國
立
交
通
大
學
電信工程研究所
博 士 論 文
中繼站輔助細胞網路之系統設計與最佳化
On the System Design and Optimization of
Relay-Assisted Cellular Networks
研 究 生:林香君
指導教授:黃家齊 教授
沈文和 教授
中
中
中
中 華
華
華 民
華
民
民
民 國
國
國
國 九
九
九
九 十
十 九
十
十
九
九 年
九
年
年 三
年
三
三 月
三
月
月
月
中繼站輔助細胞網路之系統設計與最佳化
On the System Design and Optimization of
Relay-Assisted Cellular Networks
研 究 生: 林香君
Student: Shiang-Jiun Lin
指導教授: 黃家齊
Advisor: Chia-Chi Huang
沈文和
Wern-Ho Sheen
國 立 交 通 大 學
電 信 工 程 研 究 所
博 士 論 文
A Dissertation
Submitted to Institute of Communication Engineering
College of Electrical and Computer Engineering
National Chiao Tung University
in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy
in
Communication Engineering
March 2010
中繼站輔助細胞網路之系統設計與最佳化
研究生:林香君
指導教授:黃家齊 博士
沈文和 博士
國立交通大學
電信工程研究所
中文
中文
中文
中文摘要
摘要
摘要
摘要
下一世代行動通訊系統中,中繼站輔助細胞網路架構被視為一可行且具有潛力的 網路架構。此架構佈放中繼站在傳統蜂巢式網路中,以多躍方式協助基地台與使用者 之間的訊號傳輸。它提供一個以較低成本之佈建方式來改善細胞覆蓋,提昇使用者傳 輸速率,提高細胞系統容量,以及減少使用者的上行傳輸功率。 發展中繼站輔助細胞網路之重要關鍵即是需從理論與實務等方面進行系統效能之 全面性評估。本論文考慮在一般的系統配置下,探索中繼站輔助細胞網路之系統設計 與優化。文中主要分為三大部份進行探討: 在第一部分研究中,我們針對中繼站輔助細胞系統在多細胞環境下之下行性能進 行研究。綜合考量影響系統效能之系統參數:中繼站之佈放位置、使用者之路徑選擇、 頻譜資源重用、資源配置等,以及考慮兩種使用者體驗品質,即固定頻寬分配與固定 傳輸速率分配,我們提出以基因演算法為基礎之演算法進行中繼站輔助細胞網路之系
統效能之優化。實驗結果顯示,相較於傳統網路架構,中繼站輔助細胞網路之下行細 胞容量以及使用者之傳輸速率大大地被提昇。 在論文的第二部分,我們提出中繼站輔助細胞之上行效能之設計與最佳化。在上 行效能中,使用者平均傳輸功率消耗以及上行系統的頻譜利用效率是兩個重要的效能 指標。文中考慮中繼站的佈放位置、頻率重用模式、使用者之路徑選擇以及資源分配 等系統參數進行系統設計。利用基因演算法搭配一個多重存取干擾估算演算法對中繼 站輔助細胞系統進行效能之優化。實驗結果表明,中繼站輔助細胞網路之上行細胞容 量獲得提昇,以及使用者之上行傳輸功率消耗獲得改善。 在第三部分研究中,我們考慮在似曼哈頓式環境中,多跳躍式中繼網路的傳輸排 程問題。利用似曼哈頓式環境中的高遮蔽效應,搭配在基地台與中繼站之指向性天線, 文中提出有效率之傳輸排程方法以提昇此環境下之細胞系統容量。實驗結果指出,在 似曼哈頓式環境中,基地台與中繼站搭配指向性天線,可有效提升系統頻譜效能。 本論文從理論與實務兩方面,針對中繼站輔助細胞網路進行研究。我們考慮在不 同的系統配置下,中繼站輔助細胞網路之上行與下行之設計優化與理論效能。我們亦 考量在似曼哈頓環境中,中繼站輔助細胞網路之實際的傳輸排程問題。綜合實驗結果 說明,中繼站輔助細胞網路可提昇使用者傳輸速率,提高細胞系統容量,以及減少使 用者的上行傳輸功率,並且提供似曼哈頓環境中較好的細胞覆蓋。
On the System Design and Optimization of
Relay-Assisted Cellular Networks
Student:Shiang-Jiun Lin
Advisor:Dr. Chia-Chi Huang
Dr. Wern-Ho Sheen
Department of Communication Engineering
National Chiao Tung University
Abstract
Deploying fixed relay stations (RSs) in traditional mobile cellular networks is widely
recognized as a promising technology in next generation mobile communication systems to
improve cell coverage, user throughput and system capacity, to save transmit power of a
mobile station (MS) in the uplink, and to provide a low cost deployment for coverage
extension.
One crucial step toward developing such a relay-assisted cellular network is to fully
evaluate its performance from both theoretical and practical points of view. In this
dissertation, we aim to explore the system design and the optimization of relay-assisted
cellular networks in multi-cell environment by considering general system configurations.
limits of a general relay-assisted network with optimized system parameters in a multi-cell
environment. Two types of quality of end-user experience (QoE), i.e., fixed bandwidth
allocation and fixed throughput allocation, along with two path selection methods, i.e.,
spectral-efficiency based and signal-to-noise-plus-interference ratio based are investigated.
A genetic algorithm (GA) based method is proposed for joint optimization of system
parameters, including the number of RSs and their locations, frequency reuse pattern, path
selection and resource allocation so as to maximize the system spectral efficiency.
Numerical results show that significant improvement on the system spectral efficiency and
the user throughput are achieved in the relay-assisted cellular network.
In the second part, the aim is to study the uplink performance of a relay-assisted
cellular network. Two performance measures, average power consumption of mobile
stations and uplink system spectral efficiency, are optimized by jointly considering the
system parameters of RSs’ locations, reuse patterns, path selections and resource allocation.
GA-based method along with a method of MAI (multiple access interference) estimation is
applied to solve the optimization problem. Numerical results show that with proper
deployment of RSs both power consumption of MSs and the system capacity are
remarkably improved in the uplink.
In the third part, we investigate the important issue of resource scheduling for
multi-hop relay networks in the Manhattan-like environment. New resource scheduling
methods are proposed for the multi-hop relay network with directional antennas equipped at
In this dissertation, the theoretical performance in both downlink and uplink with
general configurations in relay-assisted cellular networks is presented. The practical issues
of resource scheduling of relay-assisted cellular networks in the Manhattan-like
environment is also addressed. With comprehensively evaluations, we can conclude that a
relay-assisted cellular system is with the benefits to improve the system capacity and the
user throughput, to save transmit power of an MS in the uplink, and to provide better
Acknowledgements
It is a great pleasure to thank those who made this dissertation possible. First of all, I
heartily thank my advisors, Professors Chia-Chi Huang and Wern-Ho Sheen. In addition to
the solid research training, they also set a good example for me to be positive and optimistic
toward every challenge. With their guidance, advice and encouragement, it was in the end
what made this work accomplished.
Special thanks to Professor Dr.-Ing. Bernhard Walke in RWTH Aachen University,
Aachen, Germany and Professor Jenq-Neng Hwang in University of Washington, WA, USA,
who broadened my perspective of thought and made me more confident during my visit
with their research groups. Thanks also go to my doctorial committee members, Professors
Chung-Jr Chang, Jhy-Horng Wen, Ching-Yao Huang, Ray-Guang Cheng, and Yuh-Ren Tsai,
for their valuable comments and suggestions to make this work more complete.
I would also like to show my gratitude to my lab mates in both the Wireless
Communication Lab and Broadband Radio Access System (BRAS) Lab. Their company
made my Ph.D. life more wonderful and joyful.
This dissertation is dedicated to my family — my parents, my brother, and my
husband — for their love, support and understanding; this great power encourages me
deeply and endlessly.
Last but not least, I offer my regards and blessings to all of those who supported me
Contents
中文摘要 中文摘要中文摘要 中文摘要... i Abstract ...iii Acknowledgements... vii Contents...viiiList of Figures ...xii
List of Tables ... xv
Acronyms ... xvi
Chapter 1 Introduction ... 1
1.1 Evolution of Cellular Communication Systems... 2
1.2 Requirements of IMT-Advanced Systems... 3
1.3 Key Technologies toward IMT-Advanced Systems ... 6
1.3.1 Transmission Technology and Multiple Access Scheme – OFDMA ... 6
1.3.2 Carrier Aggregation ... 7
1.3.3 Multiple-Input Multiple-Output Antenna Technology ... 7
1.3.4 Coordinated Multi-Point Transmissions and Receptions ... 8
1.3.5 Relaying Technology ... 9
1.4 Overview of Relay-Assisted Cellular Networks... 9
1.4.1 Classifications of Relay Stations ... 10
Chapter 2 Downlink Performance and Optimization of Relay-Assisted Cellular
Networks in Multi-cell Environments ... 15
2.1 Background... 16 2.2 System Setups ... 17 2.2.1 Cell configuration... 17 2.2.2 Relaying technology ... 18 2.2.3 Propagation Models ... 21 2.2.4 Antenna Configurations ... 23
2.2.5 Power Setting of BS and RS ... 23
2.2.6 Path Selection ... 25
2.2.7 Frequency Reuse over RS-MS Links... 25
2.3 Optimization of System Parameters ... 26
2.3.1 Objective Function ... 26
2.3.1.1 Fixed Bandwidth Allocation ... 27
2.3.1.2 Fixed Throughput Allocation ... 29
2.4 Genetic-Based Optimization... 31
2.4.1 Overview of Genetic Algorithm ... 31
2.4.2 Optimization via Genetic Algorithm ... 33
2.5 Simulation Results... 35
2.5.1 Single Cell ... 36
2.5.1.1 Frequency Reuse over RS-MS Links... 46
2.5.1.2 Shadowing Effects ... 50
2.5.1.3 Sectorization ... 52
2.6 Summary ... 56
Chapter 3 Uplink Performance and Optimization of Relay-assisted Cellular Networks ... 57
3.1 Background... 58
3.2 System Setups ... 58
3.3 Problem Formulation... 59
3.3.1 Measure 1—Minimization of Average MS’s Transmit Power... 60
3.3.2 Measure 2—Maximization of Uplink System SE ... 62
3.4 Genetic-Based Optimization... 65
3.4.1 MAI Estimation Algorithm ... 67
3.5 Simulation Results... 68
3.5.1 Measure 1—Minimization of Average MS’s Transmit Power... 68
3.5.2 Measure 2—Maximization of Uplink System SE ... 77
3.6 Summary ... 84
Chapter 4 Resource Scheduling with Directional Antennas for Multi-hop Relay Networks in a Manhattan-like Environment... 85
4.1 Background... 86
4.2 System Setups and Propagation Models ... 93
4.2.1 System Setup... 93
4.2.2 Propagation Models and Antenna Pattern... 96
4.3 Resource Scheduling Methods ... 98
4.3.2.2 Method-2 ... 105 4.4 Numerical Results ... 109 4.5 Summary ... 116 Chapter 5 Conclusions ... 117 References ... 120 Appendix ... 127 Vita... 130
List of Figures
Figure 1. Examples of (a) contiguous carrier aggregation, and (b) non-contiguous carrier
aggregation. ... 7
Figure 2. An example of CoMP joint processing. ... 8
Figure 3. The multi-cell architecture
(
3,3, 3 ... 19)
Figure 4. (a) A detailed layout of a cell, and (b) the radio resource allocation. ... 20
Figure 5. A simplified shadowing model. ... 22
Figure 6. The general operation principle of GAs... 32
Figure 7. Optimal RSs’ positions and throughput distribution for FBA-SE. ... 38
Figure 8. CDF of user throughput for FBA-SE... 39
Figure 9. Convergence behavior of the proposed GA for FBA-SE (N = 6) under different control parameters (Npop, , β Pmut). ... 41
Figure 10. Complementary CDF of bandwidth consumption for FTA-SE. ... 44
Figure 11. System SE of four system configurations. ... 45
Figure 12. Throughput distribution (bps per unit area) of different frequency-reuse patterns for FBA-SE (N=6). ... 47
Figure 13. System SE of different frequency-reuse patterns (N=6). ... 48 Figure 14. Throughput distribution (bps per unit area) of FBA-SE under shadowing effects. 51 Figure 15. Optimal RSs’ positions and bandwidth consumption (Hz per unit area) for
optimization of B1, B2 and B3 in Figure 3 for FTA-SE... 55
Figure 17. The operation of genetic algorithm... 66
Figure 18. Optimal RSs’ positions and uplink transmit power distribution (in dBm). ... 71
Figure 19. Complement CDFs of uplink transmit power. ... 72
Figure 20. Transmit power distributions (in dBm) of different frequency-reuse patterns. ... 74
Figure 21. Optimal RSs’ positions and uplink transmit power distribution (in dBm) in shadowed environment... 76
Figure 22. Optimal RSs’ positions and uplink throughput distribution. ... 78
Figure 23. CDF of link SE for PM=15 dBm. ... 79
Figure 24. Optimal RSs’ positions and uplink SE distribution (bps/Hz) in shadowed environment... 82
Figure 25. Relay-assisted cell architecture in a Manhattan-like environment—Scenario 1. ... 88
Figure 26. Multi-cell setup of Scenario 1... 89
Figure 27. Transmission frame structure of Scenario 1. ... 90
Figure 28. Relay-assisted cell architectures in a Manhattan-like environment—Scenario 2... 91
Figure 29. Frequency reuse pattern in the multi-cell environment of Scenario 2. ... 92
Figure 30. The deployment of BS and four RSs and their serving areas. ... 94
Figure 31. The relevant distances from BS to determine the path loss and the probability of having LOS. ... 95
Figure 32. Resource scheduling with omni-directional antennas. ... 99
Figure 33. Two phases of transmissions in Method-1, (a) Phase 1 and (b) Phase 2. ... 101
Figure 34. Two phases of transmissions of the neighboring cells in Method-1, (a) Phase 1 and (b) Phase 2. ... 103
Figure 36. Two phases of transmissions in Method-2, (a) Phase 1 and (b) Phase 2. ... 106
Figure 37. Two phases of transmissions of the neighboring cells in Method-2, (a) Phase 1 and (b) Phase 2. ... 107
Figure 38. The frame structure of Method-2... 108
Figure 39. The CDF of SINR for different scheduling methods... 112
List of Tables
Table 1. IMT-Advanced requirements... 5
Table 2. Important parameters for four system setups. ... 40
Table 3. Important parameters for frequency reuse patterns (N=6). ... 49
Table 4. System parameters of Measure 1 for N = 0 to N = 10. ... 70
Table 5. System parameters for different frequency-reuse patterns of Scenario 1, N = 6. ... 75
Table 6. System parameters of Measure 2 for N = 0 to N = 10. ... 80
Table 7. System parameters for different frequency-reuse patterns of Measure 2, N = 6. ... 83
Table 8. The propagation loss model for the urban micro-cell environment. ... 97
Table 9. OFDMA parameters for system-level simulation. ... 110
Table 10. The used MCS. ... 111
Acronyms
3GPP 3rd Generation Partnership Project
AF amplify-and-forward
AMPS Advanced Mobile Phone System
AWGN Additive White Gaussian Noise
BS base station
CDF cumulative distribution function
CDMA code division multiple access
CoMP coordinated multi-point transmissions and receptions
DF decode-and-forward
DSP digital signal processing
EDGE Enhanced Data rates for GSM Evolution
ETACS European-TACS
FBA fixed bandwidth allocation
GA genetic algorithm
GPRS General Packet Radio Service
GSM Global System for Mobile communications
IEEE Institute of Electrical and Electronics Engineers
IMT-2000 International Mobile Telecommunications - 2000
ITU-R International Telecommunication Union - Radio
communication sector
ISI inter-symbol interference
LOS line of sight
LTE Long Term Evolution
LTE-Advanced Long Term Evolution- Advanced
MAI multiple access interference
MCS modulation and coding scheme
MIMO multiple-input multiple-output
MS mobile station
NLOS non line of sight
OFDM orthogonal frequency-division multiplexing
PSD power spectral density
QoE quality of end-user experience
QoS quality of service
RF radio frequency
RS relay station
SE spectral efficiency
SINR signal-to-noise-plus-interference ratio
SMS short message service
TACS Total Access Communication System
TDMA time division multiple access
VLSI very large scale integration
Chapter 1
Introduction
Wireless communications and networks over the last decades have experienced rapid
growth. Thanks to the advanced development in wireless access techniques, and the
dramatic progress in digital signal processing (DSP) and very-large-scale integration (VLSI)
circuits. To further fulfill the increasing demand for various wireless applications and to
better provide ubiquitous services with good quality to users, the evolution trend is still
ongoing and will continue in the future.
Among wireless communications, cellular systems are one of the most successful
wireless applications in the world and have tremendously changed our daily lives. The
cellular radio idea was first emerged by Bell Laboratories in 1940s [1], the cellular plan was
submitted to FCC (Federal Communications Commission) in 1971 [2], and the first cellular
system was commercialized in 1980s [3]. The essential features of cellular concept are
summarized by frequency reuse and cell splitting [1]. A cellular system divides a service
area into multiple cells, where each cell is covered and served by a base station (BS). Due to
can be reused when the co-channel interference is not objectionable. In order to support the
growth in traffic, a single cell can be further split into several smaller cells with lower
power so as to reuse frequency more times, which is known as cell splitting. Cellular calls
are transferred from one BS to another as a mobile station (MS) moves from cell to cell.
These characteristics provide cellular networks with a number of advantages, such as
spectrum efficiency improvement, system capacity increment, and BS transmission power
reduction, over alternative solutions.
1.1
Evolution of Cellular Communication Systems
In 1980s, Advanced Mobile Phone System (AMPS) was developed by Bell Labs and
launched in United States to afford wireless voice services by using analog signaling with
frequency division multiple access (FDMA) [3]-[5]. Meanwhile, Total Access
Communication System (TACS) and its extended version, European-TACS (ETACS), were
used in some European and Asian countries. These are known as the first generation mobile
communication systems (1G).
With more demands other than the voice services, the digital mobile communications
were started in 1990s, known as the second generation mobile communication systems (2G),
including Global System for Mobile Communications (GSM), IS-136, which are time
division multiple access (TDMA) systems, and IS-95, which is a code division multiple
access (CDMA) based system [4], [5]. 2G systems provided more efficient transmissions in
terms of spectral utilization and power consumption by using digital signaling. Moreover,
systems were with enhanced functionality as compared to 2G, named 2.5G or 2G
transitional, such as General Packet Radio Service (GPRS) and Enhanced Data rates for
GSM Evolution (EDGE) for GSM.
In the late 1990s, International Telecommunication Union - Radio communication
Sector (ITU-R) had defined International Mobile Telecommunications - 2000 (IMT-2000) as
framework of the global standard 3G [6]. Evolved from narrowband to wideband, 3G
wireless communication systems allow people access a wider range of advanced multimedia
applications anytime and anywhere, such as video conferencing, Voice-over-IP (VoIP),
faster web browsing, gaming, and audio/video streaming. Main trends of 3G systems are
Wideband Code Division Multiple Access (WCDMA) and CDMA2000.
In fact, such evolution trend is not over yet. Next generation wireless communication,
known as 4G (the forth generation mobile communication systems), is envisioned to provide
high-data-rate multimedia services, ubiquitous network connectivity, and seamless services
in a wide variety of environments, such as indoors, outdoors, low-mobility, and
high-mobility, at an affordable cost [5]. ITU-R has specified the next generation 4G mobile
systems with new capabilities of IMT which go beyond those of IMT-2000 as
IMT-Advanced [7].
1.2
Requirements of IMT-Advanced Systems
The IMT-Advanced system is expected to afford access to telecommunication services
with various applications in various ways. In [8], it is specified that IMT-Advanced systems
support mobility applications from stationary (0 km/h) to high speed vehicular (120 to 350
km/h), and provide a wide range of data rates and service demands in multi-user
capability to provide high-quality multimedia applications.
The key features of IMT-Advanced systems are summarized in Table 1. As can be seen,
IMT-Advanced systems support peak data rates of up to approximately 100 Mbps for high
mobility access and up to approximately 1 Gbps for stationary or low mobility wireless
access, which makes multimedia applications, such as video on demand, much more
capable. In addition to peak data rate, IMT-Advanced has also specified the targeted spectral
efficiency in terms of peak, cell, and cell edge user perspectives for different test
environments and antenna configurations. For example, the minimal requirements of
average spectral efficiency in downlink should be 3 bps/Hz, 2.6 bps/Hz, 2.2 bps/Hz, and 1.1
bps/Hz for indoor, microcellular, base coverage urban, and high speed environments,
respectively, on the antenna configurations of 4 at the transmitter side and 2 at receiver side.
Scalable and wider bandwidth up to and including 40 MHz should be supported in
IMT-Advanced systems to achieve peak data rate requirements.
Moreover, latency and handover requirements are also specified in IMT-Advanced.
The control plane latency, which is measured as the transition time from different
connection modes, e.g., from idle mode to active state, should be less than 100 ms, while
the user plane latency, which is known as transport delay, should be less than 10 ms in
unloaded conditions for small IP packets for both downlink and uplink. To support the
smooth handover across sites/networks, the handover interruption time should be within
27.5 ms for intra-frequency handover, and be within 40 ms and 60 ms for inter-frequency
handover in a spectrum band and between spectrum bands, respectively.
Table 1. IMT-Advanced requirements
Metrics IMT-Advanced Requirements
Peak data rate 1 Gbps for stationary or low mobility 100 Mbps for high mobility
Bandwidth (MHz) 40
User plane latency (ms) 10 Control plane latency (ms) 100
Intra-freq 27.5
Handover interruption time (ms)
Inter-freq
-within a spectrum band -between spectrum bands
40 60 DL 15
Peak spectral efficiency (bps/Hz)
(Antenna configurations of DL 4 × 4, UL 2 × 4) UL 6.75
DL Indoor: 3
Microcellular: 2.6 Base coverage urban: 2.2 High speed: 1.1
Average spectral efficiency (bps/Hz)
(Antenna configurations of DL 4 × 2, UL 2 × 4)
UL Indoor: 2.25
Microcellular: 1.8 Base coverage urban: 1.4 High speed: 0.7
DL Indoor: 0.1
Microcellular: 0.075 Base coverage urban: 0.06 High speed: 0.04
Cell edge spectral efficiency (bps/Hz)
(Antenna configurations of DL 4 × 2, UL 2 × 4)
UL Indoor: 0.07
Microcellular: 0.05 Base coverage urban: 0.03 High speed: 0.015
1.3
Key Technologies toward IMT-Advanced Systems
In order to meet the higher data rate requirements and to provide better quality of
service (QoS) to users, technology advancements in transmissions, multiple accesses,
advanced antenna systems, scalable bandwidth, and cellular architectures have been fully
exploited in next generation mobile systems. Two standard proposals toward next
generation mobile communization systems drawn mainly attentions are 802.16m
standardized by the Institute of Electrical and Electronics Engineers (IEEE) [9], and Long
Term Evolution- Advanced (LTE-Advanced) standardized by the 3rd Generation
Partnership Project (3GPP) [10].
In September 2009, both 3GPP LTE-Advanced and IEEE 802.16m have been
submitted to ITU-R as 4G candidates. The potential key technologies toward
IMT-Advanced systems which are comprehensively investigated by these standard bodies
are summarized as follows.
1.3.1
Transmission Technology and Multiple Access Scheme – OFDMA
Orthogonal frequency-division multiplexing (OFDM) is an effective modulation
scheme to combat inter-symbol interference (ISI) in a high-rate environment. By using
parallel orthogonal subcarriers along with cyclic-prefix, ISI can be removed completely as
long as the cyclic-prefix is lager than the maximum delay spread of the channel [11].
OFDM can also be used as an effective multiple access scheme, known as orthogonal
1.3.2
Carrier Aggregation
One reasonable way to fulfill the targets of very high peak-data rate for IMT-Advanced
is to increase the transmission bandwidth. Wide and scalable bandwidth up to and including
40 MHz, which may be carried by single or multiple RF (radio frequency) carriers, should
be supported in IMT-Advance [8]. The carrier aggregation method is then investigated
where several contiguous or non-contiguous component carriers are aggregated on the
physical layer to provide the necessary bandwidth for higher data rate transmissions [9],
[10]. In Figure 1 (a), an example of contiguous carrier aggregation is illustrated, where three
contiguous component carriers with 20 MHz bandwidth of each is aggregated into a wide
60 MHz bandwidth; while in Figure 1 (b), two non-contiguous component carriers with 20
MHz are aggregated to provide 40 MHz bandwidth. With the carrier aggregation methods,
the bandwidth and peak data rate requirements of IMT-Advanced system might be met.
Figure 1. Examples of (a) contiguous carrier aggregation, and (b) non-contiguous carrier aggregation.
1.3.3
Multiple-Input Multiple-Output Antenna Technology
multiple antennas at communication devices in both transmitter and receiver sides, is used
to substantially enhance the capacity of the transmission. It has been studied that the
capacity of MIMO systems is linearly increased with the minimum number of transmit and
receive antennas in a flat fading channel [12]. The higher order MIMO and advanced
MIMO technologies, including beamforming and spatial multiplexing, will be
well-integrated into next generation wireless communication system to achieve the higher
spectral utilization.
1.3.4
Coordinated Multi-Point Transmissions and Receptions
One way to improve the link quality of cell-edge users is to coordinate and combine
signal transmissions and receptions from/to multiple cell sites, which is known as
coordinated multi-point transmissions and receptions (CoMP). The coordination can be as
simple as inter-cell interference coordination, i.e., coordinated scheduling/beamforming, or
can be more advanced as the same data transmission from multiple cell sites, i.e., joint
processing [10]. Figure 2 shows an example of joint processing scheme. CoMP makes it
possible for users who are scattered in the cell to enjoy more consistent performance and
1.3.5
Relaying Technology
Reduction the propagation loss between the transmitter and the receiver is also a way
to increase the data rate. By setting relay stations (RSs) into the traditional cellular networks,
the transmission between a BS and an MS can be divided into multiple hops. In each hop,
the propagation loss then can be reduced, and higher order modulation coding scheme
(MCS) can be applied so that the transmission rate can be enhanced. Relaying technology is
introduced to improve the user throughput and to enhance the system capacity [9], [10],
[13].
Each key technology mentioned above has drawn lots of research attention. However,
it is noted that even though these technologies have been studied, it does not necessarily
mean that all of them will be included in the specifications for the next generation mobile
communication systems. The introduced complexity and the obtained gain of each
technology will be detailed evaluated.
The comprehensive study of all key technologies is out of the scope of this dissertation.
In this dissertation, we aim to investigate relaying technologies and relay-assisted cellular
networks.
1.4
Overview of Relay-Assisted Cellular Networks
Deploying fixed RSs in traditional mobile cellular networks to relay information from
a BS to an MS, and vice versa, which is known as relay-assisted cellular networks [13].
Relay-assisted cell architecture is expected to be an alternative of cost effective cell
architecture for the wireless communication systems. Very recently, the first commercial
to improve the performance of IEEE 802.16e wireless mobile broadband networks [14].
Relay-assisted cellular systems have been recognized with the following potential
benefits compared to conventional cellular architectures. At the link level, by exploiting
cooperative diversity, RSs can be used to enhance user throughput, to improve outage
probability, and to reduce error rate [15]-[24]. At the system level of cellular systems, RSs
can be deployed to improve system capacity, to extend cell coverage, to save transmit power
(in the uplink), and to provide more uniform data rates to users who are scattered over a cell.
In addition, since the transmit antennas of both ends of a relay link (BS ↔ RS) and/or an access link (BS, RS ↔ MS) are closer to each other, per user throughput can be improved as well. Furthermore, RSs have no direct backhaul connections to the network, so it is much
simpler and easier to deploy than a BS. Such benefit allows flexible and fast network
roll-out and is easy to adapt to traffic load [25]-[58].
With great application potential, the relay technology has also been adopted in IEEE
802.16m [9] and 3GPP LTE-Advanced [10] as one of the key technologies toward next
generation mobile systems.
1.4.1
Classifications of Relay Stations
Relay-assisted networks can be classified into different categories depending on their
characteristics. For example, a wireless relay-assisted network can be classified as
homogeneous relaying or heterogeneous relaying [29]. Homogeneous relaying uses the same
radio access technology for all of its connections including relay links (BS ↔ RS) and access links (BS, RS ↔ MS), while heterogeneous relaying uses different access technologies for
The connection can be in-band connection (in-band relaying) or out-band connection
(out-band relaying). If the BS-RS link shares the same band with direct BS to MS link, it is
referred as in-band relaying; if the BS to RS link does not operate in the same band as direct
BS to MS links, it is called out-band relaying scenario [10].
Another example of classification is that RSs can be categorized as either
amplify-and-forward (AF) or decode-and-forward (DF) RSs according to the forwarding
strategy [29]. An AF RS simply amplifies and retransmits the received analog signal to the
destination, while a DF RS decodes the received signal and re-encodes before re-transmission.
The AF RS has a simpler signal processing and a lower transmission delay but suffers from
noise enhancement, as compared with the DF RS.
The RSs can also be distinguished as fixed, nomadic and mobile RSs depending on their
mobility [9], [13]. RSs may be permanently installed in certain locations, i.e. attached to
buildings, which are known as fixed RSs, or they may be mobile, i.e. traveling with
transportation vehicles, which are mobile RSs. Besides, nomadic RSs are the RSs which may
be temporarily deployed in certain locations for a period of time to assist data transmissions.
1.4.2
Relay Operation Modes
As mention to the operation modes of RSs, two general types of RSs have been classified:
transparent RSs and non-transparent RSs, which are with respect to the knowledge in MSs. In
the transparent mode, an MS is not aware of whether or not it communicates with the network
via an RS; while in the non-transparent mode, an MS is aware of whether or not it is
communicating via an RS. In IEEE 802.16j and 802.16m, they are simply referred as
non-transparent RSs and transparent RSs [9], [13], while in 3GPP LTE-Advanced they are
Non-Transparent Relay (Type I Relay)
A non-transparent RS operates like a BS, except that there is no backhaul connection to
the core network. All control signaling and data transmissions between a BS and an MS are
forwarded by RSs in the non-transparent mode [9], [10], [13]. The non-transparent RS
controls its own cell, which appears to an MS as a separate cell, so that an MS can camp on
the RS, just like camping on the BS. The non-transparent RS can operate in both centralized
and distributed scheduling in the in-band or out-band of the BS operation. Besides the
throughput enhancement, the non-transparent RS may be located at the cell edge to cover the
area that is originally not covered by the BS, which is known as coverage extension.
Transparent Relay (Type II Relay)
On the other hand, in the transparent relay mode, the control signaling from a BS can
directly reach MSs and only data traffic is forwarded by an RS [9], [10], [13]. The transparent
RS is usually located within the coverage of the BS and is under the BS’s supervision so that
only centralized scheduling is supported in the transparent mode. The MS should camp on the
BS and it may not be aware of the existence of the RS. The main objective of the transparent
relay is to enhance the user throughput and to increase the system capacity by achieving
multipath diversity.
1.5
Problem and Motivation
The concept of relay-assisted cellular networks, the potential benefits, and the detailed
relaying technologies are discussed in Section 1.4. With the basic knowledge, the crucial step
operations of RSs, the reuse pattern among RSs, and the scheduling method of data
transmissions among BSs, RSs, and MSs are important design issues reflecting the system
performance. How RSs effectively and efficiently assist cellular systems has been a topic of
extensive research in both academia and industry.
From the previous literature, however, the performance evaluation of relay-assisted
cellular networks has been mostly done for very specific system scenarios, such as fixed
number of RSs and locations, fixed reuse pattern, or seeking optimal RSs’ positions with a
simplified one-dimensional model. Furthermore, although several works have been done to
evaluate the system performance in some environments which are especially suitable for
deploying RSs such as the Manhattan-like environment, previous research has mostly focused
on the aspects of coverage extension and end-to-end user throughput enhancement.
In this dissertation, we aim to fully investigate a general relay-assisted network in a
multi-cell environment both in the downlink and in the uplink from the information-theoretic
point of view. By jointly considering RSs’ locations, reuse patterns, path selections and
resource allocation, in the downlink, two types of quality of end-user experience (QoE): fixed
bandwidth allocation (FBA) and fixed throughput allocation (FTA), are investigated along
with two path selection methods: spectral efficiency (SE) based and
signal-to-noise-plus-interference ratio (SINR) based; in the uplink part, two performance
measures: average MS’s power consumption and uplink system spectral efficiency, are
optimized.
In addition, from the practical point of view, we aim to evaluate the overall system
capacity enhancement for the relay-assisted network in the Manhattan-like environment with
new scheduling methods proposed for the system where directional antennas are equipped at
Detailed literature review, problem formulation, and optimized solutions corresponding
to each topic will be provided in the following sections.
1.6
Organization of the Dissertation
This dissertation consists of three themes. The first part is to investigate the downlink
performance and optimization of relay-assisted cellular networks in multi-cell environments.
The second part aims to look into the uplink performance and optimization of a relay-assisted
cellular network. The third part studies resource scheduling with directional antennas for
multi-hop relay networks in a Manhattan-like environment.
The rest of this dissertation is organized as follows. In Chapter 2, the adopted system
setups, including multi-cell architecture, relaying technology, propagation models, antenna
configurations, power setting criteria, path selection methods, and frequency reuse patterns
for downlink performance evaluation, are addressed. The joint optimizations based on GA for
maximizing system capacities of different system configurations are proposed. The numerical
results and the summary are then provided and discussed. In Chapter 3, those of system
settings for uplink evaluation are presented. Both the minimization of average MS’s transmit
power and the maximization of uplink system capacity are formulated and solved by the
proposed GA-based algorithm and MAI estimation algorithm. Also, the numerical results of
uplink optimization and the summary are indicated. In Chapter 4, we first show the system
setups and the propagation models adopted for multi-hop relay networks in a Manhattan-like
environment. We propose two efficient resource scheduling methods with directional
Chapter 2
Downlink Performance and Optimization
of Relay-Assisted Cellular Networks in
Multi-cell Environments
In this chapter, we investigate the downlink performance limits of a general relay-assisted
network with optimized system parameters in a multi-cell environment. A genetic algorithm
(GA) based method is proposed for joint optimization of system parameters, including the
number of RSs and their locations, frequency reuse pattern, path selection and resource
allocation so as to maximize the system spectral efficiency. Two types of quality of end-user
experience (QoE), i.e., fixed bandwidth allocation (FBA) and fixed throughput allocation
(FTA), are studied along with two path selection methods, i.e., spectral-efficiency (SE) based
and signal-to-noise-plus-interference ratio (SINR) based. The background, system setups, the
objective function, the proposed optimization algorithm and the numerical results are
2.1
Background
As mentioned in Section 1.5, one crucial step in developing a relay-assisted cellular
network is to fully evaluate its performance from both theoretical and practical points of view.
The setups and the performance of relay-assisted networks have been a topic of extensive
research in both academia and industry [37]-[44].
In [37], a relay-assisted network was studied in a multi-cell environment with six RSs in
a cell, where a frequency reuse scheme over the relaying links was proposed to improve the
system spectral efficiency. In [38], the issues of RS positioning and spectrum partitioning
were investigated with RSs located on the lines connecting BS and the six vertices of a
hexagonal cell. Again, they considered the case of six RSs in a cell. The RSs’ positions were
optimized along the line to maximize the user throughput at cell boundary. In [39], the
performance of a relay-assisted OFDMA network was evaluated for the specific setup of three
RSs in a cell with and without intra-cell resource reuse; numerical results showed that the
relay-assisted network significantly outperforms the conventional cellular network with
respect to system capacity and coverage. Very recently, the IEEE 802.16j multi-hop relay
networks were evaluated in [40]-[44]. In particular, the downlink capacity was simulated in
[40] with one RS or three RSs in a sector for different modes of RS operations, including the
transparent and non-transparent RSs with centralized or distributed scheduling. In [41] the
deployment of RSs for coverage extension was investigated, and in [42], [43], the issue of
placement of BSs and RSs was considered with [42] focusing on the coverage extension
So far, as discussed above, the performance evaluation and optimization of the
relay-assisted cellular networks has been limited to very specific system configurations: with
a fixed number and location of RSs and/or using fixed reuse patterns.
In this chapter, our aim is to investigate the downlink optimization and performance
limits of a general relay-assisted network in a multi-cell environment from an
information-theoretic point of view. Two types of quality of QoE, FBA and FTA, are
explored along with two path selection methods, SE based and SINR based. A GA-based
method is proposed for joint optimization of the system parameters including RS’s positions,
reuse pattern, path selection, and resource allocation among different links to maximize the
system spectral efficiency. The theoretical performance serves as a benchmark. For more
practical relay-assisted cellular networks, where the effects of MCSs and signaling overhead
that enables the RSs’ operation need to be taken into consideration.
2.2
System Setups
This section describes the system setups and parameters we adopt in this work to
evaluate the downlink performance in relay-assisted cellular systems.
2.2.1
Cell configuration
We study a multi-cell network that consists of BSs, fixed RSs, and MSs. Figure 3 is such
an example, where RSs are deployed in the sectors of a sectorized network to improve the
system performance. The cell architecture is described by a three-tuple,
(
Kcluster,Ks ector,Kband)
,where Kcluster, Ks ector, and Kband are the size of the cluster, the number of sectors in a cell,
and the number of frequency bands used in the sectors of a cell, respectively. For example,
be regarded as the design area in which RSs are deployed for performance enhancement. The
BSs of these cells are designated as B ii, = ⋅⋅⋅1, ,K.
Figure 4 (a) is a more detailed layout of a cell, for example, i-th cell, with no
sectorization. The BS is located at the center of the cell, D is the cell radius, Ni RSs are
deployed to improve the cell performance, ri j, is the position vector of the j-th RS, denoted
by Ri j, , and m is the MS's position vector. The MSs are assumed to be uniformly
distributed over the cell region Ωi. The number of RSs can be different from cell to cell in its most general case.
2.2.2
Relaying technology
In this dissertation, we assume the RSs operate in the in-band, homogeneous relaying,
and DF mode which means the RSs decode the received signal first and then forward it to MS
using the same radio technology as the BS in the same frequency band. An MS can
communicate with the BS either through the direct path or the two-hop path (via an RS) that
constitutes the BS-RS and RS-MS links. Two-hop relaying is considered as the most common
scenario in practical applications because of the excessive delay incurred in more than
two-hop relaying. Figure 4 (b) shows a practical downlink radio resource allocation scheme,
where orthogonal radio resources are allocated to the direct and two-hop paths, respectively.
The radio resource for the two-hop path is further divided into two parts: one for the BS-RS
link and the other for the RS-MS link. With this type of resource allocation, RSs are not
Sectors denoted by the same letter use the same frequency. Fixed RS BS 2 Z 3 Z 1 Z 2 Y 3 Y 1 Y 1 X 2 X 3 X 1
Ω
2Ω
Ω
3 1 X 1 X 1 X 1 X 1 X 1 X 1 X 1 X 1 X 1 X 1 X 2 X 2 X 2 X X2 2 X 2 X 2 X 2 X X2 2 X 2 X 3 X X3 3 X X3 X3 X3 3 X 3 X 3 X 3 X 3 X 1 Y 1 Y Y1 1 Y 1 Y 1 Y 2 Y 2 Y Y2 Y2 2 Y Y2 3 Y 3 Y 3 Y Y3 3 Y Y3 1 Z 1 Z 1 Z 1 Z 1 Z 2 Z 2 Z 2 Z 2 Z 2 Z 3 Z 3 Z Z3 3 Z Z3,1 i
R
,2 iR
, i i N R ,1 ir
m
, i Nr
,2 ir
D
MS MS iB
iΩ
,1 im r
−
2.2.3
Propagation Models
The path and shadowing losses are treated separately from the small scale fading. For the
path loss, the line-of-sight (LOS) and non-line-of-sight (NLOS) models for the suburban
macro-cell environment in [29] are adopted; that is
10 ( ) 23.8log ( ) 41.9 dB LOS path L d = d + (2.1) and 10 ( ) 40.2 log ( ) 27.7 dB NLOS path L d = d + (2.2)
where d is the separation (in meters) between the transmitter and the receiver. The LOS
model is used for the BS-RS link because RSs are often mounted over the rooftops, whereas
the NLOS model is for the BS-MS and RS-MS links. Also, the NLOS model is used for the
calculation of MAI.
For the shadowing loss, a simplified model given in (2.3) is adopted mainly for verifying
the effectiveness of the proposed method in a shadowed environment. Some other shadowing
models can be used as well.
dB, if is in a shadowed area ( ) 0 dB, otherwise shadow m L m =δ (2.3)
In particular, the shadowed environment in Figure 5, which consists of 4 obstacles, will
be used in Section 2.5.1.2 for numerical results. In this setup, an MS is said to be in a
shadowed area if the LOS between the BS (RS) and the MS is blocked by an obstacle. No
MS MS BS (dB) shadow L =δ (dB) shadow L =δ RS
2.2.4
Antenna Configurations
RS and MS are equipped with one omni-directional antenna, respectively, whereas
both omni-directional and sectored antenna configurations are investigated for BSs. For the
sectored antenna, the antenna pattern proposed in [59] is adopted, which is
2 3 ( ) min 12 , m dB, dB Aθ θ A θ = − (2.4)
where −180° ≤ ≤θ 180° is the angle between the direction of interest and the bearing direction of the antenna, θ3dB = °70 is the 3-dB beamwidth, and Am =20 is the maximum attenuation.
2.2.5
Power Setting of BS and RS
A pre-specified spectral efficiency (SE) for users at the cell boundary is used for setting
up the transmitted power of a BS and its subordinate RSs. Let S= f
(
SINR)
(in bits per second per hertz, bps/Hz) denote the link SE as a function of average SINR which is definedby 2 1 0 0 ( ) E[ ] SINR= p g Lt t all d gr h N I − ⋅ ⋅ ⋅ ⋅ + , (2.5)
where p is the transmit power spectral density (PSD), t g and t g are the transmit and r
receive antenna gains, respectively, Lall( )d ≐Lpath( )d ⋅Lshadow is the composite effect of the path and shadowing losses in linear scale, h is a complex channel gain due to the small-scale fading, E i
[ ]
denotes the expectation operation, and N0 and I0 are the PSDsof additive white Gaussian noise (AWGN) and MAI, respectively.
For AWGN channels,
(
SINR)
log 1 SINR2(
)
f = + , (2.6)
where h is a constant in (2.5). For fading channels, on the other hand, f
(
SINR)
may not assume a close form as in (2.6) and needs to be evaluated numerically, depending on theconsidered fading characteristics and whether the channel state information is available at
transmitter [60]. In any case, for a specific SE S, the required SINR can be found by
( )
1SINR= f− S .
Let Sedge be the targeted SE for an MS at the cell boundary, the transmit PSD of the BS
is then set as
(
)
edge 0 0 2 1 SINR = watts/Hz ( ) E i i B t all r B M N I p g L− D g h → ⋅ + ⋅ ⋅ ⋅ , (2.7)where SINRedge = f−1
( )
Sedge . Likewise, the transmit PSD ofR
i j, is set as(
)
(
)
, , edge 0 0 2 1 , SINR = watts/Hz - E i j i j R t all i j r R M N I p g L− D r g h → ⋅ + ⋅ ⋅ ⋅ , (2.8)where ri j, denotes the Euclidean distance of the position vector ri j, . Note that with the
power settings in (2.7) and (2.8), the coverage of RSs is entirely within that of the BS. In this setup, RSs are mainly used to improve system capacity, user throughput and to remove
2.2.6
Path Selection
Path selection is a procedure to determine whether the direct path or the two-hop path is
to be chosen by a BS to communicate with an MS. Two types of path selection will be
investigated: SINR based and SE based. For the SINR-based path selection, the direct path is
selected if
( )
{
( )
}
, ,
SINR max SINR
i i j i j B M R M R m m → ≥ →
; otherwise, the two-hop path through Ri k,
is selected, where SINR
( )
i B→M m and
( )
, SINR i j R →M mare the received SINR over the
-MS
i
B and Ri j, -MS links, respectively, and
{
{
( )
}
}
, ,
, arg max SINR i j
i j i k R M R R = → m . Let
( )
i B M S → m ,( )
, i i j B R S → m and( )
, i j R MS → m be the SEs of the Bi-MS, B R , and i- i j,
, -MS
i j
R links, respectively. For the SE-based path selection, the direct-path is selected if
( )
{
,( )
}
, max i i i j i j B M B R M RS → m ≥ S → → m ; otherwise the two-hop path through Ri k, is selected, where
( )
, , , , , , , ( ) ( ) 1 1 1 ( ) ( ) ( ) ( ) i i j i j i i j i i j i j i i j i j B R R M B R M B R R M B R R M S m S m S m S m S m S m S m → → → → → → → → ⋅ = = + + (2.9)is the effective SE of the Bi-Ri j, -MS link [61], and
{
{
( )
}
}
, , , arg max i j i j i k B R M R R = S → → m .
2.2.7
Frequency Reuse over RS-MS Links
In addition to frequency reuse in the co-channel cells, the frequency band for the RS-MS links in a cell can be reused as well, thanks to the spatial separation between RSs. To exploit this advantage, RSs in a cell are divided into L reuse groups, where
, 1, ,
i
pattern can be specified by the set
{ }
, 1 Gi Gi l L l= ∀i ≐ , where{ }
, , G l i l = Ri k is the set of RSs in the l-th group of cell i. Obviously, ,1 = G L i i l l N =
∑
, where Gi l, is the cardinality of the set,
Gi l. The number of reuse groups is the same for all co-channel cells in this study. In its
most general case, some reuse groups in a particular cell may be empty; that is, it contains
no RSs.
2.3
Optimization of System Parameters
In this section, the RSs’ positions and the frequency reuse pattern are jointly optimized
over the design area
1
K i i=
Ω≐
∪
Ω to maximize the system SE, under different QoE criteria and path selection methods.2.3.1
Objective Function
Let TΩ and WΩ be the aggregate throughput and the total allocated bandwidth over the design area Ω, respectively. The system SE SΩ is then defined by
T S W Ω Ω Ω ≐ . (2.10)
Our objective is to search for the optimal set of RSs’ positions ϒ≐
{ }
ri j, and the reuse pattern G≐{ }
Gi so that the SE SΩ is maximized.Two types of QoE criteria will be investigated along with two path selection methods
represent two extremes of QoE criteria, and real systems may lie between these two.
2.3.1.1
Fixed Bandwidth Allocation
In FBA, a fixed downlink bandwidth per unit area wd (in Hz per unit area) is
allocated to an MS. Therefore, , , ( ) ( ) ( ) i i i j i j d B M B R R M w =w → m =w → m +w → m for an MS located at m , where ( ) i B M
w → m is the bandwidth allocated to the Bi →MS link,
, ( )
i i j
B R
w → m to the Bi →Ri j, link, and
, ( )
i j
R M
w → m to the Ri j, →MS link, respectively. Furthermore, the total allocated bandwidth over Ω is calculated by
B M B R R M WΩ =W → +W → +W → , (2.11) where
{
}
max i B M B M i W → = W → , (2.12) , 1 max i i i j N B R B R i j W → W → = = ∑
(2.13) and{
G,}
1 max , 1, , i l L R M M i l W → W → i K = =∑
= ⋅⋅⋅ (2.14)are the aggregated downlink bandwidth allocated to the B→MS,B→R, and R→MS links, respectively. In (2.12)-(2.14), ( ) i i Bi B M m B M W → w → m dA ∈Ω =
∫
, (2.15) , , , ( ) i i j i i j Ri j B R B R m W → w → m dA ∈Ω =∫
, (2.16)and , , , , , G G max ( ) , i l i j R i j i l i j M m R M R W → w → m dA ∈Ω ∈ =
∫
(2.17) where i B Ω and , i j RΩ are the coverage areas of Bi and Ri j, , respectively. Note that given ϒ and the path selection method, the coverage areas of the
i B Ω and , i j R Ω are determined under the power settings in (2.7) and (2.8). In addition, in (2.11), we have used the fact that
the co-channel regions are allocated with the same bandwidth, and thus, the maximum
bandwidth required among the co-channel regions is used in the calculation of the total
bandwidth. Recall that
( )
i B M S → m ,( )
, i i j B R S → m and( )
, i j R MS → m are the SEs of the Bi→MS,
,
i i j
B →R , and Ri j, →MS links, respectively. Using these notations, the throughputs per unit area supported for those links are given by
( ) ( ) ( ) i i i B M B M B M t → m =w → m S ⋅ → m , (2.18) , ( ) , ( ) , ( ) i i j i i j i i j B R B R B R t → m =w → m S ⋅ → m (2.19) and , ( ) , ( ) , ( ) i j i j i j R M R M R M t → m =w → m S ⋅ → m . (2.20)
In addition, the effective throughput
, ( )
i i j
B R M
t → → m for the two-hop path (via R ) is i j,
obtained by
{
}
, ( ) min , ( ), , ( )
i i j i i j i j
B R M B R R M
, , , , ( ) ( ) ( ) ( ) i j i i j i i j i j R M B R d B R R M S m w m w S m S m → → → → = ⋅ + , (2.21) , , , , ( ) ( ) ( ) ( ) i i j i j i i j i j B R R M d B R R M S m w m w S m S m → → → → = ⋅ + (2.22) and , , , , , ( ) ( ) ( ) ( ) ( ) i i j i j i i j i i j i j B R R M B R M d B R R M S m S m t m w S m S m → → → → → → ⋅ = ⋅ + . (2.23)
Using (2.18) to (2.23), the aggregate throughput (in bps) can be calculated as follows.
, G 1 1 i i l K L B i l TΩ T T = = = +
∑
∑
, (2.24) where ( ) i i Bi B m B M T t → m dA ∈Ω =∫
(2.25) and , , , , , G G ( ) i l i i j Ri j i j i l B R M m R T t → → m dA ∈Ω ∈ =∑ ∫
. (2.26)2.3.1.2
Fixed Throughput Allocation
In FTA, a targeted downlink throughput per unit area t (in bps per unit area) is d
supported for an MS, no matter where it is located. To achieve this, the bandwidth allocation for the direct path is
( ) ( ) i i d B M B M t w m S m → → = . (2.27)
For the two-hop path via Ri j, , from Lemma 2 in the Appendix, the best bandwidth
allocation is to make , ( ) , ( ) i i j i j B R R M d t → m =t → m =t . As a result, we get , , ( ) ( ) i i j i i j d B R B R t w m S m → → = (2.28) and , , ( ) ( ) i j i j d R M R M t w m S m → → = . (2.29)
By substituting (2.27) – (2.29) into (2.15) – (2.17), respectively, the aggregate bandwidth can be calculated as in (2.11). Furthermore, in this case,
1 i K d m i TΩ t dA ∈Ω = =
∑∫
(2.30)Note that WB→M , WB→R and WR→M in (2.12) – (2.14) are derived under the assumption of a fully-loaded system, that is, there is one user per unit area. In practice, a radio resource allocation, as illustrated in Figure 4 (b), can subsequently be done depending on how many users are to be supported in a cell. Let Wreq be the bandwidth required to
support a total of Nuser users in a cell. For FBA, Wreq =Nuser⋅Wd, where W (Hz) is the d