n g t h e co v e r a ge holes, femto BSs can also be deployed under the coverage of macro BS network to imoprove the QoS that uer experiences. In this condition, we call it as the macro/femto BS overlapping network. Because femto BSs can be deployed by users in everywhere which needs to improve the user QoS, it is difficult for service providers to optimize the performance of femto BS networks through cell planning.

(2) Huge number of femto BSs

Although femto BS was proposed just few years ago, femto BS already outnumbered traditional base stations by the end of 2010. Furthermore, now femto BSs are deployed at a rate of five millions per year [3]. It can be expected that how to control the huge number of femto BSs in the cellular network would become an important research topic.

10

(3) User priority

Because the femto BS and the backhaul connection are provided by users, it is reasonable that users will require different user access priorities and QoS requirements when the femto BS is dealing with the access request from different users. Based on the 4G wireless communications standards [15]-[16], three different access modes are supported by femto BS:

a) Closed Subscriber Group (CSG)

A CSG consists of a set of subscribers authorized by the femto BS owner or service provider. The CSG femto BS supports only users in the authorized CSG. A femto BS can belong to many different CSGs.

b) Open access (also known as Open Subscriber Group (OSG))

The open access femto BS supports all users within its coverage.

c) Hybrid access.

A hybrid femto BS supports both the authorized CSG users and non-CSG users, although the non-CSG users have only limited access.

Apparently, femto BSs will have different interference impacts on the surroundings when the associated access modes are different.

(4) Self-Organization Network (SON)

The self-organization Network is a concept that enables the femto BSs to adjust themselves with the minimum human manipulation. Here, we divide the SON into two stages, which are self-configuration and self-optimization.

In the macro BS networks, the radio parameters, such as the operating frequency bands and radiation powers, are set by system providers based on detailed cell planning. However, it would not be possible for users to set the control parameters of femto BSs by themselves. Therefore, femto BSs need the capability to set control parameters automatically. For example, femto BSs need to synchronize with the cellular network at the initialization stage. Moreover, femto BSs should also set its radiation power during the initialization process. The process that femto BSs set all the control parameters at the

initialization stage is called self-configuration.

In addition to self-configuration, the concept of self-optimization was also proposed in the studies of SON. The purpose of self-optimization is to adjust the operation of femto BS dynamically with the changes of the surroundings and users’ QoS requirements. Some optimizations need the joint cooperation between neighbor BSs, which include both femto BSs and macro BSs.

(5) Operation Modes

In the cellular network, the macro BS and micro BS are always in the normal operational mode even there is no active user under their coverage. However, femto BS has multiple states during its operation. Based on [15]-[16], the power of femto BSs can be turned on/off by the users or the backhaul connection. Furthermore, femto BSs can step into low duty mode when there is no user under its coverage. Therefore, femto BS changes between multiple states during its operation, as illustrated in Fig. 2-2.

In Fig. 2-2, femto BS enters the initialization state when power on. In the initialization state, procedures such as time/frequency synchronization should be performed. In the end of initialization state, the femto BS should attach with the service provider’s core network successfully. It is worthy to note that the femto BS is prohibited from turning on its radio frequency component before it finishes the attachment process with the core network. After attaching with service provider’s core network, the femto BS enters the operational state. However, femto BS will revert to the initialization state when it becomes unattached to the service providers core network or fails to meet operational requirements [16].

12

Table 2-1 Comparisons of femto BSs with other candidate technologies

In the operational state, femto BS can transfer between normal and low-duty operation mode depending on the traffic loading of femto BS. In low-duty operation, the femto BS alters its operation mode during the available intervals (AI) and unavailable intervals (UAI) respectively. During the AI, the femto BSs may become active on the air interface for activities such as paging, boradcasting system information, and data transmission. During the UAI, femto BS turns off its radiation power to reduce the interference to neighbor cells. Femto BS may also take the chance of UAI to synchronize with the overlaid macro BS or measuring the interference from neighbor cells. Although the low-duty operation may decrease the mutual interference, it is also required that the low-duty operation should not disturb the normal operations of the cellular network and the user QoS [16]. The comparisons of femto BS and candidate access technologies are listed in Table 2-1.

2.3 Benefits of Femto BS

Because of the features that femto BS obtains, femto BS brings many benefits to the cellular networks and the users. The advantages of femto BS include [3]-[10]:

(1) Coverage holes compensation

For the cellular network, the coverage holes in the cellular network can be compensated by the deployment of femto BSs. Because of the isolation of coverage holes from the coverage of cellular network, femto BSs can reuse the frequency spectrum without interfering neighbor BSs and so the area spectral efficiency (bits/s/Hz/m2) [17] of the cellular network also increases.

Femto BS Micro BS WLAN AP Relay Station DAS

Spectrum Licensed

/Unlicensed

Licensed Unlicensed Licensed Licensed

Cell Plan No Yes No Yes Yes

Installation User Service provider User Service provider Service provider

Backhaul Cable/DSL Telephony

network

Cable/DSL No Telephony network

QoS Guarantee Hard hard Soft hard hard

(2) Channel quality & spectrum efficiency

The channel qualities between the macro BS and indoor users are always affected by the indoor penetration loss and multipath effects. Because of poor channel quality, macro BSs need to assign more radio resource for indoor users to fulfill the users’ QoS. With the deployment of femto BSs, the spectrum efficiency of the whole cellular system will be improved because the channel quality improves.

(3) Load balancing

Femto BS also helps the macro BS network to achieve load balancing. In the macro/femto BS overlapping network, macro BSs can offload the indoor traffic requirement to the femto BSs. Then, macro BSs could save more resource to serve outdoor users, handover users and roaming users. So, outdoor users also benefit from the deployment of femto BSs in both the air link and backhaul connection.

(4) Energy efficiency

To communicate with the macro BS network, indoor UEs need to radiate more radiation power to conquer the weak channel quality. Now, by connecting with the femto BS, UEs consume less power for good connection quality and so both the energy efficiency in packet transmission and the battery life of UEs increase.

2.4 Research Topics of Femto BS

Although femto BS brings many advantages to both the cellular network and the users, femto BS also increases the complexity of cellular network. Without cell planning, femto BS needs intelligent mechanisms to adjust itself based on users’ requirements and the surroundings. In this section, we will introduce the preliminary studies about femto BS and their achievements.

2.4.1 Deployment Issue

It is difficult to quantify the influence of the deployment of femto BSs because the randomness of their locations. Many analysis of the femto BSs were achieved through simulations. In [5], a system level simulation was constructed by assuming a hexagonal macro BS network, which was combined with 19 macro BSs. The area of macro BS network was divided into multiple grid areas and the locations of femto BSs were

14

randomly selected from a grid with 20 m separation. In [18], a detailed apartment model was proposed for the research of femto BS in the LTE system. In [19], the deployment problem was analyzed by selecting the best configuration of femto BSs among many fixed testing points. To maximize the Shannon capacity in the building, the capacity was formulated as an equation related to the locations, radiation powers and channel selections of the femto BSs. Mixed integer programming was used to solve the optimal solution. Xiang et al. proposed a joint channel allocation and fast power control scheme [20]. By assuming femto BSs could sense and reuse the frequency spectrum, the downlink spectrum sharing problem in [20] was formulated as a mixed integer nonlinear programming problem and decomposition methods were applied to solve the problem. In [21], Liu et al. proposed a mathematical model to capture the unique building features. Based on the model in [21], a set of novel transformation strategies were provided to formulate the deployment issue into a mixed-integer convex program (MICP). Accordingly, an effective global optimization algorithm based on convex relaxation of the formulated MICP within a branch-and-bound framework was applied. Liu‘s works in [21] guaranteed a global optimal solution.

2.4.2 Interference Analysis and Mitigation

Because of the random distributions of femto BS network and different operation modes, femto BSs will produce strong interference if the joint interference is not solved appropriately. In [15], six interference scenarios of femto BS networks are plotted:

1) Femto user -> macro BS 2) Femto BS -> macro user 3) Macro user -> femto BS 4) Macro BS -> femto user 5) Femto user -> femto BS 6) Femto BS -> femto user

Macro user is the user who is served by macro BS and femto user is the user who is served by femto BS. In Fig. 2-3, the black solid lines represent data connection and the read dash lines represent interference.

In femto BS interference mitigation algorithm, most of the analyses and proposals are based on two popular radio access technologies: i) CDMA (Code Division Multiple Access) system, and ii) OFDMA system. Here, we will also introduce the preliminary studies based on their access technologies.

2.4.2.1 CDMA System

To analyze the interference that femto BS creates to the macro/femto BS overlapping network, Chandrasekhar and Andrews provided new mathematical models and analysis for the uplink interference problem in the two-tier CDMA-based CSG femto BS networks [22]. In [22], sectoring receiver antennas and time hopping-CDMA mechanism were proposed to be embedded in the femto BS to avoid mutual interference between the macro BS and femto BSs. Das and Ramaswamy investigated the reverse link capacity of femto cells by modeling inter-cell interference as a Gaussian random variable [23]. For CDMA femto cells, power control or saving a “macro BS only” spectrum was proposed by many studies [24]-[26]. In [27], Arulselvan et al. proposed a “geo-static scheme”, which to enable the femto BS to adjust power level in radio frequency based on its physical distance to the macro BS. Based on this adaptive power control scheme, the femto BS network locally achieved a target data rate that is centrally computed by the network.

2.4.2.2 OFDMA System

Chu et al. proposed a decentralized resource allocation scheme for the OFDMA downlink of a shared spectrum hybrid macro/femto network [28]. In [28], each femtocell randomly selects a subset of OFDMA resources for transmission. The proposed approach in [28] is simple in implementation. However, the random selection approach cannot provide the optimal system performance and QoS guarantee to UEs. To eliminate mutual interference, many studies proposed advanced algorithms baed on different directions, which include: a) Frequency planning, b) Power control, c) SON, d) Optimization problem, and e) Game Theorem.

16

a) Frequency plan

In [29]-[31], the authors discussed how to assign frequency carriers to femto BSs through the given frequency plan in macro BS networks. In these studies, fractional Frequency Reuse (FFR) was applied in the macro BS network. Then, femto BSs were proposed to reuse the macro BS spectrum to improve the spectrum efficiency. In [32], Ghosh et al. analyzed the improvement of FFR in the heterogeneous network. Their results can also be applied to the FFR in the macro/femto BS overlapping network. However, there is one implementation problem in this approach: How to decide if the femto BS could reuse the macro BS spectrum? To solve this problem, G¨uvenc et al. proposed a “interference-limited coverage area” (ILCA), which is an area within a contour where the received power levels from the macro BS and femto BS are the same [33] . The ILCA will be compared with a threshold (e.g., the area of a user’s premises); if it is larger than the threshold, the femto BS is allowed for co-channel operation (i.e., it is in outer region). Otherwise, femto BS is in the inner region and it cannot reuse the macro BS spectrum. In [34], based on the objective to increase the system spectral efficiency, Bai et al. discussed the tendency of macro BS/femto BS to reuse or to partition the spectrum when the serving user is in different locations of the macro BS coverage. Then, a hybrid frequency allocation algorithm was proposed to improve the spectrum efficiency in the macro/femto BS overlapping network.

b) Power control

In [35], Li et al. formulated the downlink power control problem for femto BSs that operate in the same frequency carrier with macro BSs. Both centralized and distributed solutions were given jointly with a dynamic channel re-allocation procedure to assure the QoS of users. In [36], a distributed utility-based SINR adaptation was proposed for femto BS networks to alleviate cross-tier interference at the macro BS, which was interfered by overlaid femto BSs.

To briefly summarize, the interference elimination approaches above proposed to eliminate the interference between the macro/femto overlapping network by the popular techniques in the cellular netowrks, such as directional antennas, power control, and frequency participation. Next, we will introduce the studies about how to decrease the mutual interference through SON algorithm.

C) SON algorithm

The approaches of SON algorithms can be divided into three cooperation levels, which are shown in Fig. 2-4. Note that the three levels can co-exist in one control algorithm. i) Self-Measurement

In self-Measurement, femto BS adjusts its operation parameters by measuring the environment itself. In [37], several heuristic frequency assignment schemes were proposed and compared. Based on their simulations, the LIP (Least Interference Power) scheme, which new femto BS selects the frequency band that has the minimum the received total interference power at the receiver side of itself, is the best practical scheme. However, the performance of LIP scheme is sensitive to the order of femto BSs turning on its radiation power. Furthermore, each femto BS can only access one frequency carrier, which limits the system capacity. To solve this problem, Garcia et al. proposed an “autonomous component carrier selection” approach [38]. First, each femto BS selects one least interfered primary carrier from a set of carriers based on its measurement. Then, allocation of additional secondary component carriers is possible if and only if the performance impact on neighboring cells is estimated to be acceptable. In [39], Sundaresan and Rangarajan proposed a distributed random access scheme (DRA). Accoring to DRA, the femto BS decides which resource blocks it occupies based on a hash table. The hash table is generated individually by each femto BS and the size of hash table is decided by the interfering degree, which is also measured by the femto BS itself. Femto BSs will rehash the hash table in the collided resource blocks. The details of resource blocks of OFDM system will be explained in Chap. 5.

18

Many studies also applied cognitive radio technique to realize the SON algorithm [40] -[43]. In [40], Lien et al. proposed a cognitive radio resource management (CRRM) scheme for femto BS networks. In CRRM, femto BSs periodically sense the channel to identify which resource block is occupied by the macro BS network. In subsequent data frames, femto BSs only allocate “non-occupied” resource blocks sensed in the sensing phase. To achieve optimal spectrum utility, femto BSs are required to record the following parameters: (i) the traffic loading of the macro BS network, (ii) radio resource allocation correlation probability of the macro BS network, and (iii) percentage of correlated radio resource allocation of the macro BS network. In [41], a localized dynamic spectrum access approach was proposed in a macro BS/femto BS overlapping network. In [41], femto BSs reuse the spectrum for macro-PU/femto-PU, which are primary users served by macro BS and femto BS respectively, by sensing the idle spectrum. Simulation results showed that throughput improves if spectrum sensing is achieved by femto BSs. It is because femto BSs are usually with better sensing capability. In [42], Jin et al. proposed to combine cognitive radio and multi-hop cooperative communication in the macro/femto BS overlapping network. By requiring every wireless device to be equipped with frequency-agile spectrum sensing units, Jin et al. developed an optimization framework for location-aware cooperative resource management, with jointly employing power control, multi-hop cooperative communication and flow management techniques. Based on stochastic geometry and homogeneous Poisson point process (HPPP), Cheng et al. proposed several corresponding downlink spectrum sharing schemes between femto BSs and macro BSs as well as among femto-BSs [43]. Moreover, by requiring femto BS to measure location information and avoidance region, the proposed Distance Sense Multiple Access (DSMA) and controlled-underlay schemes in [43] provided much more throughput than that in traditional interweave and slotted Aloha schemes.

To summatize, the Self-Measurement approach is easy to be implemented. Without information exchange between UEs and other BSs, the femto BS does not produce much control overhead to the backhaul network. However, the drawback of Self-Measurement approach is: the measurement from the femto BSs does not represent the measuremet of users. To fulfill users’ QoS requirements, femto BSs need the measurement reports from users.

ii) Users’ Reports

In cellular network, users’ reports are already applied in many control algorithms, such as handover process or frequency carrier selection [15]. In the femto BS networks, users’ report is extended to modify the control parameters of femto BS network. In [44], Claussen et al. proposed a novel mobility-event based self-optimization approach to adjust the femto BS radiation power. In this approach, they tried to minimize the increase of unnecessary mobility events, such as passing and handover events. It was shown that mobility event based self-optimization of coverage can both significantly reduce the total number of mobility events caused by femto cell deployments and improve the indoor coverage. In [45], L´opez-P´erez et al. proposed two SON approaches for femto BS in the downlink direction. One is the femto BS selects the least interfered frequency carrier it detects from neighbor BSs. Another one is femto BS selects the least interfered frequency carrier that users measure. Simulations result showed the user based approach gets better performance. Although the femto BS networks can get better performance from the users’ report, the number of calculations in each femto BS would increase exponentially with the number of users and the number of carriers. Furthermore, requiring UEs to perform measurements may enhance the power consumptions of UEs, which are typically power limited.

iii) Inter-BS Cooperation

To optimize the bandwidth efficiency and resource allocation, many researches proposed the capability that BSs exchanging information with neighbor cells through air links or backhaul connections [46]-[49]. In [46], Amirijoo et al. proposed that network detects an outage area autonomously based on measurements, which from both UEs and neighbor BSs. Then, the network alters the configuration of surrounding BSs to compensate the outage-induced coverage. In [47], Li et al. enhanced the joint cooperation of femto BSs by also requiring the information exchange between BSs.

However, even the system performance can be improved by the inter-BS information exchange, the propagation delay of backhaul connection is too long to allow dynamic cooperation between femto BSs and macro BSs [48]. To facilitate the information exchange, information exchange through air links was proposed in many studies. In [49], Adhikary et al. proposed a novel approach for the femto BSs to reuse the macro BS spectrum by listening to the resource allocation map, which is broadcasted by macro BS over the time slots. Furthermore, the femto BS also gets the locations information of UEs

20

through Global Positioning System. Then, femto BS will reuse the macro BS spectrum by limiting joint interference.

To briefly summarize, the inter-BS cooperation improves the system performance futher because of more information gathered during the process. However, it may also increase the signaling overhad and the loading of compulations to the cellular netowrks.

d) Optimization problem

Interference problem can also be solved by using the tools of optimization problem. In [50], L´opez-P´erez et al. proposed “dynamic frequency planing” by modeling the frequency allocation problem as a mixed integer programming. In the backhaul network, a centralized controller is responsible to gather all the measurements from users and BSs. Greedy algorithms were used in the simulations and the result showed the macro BS femto BS joint cooperation would conduct the best performance during the simulation. In [51], femto BSs were grouped based on the mutual interference information. Then, a central controller determined the minimum number of orthogonal sub-channels for each group to provide target performance. The transmission power of each femto BS was adjusted based on the received signal strength indication (RSSI) in a distributed manner. However, the above optimization problems require high complexity and centralized computations, which increase the difficulty to be implemented in the femto BS network.

e) Game theorem

Game theorem is also applied by many researchers to analyze spectrum allocation problem in the macro/femto BS overlapping network. In [52], Chen et al. proved the existence of the unique optimal solution of the channel allocation problem. Furthermore, they also proposed A DANCE mechanism for a general femtocell channel allocation problem. In [53], Lien et al. proposed the cognitive radio resource management scheme for femtocells to mitigate cross-tier interference. Under such cognitive framework, a strategic game was further developed for the intra-tier interference mitigation.

2.4.3 Load Balancing

In the section 2.3, we have introduced that femto BS can share the loadings of macro BS networks. To achieve the objective of load balancing, some studies suggested letting the UEs to prefer the femto BS on the BS selection stage. In [32], [54], the concept of

“range expansion” (also called cell biasing), where a UE may associate with a femto BS even though the received power from the the macro base-station on the downlink is higher, was demonstrated. However, it is obvious that this approach can lead to more interference from the macro BS at the UE which is associated with the femto BS. Therefore, a joint cell-association and scheduling for femto BSs and macro BSs had been discussed for downlink systems [54]. In [32], range expansion was combined with a TDM (Time Division Multiplexing) based interference cancellation approach to improve the overall user experience compared to a macrocell network. In [55], G¨uvenc et al. studied the impact of range expansion and number of femto BSs on both sum capacity and fairness of heterogeneous networks. Moreover, a new cell selection method, which adaptively expands the range of femto BSs based on the resource-specific SINR measurements, was proposed.

2.4.4 CSG/OSG Conflict

Different user priorities enhance the complexity of interference problem in femto BS networks. In [56], L´opez-P´erez et al. investigated the influence of CSG femto BS network through simulation. In the downlink direction, it had been demonstrated that the CSG femto BS network would decrease the total cell throughput by around 15% with respect to that of OSG femto BS network. Furthermore, CSG femto BS also increases the error reception events of outdoor users. In [57]-[58], Jo et al. proposed lemmas which provide expressions of the SINR distribution for various zones within a cell as a function of the macro BS-femto BS distance. Based on their analysis, it showed that indoor users preferring closed access and outdoor users preferring open access. Moreover, the conflict is most pronounced for femtocells near the cell edge of macrocell. To solve this problem, some studies proposed to enable the CSG femto BS to share resource to outdoor users so that a specified minimum data rate can be achieved [56]-[58]. In other words, hybrid mode is preferred to the system in the downlink direction. In the uplink direction, analysis results had shown a more complicated phenomenon [59]. In [59], Xia et al. concluded that the best approach depends heavily on whether the multiple access scheme is orthogonal (e.g. OFDMA) or non-orthogonal (CDMA). In a TDMA (Time Division Multiple Access)/OFDMA (Orthogonal Frequency Division Multiple Access) network, CSG is typically preferable at high user densities, whereas in CDMA, OSG provides significant gain of more than 300% for indoor user by reducing the near-far problem

22

experienced by the femto BS. Therefore, it is suggested that the interests of the femto BS owner and the network operator are more compatible than typically believed, and that CDMA femto BS should be configured for OSG whereas OFDMA or TDMA femto BS should adapt to the density of users.

2.5 Conclusion

In this chapter, we have introduced the background of femto BS. Femto BS has the flexibility to be deployed randomly by users. Femto BS can also provide OSG/CSG/Hybrid access modes to different users. Within the help of femto BS, cellular network can compensate the coverage holes and improve user QoS. Because of better indoor channel quality and frequency reuse factor, the spectrum efficiency also improves. Femto BS can also share the loading of macro BS networks. Moreover, the energy efficiency and battery life of UEs will also be increased.

However, femto BS also brings many challenges to the cellular network. In this chapter, we have introduced four major challenges: 1) Deployment issue, 2) Interference mitigation, 3) Load balancing, and 4) CSG/OSG conflict. To eliminate joint interference problem caused by femto BS networks, traditional approaches such as frequency plan and power control were proposed by many researchers. However, not only traditional approaches, many novel algorithms were constructed based on SON algorithm, optimization problem, and game theorem.

C

HAPTER

3

3-D

F

EMTO

BS

D

EPLOYMENT MODELS

AND

A

NALYSIS

In this chapter, we will analyze how to deploy the femto BS to achieve ubiquitous coverage. In section 3.1, we introduce our analysis model and tools. In section 3.2, we analyze the range of the feasible femto BS density to achieve ubiquitous coverage. In section 3.3, numerical results are provided to prove our analysis model. In section 3.4 we discuss how to apply our analysis model to improve the deployment of femto BSs. Finally, we conclude our contribution in section 3.5.

3.1 Analysis Model

To estimate the performance of femto BS network, we perform two important assumptions in our studies. The first is three-dimensional analysis and the second is applying HPPP in modeling the random distributions of femto BSs.

3.1.1 Three-Dimensional Analysis

In the past, most of the studies about cellular network concentrated on the 2-D analysis model. However, the scenario of femto BS networks is different from that of traditional cellular network because femto BSs are deployed and installed by users to fulfill user

24

Fig. 3-1 Femto BS network analysis model

QoS in the indoor environment. Furthermore, it is sxpected that most of the femto BSs are deployed in the urban areas, where the complex surroudings create coverage holes in buildings. Therefore, to generate a more realistic analysis, a 3-D special model is more appropriate than the traditional 2-D plane analysis in analyzing the femto BS networks. In our analysis, we create an innovative model by assuming the femto BS networks are deployed in a 3-D space, which is shown in Fig. 3-1. In Fig. 3-1, one target user,

T

U

, is located under the coverage of one macro BS. We will analze the signal strength

and interference that

U

_T receives. To simplify the analysis, the joint interference from other macro BSs are ignored by considering the macro BS or femto BS network

dominates the combination of interference. From the

U

T’s point of view, by considering

the

U

_T located in the center of a sphere space, femto BSs are randomly deployed around the

U

_T . R_m is the distance between the user and the macro BS.R_n is the distance between the user and its nth nearest femto BS, Fn.

In our works, we apply the PDF of Rn to estimate the signal strength received by

U

T .

By considering the Hata empirical path loss model, the received signal strength,Un, can

be calculated by (3.1) [60]. . (dB), ) ( log 10η ₁₀ ε δ − ≥ − = fn fn f n n n P R R U (3.1)

Here, P_fn is the transmission power of femto BS, F_n, and δ _fn is the path loss constant between

U

_T and Fn. ηf is the path loss exponent of femto BS networks and

ε _{is assumed to be small and can be ignored. From (3.1), it is clear that we need to}

obtain the PDF of ln(R_n) for the calculation of U_n. In the next section, we provide the details about how to model the random distributions of femto BS networks.

3.1.2 Homogeneous Poisson Point Process

In order to estimate the PDF of Rn and ln(Rn), we utilize the tools of stochastic geometry [61]-[62] in our works. Stochastic geometry, also known as spatial statistics, which means the statistical modeling of spatial relationships, gives researchers many tools to study the behavior over many spatial realizations of a network whose nodes are placed according to some probability distributions. Stochastic geometry has already applied in many researches about wireless communications [63]-[65]. In CDMA system, Musa et al. had published a serious of analysis about DS-CDMA system by using stochastic geometry to model the interference [66]-[69].With the advance of wireless communications, stochastic geometry and related techniques had been widely applied to ad hoc networks [70]-[74], wireless LAN [75], cognitive radio [76], cellular systems [77], relay networks [78]. In Table 3-1, we quoted some popular point processes for wireless network from [65]. In our analysis, we apply homogeneous Poisson point process (HPPP), which is one of the most fundamental models in stochastic geometry, to analyze the distributions of femto BS networks. Next, we will introduce how we apply HPPP in our study.

Homogeneous Poisson point process (HPPP)

HPPP [61] has been widely used in various studies such as the performance of random networks [71]-[72] and stochastic features of interference [80]-[81]. Based on HPPP, we assume that the femto BSs are uniformly distributed around

U

_T with densityλ. Because of uniform distribution in the 3-D space, the PDF of the number of femto BSs in the area can be represented by (3.2) [82].

. 3 / 4 , ! ) exp( ) ( ) , , ( Pr r3 x x x X

υ

π

λυ

λυ

υ

λ

= − = (3.2)

26

Table 3-1 Common spatial models [65]

Point Process Key Properties Example Ref.

Poisson (PPP)

Mutual independence between node locations

Ad hoc networks with pure random channel access.

[71]

Binomial Similar to PPP as far as i.i.d.

node locations, but with a fixed number of nodes in a given area.

A known number of relays or mobile users deployed at random in a cell of known size

[79]

Poisson cluster (PCP)

Clustering of nodes, with independence between cluster locations.

Sensor networks, military platoons, an urban network with dense hotspots.

[70]

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.

[22]

Matern hard Core

Minimum distance between nodes.

Carrier sensing wireless networks with collision avoidance, e.g. WiFi.

[63]

Determinantal Repulsion between nodes,

e.g. Ginibre Process.

Networks with soft minimum distance.

[64]

Here, x is the number of femto BSs in the sphere. r and υ are the radius and volume of the sphere, respectively. From (3.2), it is clear that the complimentary CDF of R_n can be represented by the

Pr

_X

(

x

,

λ

,

υ

)

.

∑

∑

− = − = − = = ≥ 1 0 3 3 1 0 . ! / ) 3 / 4 exp( ) 3 4 ( ) , , ( Pr ) Pr( n x x n x X n r x r x r R λ υ πλ πλ (3.3)

Then, we can obtain the PDF of R_n, denoted by Pr (r)

n R , ) 3 / 4 exp( ) ( ) 3 / 4 ( 3 )) Pr( 1 ( ) ( Pr 3 3 r n r r r r R r n n Rn πλ πλ ₋ Γ = ∂ ≥ − ∂ = (3.4)

where Γ(n) is gamma function. In the next paragraph, we will show that Pr (r)

n R