On the Spectral Efficiency and Energy Efficiency of the Cloud Radio Access Network Architecture

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2017 On the Spectral Efficiency and Energy Efficiency of the Cloud Radio Access Network Architecture

Ghods, Fatemeh

Ghods, F. (2017). On the Spectral Efficiency and Energy Efficiency of the Cloud Radio Access Network Architecture (Unpublished doctoral thesis). University of Calgary, Calgary, AB. doi:10.11575/PRISM/27196 http://hdl.handle.net/11023/4104 doctoral thesis

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On the Spectral Eﬃciency and Energy Eﬃciency of

the Cloud Radio Access Network Architecture

Fatemeh Ghods

A THESIS

SUBMITTED TO THE FACULTY OF GRADUATE STUDIES

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE

DEGREE OF DOCTOR OF PHILOSOPHY

GRADUATE PROGRAM IN ELECTRICAL AND COMPUTER ENGINEERING

CALGARY, ALBERTA

SEPTEMBER, 2017

c Fatemeh Ghods 2017 Abstract

Providing support for high consumer data traffic and maintaining high system efficiency are key requirements of the fifth generation (5G) wireless network design. The high costs associated with the widespread installation of the network base stations (BSs) and spectrum acquisition makes them impractical for accommodating the high traffic load. What is more, the continuous operation of the BSs also has a significant consequence in causing elevated levels of carbon dioxide (CO2) emissions. To meet the key requirements of high spectral efficiency (SE), maintain low levels of cost, and high energy efficiency (EE), cloud-radio access network (cloud-RAN) has been proposed as a promising architectural solution. Moreover, new waveforms (e.g., filter bank multicarrier (FBMC)) have been suggested as alternatives to the traditional orthogonal frequency division multiplexing (OFDM) to satisfy the astounding growth in the traffic load. This thesis aims to enhance capacity and reduce the network power consumption. First, the effect of cooperative transmission in combination with the cloud-

RAN architecture on network-level achievable data rate along with EE and SE is studied.

Mathematical tools from stochastic geometry are utilized, to analytically characterize SE and EE. Moreover, the ability to increase the power savings is investigated by incorporating a tunable downlink distance-based fractional power control (D-FPC) mechanism into the cloud-RAN architecture. Using tools from stochastic geometry, the network-level coverage probability and EE are examined. Second, the throughput reliability/SE/EE of a cloud-

RAN incorporating the D-FPC mechanism along with cooperative joint transmissions is analyzed by adopting a stochastic geometry-based approach. Lastly, taking into account feasibility of two-fold data rate improvement within FBMC waveform, this thesis studies and experimentally examines FBMC waveform to evaluate this new waveform and compares it with OFDM waveform. Moreover, the linearity requirements of power ampliﬁer (PA) using memoryless and memory polynomial digital predistortion (DPD) techniques are also

ii examined through a very nonlinear PA (Doherty) and a moderately linear PA (Class AB) to explore the behavior of OFDM and FBMC signals. Overall, this thesis provides critical insights to the cloud-RAN system designer for selecting appropriate architectural approach and waveform to achieve desired performance regarding energy, spectral, and PA eﬃciency.

iii Acknowledgments

I would like to start oﬀ by praising and thanking God, whom by his grace I am here today.

Secondly, I would like to express my sincere gratitude to my research supervisor Prof.

Abraham O. Fapojuwo and my research co-supervisor Prof. Fadhel M. Ghannouchi for believing in me and providing invaluable guidance and relentless support throughout this research. I appreciate all their contributions of time, ideas, and funding to make my Ph.D. experience productive and stimulating. My sincere thanks also goes to Prof. Mohamed

Helaoui, and Dr. Andrew K. Kwan for their scientiﬁc advice and knowledge and many insightful discussions and suggestions. Furthermore, I am grateful to the thesis examiners:

Prof. Laleh Behjat, Prof. Vassil Dimitrov, Prof. Majid Pahlevani, Prof. Roshdy Hafez, for their time and eﬀort to evaluate the thesis and for for their insightful comments and encouragement. In particular, I am grateful to Prof. Laleh Behjat for her continuing support.

I am extremely grateful to my family: my parents, my sisters and brothers, and my sisters/brothers in law for their love, prayers, and sacriﬁces for educating and preparing me for my future.

I thank my entire fellow labmates in Wireless Networking Research Laboratory and iRa- dio Laboratory for the stimulating discussions, their support and all the fun we have had in the last four years. Thanks you, Dr. Kasun Hemachandra, Ismail Kamal, Dr. Kazi

Ashrafuzzaman, Dr. Jaya Rao, Dr. Xiaobin Yang, Dr. Mayada Younes, Mohsin Aziz,

Isaac Osunkunle, Jonathan Kwan, Hai Wang, Okechukwu Ochia, Simon Windmuller, Akash

Melethil, and Dr. Maryam Jouzdani.

Last but not the least, my thanks go to all the people who have supported me to complete the research work directly or indirectly.

iv To My Life-Coaches, My Parents I owe it all to you

v Table of Contents

Abstract ...... ii

Acknowledgments ...... iv

Table of Contents ...... vi

List of Figures ...... x

List of Tables ...... xii

1 Introduction ...... 1

1.1 Context and Motivation ...... 1

1.2 Problem Statement ...... 4

1.3 Objectives and Contributions ...... 6

1.4 Thesis Outline ...... 7

2 Literature Review ...... 9

2.1 Adopted Mathematical Tool and Waveform ...... 9

2.1.1 Stochastic Geometry Tool for Analyzing cloud-RAN Performance . . 9

2.1.2 FBMC Waveform ...... 10

2.2 Cooperative Transmission/Power Control for SE/EE improvement ...... 13

2.2.1 Cooperative Transmission Mechanism for SE enhancement ...... 14

2.2.2 Power Control Mechanism for EE enhancement ...... 15

2.2.3 Present Thesis Compared to the Related Works on Cooperative Transmission/

Power Control Method ...... 16

2.3 FBMC and OFDM-based Research Works ...... 19

2.3.1 Present Thesis Compared to the FBMC and OFDM-based Related

Works ...... 21

3 Energy Eﬃciency and Spectral Eﬃciency of cloud-RAN Incorporating Power

Control or Cooperative Transmission ...... 23

vi 3.1 Introduction ...... 23

3.2 Incorporating Cooperative Transmissions ...... 24

3.2.1 Downlink System Model ...... 24

3.2.2 Performance Analysis ...... 28

3.2.3 Numerical and Simulation Results with Discussion ...... 31

3.3 Incorporating Distance-Based Power Control ...... 33

3.3.1 Downlink System Model ...... 33

3.3.2 Distance-Based Fractional Power Control ...... 34

3.3.3 Performance Analysis ...... 35

3.3.4 Numerical and Simulation Results with Discussion ...... 39

3.4 Summary ...... 43

4 Throughput Reliability Analysis of cloud-RAN Networks Incorporating Power

Control along with Cooperative Transmission ...... 44

4.1 Introduction ...... 44

4.2 Downlink System Model ...... 45

4.2.1 Cooperation Model ...... 45

4.2.2 Spectrum Allocation ...... 46

4.2.3 Power Control Model ...... 46

4.3 Throughput Reliability Analysis ...... 47

4.3.1 Throughput Reliability Results ...... 48

4.3.2 Per-user Achievable Average Throughput ...... 52

4.4 EE and SE Analysis ...... 53

4.4.1 Cloud-RAN Energy Eﬃciency ...... 53

4.4.2 Cloud-RAN Spectral Eﬃciency ...... 55

4.5 Numerical and Simulation Results with Discussion ...... 56

4.6 Summary ...... 64

vii 5 5G Signaling/Evaluation ...... 65

5.1 Introduction ...... 65

5.2 Filter Bank Multi Carrier Waveform ...... 66

5.3 Digital predistortion ...... 67

5.4 Power Ampliﬁer Behavioral Modeling ...... 69

5.4.1 Memoryless Model ...... 70

5.4.2 Memory Polynomial Model ...... 70

5.5 Evaluation Metrics ...... 71

5.5.1 PAPR ...... 71

5.5.2 ACPR ...... 72

5.5.3 EVM ...... 72

5.6 Signal Generation ...... 73

5.7 Power Ampliﬁer Characterization Setup ...... 74

5.8 Experimental Results and Discussion ...... 75

5.8.1 EVM and ACPR Results before applying DPD ...... 76

5.8.2 EVM and ACPR results with DPD ...... 78

5.9 Summary ...... 84

6 Conclusions ...... 85

6.1 Major Research Findings ...... 85

6.2 Thesis Conclusions ...... 87

6.3 Engineering Signiﬁcance of the Thesis Findings and Conclusions ...... 87

6.4 Thesis Limitations and Future Directions ...... 88

Bibliography ...... 92

A3 Appendices to Chapter 3 ...... 106

A3.1 Derivation of Average Achievable Rate (General Case) ...... 106

A3.2 Derivation of Average Achievable Rate (Special Case) ...... 107

viii A3.3 Derivation of Optimal RRH Density (Special Case) ...... 108

A3.4 Coverage Probability Derivation ...... 109

A4 Appendices to Chapter 4 ...... 111

A4.1 PROOF of Proposition 4.1 ...... 111

A4.2 PROOF of Proposition 4.4 ...... 114

ix List of Figures and Illustrations

1.1 The cloud-RAN architecture ...... 3

2.1 OFDM transmitter versus FBMC transmitter [1] ...... 10

2.2 FBMC spectrum overlap 2 − 4 versus OFDM spectrum ...... 12

2.3 FBMC overlap 4 frame versus OFDM frame ...... 13

3.1 An illustrative cloud-RAN architecture...... 27

3.2 Per user average achievable rate versus RRH density for diﬀerent numbers of

cooperative RRHs (K = 1, 2, and 3)...... 32

3.3 Spectrum Eﬃciency vs. RRH density for diﬀerent numbers of cooperative

RRHs (K = 1, 2, and 3)...... 33

3.4 Energy Eﬃciency vs. RRH density for diﬀerent numbers of cooperative RRHs

(K = 2, and 3)...... 34

−3 2 3.5 Unconditional coverage probability vs. SIR threshold (λ = 1×10 RRHs/m ,Rcell = 15 m)...... 41

3.6 The per user average achievable rate vs. cell radius (λ = 1 × 10−3 RRHs/m2) 42

−3 2 −3 2 3.7 EE vs. cell radius (λ = 1 × 10 RRHs/m , λu = 2 × 10 users/m ) . . . . 43

4.1 Throughput reliability for 6 RRH operational scenarios vs. SIR threshold

−3 2 (λ = 1 × 10 RRHs/m ,Rc = 50 m)...... 58 4.2 Throughput reliability vs. cluster radius (λ = 1 × 10−3 RRHs/m2, θ =

2.716 nats/sec (or T = 11.5 dB)) ...... 59

4.3 Per user average rate vs. RRH Density (Rc = 50 m) ...... 60

4.4 Energy Eﬃciency vs. RRH density (Rc = 50 m, = 0.5 (HFPC)) ...... 62

4.5 Spectrum Eﬃciency vs. RRH density (Rc = 50 m, = 0.5 (HFPC)) . . . . . 63

5.1 Typical power and eﬃciency behavior of a power ampliﬁer ...... 68

x 5.2 Predistortion schematic ...... 69

5.3 Graphical deﬁnition of the ACPR...... 72

5.4 Graphical deﬁnition of the error vector...... 73

5.5 Narrow band FBMC ...... 74

5.6 a) block diagram of the measurement setup for Class AB PA, b) Class AB

measurement setup...... 76

5.7 a) block diagram of the measurement setup for Doherty PA, b) Doherty PA

measurement setup...... 77

5.8 the PAPR CCDF of original signals in dB for both 64-QAM and QPSK mod-

ulation schemes...... 78

5.9 The EVM of the OFDM and FBMC signals versus IPBO including AM-AM

characteristics; a) measured by Class AB PA, b) measured by Doherty PA. . 79

5.10 The frequency spectra of FBMC overlap 4; a) measured by Class AB PA, b)

measured by Doherty PA...... 82

5.11 The EVM and ACPR of the OFDM and FBMC signals after applying predis-

tortion. a) measured by Class AB PA, b) measured by Doherty PA. . . . . 83

xi List of Tables

2.1 Frequency domain prototype ﬁlter coeﬃcients ...... 11

2.2 Diﬀerences and similarities between the network resource management tech-

niques and network performance analysis metrics/tools investigated in this

thesis and selected related works in the literature...... 18

2.3 Diﬀerences and similarities between the evaluation metrics/tools and DPD

techniques investigated in this thesis and selected related works in the literature. 22

4.1 The assumed parameters values ...... 57

xii List of Symbols

α ...... Path loss exponent h ...... Rayleigh fading channel power gain

N ...... AWGN power

ϕ ...... Location of RRHs

λ ...... Density of RRHs

λu ...... Density of users

λopt ...... Optimal density of RRHs

...... Power control coeﬃcient

pmax ...... RRH maximum transmit power

pmin ...... Predeﬁned minimum received power for acceptable communication

Pi ...... Transmit power of cooperating RRH i

Pj ...... Transmit power of interfering RRH j

Ptot,RRH ...... Total power consumed per RRH

p0 ...... RRH consumed power at the minimum non-zero output power per transceiver chain p0 ...... The transmit power by an RRH to a user at any location inside the RRH

coverage area

Pout ...... RF output power

xiii Pin ...... RF consumed power

PDC ...... DC power

P AE ...... Power-added eﬃciency

ηD ...... Drain eﬃciency

∆ ...... Slope of the load-dependent power consumption

NTRX ...... Number of transceiver chains

Nu ...... Number of users in an RRH coverage area

K ...... Random number of RRHs in a cluster

B ...... Total spectrum available to each cluster b ...... Per user bandwidth

A1, ..., AK . . . . . Locations of RRHs in the cluster A

Rcell ...... Radius of RRH

Rc ...... Radius of a cluster

r1 = r ...... Distance of the typical user to its nearest RRH in its associated cluster

ri ...... Distance between a cooperating RRH i and the desired user (for i ∈ {2, 3,...,K})

Rj ...... Distance between an interfering RRH j outside of the cluster and the typical

user (for j ∈ ϕ\{A1, ..., AK })

xj ...... Distance between an interfering RRH j and its own user within RRH j’s coverage area

R ...... Achievable rate

xiv R¯ ...... Average achievable rate

Pcov ...... Coverage probability

I ...... Inter-cluster interference

T hrReliab . . . . . Throughput reliability

θ ...... Throughput threshold

T ...... SIR threshold

xv List of Abbreviations

ACLR ...... Adjacent Channel Leakage Ratio

ACPR ...... Adjacent Channel Power Ratio

AM/AM . . . . . AMplitude-to-AMplitude

AM/PM . . . . . AMplitude-to-Phase

AWGN ...... Additive White Gaussian Noise

BBU ...... BaseBand processing Unit

BER ...... Bit Error Rate

BS ...... Base Station

CAPEX ...... CAPital EXpenditure

CCDF ...... Complementary Cumulative Distribution Function cloud-RAN . . Cloud-Radio Access Network

CO2 ...... Carbon dioxide

CP ...... Cyclic Preﬁx

DC ...... Direct Current

D-FPC ...... Distance-based Fractional Power Control

DPD ...... Digital PreDistortion dB ...... decibel dBc ...... decibel below the main carrier power

xvi EE ...... Energy Eﬃciency

EVM ...... Error Vector Magnitude

FBMC ...... Filter Bank MultiCarrier

FPC ...... Fractional power control

Full PC ...... full Power Control

4G ...... Fourth Generation

5G ...... Fifth-Generation

H-C-RAN . . . . Heterogeneous Cloud-RAN

HetNets ...... Heterogeneous networks

HFPC ...... Half Power Control

IFFT ...... Inverse Fast Fourier Transform

IPBO ...... Input Power BackOﬀ

LTE ...... Long-Term Evolution

LUT ...... Look-Up Table

MAC ...... Media Access Control

MHCP ...... Matern Hard-Core Point process

MP ...... Memory Polynomial

No PC ...... No Power Control

OFDM ...... Orthogonal Frequency Division Multiplexing

xvii OFDMA . . . . . Orthogonal Frequency Division Multiple Access

OOB ...... Out Of Band

OPEX ...... OPerational EXpenditure

OQAM ...... Oﬀset Quadrature Amplitude Modulation

PA ...... Power Ampliﬁer

PANC ...... Power Ampliﬁer Nonlinearity Cancellation

PAPR ...... Peak to Average Power Ratio pdf ...... probability density function

PPP ...... Poisson Point Process

PSD ...... Power Spectral Density

QoS ...... Quality of Service

RF ...... Radio Frequency

RRH ...... Remote Radio Head

SE ...... Spectral Eﬃciency

SINR ...... Signal-to-Interference-plus-Noise Ratio

SIR ...... Signal-to-Interference Ratio

UE ...... User Equipment

VSA ...... Vector Signal Analyzer

VSG ...... Vector Signal Generator

GPIB ...... General Purpose Interface Bus

xviii Chapter 1

Introduction

1.1 Context and Motivation

The drastic growth rate in recent usage of smart-phones and tablets has led to a dramatic in-

crease in global mobile data traﬃc. For example, 2014 had close to 30-fold increase in global

mobile data traﬃc in comparison to the traﬃc in the entire global Internet in 2000 [2].

Hence, in response to this issue, work is ongoing in both industry and academia towards

developing the ﬁfth-generation (5G) wireless standard, aiming at 20 Gbps peak data rate at

106/km2 device density [3]. While the widespread installation of the network base stations

(BSs) can support the increasing data traﬃc demands, it comes at a great expense in CAP- ital EXpenditure (CAPEX) and OPerational EXpenditure (OPEX) [4]. What is more, the continuous operation of the BSs also has a signiﬁcant consequence in causing high levels of carbon dioxide (CO2) emissions, accentuated by the fact that cellular networks are a major energy consumer.

On one hand, recent statistics indicate that the demand for information and communications technology contributes up to 2% of the global energy consumption and 2% in CO2 emissions [5], hence the need for energy-efficient communication in telecommunication networks. On the other hand, the increase in the rate of data traffic has consistently outpaced the rate of growth in new spectrum acquisition. Hence there is a considerable amount of interest to boost the spectral efficiency (SE) performance significantly.

The cloud-radio access network (cloud-RAN) architecture is considered as a network innovation on the road to 5G wireless networks. It provides capacity enhancement to meet the dramatic increase in data traﬃc demands [6, 7]. As an emerging technology, it has a high potential to reduce the energy consumption and to increase the network capacity using

1 centralized processing and distributed antenna units [8,9]. As indicated in [4], and [10], the centralized processing makes more sense in data-centric infrastructure, and therefore cloud-

RAN beneﬁts from centralized processing of signals from the distributed remote radio heads

(RRHs), increasing the feasibility of having a cheaper deployment. It has been reported in [7] that the cloud-RAN architecture can provide up to 70% savings in the OPEX merely due to moving the cooling operation from the individual BSs to the centralized processing units. Moreover, in comparison with the traditional long-term evolution (LTE) network, cloud-RAN saves 10 to 15% of CAPEX [11].

As shows in Figure 1.1, the cloud-RAN is composed of the centralized baseband processing units (BBUs), distributed RRHs, and high-speed, low latency optical ﬁber links in the fronthaul that interconnect BBUs and RRHs. BBUs undertake the baseband processing and resource allocation tasks, serving as virtual BSs and, referred to as cloud. Each RRH com- prises the transceiver and antennas that transform the baseband signal to radio frequency

(RF) signal which is transmitted to the users [12]. The high-speed optical ﬁber links in the fronthaul which can support low latency and high bandwidth communications, both of which are critical for the fast and timely processing performed at the BBUs resulting in network capacity enhancement [12].

Indeed, cooperative transmission within a cloud-RAN architecture potentially brings the next performance leap to solve the capacity crunch problem caused by the exponential growth in mobile data traﬃc. Cooperative transmission not only enhances the network achievable rate but also mitigates network interference resulting in less energy consumption and improved spectrum utilization. Aside from this, it is feasible to achieve higher savings in energy by tuning the RRH transmit power within a cloud-RAN. In this regard, a distance-based fractional power control (D-FPC) mechanism is taken into account in this thesis. Adjusting an RRH transmit power by the distance between the RRH and a typical user is a viable solution to realize major improvement in energy eﬃciency (EE) of cloud-RANs.

2 BBU pool = cloud

Fiber fronthaul Links BBU1

BBU4 BBU2

BBU3

Base Band Unit (BBU) BBU Remote Radio Head (RRH) User Equipment Wireless Link

Figure 1.1: The cloud-RAN architecture

Moreover, for the future 5G networks, new waveforms have been proposed as alternatives to the orthogonal frequency division multiplexing (OFDM) to achieve higher data rate (eg.

filter bank multicarrier (FBMC), generalized frequency division multiplexing (GFDM), and universal filtered multi-carrier (UFMC)). Despite the OFDM’s advantages as the de facto waveform standard in wireless networks [13–15] for the past two decades [16], its drawbacks led to the considerable amount of interest in new waveforms. The insertion of cyclic prefix

(CP) to mitigate intersymbol interference and its spectral leakage in neighboring sidebands

(known as out of band (OOB) emission), induces a loss of the SE in OFDM–based systems.

Filter bank multicarrier (FBMC) is a major candidate waveform for 5G [16]. Its good concentrated frequency localization caused by using prototype filters [17] significantly reduces the OOB emission. Besides, FBMC does not require CP but instead uses offset quadrature

3 amplitude modulation (OQAM) along with ﬁlter bank leading to the higher data rate and, thus, boosted SE [18]. Instead of ﬁltering across the full frequency band as done in OFDM,

FBMC filters on a per subcarrier basis, providing an excellent control for the filter bank and emission of subcarriers. Indeed, the choice of the prototype filter differentiates FBMC from

OFDM. If adopted, FBMC would serve as an evolution of OFDM that is likely to coexist with OFDM [16].

Collectively, the increase in data traﬃc requirement along with the growth in global power consumption underscores the need to achieve high EE in cellular networks in addition to the

SE. To this end, the use of cooperative joint transmissions by the RRHs and the downlink power control technique in the cloud-RAN architecture is expected to address the SE and

EE crunch problem. As such, not only energy is utilized more efficiently due to power control, but the spectrum is also used more efficiently as evidenced by the improvement in achievable data rate and mitigation of interference. Moreover, using offset quadrature amplitude modulation along with filter bank in FBMC waveform improves data rate.

1.2 Problem Statement

The main problem addressed in the thesis is how to increase the SE (to cater for the increasing data traﬃc demand) and EE (to reduce the OPEX and achieve a clean environment) by utilizing the cloud-RAN architecture. While enhancing the SE and EE performance beneﬁts the network operator, it is equally important that the performance improvement achieved does not compromise the user’s quality of service (QoS). Currently, cloud-RAN is work-in-progress as a network architecture which requires more in-depth investigations to fully understand its capabilities and limitations. While there has been fairly large body of work on the performance of heterogeneous and homogeneous cellular networks, the performance analysis of cloud-RANs architecture need more indepth study. Furthermore, the existing cloud-RAN studies lean towards enhancing the performance by using optimization

4 techniques, such as ﬁnding optimal RRH placement, fronthaul capacity, and BBU processing of resources to ensure EE [12,19]. Thus, the works addressing the impact of multiple cloud-

RAN operating conditions/parameters on SE and EE performance have been few and far between, as most of the investigations are typically done for a speciﬁc cloud-RAN operating condition/parameter.

Thus, this thesis tackles the problem of assuring user’s QoS in cloud-RANs, considering the cloud-RAN operating conditions of RRH cooperation or RRH power control or both.

The QoS metric is the per user achievable throughput (i.e. achievable data rate) and the probability that the achievable throughput exceeds a speciﬁed throughput threshold, referred to as throughput reliability in this thesis, is derived. Knowledge of the throughput reliability enables the calculation of the per user achievable average rate which, in turn, is used for computing the EE and SE. The thesis adopts a stochastic geometry-based approach which incorporates interference mitigation via cooperative joint processing or power control or both of them, to enhance the SE and EE performance in cloud-RANs. Under the settings considered, cooperation and power control enable the RRHs to be opportunistically operated by the interference and load conditions such that both the SE and EE are maintained at a high level at all times.

Also, the proposal for the FBMC waveform for use in 5G networks with the goal of improving data rate is still in its infancy, and many issues are still open, especially experimental performance analysis of FBMC waveform is still lacking in the literature. However, most of the existing works on FBMC waveform are focused on theoretical or simulation analysis of this new waveform and they lack clear insights on FBMC characteristics and the DPD impacts on the quality of received FBMC signals that can be achieved by experimental in- vestigation. Thus, this thesis also experimentally examined FBMC waveform to understand its capability and limitation as an alternative to OFDM to address the problem of increasing data rate demand in cellular networks, especially cloud-RAN.

5 1.3 Objectives and Contributions

This thesis develops a stochastic geometry based analytical approach for calculating the throughput reliability of a cloud-RAN comprising randomly distributed RRHs and randomly located users. Cooperative joint transmission by the RRHs and a tunable distance-based

RRH transmit power control mechanism are employed to achieve power savings and high throughput reliability. The analytical result for the throughput reliability serves as input to the analysis of per-user achievable average rate and cloud-RAN network-level performance metrics of SE and EE. The analytical results are validated by Monte Carlo simulation results with good agreement, thus conﬁrming the accuracy of the developed analytical approaches.

Moreover, to meet high data rate demands, FBMC as a promising candidate waveform for 5G and as alternatives to the traditional OFDM waveform is examined in this thesis.

Thus, this thesis investigates FBMC signals comprising memoryless and memory polynomial

DPD techniques to achieve highly eﬃcient PA and simultaneously satisfy user’s QoS. The experimental approach is used to evaluate this new waveform considering diﬀerent values of the overlapping factor, selected in the range from one to four and then comparing its performance against that of the traditional OFDM through the adjacent channel power ratio

(ACPR) and the error vector magnitude (EVM) metrics.Besides, because the power ampliﬁer

(PA) is considered as the most energy ineﬃcient component of a wireless transmitter, it is an essential requirement to design a PA that maintains linearity while operating at high power eﬃciency. The linearity requirements of PAs using memoryless and memory polynomial digital predistortion (DPD) techniques is also studied in this thesis. A very nonlinear PA

(Doherty) and a moderately linear PA (Class AB) are used to investigate the behavior of

OFDM and FBMC signals regarding the ACPR and the EVM.

Speciﬁcally, the contributions of this thesis are sixfold:

• Analytical derivation of achievable average rate/throughput/coverage probability in

cloud-RAN:

6 – Derivation of analytical results for the achievable average rate under RRH cooperation

(chapter 3)

– Derivation of analytical results for the coverage probability and achievable average

rate under D-FPC (chapter 3)

– Derivation of analytical results for throughput reliability, achievable average rate, and

throughput under RRH cooperation along with D-FPC (chapter 4)

• Analytical derivation of the SE and EE in a cloud-RAN:

– Derivation of analytical results for the SE and EE under RRH cooperation (chapter 3)

– Derivation of analytical results for the EE under D-FPC (chapter 3)

– Derivation of analytical results for SE and EE under RRH cooperation along with

D-FPC (chapter 4)

• Derivation of analytical results for the optimal RRH density that maximizes the EE in

a cloud-RAN under RRH cooperation (chapter 3)

• Recommendation of minimum acceptable input power backoﬀ (IPBO) for FBMC and

OFDM signals regarding EVM, under the case study (chapter 5)

• Comparing FBMC signals performance with OFDM signal regarding the ACPR and

EVM metrics measured by Class AB PA (chapter 5)

• Experimental results for the ACPR and EVM in FBMC signals under memoryless and

memory polynomial DPD schemes measured by Doherty PA (chapter 5)

1.4 Thesis Outline

This thesis is organized into six chapters and several appendices. Chapter 2 presents a review of the previous works related to each of the problems that are mentioned in this thesis. Applying a stochastic geometry-based approach, in chapter 3, the eﬀect of cooperative

7 transmission or D-FPC in combination with the cloud-RAN architecture on network-level achievable data rate/coverage probability is studied. Followed by EE/SE analysis for downlink transmissions in cloud-RAN architecture. Then, the signiﬁcance of the analytical results via numerical results and their interpretation are presented.

Chapter 4 also adopts a stochastic geometry-based approach to evaluate the eﬀects of cooperative RRH transmission along with tunable power control mechanism on per user achievable throughput and the probability that the achievable throughput exceeds a speciﬁed throughput threshold. Then, presents an analytical derivation of EE and SE, followed by numerical and simulation results and discussion, where interference mitigation that results from cooperation and power control enhances the SE and EE performance in cloud-RAN.

The FBMC waveform examined in chapter 5, where the linearity requirements of PA by memoryless and memory polynomial DPD is studied. Then, the performance of the FBMC signals with different values of overlapping factor, in the range from one to four, is evaluated regarding ACPR and EVM. Moreover, FBMC and OFDM are compared regarding peak to average power ratio (PAPR), ACPR, and EVM. Finally, chapter 6 concludes the thesis with statements on the research findings and their significance along with the limitations and potential research directions for the future.

8 Chapter 2

Literature Review

2.1 Adopted Mathematical Tool and Waveform

2.1.1 Stochastic Geometry Tool for Analyzing cloud-RAN Performance

The stochastic geometry is an emerging analysis framework that enables tractable analysis of wireless network performance on a wide scale [20–23]. It is a branch of applied probability that models the location of the network BSs and users as the spatial point process,

(e.g., poisson point process (PPP) or the matern hard-core point process (MHCP)) [24,25].

Distinct from the Wyner models [26,27], stochastic geometry enables to incorporate channel models (e.g., small scale fading and large scale path loss) along with the probabilistic nature of the media access control (MAC) layer behavior into a single framework. In the Wyner model, the user locations are ﬁxed [27] and only one or two interfering cells are considered, which result in total interference of single random variable with some distribution like a log-normal [28]. Distinct from the stochastic geometry, some other models considered interference from interferers with the same distance, which is far from reality [28]. These models including Wyner model cannot capture the essential aspects of cellular networks, whereas stochastic geometry includes random user locations and fading [27].

Both theoretical [29–32] and empirical [33,34] studies justify the accuracy of using PPP for modeling the location of the network BSs which result in wide use of PPP model in the cellular networks [35–37]. For analytically modeling the remote radio heads (RRHs) spatial distribution, this research will employ the PPP because of its analytical tractability in deriving closed form expressions for key network performance metrics [20, 33]. However, other special point processes like MHCP can be considered to avoid existence of overlapping

9 points which can happen in PPP. Moreover, due to the random spatial distribution of the

RRHs and users, the analytic development of cloud-RAN performance in this research will be based on the stochastic geometry framework, to model interference, capture the location of RRHs and analyze the coverage probability by averaging over all potential geometrical patterns [22].

2.1.2 FBMC Waveform

Figure 2.1 shows a general overview of ﬁlter bank multicarrier (FBMC) transmitter compared to orthogonal frequency division multiplexing (OFDM) transmitter. However, FBMC like

OFDM divides the spectrum into orthogonal sub-bands, and performs ﬁltering for each subcarrier. Moreover, despite OFDM that needs cyclic preﬁx (CP) to avoid interference, in

FBMC there is no need for CP due to use of the oﬀset quadrature amplitude modulation

(OQAM) modulation along with ﬁlter bank [18].

Cyclic Input IFFT Channel Prefix

a) OFDM transmitter

Digital Input IFFT Channel Filters

Filter Bank

b) FBMC transmitter

Figure 2.1: OFDM transmitter versus FBMC transmitter [1]

In digital communications, symbols are affiliated with pulse shapes that show the density of symbol energy in time or frequency domain [38]. Using prototype filters (modified filter

10 Table 2.1: Frequency domain prototype ﬁlter coeﬃcients

Overlap factor Prototype ﬁlter coeﬃcients 1 1 2 1, −0.707 3 1, −0.911438, 0.411438 4 1, −0.97196, 0.707, −0.235147 design for a particular application) enables very good concentrated frequency localization [17] in FBMC waveform, which results in reduced OOB emission in FBMC compared to OFDM.

In FBMC, by utilizing filter bank results in redesigned of the waveform with a very small sideband (caused by good frequency localization) [39] and very short ramp-up and ramp- down [40]. In FBMC, prototype filters are characterized by the overlapping factor, in the range from one to four, that obtained by applying table 2.1 frequency-domain coefficients to design prototype filter [41]. The FBMC overlapping factor implies the number of multicarrier symbols that overlap in the time domain, equivalent to the number of frequency coefficients that are used between the FFT filter coefficient in the frequency domain [41].

As illustrated in Figure 2.2, OFDM has a signiﬁcant OOB emissions compared to FBMC overlap 3, and 4. This means eﬃcient use of allocated spectrum can be achieved in FBMC signals and can be feasible to occupy spectral holes for spectrum-sensing applications like cognitive radio.

This research used the European union seventh framework program of physical layer for dynamic spectrum access and cognitive radio (EU FP7 PHYDYAS) project’s FBMC which is generated by using the Nyquist ﬁlter as it shown in [39]. Figure 2.3 compares OFDM and

FBMC overlap 4 frames in the time domain, as an example. The generation of OFDM and

Figure 2.2: FBMC spectrum overlap 2 − 4 versus OFDM spectrum

FBMC transmit signal X(t), are represented in (2.1) and (2.2), respectively [16].

+∞ υ−1 X X 2πj(t−nT )/T X(t) = Sq[n]p(t − nT )e n=−∞ q=0 t − T/2 p(t) = Π( ) ∗ h(t) T   (2.1) t 1, if |t| ≤ T/2, Π( ) = T  0, otherwise π πt t − T /2 h(t) = sin( )Π( 0 ) 2T0 T0 T0 where Sq[n] is a complex-valued symbol transmitted on the qth subcarrier and at the instant nT . p(t) is obtained by convolving rectangular pulse Π(.) of width T and half-sine wave of width T0 (roll-oﬀ period). h(t) is the impulse response of the ﬁlter, υ is the number √ of subcarriers, and j = −1. The OFDM symbol period is denoted by T , and ∗ denotes

12 TFFT

CP Symbol 1 CP Symbol 2

a) OFDM

Symbol 1. I

Symbol 1. Q

TFFT/2 Symbol 2. I

Symbol 2. Q

b) FBMC

Figure 2.3: FBMC overlap 4 frame versus OFDM frame convolution. +∞ υ−1 X X X(t) = Aq[n]H(t − nT/2) n=−∞ q (2.2)

j(q+n)π/2 jπqt/T Hq(t) = H(t)e e where Aq[n] is a real symbol transmitted on the qth subcarrier and at the instant nT . H(t) is a prototype ﬁlter impulse response. Here, data symbols are spaced at T/2 along the time axis. Moreover, (ej(q+n)π/2) implies the phase shift which is equivalent to zero when q + n is an even number and is π/2 for other values. Hence, in FBMC the orthogonality is achieved by using half-symbol space delay between the in-phase (I) and the quadrature

(Q) components of QAM symbols with half-Nyquist pulse shapes which is known as oﬀset quadrature amplitude modulation (OQAM).

2.2 Cooperative Transmission/Power Control for SE/EE improvement

The deﬁnition of cooperative transmission means joint transmission by all RRHs in a cluster to the desired user, whereas power control means tuning transmit power. The concept of cooperative transmission/power control has been used in traditional cellular networks by the

13 previous researchers to enhance the outage probability performance. This Section reviews the works in literature and compares them with the work done in the present thesis.

2.2.1 Cooperative Transmission Mechanism for SE enhancement

The performance improvement achievable via cooperative transmission in cellular networks has been previously analyzed using various techniques, based on new insights into mitigating inter-cell interference and reducing outage probability. Using the stochastic geometry framework, reference [42] analyzed the outage probability of a cellular network where a group of

BSs inside a cluster area cooperatively transmits to a user equipment (UE) located near the cluster edge or cluster center. To alleviate high interference at the UEs near the cluster edge, the frequency subchannels assigned to the cluster edge BSs are diﬀerent than those assigned to the cluster-interior BSs. Besides, reference [42] uses the channel inversion power control policy at each BS. The work by Tanbourgi et al. [43] also adopted the stochastic geometry tool to characterize the signal-to-interference-plus-noise ratio (SINR) distribution at a typical user in a traditional cellular network with non-coherent joint-transmissions by cooperating

BSs, considering cooperating mechanisms of user-centric clustering and channel-dependent cooperation activation. The key insights from [43] are that BS cooperation improves the

SINR gain, which is better at large path loss exponent, and the SINR outage probability decreases exponentially with increasing BS density. The cooperative transmission concept is implicit in cloud-RANs, and its impact has been studied in the literature. Ha et al. [12] developed optimal and low-complexity algorithms that minimize the total transmission power of cooperative RRHs in a cloud-RAN under the constraints of processing power at the BBUs, fronthaul capacity, and required QoS of users. Two related problems were solved iteratively: fronthaul constrained power minimization problem and power and fronthaul capacity trade- oﬀ problem, with the goal of determining the RRHs that can cooperatively and eﬃciently transmit to the users with the requested service.

14 2.2.2 Power Control Mechanism for EE enhancement

Previous studies have been conducted on power control of wireless networks. The authors in [44] introduced a fractional power control model that demonstrates a trade-off between transmitting at fixed power and channel inversion. But as noted by the authors, channel inversion of exponentially distributed channel power gain (i.e. Rayleigh distributed channel amplitude gain) is undefined. Auer et al. [45] proposed a linear power consumption model where power consumption of different BS types (Macro, RRH, Micro, Pico, Femto) is obtained experimentally. Recently, a linear and parameterized component-based power model for cloud-RAN is introduced in [46], where the authors claim 33.3% power saving in cloud-RAN is due to 87.4% power reduction in the cooling system.

Previous studies have also been conducted on power control and energy efficiency (EE) of cloud-RANs. The authors in [19] analyzed the EE expressed in Joules − per − bit, of cloud-RAN under specified QoS constraints, accounting for the circuitry energy consumption. Besides, [19] determined the optimal size (radius) of the cooperating region at which the energy consumed per bit is minimized. Liu and Lau [47] tackled the problem of optimal joint power and antenna selection to achieve energy-efficient large distributed multiple input, multiple output (MIMO) cloud-RANs. It is shown that the capacity of a very large distributed

MIMO cloud-RAN scales according to the order of a factor equal to the product of the number of users, path loss exponent, and logarithm of the number of antennas [47]. The transmit power in the uplink and downlink must be controlled to avoid signiﬁcant interference, maximize system capacity and EE. Currently, there are very few power control algorithms to adapt to the centralized management structure of the cloud-RANs [48]. The authors in [48] proposed a power allocation algorithm for uplink transmissions in cloud-RANs, where the proposed algorithm is applied to solving a capacity optimization problem. Liu el al. [49] proposed algorithms for the joint wireless power control and fronthaul rate allocation in the uplink that maximize the throughput in orthogonal frequency division multiple access

15 (OFDMA)-based cloud-RAN. The proposed joint optimization algorithms exhibit signiﬁcant performance gain relative to individually optimizing wireless power control or fronthaul rate allocation.

2.2.3 Present Thesis Compared to the Related Works on Cooperative Transmission/Power

Control Method

Compared to the works above, this thesis exhibits similarities. The present work is similar to [12, 42, 43] regarding RRH (or multicell) cooperation, and studies the power control and

EE of cloud-RANs as in [48,49] and [19,47], respectively. Concerning the analysis tool, this thesis adopts the stochastic geometry framework for cloud-RAN performance analysis, the same tool as used in [42,43] for the SE performance analysis of traditional cellular networks with multicell cooperation. This research distinguishes from the above previous works in six respects. First, the present thesis analyzes the throughput reliability, EE, and SE of cloud-RANs when applying RRH cooperation/power control policy and a combination of them. While [47–49] also involve cooperation and power control, their analysis focus is on the system-level performance metrics of SE and sum-rate [49], sum-rate [47], and system capacity [48] whereas this thesis addresses in a holistic manner both the user-level and network-level performance metrics of throughput reliability, and EE and SE, respectively.

Second, unlike [48] and [49] that focused on the uplink transmissions, the current thesis studies the downlink transmissions with a goal to reduce the RRH transmission power thus increasing network EE and simultaneously enhancing the user data rate; this somewhat conflicting objective is achieved through joint RRH cooperation and power control. Third, this research adopts a pre-defined distance-based power control policy and studies its impact on cloud-RAN performance. The works [47–49] determine the transmission power as a solution to the formulated resource allocation problem, without explicit specification of a power control policy as done in this thesis. Fourth, unlike [44], this research adopts a D-FPC mechanism, which is applicable to any distribution of distance. Fifth, distinct from [45, 46]

16 that propose a power model to realize the amount of power used in wireless networks and cloud-RAN, this thesis investigates a D-FPC mechanism to calculate the amount of possible energy saving in the cloud-RAN. Finally, to manage the analysis complexity arising due to the combined RRH cooperation and power control, this thesis studies the single input, single output cloud-RAN to determine the throughput reliability, EE and SE, diﬀerent from [47] that studied the maximum average weighted sum-rate of MIMO cloud-RAN.

Table 2.2 lists the main diﬀerences and similarities between the network resource management techniques and network performance analysis metrics and tools investigated in this thesis and those in the literature.

17 Table 2.2: Diﬀerences and similarities between the network resource management techniques and network performance analysis metrics/tools investigated in this thesis and selected related works in the literature.

Net. Resource Network Performance Analysis Mgmt. Tech. Analysis Metrics Tool Network Power Rate/ Thr. EE/ Coop. Control Capacity Reliab. Tx. Power SE SG Opt. Downlink Thesis Cloud-RAN Yes Yes Yes Yes Yes Yes Yes Yes Downlink Total [12] Cloud-RAN Yes No Yes No Tx. Power No No Yes Uplink [19] Cloud-RAN No No No No EE No No Yes

[42] Cellular Yes No Coverage No No Yes Yes Yes

[43] Cellular Yes No SINR No No Yes Yes Yes Wireless [44] Network No Yes Outage No No No Yes No Wireless [45] Network No No No No EE No No No

[46] Cloud-RAN No No No No Yes No No No Downlink MIMO [47] Cloud-RAN No No Yes No Yes No No Yes Uplink [48] Cloud-RAN No Yes Yes No No No No Yes Uplink [49] Cloud-RAN No Yes No Yes No Yes No Yes

18 2.3 FBMC and OFDM-based Research Works

Currently, FBMC waveform as an emerging technology requires more indepth study to understand its capabilities and limitations. While the majority of existing works are focused on theoretical or simulation analysis of FBMC [50–56], only a limited number of them investigate it experimentally [57]. Hence, these works lack clear insights on the FBMC characteristics as well as clear understanding of the DPD impacts on FBMC signals passed through PAs, in the real world.

The performance of FBMC waveform as one of the 5G candidate waveforms has been studied recently by previous researchers especially in comparison to OFDM waveform. Adopt- ing baseband amplitude clipping using Bussgang noise cancellation (BNC) [58], reference [50] reduced peak to average power ratio (PAPR) of the OFDM and FBMC with the overlapping factor of four. Simulation results for transmitting over additive white Gaussian noise

(AWGN) and Rayleigh fading channels reveal that FBMC outperforms OFDM regarding bit error rate (BER) with and without clipping. Bouhadda et al. [51] studied the eﬀect of PA and nonlinear distortion caused by memoryless PA on the BER of OFDM and FBMC signals.

A polynomial approximation was developed to calculate BERs of the diﬀerent PA models.

However, analytical and simulation results show similar BER performance for both OFDM and FBMC signals in the case of amplitude distortion, but OFDM outperforms FBMC in the event of phase distortion due to FBMC’s signiﬁcant sensitivity to nonlinear distortion. The authors in [59] studied the impact of nonlinear distortion caused by memoryless PA on the spectral performance achieved by narrowband FBMC signal compared to that of OFDM.

The experimental results show FBMC has better spectral containment and better Notch power ratio (NPR) than OFDM in high IPBO.

The concept of predistortion has also been conducted to compensate for nonlinear am- pliﬁed OFDM and FBMC signals. The authors in [52] applied two diﬀerent DPD techniques to overcome distortion in OFDM and FBMC signals. Simulation results exhibit that pre-

19 distortion works better for OFDM than FBMC. However, by separately predistorting phase and amplitude distortions, FBMC shows the same performance as OFDM, where the performance is evaluated by computing symbol error rate (SER). The impact of predistortion on the BER performance of FBMC signal was also investigated in [53]. Modeling in-band nonlinear distortion by a complex gain and nonlinear noise, authors proposed an iterative technique named PA nonlinearity cancellation (PANC) as DPD method to remove the noise distortion for memoryless PA. The authors in [60] also proposed a ﬂexible and low complexity DPD model for non-continuous FBMC transmissions which linearized a particular range of frequency. Simulations exhibit 15 dB adjacent channel power ratio (ACPR) improvement in FBMC signal by using their frequency optimized DPD method. The work by

Gebremicael et al. [57] also compared OFDM and FBMC signals by investigating dual band

RF input signals with 1 MHz FBMC, 10 MHz FBMC and 10 MHz OFDM passed through the PA. Experiments were performed to analyze the impact of OFDM and FBMC signals’ characteristics on the PA’s behavioral model concerning memory depth, nonlinear order, crest factor, and adjacent channel leakage ratio (ACLR) enhancement by applying memory polynomial DPD. Recently, Bulusu et al. [54] declared that LTE–like FBMC systems on nonlinear devices could coexist with professional mobile radio (PMR) and public protection and disaster relief (PPDR) as in linear devices under the condition of having suitable PAPR.

Whereas, LTE–based OFDM system fails in the similar situation. The authors in [55] predict power spectral density (PSD) regrowth of FBMC systems using nonlinear memoryless Saleh’s

PA model. Based on cumulants, a polynomial approximation on amplitude-to-amplitude

(AM/AM) and amplitude-to-phase (AM/PM) distortion characteristics are presented to predict spectral regrowth of FBMC systems. The authors claim that predicting PSD regrowth is vital to overcoming spectrum localization lost in FBMC caused by PA nonlinearity.

Previous studies have also examined the role of overlapping factor in FBMC–based systems. Using simulation, [56] analyzed the impact of FBMC overlapping factor on system

20 complexity and sideband spectrum leakage of the staggered multi tone modulation systems.

Simulation results reveal that overlapping factor of four shows the best sideband suppres- sion (three–fold better than OFDM with four–fold complexity degradation as compared to

OFDM). Also, the authors claim that increasing overlapping factor results in a decrease in sideband.

2.3.1 Present Thesis Compared to the FBMC and OFDM-based Related Works

Compared to the above works, this research displays similarities, complements some of the works, and provides further insights related to predistortion of FBMC signals from linearity, spectral eﬃciency and power eﬃciency perspectives of the wireless transmitters. Similar to [50,57,59,60] this work compares OFDM and FBMC signals regarding ACPR and studies the impact of FBMC overlapping factor as in [57]. Concerning DPD techniques, this thesis accounts for memoryless and memory–based DPD as in [51–53, 55, 59] and [52, 57, 60].

This research differentiates from the related works cited in four aspects. First, both memoryless and memory polynomial DPD purport to investigate the memory effects along with nonlinearity on both FBMC and OFDM signals. Second, unlike [50–56, 60] that generate or evaluate FBMC and OFDM signals by simulations or theoretical approach, this thesis like [57, 59] experimentally investigates FBMC and OFDM signals using a wide band test bench that includes two amplifiers: a mildly nonlinear class AB amplifier and strongly nonlinear Doherty amplifier. While [57, 59] also involve experimental results, their focus is on the dual band FBMC signal concerning ACPR, and the narrow band (1MHz) FBMC signal regarding spectral performance, respectively, whereas the current thesis adopts DPD techniques to study the impact of overlapping factor in single wide band FBMC signals.

Moreover, in addition to ACPR, error vector magnitude (EVM) is calculated, and the eﬀect of PA mean input power is addressed. Third, the impact of diﬀerent PA IPBO on EVM is studied in this thesis. Finally, distinct from the works above which determine BER and SER as in [50,51,53] and [52], or ACPR as in [50,57], in this research both the ACPR and EVM

21 are computed for OFDM and FBMC signals with diﬀerent overlapping factors before and after applying DPD. Table 2.3 summarizes the main diﬀerences and similarities between the performance metrics and tools used in this thesis and those in the literature.

Table 2.3: Diﬀerences and similarities between the evaluation metrics/tools and DPD techniques investigated in this thesis and selected related works in the literature.

Evaluation Evaluation DPD Metrics Tools Techniques Waveform BER/ Anal./ ACPR EVM SER Exper. Simu. ML MB Single wide band Thesis FBMC Yes Yes No Yes No Yes Yes OFDM & [50] FBMC Yes No Yes No Yes No No OFDM & [51] FBMC No No Yes No Yes Yes No OFDM & [52] FBMC No No Yes No Yes Yes Yes

[53] FBMC No No Yes No Yes Yes No

[54] FBMC No No No No Yes No No

[55] FBMC No No No No Yes No No OFDM & [56] FBMC No No No No Yes No No Dual band [57] FBMC Yes No No Yes No No Yes Narrow band [59] FBMC Yes No No Yes No No No OFDM & [60] FBMC Yes No No No Yes Yes No

22 Chapter 3

Energy Eﬃciency and Spectral Eﬃciency of

cloud-RAN Incorporating Power Control or

Cooperative Transmission1

3.1 Introduction

The use of cooperative transmission in combination with the cloud-RAN architecture is expected to offer the much sought after relief to address the explosive growth in data traffic due to offsetting interference by the gain in the received signal power from cooperation.

Thus, the eﬀect of cooperative transmission on network-level achievable data rate along with

EE and SE for downlink transmissions in cloud-RAN architecture is studied in this chapter.

Moreover, the cloud-RAN along with power control mechanism can potentially offer additional energy reduction (i.e. each RRH radiates just the minimum power required for quality communication based on its distance to each user). Thus, a tunable D-FPC mechanism is also considered in this chapter and its effects on network-level coverage probability, along with EE of cloud-RAN are studied. Specifically, this chapter’s contributions are:

• Analytical derivation of achievable average rate in cloud-RAN under RRH cooperation.

• Derivation of analytical results for SE and EE with cooperating RRHs in a cloud-RAN.

1The content of this chapter has generated two papers: – Published as a conference paper [61], F. Ghods, A. O. Fapojuwo, and F. M. Ghannouchi, En- ergy efficiency and spectrum efficiency in cooperative cloud radio access network, in 2015 IEEE Pacific Rim Conference on Communications, Computers and Signal Processing (PACRIM), Aug 2015, pp. 280-285. – Published as a conference paper [62], F. Ghods, A. O. Fapojuwo, and F. M. Ghannouchi, Energy efficiency analysis of a C-RAN with distance-based power control, in 2017 IEEE 30th Canadian Conference on Electrical and Computer Engineering (CCECE), April 2017, pp. 1-5.

23 • Derivation of analytical results for the optimal RRH density that maximizes the EE

in a cloud-RAN under RRH cooperation.

• Analytical results for the coverage probability and achievable average rate in a cloud-

RAN under D-FPC.

• Analytical results for the EE in a cloud-RAN under D-FPC.

The rest of this chapter is organized as follows. Section 2 describes the cloud-RAN model incorporating cooperative transmissions, where all the network model assumptions are stated.

Then, analysis of SE and EE is presented and the signiﬁcance of the analytical results via numerical results and their interpretation are demonstrated. In Section 3 the cloud-RAN model assumptions incorporating D-FPC are stated. Followed by analysis of the coverage probability and achievable average rate and EE in a cloud-RAN under D-FPC. Then, a comparison of simulation results using D-FPC is presented and discussed. Finally, the chapter is concluded in a summary Section.

3.2 Incorporating Cooperative Transmissions

3.2.1 Downlink System Model

As the cloud-RAN operating conditions of RRH cooperation and RRH transmit power control are of interest in this work, the cloud-RAN downlink system model developed in this chapter is on the radio access segment of cloud-RAN. Transmissions in the downlink (i.e. from RRHs to users) are studied where each RRH is equipped with one antenna and each

UE also has a single antenna (i.e. single input, single output downlink transmission model is studied). The radio access segment is governed by the assumptions listed in the following two subsections which include the common assumptions used for both cooperative transmission and power control in all the thesis’s chapters and the assumptions that are peculiar to cooperative transmission.

24 3.2.1.1 Common Assumptions in both Cooperative Transmission and Power Control

3.2.1.1.1 Network architecture

The cloud-RAN architecture consists of the distributed RRHs and the centralized BBUs.

Each RRH is equipped with one antenna, for simplicity and not to dilute the gains of

centralized processing with that of multiple input multiple output technology, where multiple

antennas are used. The locations of the RRHs are distributed over the cloud-RAN service

area as a PPP denoted by ϕ with intensity λ. The PPP is assumed for analytic tractability,

consistent with previous works, e.g. [20,63,64]. The RRH maximum transmit power is pmax. To represent the worst case analysis, all RRHs are assumed to be active with at least one user

to serve in their respective coverage areas which, for analytic tractability, is also assumed to

be circular in shape with radius Rcell for simplicity (a more precise model is consideration of Voronoi cell but this results in major analytical complications [28]). The locations of users

are assumed to be distributed over the cloud-RAN service area as a PPP with intensity λu. However, based on the fact that the PPP distribution becomes a uniform distribution in a bounded area [37], users are uniformly distributed across the RRH coverage area.

3.2.1.1.2 Radio Channel Model

The channel is modeled by a distance-dependent path loss and small-scale fading. Similar to [33], large-scale shadow fading is neglected as it is assumed to be overcome with slow

−α power control. The distance dependent path loss is modeled by ri , where α is the path loss

exponent and ri is the distance between the desired user and RRH i. The small-scale fading amplitude (envelope) is assumed to be Rayleigh distributed, and thus h, the Rayleigh fading

channel power gain (i.e. amplitude squared) is an exponentially distributed random variable

with unit mean. In addition to path loss and small-scale fading, AWGN is considered whose

power is symbolized by N.

3.2.1.1.3 Multiple Access Technique

The multiple access technique for resource allocation is assumed to be the orthogonal fre-

25 quency division multiple access (OFDMA), the de facto access technique in the current

4G standards. OFDMA is assumed as the spectrum allocation scheme for the cloud-RAN.

For the OFDMA-based cloud-RAN considered in this work, the total available spectrum is

divided into a ﬁnite number of equal bandwidth subcarriers.

3.2.1.2 Assumptions Speciﬁc to Cooperative Transmission

3.2.1.2.1 Cooperation Model

Partitioning the cloud-RAN service area into cluster areas, the cooperation model consists

of joint transmission by all the RRHs in a cluster to the desired user. For a cluster of radius

2 Rc, the random number of RRHs in the cluster is denoted by K (E[K] = πλRc ), where

A1, ..., AK are their respective locations in the cluster area. Due to the cooperative joint transmission by the RRHs in the cluster, the received signal power by a user in the cluster is the coherent sum of the power received from all the cooperating RRHs. Without loss of generality, the desired user is located at the origin of a cluster area. In Figure 3.1 a simplified network architecture is depicted where six different distances are shown which are defined as follows:

• r1 = r: distance of the typical user to its nearest RRH in its associated cluster.

• ri: distance between a cooperating RRH i and the desired user (for i ∈ {2, 3,...,K}).

• Rj: distance between an interfering RRH j outside of the cluster and the typical user

(for j ∈ ϕ\{A1, ..., AK }).

• xj: distance between an interfering RRH j and its own user within RRH j’s coverage area.

• Rcell: cell radius.

• Rc: cluster radius.

26 BBU pool

x3 x 2

BBU1 R

R 2

Fiber fronthaul r2 Links BBU BBU r 4 2 User R R4 1

c 3 R r x Rcell 1 x BBU 4 3

Cluster A Base Band Unit (BBU) BBU Remote Radio Head (RRH)

User Equipment

Figure 3.1: An illustrative cloud-RAN architecture.

For illustration, cluster A, the cluster of interest, in Figure 3.1 contains three cooperating

RRHs which jointly and coherently transmit to the desired user. Figure 3.1 shows four RRHs which are located outside of cluster A belonging to some other clusters in the service area.

These RRHs are potential sources of inter-cluster interference to all the users in cluster A.

3.2.1.2.2 Centralized Processing Model

Each cluster of cooperating RRHs has its own associated BBU for resource and interference management. For example, to avoid intra-cluster interference, the BBU refrains from assigning the same frequency channel to parallel transmissions in the cluster. Thus, potential interference to the desired user comes from all the simultaneous transmissions by the RRHs located outside of the cooperating cluster.

The multiple access technique for resource allocation is assumed to be the OFDMA as mentioned in Section 3.2.1.1.3. The total spectrum available to each cluster is denoted by

B divided among the fully utilized subchannels. The subchannels are equally allocated to

27 the users within the RRH coverage area. Hence, the average number of users per RRH

λu coverage area, denoted by E[n], is calculated by E[n] = λ , and the per user bandwidth (b) is determined by: B b = (3.1) E[n] × K

3.2.2 Performance Analysis

3.2.2.1 Average Achievable Rate

By the Shannon law [65], the achievable rate (R) by a user located at a certain distance to

its serving RRH within the RRH coverage area is given by: R =4 b ln[1+SINR] where SINR

is the received signal-to-interference plus noise ratio at the user, consequence of the assumed

downlink transmission.

Theorem 1: For the cloud-RAN system conﬁguration shown in Figure 3.1, the per user

average achievable rate (R¯) is given by:

1) General Case: (general with respect to α, λ, K, Pi, and N)

Z Z ∞ −xN ¯ −πλr2 e 2/α 2/α R = b e exp(−(xPi) πλς) × (1 − exp(−(xPi) πλ(t − ς))) dx 2πλr dr r>0 x=0 x (3.2)

where Pi and Pj represent the transmit power of cooperating RRH i and interferer RRH

2y1−α/2 2 2 −α/2 2π csc(2π/α) j, respectively. In (3.2), ς = α−2 2F1 1, 1 − α ; 2 − α ; −y and t = α , where

Rc 2 2F1 (., .; .; .) the Gauss hypergeometric function, y = ( 1/α ) , and csc(x) is the Cosecant (xPj ) of x. From (3.2) it is feasible to increase the achievable rate as the RRH density increases

or as the per user bandwidth increases due to direct proportionality between R¯ and λ, and

also R¯ and b.

Proof: Provided in Appendix A3.1.

2) Special Case: Interference limited (i.e. N = 0), ﬁxed transmit power Pi = Pj = pmax, for all i and for all j, and α = 4

¯ 0.5 2 R = % Γ(0, pmax π λ/2) (3.3)

28 2 ∞ πλRc R z−1 −ι where 0 < << 1,% = 2b(e −1), Γ(z, t) = ι=x ι e dι is the upper-incomplete gamma function. From (3.3), the per user average achievable rate R¯ has a linear relationship with the per user bandwidth b and a nonlinear relationship with the RRH density λ. It implies that increasing both b and λ will improve R¯ due to the feasibility of associating higher bandwidth to each user and stronger received power gained from cooperation, respectively.

Proof: Provided in Appendix A3.2.

3.2.2.2 Network Spectrum Eﬃciency

The network SE is calculated as a ratio of the total network average achievable rate to the total bandwidth utilized as: λ × R¯ SE = u (3.4) B

1) Special Case: Interference limited (i.e. N = 0), ﬁxed transmit power Pi = Pj = pmax, for all i and for all j, and α = 4

%λ Γ(0, p0.5 λ/2) SE = u max (3.5) B

From (3.5), since SE is a scaled version of R¯, the SE like R¯ has a nonlinear relationship with the RRH density λ. Also, the SE has a linear relationship with user density λu because from 3.4, increasing λu will improve the total network average achievable rate and so that enhances the SE.

3.2.2.3 Network Energy Eﬃciency

The network EE is calculated as a ratio of the total network average achievable rate to the total power consumed by the network. This Section adopts the linear approximation for total power consumed per RRH (Ptot,RRH ) consisting of consumed power at the minimum non- zero output power (p0) per transceiver chain plus RF output power (Pout) can be determined by [45]: Ptot,RRH = NTRX p0 + ∆Pout where ∆ is the slope of the load-dependent power consumption and NTRX is the number of transceiver chains. Mathematically, the EE is

29 given by: λ × R¯ EE = u (3.6) λ × (NTRX p0 + ∆Pout)

1) Special Case: Interference limited (i.e. N = 0), ﬁxed transmit power Pi = Pj = pmax, for all i and for all j, and α = 4

%λ Γ(0, p0.5 λ/2) EE = u max (3.7) λ(NTRX p0 + ∆Pout)

It is seen from (3.7) that, by increasing the RRH density, there is an increase in the EE.

However, the network power consumption also increases with λ resulting in EE degradation.

Hence, there exists an optimum RRH density for which the EE is maximum.

3.2.2.4 Energy Eﬃciency Maximization

A single objective optimization is studied in order to ﬁnd the optimal RRH density that maximizes the EE. The EE maximization problem is formulated as follows:

Maxλ EEλ (3.8) s.t λ > 0 where EE is given by (3.7).

1) Special Case: Interference limited (i.e. N = 0), ﬁxed transmit power Pi = Pj = pmax, for all i and for all j, and α = 4

The optimal RRH density for the interference limited scenario with a ﬁxed RRH transmit power and α = 4, is calculated by setting the ﬁrst derivative of EE in (3.7) with respect to

λ to zero and solving for : √ 2 3 4 c c − 12c c + 3c2 + 4c2 2 4 √ 1 3 4 2 λopt = 3 (3.9) 6 4 c1c4

µ 3µ$2 $2 µ 2 3 where c1 = 4 − 8 , c2 = µ + 2 − $µ, c3 = 2 (g + 1) + $, c4 = (27c1 + 2c2 − 9c1c2c3 + p 2 3 2 3 2 1/3 0.5 2 4(−c2 + 3c1c3) + (27c1 + 2c2 − 9c1c2c3) ) , $ = 0.5 pmax π , g = −(0.577216+ln($)), µ =

2 πRc .

Proof: Provided in Appendix A3.3.

30 Substituting c1, c2, c3, c4, in (3.9) and then substituting the result into 3.6 shows that the optimal EE depends on the cluster radius Rc and RRH transmit power (they appeared in the terms µ and $, respectively). In essence, a network operator can maximize EE of a cloud-RAN by an appropriate choice of cluster radius and RRH transmit power setting.

3.2.3 Numerical and Simulation Results with Discussion

In this Section, numerical results are presented using the analytical expressions in Section

3.2.2. The assumed network parameter values are speciﬁed as follows: B = 10MHz, λu = 3 × 10−3 users/m2 (to be appropriate for the chosen λ), α = 4 (any α > 2 is applicable), pmax = 20 W = 43 dBm, and Ptot,RRH = 503.2 W (is chosen based on the experimental result in [45]) for 1 antenna, 1 carrier, tri-sectored RRH coverage area (NTRX = 3). Furthermore, N = 0, hence only interference limited case is considered such that SINR ≈ SIR, the signal to interference ratio. Results are obtained for networks with cooperating and non-cooperating

RRHs operational scenarios as follows:

• with no cooperation (K = 1).

• with two cooperating RRHs (K = 2).

• with three cooperating RRHs (K = 3). where centralized processing is enabled for the two cooperating scenarios. Figure 3.2 shows the per user average achievable rate as the RRH density increases, for the three operational scenarios considered. Increasing the RRH density (i.e. deploying a higher number of RRHs) results in average rate enhancement because the gain in the received signal power from the cooperating RRHs far outweigh the increase in the interference level. The result shows that up till λ equals to 0.1, 0.2, and 0.3 RRHs/m2 (for the scenarios K equals to 1, 2, and 3 respectively) leads to an improvement in the average rate. However, beyond those values the average rate starts to decrease meaning the interference is so large to oﬀset any gains

31 from cooperation. It also demonstrates that RRHs beneﬁts from cooperation up to a higher

density (i.e.λ = 0.2 RRHs/m2 for K = 2) than having no cooperation (λ = 0.1 RRHs/m2).

Figure 3.3 depicts the SE performance for diﬀerent RRH density for the cooperating

(K = 2, 3) and non-cooperating (K = 1) operational scenarios. As expected, from (3.4) the SE exhibits a similar behavior as the per user average achievable rate but weighted by a constant scaling factor. It is seen that increasing the RRH density increases the total achievable rate and, hence, the SE performance but this is to a certain extent because, for each operational scenario, the SE performance tends to decrease as the RRH density becomes large, consequence of increased interference. As expected, comparing the results for the operational scenarios shows that it is possible to realize twofold improvement in the

SE using cooperation due to an increase in the received signal power. Figure 3.4 illustrates

x 109 2 K = 1 K = 2 1.5 K = 3

0.5

Average Achievable Rate (Nps) 0 0 0.1 0.2 0.3 0.4 0.5 RRH Density (λ)(m−2)

Figure 3.2: Per user average achievable rate versus RRH density for diﬀerent numbers of cooperative RRHs (K = 1, 2, and 3).

the EE for the operational scenarios of having and not having cooperation. Note that,

using (3.7), increasing the RRH density improves the average achievable rate but at the

same time it increases the network power consumption along with increasing the number

of interferers thus resulting in degraded EE performance after a certain λ value (λ equals

to 0.05, 0.1, and 0.2 RRHs/m2 for the scenarios K equals to 1, 2, and 3, respectively from

Figure 3.4). As shown in Figure 3.4, there is an optimal value of RRH density at which the

32 )

−2 0.5 K = 1 0.4 K = 2 K = 3

0.3

0.2

0.1

Spectrum Efficiency (Nps/Hz/m 0 0 0.1 0.2 0.3 0.4 0.5 RRH Density (λ)(m−2)

Figure 3.3: Spectrum Eﬃciency vs. RRH density for diﬀerent numbers of cooperative RRHs (K = 1, 2, and 3).

EE is maximum for each operational scenario, which can also be found by solving (3.9) for the cooperating scenarios. Furthermore, comparing the cooperating and non-cooperating scenarios reveals that cooperation beneﬁts from intra-cluster interference mitigation and subsequent SIR enhancement, consequently resulting in improved EE performance. Hence, up to three-fold improvement in EE is achievable via cooperation. Worthy to mention, comparing Figure 3.3 and Figure 3.4 performance degradation will happen in denser RRH deployment for EE than SE. That is due to increase in the network power consumption by employing more RRH results in faster decrease in EE performance.

3.3 Incorporating Distance-Based Power Control

3.3.1 Downlink System Model

The cloud-RAN architecture consists of two major parts: the centralized BBUs and the radio access segment comprising a set of RRHs that the available spectrum is equally divided among them. The radio access segment is governed by the assumptions listed in

Section 3.2.1.1.

33 x 104 4 K = 1 K = 2 3 K = 3

1 Energy Efficiency (Nats/J) 0 0 0.1 0.2 0.3 0.4 0.5 RRH Density (λ) (m−2)

Figure 3.4: Energy Eﬃciency vs. RRH density for diﬀerent numbers of cooperative RRHs (K = 2, and 3).

3.3.2 Distance-Based Fractional Power Control

For the downlink transmission model, it is assumed that all the RRHs utilize the distance-

α proportional fractional power control (D-FPC) model given by ri where is the power

control coeﬃcient, ∈ [0, 1] [44, 66] and ri is the distance between an RRH i and its user. The D-FPC is a technique that assigns transmit power based on the distance between an

RRH and its users. D-FPC maximizes EE as it mitigates total interference power and minimizes network power consumption. Let pmax and pmin denote the maximum transmit power by an RRH and the predeﬁned minimum received power for acceptable communication, respectively. By D-FPC, the transmit power of RRH j is given by [67]:

pmin α pj = pmax( ) ri 0 < ri ≤ Rcell (3.10) pmax

where the value = 0 means no power control, where pmax is assigned to all the RRHs regardless of their distance to their users. The value = 1 means full power control (Full PC)

where minimum transmit power is allocated to all RRHs. Fractional power control (FPC) is

achieved when lies in the range 0 < < 1 [44], which means transmit power will lie between

p Rα the minimum and maximum power. Thus, the R value should satisfy min cell < 1 based cell pmax α on the fact that pminRcell < pmax.

34 Next, using the considered D-FPC, the transmit power p0 of RRH j to its typical

0 R Rcell 1− α 2r user at any location inside the RRH j’s coverage area is p = pminpmaxr 2 dr = 0 Rcell 2p p1− min max Rα . The ratio 2r is the probability density function (pdf) of the user locations 2+α cell Rcell in the sample RRH coverage area, which follows from the assumed uniform distribution of the user locations in the sample RRH coverage area.

3.3.3 Performance Analysis

In this Section prelude to the EE analysis, the coverage probability and the achievable average rate are derived, where the latter serves as a foundation to analyze network EE.

Speciﬁcally, two special cases are analyzed, as follows:

• Case 1: Interference limited (i.e. N = 0), half fractional power control or HFPC

(i.e. = 0.5) and α = 4.

• Case 2: Interference limited (i.e. N = 0), Full PC (i.e. = 1) and α = 4.

Due to the random spatial distribution of the RRHs and users, the stochastic geometry

tool is used to analyze the coverage probability by averaging over all potential geometrical

patterns [22].

3.3.3.1 Coverage Probability

The coverage probability is the probability that the received SINR (or SIR when the system

is interference limited) at the typical user at distance r from its closest serving RRH exceeds

a speciﬁed SINR or SIR threshold T , denoted by Pcov = Pr(SINR > T |r) or (Pcov = Pr(SIR > T |r)).

1) General Case: (general with respect to , α, and N) Under D-FPC, the general formula

for Pcov is determined as:

Pcov = Pr(SINR > T |r) = exp(−ηN − πλδ) (3.11)

35 2 2 2 α(1−) pmax where δ = (2ωR /(α − 2)) 2F1(1, 1 − ; 2 − ; −ω), η = T r ( ) /pmax, ω = cell α α pmin 2T α(1−) r ρ , ρ = , and 2F1(., .; .; .) is the Gauss-hypergeometric function. α+2 Rcell

Proof: Provided in Appendix A.3.4. Using (3.11) with N = 0, the SINR becomes signal to interference ratio (SIR) and the conditional coverage probability has a negative exponential proportionality to δ which in turn is a function of T . As T increases, less number of transmissions can achieve the SIR threshold (T ).

The expressions for Pcov for Case 1 and Case 2 are:

πλT ρ2T P = exp(− R2 ρ2 F (1, 0.5; 1.5; − )), Case 1 (3.12) cov 2 cell 2 1 2

πλT T P = exp(− R2 F (1, 0.5; 1.5; − )), Case 2 (3.13) cov 3 cell 2 1 3

2 z By using the identity 2F1(1, 0.5; 1.5; −(tan z) ) = tan z [68], eq.15.1.5], (3.12) and (3.13) respectively become:

2p 2 p 2 Pcov = exp(−πλr T/(2ρ ) arctan ρ T/2), Case 1 (3.14)

2 p p Pcov = exp(−πλRcell T/3 arctan T/3), Case 2 (3.15)

By invoking the approximation arctan(x) ≈ x [16, eq.4.4.42] for small values of x, (3.14) and (3.15) can be approximated by:

2 Pcov ≈ exp(−πλr T/2), Case 1 (3.16)

2 Pcov ≈ exp(−πλRcellT/3), Case 2 (3.17)

where the approximation is valid for small values of SINR threshold T (where its typical value in practice is around zero dB [69]) and/or when the normalized distance of the typical user to its closest RRH is much less than unity.

36 Considering (3.16), in HFPC the conditional coverage probability depends on the distance

r and T , while, in Full PC the conditional coverage probability depends on the distance Rcell and T . The reason is, in Full PC all RRHs transmit at the minimum transmit power which is deﬁned based on the Rcell value to achieve the minimum acceptable received power, so as to cover the edge users. Whereas, in HFPC, RRH transmit power is a fraction of the minimum transmit power (determined for Full PC), adjusted based on the distance r between the RRH and its user of interest and the power control parameter = 0.5.

The unconditional coverage probability (i.e., the coverage probability at any random location that the typical user may be within its RRH coverage area) is determined by:

Z −πλr2 Pr(T, λ, α, )= Pcov e 2πλr dr (3.18) r>0

where 2πλre−πλr2 is the pdf of the distance between the typical user and its nearest

RRH [33].

Substituting the expression for Pcov in (3.12) and (3.13) (or (3.14) and (3.15)) in (3.18) gives the exact value of the unconditional coverage probability. Similarly, the approximate value of unconditional coverage probability is obtained by substituting (3.16) and (3.17) in

(3.18).

3.3.3.2 Per User Achievable Average Rate

Based on Shannon’s law, the rate R in nats/sec/Hz that a typical user located at a given distance r from its closest RRH can achieve is determined by: R(r) , ln[1 + SINR(r)]. Clearly R is a nonnegative random variable because SINR(r) is random and nonnegative.

Hence, the achievable average rate R¯(r) at a given distance r is:

¯ R(r) , E[ln(1 + SINR(r))] ∞ (a) Z = Pr( ln(1 + SINR(r)) > θ ) dθ (3.19) θ=0 ∞ ∞ (b) Z dT Z dT = Pr( SINR(r) > T ) = Pcov T =0 1 + T T =0 1 + T

37 where the expectation is with respect to both the interfering RRHs and the distribution of small-scale fading [33]. The label (a) uses the fact that for any non-negative random variable

R ∞ θ X, E[X] is E[X] = x=0 Pr{X > x} dx, and (b) applies a change of variables T = e − 1 [70]. The per user achievable average rate at any location, R¯ is determined by:

Z Z ∞ ¯ dT −πλr2 R = Pcov e 2πλr dr (3.20) r>0 T =0 1 + T

where the expressions for Pcov are presented in sub-section 3.3.2.2. For example, substituting (3.16) and (3.17) in (3.20) gives:

Z ∞ Z exp(−πλr2(1 + T )) R¯ ≈ 2 2πλr dr dT, Case1 (3.21) T =0 r>0 (1 + T )

TR2 Z ∞ Z exp(−πλ(r2 + cell )) R¯ ≈ 3 2πλrdrdT, Case2 (3.22) T =0 r>0 (1 + T )

3.3.3.3 Network Energy Eﬃciency Analysis

Diﬀerent from (3.6) that approximates total power consumed by the network based on [45], this Section proposes a more accurate approximation that applied power control mechanism to calculate network power consumption.

The energy consumed in a cloud-RAN consists of consumption for [71]: i) data transmission and reception, transceiver circuits, alternating current to direct current (AC-DC) and DC-

DC conversion, cooling system, and fronthaul interfacing all consumed at the RRHs, and ii) communication protocol to support the centralized processing at the BBU pool. Recall from

Section 4.2 that only the RAN segment of cloud-RAN is of interest in this chapter. As such, the EE analysis presented here considers only the energy consumption of the RRHs. The components of RRH energy consumption can be divided into two parts: static and dynamic parts. The static part includes energy consumed in the transceiver circuits, AC-DC and

DC-DC conversion, cooling system, and fronthaul interfacing; while the dynamic part is the energy consumption in the power ampliﬁer for data transmission and energy consumption in the low noise ampliﬁer during data reception.

38 To do so, the starting point in the analysis is to derive the total power consumed by all the

2 RRHs per unit area (e.g. in W atts/km ) denoted by Pt. Pt = λpin, where pin is the power consumed by an RRH which is given by pin = P0 + ∆Ptot,RRH . The term P0 is the power consumed by an RRH in its ideal mode (when RRH is awake but not transmitting), and ∆ is the slope of the load-dependent power consumption. Ptot,RRH is the total power transmitted by an RRH to all the users at any location inside its coverage area calculated by:

Z Rcell 2r P = [N ] p p1− dr tot,RRH E u min max R2 0 cell (3.23) 2p p1− = min max [N ]Rα 2 + α E u cell where E[Nu] is the average number of users in the RRH coverage area, given by: E[Nu] =

2 λuπRcell. Next, the network EE for the general and Cases 1 and 2 are:

λ × R¯ λ × R¯ EE = u = u , General case 2∆p p1− λpin min max α λP0 + 2+α E[Nu]Rcell λ × R¯ u (3.24) = ∆ √ α , Case 1 λP0 + 2 pmin pmax E[Nu]Rcell ¯ λu × R = ∆ α . Case 2 λP0 + 3 pmin E[Nu]Rcell Substituting the expression for R¯ given by (3.21) and (3.22) into (3.24) gives the approximate value of EE for Case 1 and Case 2, respectively. Similarly, the exact value of EE is obtained by substituting exact expressions for Pcov (i.e., (3.12) and (3.13)) in (3.20).

3.3.4 Numerical and Simulation Results with Discussion

The results are obtained by assuming N = 0 (i.e, noise eﬀect is neglected), λ = 1 ×

−3 2 −3 2 10 RRHs/m (to study medium dense RRH deployment [72]), λu = 2 × 10 users/m ,

α = 4 and pmin = 0 dBm. The values P0 = 84 W , ∆ = 2.8 and pmax = 43 dBm are chosen based on the experimental results in [45]. Moreover, simulation is done to check the accuracy of the analytical results. For both analysis and simulation, the network model assumptions

(provided in Section 3.3.1) hold, except considering an inﬁnite bi-dimensional area in analysis

39 as compared to the finite two-dimensional service area in simulation with radius 30000 m to have sufficiently large area in order to minimize error. Here, three different RRH operational scenarios in terms of the power control parameter are studied, enumerated as follows.

• = 0 denoted as No PC [33].

• = 0.5 denoted as HFPC, (Case 1 Equations).

• = 1 denoted as Full PC (Case 2 Equations).

Figure 3.5 depicts the analysis and simulation results of unconditional coverage probability for three RRH operational scenarios (No PC, HFPC, Full PC), where the assumed

ﬁnite simulation service area causes a small diﬀerence between the simulation and analytical results. D-FPC enhances coverage probability till a certain value of T (e.g. about 15 dB for HFPC and 12 dB for Full PC, comparing analytical results). By controlling the transmit power in the power control scenarios, the received signal by the user of interest attains additional gain over the collective interference from all the interferers, resulting in SIR improvement and hence enhanced coverage probability. Beyond the SIR threshold of about

15 dB (HFPC) and 12 dB (Full PC), there exists a faster reduction in coverage probability than that of the No PC scenario. Moreover, Full PC has a faster reduction in coverage probability than the HFPC at large values of SIR threshold. The reason is, with Full PC,

α transmitting at minimum power (pminr ) reduces the likelihood of the successful transmissions, and hence a lower coverage probability than that of HFPC. Using the formula for ¯ R (3.20) and considering the exact expressions for Pcov ((3.12) and (3.13)), the unconditional per user achievable average rate for the three operational scenarios under different ¯ Rcell is illustrated in Figure 3.6. First note that, with no power control, R is independent ¯ of Rcell and converges to 1.49 nats/sec/Hz [33]. However, R is impacted by Rcell due to the assumed D-FPC scheme and the effect is different depending on the assumed value of the power control parameter . For both the HFPC and Full PC scenarios, R¯ initially increases

40 1 Analysis: No PC 0.9 Analysis: Full PC Analysis: HFPC 0.8 Simulation: No PC Simulation: Full PC 0.7 Simulation: HFPC

0.6

0.5

0.4

0.3

Unconditional coverage probability coverage Unconditional 0.2

0.1

0 -10 -5 0 5 10 15 20 SIR Threshold (dB)

Figure 3.5: Unconditional coverage probability vs. SIR threshold (λ = 1 × −3 2 10 RRHs/m ,Rcell = 15 m)

with Rcell because the received signal power exceeds the total interference thus satisfying the required SIR threshold. Worthy to mention, there is no constraint on transmit power to identify power control behavior. It is interesting that the two power control scenarios exhibit diﬀerent behaviors after a certain value of Rcell. From Figure 3.6, beyond Rcell = 40 m, the ¯ R achieved with Full PC decreases exponentially with further increases in Rcell, which follows from (3.17). Furthermore, with Full PC, the RRH is transmitting at minimum power

α (pminr ) resulting in unsuccessful transmission and decreasing achievable rate as Rcell increases and eventually tends to zero at large values of Rcell. On the other hand, with HFPC, the transmit power is being adapted such that the increase in the received power is counter- balanced by the increase in interference, so that the achievable average rate is not aﬀected by Rcell. Compared to the No PC scenario, the HFPC scenario provides up to 168% improvement in the achievable average rate. In Figure 3.7, the exact value of EE versus Rcell is depicted for all three RRH operational scenarios for the ﬁxed values λ = 1 × 10−3RRHs/m2

−3 2 α and λu = 2 × 10 users/m . In Full PC scenario, transmitting at lowest power (pminr )

41 4.5 HFPC 4 No PC Full PC 3.5

2.5

1.5

0.5 Per User Achievable Average Rate (nats/sec/Hz) Rate Average Achievable User Per

0 0 20 40 60 80 100 120 140 160 180 200 Cell Radius(R )(m) cell

Figure 3.6: The per user average achievable rate vs. cell radius (λ = 1 × 10−3 RRHs/m2)

boosts energy saving, which enhances EE till a certain value of Rcell (about 40 m). After this

value of Rcell, where RRH is likely to transmit to a longer distance, the achievable average rate decreases along with increasing Rcell due to unsuccessful transmissions, which decreases EE. In HFPC, the desired signal overcomes interference and thus increases the achievable

average rate, resulting in seven-fold EE enhancement. As the EE is a scaled version of R¯,

the EE in HFPC also tends to a limiting value, for which further increase in Rcell results in

no further gain in EE. Also, the EE for Full PC decreases after Rcell exceeds a certain value. The explanation for these behaviors is as given earlier for Figure 3.6.

42 0.1 HFPC 0.09 No PC Full PC 0.08

0.07

0.06

0.05

0.04

0.03 Energy Efficiency (nats/Hz/J) Efficiency Energy

0.02

0.01

0 0 20 40 60 80 100 120 140 160 180 200 Cell Radius(R )(m) cell

−3 2 −3 2 Figure 3.7: EE vs. cell radius (λ = 1 × 10 RRHs/m , λu = 2 × 10 users/m )

3.4 Summary

Employing the stochastic geometry framework to assess the EE and SE performance achievable using cooperative cloud-RAN with centralized processing was the purpose of this chapter. It is shown that RRH cooperation is beneﬁcial in terms of received signal power enhancement and interference avoidance both of which aﬀect the network EE and SE performance.

From the analytical results, it is imperative to utilize an optimal number of cooperating

RRHs for maximizing the EE. Solving the optimization problem reveals that accounting for the cluster radius and transmit power is essential to ﬁnd the optimal number of cooperating

RRHs that maximize the EE. In this chapter, the stochastic geometry tool is used to investigate the ability to mitigate interference via D-FPC. Hence, EE is maximized as tuning transmit power based on distance minimizes network power consumption and network interference power. Numerical results reveal that up to seven-fold increase in EE performance can be realized with D-FPC when the control factor is set at 0.5, thanks to the achievable average rate increment by reducing the interference eﬀect.

43 Chapter 4

Throughput Reliability Analysis of cloud-RAN

Networks Incorporating Power Control along with

Cooperative Transmission2

4.1 Introduction

This chapter tackles the problem of assuring user’s quality of service (QoS) in cloud-RANs, considering the cloud-RAN operating conditions of RRH cooperation and RRH power control. The QoS metric is the per user achievable throughput (i.e. achievable data rate) and the probability that the achievable throughput exceeds a speciﬁed throughput threshold, referred to as throughput reliability in this chapter, is derived considering RRH cooperative transmission/power control or both. Knowledge of the throughput reliability enables the calculation of the per user achievable average rate which, in turn, is used for computing the

EE and SE. The chapter adopts a stochastic geometry-based approach which incorporates interference mitigation via cooperative joint processing and power control to enhance the SE and EE performance in cloud-RAN. Under the settings considered, cooperation and power control enable the RRHs to be opportunistically operated in accordance with the interference and load conditions such that both the SE and EE are maintained at a high level at all times. Speciﬁcally, the contributions of this chapter are twofold:

• Analytical derivation of throughput complementary cumulative distribution function

(CCDF), referred to henceforth as throughput reliability, in cloud-RAN under RRH

2The content of this chapter has generated one journal paper: – Published as a journal paper in Wireless Communications and Mobile Computing [73], F. Ghods, A. O. Fapojuwo, and F. M. Ghannouchi, Throughput reliability analysis of cloud- radio access networks, Wireless Communications and Mobile Computing, vol. 16, no. 17, pp.2824-2838, 2016.

44 cooperation along with power controlled transmissions.

• Derivation of analytical results for SE and EE, also with RRH cooperation and power

control.

The novelty of our approach is the consideration of both the RRH cooperation and power

control in cloud-RAN performance analysis, using tools from stochastic geometry. To our

best knowledge, this is the ﬁrst work in the literature which combines both RRH cooperation

and power control in the context of cloud-RAN.

The rest of this chapter is organized as follows. Section 4.2 describes the cloud-RAN model assumed in the chapter, covering the diﬀerent aspects of cloud-RAN design and operation. This is followed by cloud-RAN throughput reliability analysis in Section 4.3, which serves as input to EE and SE analysis presented in Section 4.4. In Section 4.5, numerical and simulation results are presented and discussed. Finally, Section 4.6 summarizes the chapter and points out some areas for future work.

4.2 Downlink System Model

The downlink system model of the cloud-RAN is same as chapter 3, Section 3.2.1.1, and the assumed network architecture is same as Figure 3.1, plotted in chapter 3.

4.2.1 Cooperation Model

The cloud-RAN service area is assumed to be partitioned into cluster areas, where a cluster contains the set of cooperating RRHs. The cluster area is assumed to be circular in shape, for analytic simplicity, with a radius of Rc. A random number K of RRHs in a cluster (of radius Rc) cooperate by jointly transmitting to the desired user. This cooperation model is identical to joint transmission, the most advanced coordinated multi-point scenario of

LTE advanced systems [74]. Now, the locations of the cooperating RRHs in a cluster, say cluster A, are represented by A1,...,AK , where, without loss of generality, A1 denotes the

45 nearest RRH to the desired user and Aj, j = 2, 3,...,K are the other cooperating RRHs in the cluster. Similarly, the other clusters in the cloud-RAN service area will each have K cooperating RRHs. Due to the cooperative joint transmission by the RRHs in the cluster, the received signal power by a user in the cluster is the coherent sum of the power received from all the cooperating RRHs. Moreover, the users’ locations are assumed to be PPP over the cloud-RAN service area, which implies that the users are uniformly distributed across the cluster area as well as the RRH coverage area (PPP becomes uniform when the area is bounded [37]).

4.2.2 Spectrum Allocation

As mentioned in Section 3.2.1.1.3, OFDMA is the assumed multiple access technique which is selected due to its eﬃcient spectral usage and zero or negligible co-channel interference

(users are allocated orthogonal subcarriers). The total spectrum is available to each cluster of cooperating RRHs and equally allocated to all the users within each cluster area. The BBU associated with the cooperating RRHs in a cluster controls the subcarrier allocation such that each subcarrier is only allocated to one user, thus eliminating intra-cluster interference.

Hence, we focus on one cluster where the desired user resides as the cluster of interest and treat the other clusters in the cloud-RAN service area as sources of out-of-cluster interference

(also referred to as inter-cluster interference). Since, there is no intra-cluster interference, the desired user only suﬀers from inter-cluster interference, denoted by I, from RRHs in the neighboring clusters to its own cluster.

4.2.3 Power Control Model

The assumed power control model is D-FPC as explained in Section 3.3.2. in chapter 3.

46 4.3 Throughput Reliability Analysis

The objective of the analysis is to derive the expression for throughput reliability, deﬁned as

the probability that T hr, the per-user achievable throughput exceeds θ, a desired throughput threshold in a cloud-RAN with RRH cooperation and RRH transmit power control. The starting point is the expression for T hr. By Shannon’s capacity law:

S 1 S 1 T hr = log (1 + ) = ln(1 + ) = ln(1 + SINR) (4.1) 2 I + N ln 2 I + N ln 2

where T hr is in bits/sec/Hz or nats/sec/Hz accordingly, S is the total received power at the

desired user from all the K cooperating RRHs inside the cluster of radius Rc, I is the received aggregate out-of-cluster interference from all the RRHs located outside the boundary of the

cluster of interest (i.e. cluster where the desired user resides), and SINR is the received

signal-to-interference plus noise ratio at the desired user. Making use of Figure 3.1 and the

assumed propagation channel model (Section 4.2.2), the expressions for SINR is given by:

S p h r−α + PK p h r−α SINR = = 1 1 1 i=2 i i i (4.2) I + N P p h R−α + N j∈ϕ\{A1,...,AK } j j j Since ϕ, the RRH locations in the cloud-RAN service area follow the PPP with RRH density

λ (Section 4.2.1), clearly S,I,SINR and, hence, T hr are random variables. Without loss

of generality, assume that RRH 1 (whose location is A1) is the closest RRH to the desired

user. Given that the desired user is at a distance r1 = r from its closest RRH in the cluster (Figure 3.1), the conditional throughput reliability is deﬁned mathematically by:

T hrReliab(θ, λ, Rc, |r) = Pr(T hr > θ |r) (4.3)

By un-conditioning with respect to the location of the desired user in the coverage area of its

closest RRH, the unconditional throughput reliability is denoted by T hrReliab(θ, λ, Rc, ). Clearly, the expression T hrReliab(...) requires knowledge of the statistics of S,I,SINR and

T hr. Starting with the aggregate interference, generally the expression for the probability

density function (pdf) of aggregate interference in a wireless network is unknown. In essence,

47 for the cloud-RAN under study, the expression for the pdf of I, the out-of-cluster interference

(i.e. aggregate interference from all the RRHs located outside the cluster of interest) is unknown. Hence, in this chapter, instead of characterizing by its pdf, we characterize I by

−SI LI (s) = E[e ] the Laplace transform (LT) of the pdf for I which always exists because I is a strictly positive random variable. Similar to [11],[12], this chapter employs the stochastic geometry framework to obtain, in a systematic way, the Laplace transform of the pdf for I as well as evaluating the statistics of SINR and T hr. Section 4.3 presents semi-closed form results for T hrReliab(...) ﬁrst under the general case when both RRH cooperation and RRH transmit power control are active and then under cases when only some speciﬁc operating conditions are active. Section 4.3.2 provides per-user achievable average throughput results, which are the by-products of the throughput reliability.

4.3.1 Throughput Reliability Results

Proposition 4.1:

Under the cloud-RAN operating conditions that both RRH transmit power control (i.e.

0 < ≤ 1) and RRH cooperation (i.e. 0 < r < Rc < ∞) are active, the conditional throughput reliability T hrReliab(θ, λ, Rc, |r) is given by:

−Nδ −πλτ −πλκr2 T hrReliab(θ, λ, Rc, |r) = e e e (4.4)

α 2 2 2 r 2Rcell θ where τ = (2R ξ/(α − 2)) F (1, 1 − ; 2 − ; −ξ), ρ = , ϑ = α , T = e − 1, c 2 1 α α Rc (α+2)r 2 2 (α−2) 2 2 α κ = (2ϑ/(α − 2)) × (2F1(1, 1 − α ; 2 − α ; −ϑ) − ρ 2F1(1, 1 − α ; 2 − α ; −ϑρ )), δ = α(1−) pmax 2T rRcell α −T r ( ) /pmax, ξ = ( ) , and 2F1(a, b; c; d) is the Gauss-hypergeometric pmin α+2 r Rc function.

Proof: Provided in Appendix A4.1. (4.4) provides the following insight: the conditional throughput reliability is inﬂuenced by the AWGN power (ﬁrst exponential function in (4.4)), the aggregate desired signal power

48 received at the desired user from the cooperating RRHs inside the cluster of interest (second

exponential function), and the aggregate out-of-cluster interference power at the desired user

from all the RRHs outside the cluster of interest (third exponential function).

Proposition 4.2: Under the cloud-RAN operating conditions that both RRH transmit

power control (i.e. 0 < ≤ 1) and RRH cooperation (i.e. 0 < r < Rc < ∞) are active, the un-conditional throughput reliability T hrReliab(θ, λ, Rc, ) is given by:

Z −Nδ −πλτ −πλκr2 −πλr2 T hrReliab(θ, λ, Rc, )= e e e e 2πλr dr. (4.5) r>0 where, following the logic in [33], the product e−πλr2 2πλr is the pdf of the distance r between the desired user and its nearest RRH. The variables τ and κ in the exponential terms are each functions of the RRH cooperation parameter (Rc) and the RRH transmit power control parameter via complicated expressions involving special mathematical functions (e.g. the

Gauss-hypergeometric function).

Proof: (4.4) is derived given that the desired user is at a distance r from its closest RRH.

−πλr2 By un-conditioning with respect to e 2πλr the pdf for r, gives (4.5).

Corollary 4.1: At a ﬁxed Rc and, under high RRH density (i.e. λ tends to a large value), the out-of-cluster interference dominates the AWGN noise power, i.e. I >> N, such that

(I + N) ≈ I or N = 0 and SINR ≈ SIR, the signal-to-interference ratio. Setting N = 0 in

(4.5) then gives:

Z −πλτ −πλκr2 −πλr2 T hrReliab(θ, λ, Rc, )= e e e 2πλr dr. (4.6) r>0

(4.6) provides the following insight: the unconditional throughput reliability is inﬂuenced by the aggregate desired signal power received at the desired user from the cooperating RRHs inside the cluster of interest of radius Rc (ﬁrst exponential function) and the aggregate out- of-cluster interference power at the desired user from all the RRHs outside the cluster of interest (second exponential function). For a given cluster radius Rc, as λ increases the total

49 received out-of-cluster interference outweighs the aggregate received signal power from the

cooperating RRHs such that the received SIR becomes so small and most of the time falling below the desired SIR threshold leading to lower throughput reliability. In the limit when

(λ → ∞) the throughput reliability tends to zero, as expected. Note that in (4.5) and (4.6), the variables τ and κ in the exponential terms are each functions of the RRH cooperation parameter (Rc) and the RRH transmit power control parameter () via complicated expressions involving special mathematical functions (e.g. the Gauss-hypergeometric function). Hence, the impact of power control and cooperation on throughput reliability will be demonstrated via numerical computations.

Using Corollary 4.1 as basis, next we consider the special cases depending on whether or not RRH transmit power control or RRH cooperation is active.

Proposition 4.3: Under the cloud-RAN operating conditions where RRHs transmit with no power control (i.e. = 0) and only RRH cooperation (i.e. 0 < r < Rc < ∞) is active, the un-conditional throughput reliability T hrReliab(θ, λ, Rc) is given by:

Z Pr(θ, λ, α)= e−πλ%e−πλψr2 e−πλr2 2πλr dr (4.7) r>0

2 2 (α−2) 2 2 α where ψ = (2/(α − 2)) × (2F1(1, 1 − α ; 2 − α ; −1) − ρ 2F1(1, 1 − α ; 2 − α ; −ρ )), and % = (2TR2/(α − 2))ρ2 F (1, 1 − 2 ; 2 − 2 ; −T ρα), and ρ = r . In (4.7), the ﬁrst exponential c 2 1 α α Rc term accounts for the RRH cooperation while the second exponential term represents the out-of-cluster interference.

Proof: Setting = 0 in the expressions for τ and κ and then substituting the results into

(4.6) gives (4.7). Notice that the variables % and ψ in the exponential terms are each functions of the RRH

cooperation parameter Rc via complicated expressions involving special mathematical functions (e.g. the Gauss-hypergeometric function), hence at ﬁrst glance the impact of Rc on

T hrReliab(θ, λ, Rc) is not obvious. However, an inference from (4.7) is the following: for a

50 ﬁxed RRH density λ, an increase in the RRH cooperation parameter Rc implies an increase in the number of cooperating RRHs in the cluster of interest and a decrease in the number

of out-of-cluster RRHs. This means an increase in the received SIR at the desired user and,

consequently, an increase in the throughput reliability.

Proposition 4.4: Under the cloud-RAN operating condition that the RRH transmit

power control (i.e. 0 < ≤ 1) is active but with no RRH cooperation (i.e. 0 < Rc = r), the un-conditional throughput reliability, T hrReliab(θ, λ, ) is given by:

Z Pr(θ, λ, α, )= e−πλσe−πλr2 2πλr dr (4.8) r>0

2 2 2 2T r α(1−) where σ = (2ηR /(α − 2)) × 2F1(1, 1 − ; 2 − ; −η), and η = ( ) . Note cell α α α+2 Rcell that, unlike (4.5), (4.6), and (4.7), the exponential term denoting the RRH cooperation no

longer exists in (4.8) because the desired user is served only by its closest RRH. The received

aggregate interference by the desired user now comes from the other RRHs in the cloud-RAN

service area which is represented by the ﬁrst exponential term in (4.8).

Proof: Provided in Appendix A4.2. Without RRH cooperation and with distance-based power control such that the same

signal power pmin is received by the desired user at any location inside the coverage area of its closest RRH, the throughput reliability is inﬂuenced mainly by the received aggregate

interference. Clearly, the aggregate interference is worse when the desired user is near the

boundary of the coverage area of its closest RRH (i.e. r → 1) resulting in lower SIR and, Rcell consequently, low throughput reliability T hrReliab(θ, λ, ). In (4.8), σ is a function of the power control parameter through a complicated expression involving special functions (e.g. the Gauss-hypergeometric function), hence the impact of on T hrReliab(θ, λ, ) is studied via numerical calculations.

Proposition 4.5: Under the cloud-RAN operating conditions where RRHs transmit

51 with no power control (i.e. = 0) and with no RRH cooperation (i.e. 0 < Rc = r), the un-conditional throughput reliability T hrReliab(θ) is given by:

2T 2 2 T hrReliab(θ) = [− F (1, 1 − ; 2 − ; −T ) + 1]−1. (4.9) (α − 2) 2 1 α α

where T = eθ − 1 is the SIR threshold.

Proof: First set = 0 and Rc = r in the expressions for τ and κ and then substi- tute the results into (4.6). Next apply a change of variables ν = r2 and integrating with respect to ν gives (4.9). Clearly, (4.9) is independent of the RRH density λ, consistent with published results in the literature [33]. The insight from (4.9) is that, for a given environment (i.e. α is ﬁxed), T hrReliab(θ) decreases as the throughput threshold θ increases.

4.3.2 Per-user Achievable Average Throughput

The per-user achievable average throughput, E[T hr] can be determined from (4.1):

1 [T hr] = [ln(1 + SINR)] (4.10) E ln 2 E

where E[T hr] is in nats/sec/Hz. However, E[T hr] can also be determined by invoking a well-known result from probability theory: for any non-negative random variable X, the R ∞ expected value of X, E[X] = x=0 Pr{X > x} dx [70]. Since T hr is a non-negative random variable, the above result from probability theory is applied and E[T hr] is computed by:

Z ∞ Z ∞ E[T hr] = Pr{T hr > θ} dθ = T hrReliab(...) dθ (4.11) θ=0 θ=0

where Pr{T hr > θ} is the un-conditional throughput reliability (i.e. T hrReliab(...)), given

by (4.5) to (4.9). Substituting (4.5) to (4.9) into (4.11) gives the expression for per-user

achievable average throughput for the diﬀerent operating conditions of the cloud-RAN. No-

tice that, with the exception of T hrReliab(...) given by (4.9) (i.e. operating condition of no

RRH cooperation and no power control), the calculation of E[T hr] for the other cloud-RAN

52 operating conditions whose T hrReliab(...) are given by (4.6) to (4.8) each requires double integrations with no closed-form solution, and, hence, are performed numerically. As such, the insights deduced from (4.11) will be given after generating and plotting the numerical results in Section 4.5.

4.4 EE and SE Analysis

Cloud-RAN promises to enhance both the EE and SE. In this Section we quantify both the

EE and SE in a cloud-RAN under the operating conditions of RRH cooperation and RRH transmit power control. The results of Section 4.3 are leveraged in the calculation of EE and

SE.

4.4.1 Cloud-RAN Energy Eﬃciency

Energy eﬃciency is generally deﬁned as the number of information bits transmitted per unit of expended energy, measured in bits − per − Joule. In what follows, we derive the result for the EE in a cloud-RAN under the operating conditions of RRH transmit power control and RRH cooperation, adopting the models described in Sections 3.4 and 3.5, respectively.

For worst case analysis, it is assumed that all the RRHs are up (i.e. none in sleep mode).

Also the RRH distribution and user distribution are as described in Section 3.1. Using same analysis like the one presented in Section 3.3.2.4 in chapter 3, and applying RRH transmit power control along with cooperation the EE expression is derived as follows.

The starting point in the analysis is to derive the expression for Ptot,RRH , the total power transmitted by an RRH to all the users inside a cluster of K cooperating RRHs:

0 Ptot,RRH = KNup (4.12)

0 where Nu is the number of users in an RRH coverage area and p is the controlled transmit power by an RRH to the desired user (the expression for p0 will be given later). Now, according to the linear power consumption model [45], applied to an RRH with one transceiver,

53 the power consumed by an RRH, pin, is:

0 pin = P0 + ∆Ptot,RRH = P0 + ∆KNup (4.13)

where P0 is the power consumed by an RRH while it is awake but not transmitting to any user (i.e. static part) and ∆ is the slope of the transmission/reception-dependent power

consumption. Note that the second term of (4.13) implies that the power transmitted by

an RRH to all the users within its coverage area is exactly the same as that transmitted to

all the users in the coverage areas of the other RRHs within the cluster. This implication is

true due to the cooperation of all the RRHs in a cluster. Hence, the power consumed per

unit area (e.g. in W atts/km2) by all the RRHs in a cluster is:

0 Ptot,clus = λpin = λ(P0 + ∆KNup ) (4.14)

The network EE is deﬁned as the ratio of the network-level achievable throughput per unit

area to the network-level consumed power per unit area, where, without a loss in generality,

the area is taken with respect to the cluster level of a cloud-RAN. Mathematically:

λuT hr λuT hr EE = = 0 (4.15) Ptot,clus λ(P0 + ∆KNup )

Taking expectations of the random variables in both the numerator and denominator in

(4.15) gives: λuE[T hr] EE = 0 (4.16) λ(P0 + ∆ E[K] E[Nu] p )

where E[K] and E[Nu] are the average number of RRHs in a cluster and average number of users in a cluster, respectively. Based on the assumptions regarding the RRH distribution

2 2 and user distribution in Section 3.1, E[K] = λπRc and E[Nu] = λuπRcell and substituting these into (4.16) gives: λuE[T hr] EE = 2 0 2 2 (4.17) λ(P0 + ∆λλuπ p Rc Rcell) where E[T hr] is calculated using (4.11). It remains to derive the expression for p0 the transmit power by an RRH to a desired user at any location within the RRH coverage area. From

54 (3.10), under the assumed distance-based FPC model, the transmit power by an RRH to a

1− α user at distance r away is: pminpmaxr . Hence, the transmit power by an RRH to a user at any location inside the RRH coverage area is given by:

Z Rcell 1− 0 1− α 2r 2pminpmax α p = pminpmaxr 2 dr = Rcell (4.18) 0 Rcell 2 + α

2r where the ( 2 ) in the integrand is the pdf of r, which follows from the fact that users Rcell are distributed uniformly across the RRH coverage area, assumed to be circular in shape

and of radius Rcell. (4.17) oﬀers the following insights. The expression for EE is directly

proportional to E[T hr] which in turn is proportional to λ the RRH density. However, from (4.17) it is seen that the cloud-RAN EE is also inversely proportional to the RRH density.

Increasing the RRH density increases the achievable throughput, but with a concomitant

increase in power consumption (from (4.14)) and, consequently, a decrease in the EE. Hence,

a trade-oﬀ exists between energy consumption and throughput (or between EE and SE).

The trade-oﬀ between the energy consumption and throughput becomes more complex in

a cloud-RAN due to the cooperation among the RRHs in a cluster and the RRH transmit

power control mechanism. Moreover, (4.17) shows that the EE is a function of the RRH

cooperation parameter (Rc) and the RRH transmit power control parameter () where both parameters appear in the numerator and denominator. Hence, the impact of power control and cooperation on cloud-RAN EE will be demonstrated via numerical computations.

4.4.2 Cloud-RAN Spectral Eﬃciency

The SE is the rate at which the available system bandwidth is used for data transmission.

Given a certain amount of bandwidth B for a cloud-RAN, the objective is to maximize the per-user achievable throughput, E[T hr] achieved via RRH cooperation. Recall that the units for E[T hr] is in nats/sec/Hz. Hence, E[T hr] can be interpreted as the per-user SE.

If the users are distributed across the cloud-RAN service area with density λu, then SE, the

55 cloud-RAN area-wide SE, expressed in units of nats/sec/Hz/unitarea is:

SE = λu × E[T hr] (4.19) where E[T hr] is calculated using (4.11). From (4.19), the SE is a scaled version of E[T hr].

As such, the insights from (4.19) will be identical to those for E[T hr].

4.5 Numerical and Simulation Results with Discussion

This Section presents and discusses the numerical results calculated using the analytical results obtained in Sections 4.3 and 4.4. In addition, we have conducted Monte Carlo simulations to validate the accuracy of the analytical results. Instead of the infinite R2 cloud-RAN service area assumed in the analysis, in the simulations we assume a finite size two-dimensional cloud-RAN service area. To achieve a good balance in the tradeoff between solution quality (i.e. minimize the error between the finite and infinite size cloud-RAN service area) and solution efficiency (i.e. minimize the simulation run time), a radius of

3000 m is assumed for the cloud-RAN service area in the simulations. An RRH density

λ = 0.001 RRHs/m2 is assumed, which corresponds to medium dense RRH deployment [72].

2 The user density λu is set at 0.003 users/m . Note that λu > λ to ensure there is at least one user in an RRH coverage area, of radius Rcell = 15 m. The cloud-RAN is deployed in an urban environment whose propagation channel is modeled by the distance-dependent path loss (path loss exponent α = 4) and small-scale Rayleigh fading (average power of unity).

The RRH maximum transmit power pmax is 43 dBm [45] and the receiver threshold pmin is set at 0 dBm. Note that the assumed parameter values are selected to illustrate the cloud-

RAN performance and do not represent a speciﬁc cloud-RAN design. Table 4.1 summarizes the assumed parameter values, unless stated otherwise.

Results are generated for six RRH operational scenarios listed as follows:

1. Without RRH transmit power control ( = 0) and no RRH cooperation (No PC, No

56 Table 4.1: The assumed parameters values

Symbol Deﬁnition Assumed Value λ Density of RRHs deployed in the cloud-RAN 0.001 RRHs/m2 2 λu Density of users in the cloud-RAN 0.003 users/m α Path loss exponent 4 Rc Radius of the cluster in the cloud-RAN 50 m Rcell Radius of an RRH coverage area 15 m pmax Maximum transmit power by an RRH 43 dBm pmin Minimum received power for acceptable communication 0 dBm

Coop) (4.9)

2. With RRH full transmit power control ( = 1) and no RRH cooperation (Full PC,

No Coop) (4.8)

3. With RRH fractional power control ( = 0.5) and no RRH cooperation (HFPC, No

Coop) (4.8)

4. With RRH full transmit power control ( = 1) and RRH cooperation ( Full PC with

Coop) (4.6)

5. With RRH fractional power control ( = 0.5) and RRH cooperation ( HFPC with

Coop) (4.6)

6. Without RRH transmit power control ( = 0) and RRH cooperation (Only Coop)

(4.7)

The appended equation number signiﬁes the corresponding T hrReliab(...) expression, as provided in Section 4.3.

Figure 4.1 shows the throughput reliability for the six RRH operational scenarios where, for the scenarios 4, 5 and 6, the cluster radius Rc is set at 50 m. For ease of showing the results, the throughput reliability is plotted against the SIR threshold, T , instead of the throughput threshold, θ. The SIR threshold is deﬁned as the minimum received SIR for acceptable communication, given by T = eθ − 1. Hence, a one-to-one relationship exists

57 1 Analysis: No PC, No Coop Analysis: Full PC, No Coop Analysis: HFPC, No Coop 0.9 Analysis: HFPC with Coop Analysis: Full PC with Coop Analysis: Only Coop 0.8 Simulation: Full PC, No Coop Simulation: Only Coop Simulation: No PC, No Coop 0.7 Simulation: HFPC with Coop Simulation: HFPC No Coop Simulation: Full PC with Coop 0.6

0.5

0.4 Throughput Reliability Throughput

0.3

0.2

0.1

0 6 7 8 9 10 11 12 13 14 15 SIR Threshold (dB)

Figure 4.1: Throughput reliability for 6 RRH operational scenarios vs. SIR threshold −3 2 (λ = 1 × 10 RRHs/m ,Rc = 50 m)

between T and θ. For the range of values of T 5 to 15 dB considered in Figure 4.1, the

corresponding values of θ vary from 1.43 to 3.49 nats/sec. In Figure 4.1, the curves are the analytical results, while the markers denote the simulation results. There is a very good agreement generally between the simulation and analytical results, thus conﬁrming the accuracy of the analytical results. The slight disparity between the analytical and simulation results for RRH operational scenarios 3, 4, 5, and 6 is due to the assumed ﬁnite size of

cloud-RAN service area in the simulation in contrast to the inﬁnite size of service area for

the analysis. The diﬀerence becomes more pronounced for scenarios 3, 4, and 6 involving

power control and cooperation which are both sensitive to distance, the former through

the adopted distance-based power control mechanism and the latter through the cluster

radius. It is observed from Figure 4.1 that RRH cooperation provides an improvement in

throughput reliability. For example, when the result of scenario 6 is compared with that

of scenario 1, there is at least 100% increase in throughput reliability. At large value of

58 T the likelihood of the received SIR exceeding the T reduces, with a consequence of high number of unsuccessful transmissions, and hence a lower throughput reliability. It is also observed from Figure 4.1 that both fractional power control (HFPC) and full PC provide an improvement in throughput reliability, as seen from comparing the results of scenarios 3 and 1, and scenarios 5 and 6 (HFPC), and also comparing the results of scenarios 2 and 1, and scenarios 4 and 6 (full PC). Clearly, both HFPC and full PC reduce the level of out-of- cluster interference which leads to a high received SIR and, thus, an increase in throughput reliability. Moreover, the improvement in throughput reliability when cooperation is used with power control is higher than without cooperation, as expected.

1 Full PC with Coop HFPC with Coop 0.9 Only Coop

0.8

0.7

0.6

0.5

Throughput Reliability Throughput 0.4

0.3

0.2

0.1 50 100 150 200 250 300 Cluster Radius (m)

Figure 4.2: Throughput reliability vs. cluster radius (λ = 1 × 10−3 RRHs/m2, θ = 2.716 nats/sec (or T = 11.5 dB))

Figure 4.2 shows the sensitivity of the throughput reliability to the cluster radius Rc, the RRH cooperation parameter. The results are generated assuming T = 11.5 dB (or

θ = 2.716 nats/sec) for the RRH scenarios 4 and 5, and 6 with and without power control,

respectively. Clearly, the throughput reliability increases with Rc as expected, because of an

59 increase in the average number of cooperating RRHs in a cluster as Rc increases (recall that

2 E[K] = λπRc ). It is interesting that as Rc increases, the throughput reliability tends to a limiting value. This is due to the fact that the gains in the aggregate received signal power is counter-balanced by the increase in the out-of-cluster interference causing the instantaneous per-user throughput T hr to tend towards a limiting value. It is concluded from Figure 4.2 that, for the assumed parameter values, the throughput reliability tends to 0.54, 0.74, and

0.78 for RRH operation scenarios 6, 5, and 4, respectively. Figure 4.2 is useful to the cloud-

RAN system designer for selecting the cluster radius value to achieve a desired throughput reliability objective and also to determine the threshold cluster radius for which further increase in cluster radius results in no further gains in throughput reliability.

10 No PC, No Coop 9 Full PC, No Coop HFPC, No Coop 8 Only Coop Full PC with Coop HFPC with Coop 7

2 Per User Average Rate (nats/sec/Hz) Rate Average User Per

0 0 0.5 1 1.5 2 2.5 3 -3 RRH Density ( 6) (RRHs/m2) #10

Figure 4.3: Per user average rate vs. RRH Density (Rc = 50 m)

In Figure 4.3, the per-user average rate (in nats/sec/Hz) is plotted versus the RRH density in a cloud-RAN, for the six RRH operational scenarios. For scenarios 4, 5, and 6 involving RRH cooperation, the cluster radius is set at 50 m and also for scenarios 3 and

60 5 involving HFPC, = 0.5. It is seen from Figure 4.3 that, under scenario 1 for which there is neither RRH transmit power control nor RRH cooperation, the per-user achievable average rate is invariant with the RRH density, consistent with the previous results in the literature [33]. Increasing λ results in an increase in the received signal power (due to the shorter distance of the desired user to its nearest RRH) and also an increase in the aggregate interference (because of the large increase in the number of interfering RRHs).

For scenario 6 where RRH cooperation is enabled but no RRH transmit power control, it is observed that the per-user achievable average rate initially increases with the RRH density and then tends to a limiting value at high RRH density. When the RRH density is increased from a low value, there is a concomitant increase in the per-user average rate due to an increase in the received SIR. As the RRH density is further increased, the average rate tends to a limiting value because the gain from cooperation is approximately oﬀset by the corresponding increase in the out-of-cluster interference. Now, for scenarios 2, 3, 4, and 5 involving distance-based power control mechanism, the per-user average rate decreases with

RRH density whether or not RRH cooperation is enabled. The decrease in the data rate is due to the complex interaction between the power control and cooperation mechanisms.

Regardless of whether or not cooperation exists, the per-user average rate achieved with full power control is generally higher than that of fractional power control. Note also that the per-user average rates for scenarios 2, 3, 4, and 5 are generally better than those for scenarios

1 and 6, further demonstrating the beneﬁt of cooperation and power control.

Figure 4.4 presents the network EE performance for the six RRH operational scenarios.

There are four main ﬁndings from Figure 4.4. First, the cloud-RAN EE decreases with increasing RRH density. From (4.17), the increase in RRH density raises the network power consumption to a value much higher than the corresponding increase in the network throughput, thus resulting in the decrease in cloud-RAN EE. Second, for the scenarios involving no

RRH transmit power control, it is interesting to ﬁnd that RRH cooperation is not beneﬁcial

61 35 No PC, No Coop Full PC, No Coop 30 HFPC, No Coop Full PC with Coop HFPC with Coop 25 Only Coop

Energy Efficiency (nats/J) Efficiency Energy 10

0 10-5 10-4 10-3 10-2 RRH Density (6)(RRHs/m2)

Figure 4.4: Energy Eﬃciency vs. RRH density (Rc = 50 m, = 0.5 (HFPC)) to cloud-RAN EE. In fact, from Figure 4.4, the cloud-RAN EE with RRH cooperation is less than that without cooperation by 56%. The explanation is as follows: at a given cluster radius, not only the improvement in the received aggregate signal power from all the

K cooperating RRHs in the cluster is nearly cancelled out by the increased out-of-cluster interference, but cooperation also increases the network power consumption by a factor of

K, thus resulting in less network EE compared to that without cooperation when K = 1.

The third major ﬁnding from Figure 4.4 is that the distance-based power control mechanism

signiﬁcantly enhances the cloud-RAN EE than without, where with full power control pro-

viding the highest gain. From Figure 4.4, full power control and fractional power control at

= 0.5 provide 278% (approximately three-fold improvement) and 89% improvement in EE, respectively over that of the corresponding scenario without power control. Controlling the

RRH transmit power at a given RRH density results in reduced network power consumption and, consequently, an increase in the network energy eﬃciency. The fourth ﬁnding from

62 Figure 4.4 is that with power control, the beneﬁt of RRH cooperation is marginal, where the

explanation is similar to that provided above for the second ﬁnding.

0.03 No PC, No Coop Full PC, No Coop HFPC, No Coop 0.025 Only Coop

) Full PC with Coop 2 HFPC with Coop 0.02

0.015

0.01 Spectral Efficiency (nats/s/Hz/m Efficiency Spectral

0.005

0 0 0.5 1 1.5 2 2.5 3 RRH Density (6) (RRHs/m2) #10-3

Figure 4.5: Spectrum Eﬃciency vs. RRH density (Rc = 50 m, = 0.5 (HFPC))

Finally, Figure 4.5 presents the cloud-RAN SE plotted against the RRH density. As seen from (4.19), the cloud-RAN SE is a scaled version of Figure 4.3, depicting the per-user average rate, where the scaling factor is the user density. As such, the explanation provided on

Figure 4.3 also applies to the cloud-RAN SE behavior shown in Figure 4.5. From Figure 4.5, full power control and fractional power control at = 0.5 provide 108% (approximately one- fold improvement) and 85% improvement in SE, respectively as compared to the No PC, No

Coop scenario.

63 4.6 Summary

In this chapter, mathematical analysis based on stochastic geometry is performed to investigate the impact of power control and cooperation on the throughput reliability, per-user achievable average rate, EE, and SE performance of cloud-RANs. On one hand, the use of a distanced-based power control for tuning the RRH transmit power results in reduced network power consumption, and thus improves the network EE. On the other hand, cooperation provides a boost in the aggregate received signal power leading to an increase in the per-user achievable average rate and, hence, SE improvement. Thus, it is concluded that cooperation along with power control helps to enhance both the SE and EE performance of cloud-RANs. As revealed from the numerical results, it is feasible to realize close to three- fold increase in the EE along with 108% improvement in the SE of cloud-RANs. Moreover, this chapter shows that high interference makes power control inappropriate for super dense networks and cooperation gain remains significant against only up to a certain number of cooperating RRHs. However, cooperation worsens EE by up to 56%, which is overcome by using PC, while improving SE up to 108%. The significance of these findings is that it is imperative to utilize an optimal RRH density where each RRH in the cooperating cluster is configured with a certain power control setting for not only maximizing EE and SE but also for minimizing the network’s capital and operational expenditure.

64 Chapter 5

5G Signaling/Evaluation3

5.1 Introduction

According to 2016 IEEE annual report [76], two of the important challenges associated with

fifth-generation (5G) wireless network technology is the need to have significant increase in data speeds, necessitating a higher spectral efficiency (SE), and energy efficiency (EE) of the network elements. These requirements that are imposed by 5G services have drawn researchers’ attention to prospective new waveforms (e.g. filter bank multicarrier (FBMC))

[77] and advanced network architecture (e.g. cloud-radio access network (cloud-RAN)).

FBMC as an alternative to the traditional orthogonal frequency division multiplexing

(OFDM) utilizes spectrum more efficiently due to reducing the overhead of guard band required for signals with strong out of band (OOB) emission (like traditional OFDM), and avoiding the use of cyclic prefix (CP) [78]. Although, incorporating cloud-RAN with FBMC can offer a higher SE and EE, this leading edge technology (FBMC), lacks in-depth understanding of its capability and restrictions, especially regarding EE. Since, the most energy inefficient component of a wireless transmitter is the power amplifier (PA), this chapter investigates FBMC experimentally to study its characteristics and requirements in order to drive the PA at high efficiency.

This chapter experimentally examines the FBMC waveform and compares it with the

OFDM waveform. Then, it studies the linearity requirements of power ampliﬁer (PA) using memoryless and memory polynomial digital predistortion (DPD) techniques. Considering

3The content of this chapter has generated one journal paper: – Submitted as a manuscript in the IEEE Communication Magazine [75], F. Ghods, A. K. Kwan, M. Helaoui, F. M. Ghannouchi A. O. Fapojuwo, Analysis and mitigation of the eﬀect of transmitter’s nonlinearity for 5G FBMC signals, IEEE Communication Magazine, 2017.

65 FBMC with different values of overlapping factor, in the range from one to four, the signals’ performance is evaluated through the adjacent channel power ratio (ACPR) and the error vector magnitude (EVM) metrics. Moreover, FBMC and OFDM are compared concerning peak to average power ratio (PAPR), ACPR, and EVM, and the signals are assessed over different PA input power backoff levels. Specifically, this chapter’s contributions are threefold:

• Recommendation of minimum acceptable input power backoﬀ (IPBO) for FBMC

and OFDM signals regarding EVM, under the case study.

• Comparing FBMC signals performance with OFDM signal in terms of the ACPR

and EVM metrics measured by Class AB PA.

• Experimental results for the ACPR and EVM in FBMC signals under memoryless

and memory polynomial DPD schemes measured by Doherty PA.

The rest of this chapter is organized as follows. First, the FBMC waveform, and digital predistortion are deﬁned. Followed by introducing PA behavioral models (memoryless and memory polynomial DPD) and the performance evaluation metrics. Then the generation of the OFDM and FBMC signals are discussed. Following that, the chapter studies how to satisfy PA linearity characteristics applying both memoryless and memory polynomial DPD, measured by Class AB and Doherty PAs. A comparison of experimental results using DPD on the signals is presented; and ﬁnally, the chapter is summarized in the last Section.

5.2 Filter Bank Multi Carrier Waveform

FBMC waveform is a primary candidate of 5G networks [16] that uses prototype ﬁlters to provide very good concentrated frequency localization [17], results in low out of band

(OOB) emission. Moreover, it does not require cyclic preﬁx (CP), thanks to the use of oﬀset

66 quadrature amplitude modulation (OQAM) along with ﬁlter bank which leads to about

two-fold increase in data rate and higher spectral eﬃciency (SE) [16].

As an emerging technology, FBMC waveform requires more in-depth study. This chapter

provides clear insights on the FBMC characteristics and the impact of DPD on its perfor-

mance compared to the OFDM via extensive experiments.

5.3 Digital predistortion

The PA is the most energy consuming component in any transmitter system due to the high

energy waste (e.g. more than 50% of produced power is converted to heat energy) [79]. The

eﬃciency of a PA is the amount of radio frequency (RF) power consumed (Pin) to achieve

the required RF output power (Pout) which is calculated by a metric called power-added eﬃciency (PAE). PAE implies how eﬃciently a PA converts direct current (DC) power to

RF power which also shows power loss of PA, given by the following equation [80].

P − P P AE = out in (5.1) PDC 1 = η (1 − ) (5.2) D G where PDC is the power from DC power supply to the device. The ηD is the drain eﬃ- ciency which is the ratio of Pout to PDC [80], and G is the RF power gain (function of the instantaneous amplitudes of the signal).

From the above expressions and Figure 5.1, we can see that in order to achieve higher

eﬃciency, one needs to operate at higher input power. However, at such power levels the

input-output relationship of the PA ceases to be linear resulting in inter-modulation distor-

tions [81] where linearity is deﬁned as the linear signal conversion between input and output.

This is illustrated in Figure 5.1. This problem is referred to as the linearity-eﬃciency trade-

oﬀ [82]. Thus, it is a key criteria to design a PA that maintains linearity while operating

at high eﬃciency [83]. As shown in Figure 5.1, high power eﬃciency is achieved by operat-

67 ing in nonlinear region, while operating in linear region causes low efficiency. Operating in nonlinear region of PA results in significant out of band (OOB) distortion, which provides unwanted interference in adjacent frequency channels. Moreover, PAs in wideband systems operate and exhibit thermal and electrical memory effects which mean PA power gain is not constant over time, and varies with the current and previous input signal values.

Output Power Linear output (dBm) Efficiency Saturation

PSat Pout-pd 3 dB Compression point Pout Desired output

Pin Pin-pd Input Max correctable Pin Power (dBm)

Figure 5.1: Typical power and eﬃciency behavior of a power ampliﬁer

To drive PA at high eﬃciency mode, DPD techniques are used to compensate for PA nonlinearity at the expense of implementation complexity. Both memoryless and memory polynomial (MP) model are considered to investigate the eﬀect of memory along with nonlinearity on OFDM and FBMC signals.

The DPD is the inverse function of the normalized PA response applied on the original baseband input signal that results in linear gain at the output of PA. Figure 5.2 shows the input signal (x(n)) passed through the normalized inverse (predistortion) function of g(.) denoted by f(.), where g(.) is the PA’s nonlinear transfer function. Thus, a linear relationship between x(n) and y(n) is produced, where z(n) is the intermediate signal produced by f(.).

68 Hence, Figure. 5.2 should satisfy the following equation [81]:

y(n) = g(f(x(n))) ' G × z(n) (5.3)

f(x) = g(y/G)−1 (5.4) where G =4 G(|x(n)|) is function of the instantaneous amplitudes of the signal.

x(n) z(n) y(n) f (.) g (.) Predistortion PA Function Function

Figure 5.2: Predistortion schematic

5.4 Power Ampliﬁer Behavioral Modeling

To model the nonlinearity of the PA and obtain its reverse model for the purpose of linearization, PA behavioral modeling is necessary. The PA behavioral modeling is a black box modeling procedure that provides a mathematical formulation relating the input and output of the black box. This black box, in our case, is the power ampliﬁer. The behavioral modeling of the PA’s reverse function is equal to the post-distortion function as shown in

(5.4).

In this thesis, depending on the bandwidth of the signal, both memoryless and memory- based behavioral model have been considered to compensate for PA nonlinearity. Thus, the capability of using the look-up table (LUT) as a memoryless model, and MP [84] as a memory-based model, to linearize the system is evaluated. The LUT is chosen for its simplicity and to compensate for the static nonlinearity of the system while MP is used to enhance accuracy due to accounting for the memory eﬀect exhibited by the transmitter.

Indeed, MP is expected to show a better performance when modeling PAs with signals experiencing memory eﬀects.

69 5.4.1 Memoryless Model

In order to understand the behavioral modeling of a PA, consider Fig. 5.2. The LUT algorithm is a low complexity memoryless behavioral model of PA [85]. LUT generates static nonlinearity of PA by taking the instantaneous complex gain characteristics of PA. It uses averaging or polynomial ﬁtting of the raw data to derive the PA behavioral model [84].

The output signal of the PA i.e. y(n) using an LUT based model is calculated by the following equation [81].

y(n) ' G × z(n) (5.5) where z(n) is the input to the PA and G is function of the instantaneous amplitudes of the signal. It should be emphasized here that the above equation relates the input to the PA to its output i.e. the forward model. Obtaining an inverse model can be achieved in a straight forward manner by swapping the input and the output in the above equation.

5.4.2 Memory Polynomial Model

As mentioned earlier, LUT models the memoryless forward/reverse behavior of the PA.

This leads to simplicity in its implementation. However, in practical systems, if we increase the bandwidth of the signal, the associated memory effects cannot be ignored. Hence, for improved accuracy, these effects have to be considered. MP is a widely used model to model/mitigate the nonlinearity of the PA in the presence of memory effects. Thus MP model [86] is a more complicated behavioral model than LUT, which compensates for memory effects caused by large bandwidth signals. MP is a simplified version of Volterra series that only keeps the diagonal terms in the Volterra series to alleviate its complexity. It considers the dynamic memory effects of PA. The output of the PA when using MP is given by

(5.6) [84]. N O X X k−1 y(n) = ai,k z(n − i)|z(n − i)| (5.6) i=0 k=1 where N and O are the memory depth of the PA and nonlinearity order, respectively.

70 x(n − i) is the complex modulated input signal with delay equal to i. The term ai,k are the MP model coeﬃcients that are extracted using a least squares approach [87]. Similarly, the coeﬃcients for the reverse model can be obtaining by swapping the input and the output in the above equation and using the Least Squares approach.

5.5 Evaluation Metrics

One of the most important performance evaluation factors of the PA and transmitters is linearity. Since nonlinearity causes spectral regrowth into adjacent channels in the frequency domain, the ACPR is a suitable evaluation metric of PA linearity. Also, EVM is another linearity metric to quantify the in-band distortion of the transmitter in the time domain.

This chapter evaluates the PA and transmitter functioning while using FBMC waveform and then compare its performance against that of the traditional OFDM through the ACPR and the EVM metrics. Moreover, the signal’s statistics, PAPR and probability density function of the original FBMC and OFDM signals that inﬂuence the behavior of PA are measured and compared in this thesis.

5.5.1 PAPR

PAPR is deﬁned as the ratio of the peak power of the signal to its average power, which shows the extreme of the peak in the signal waveform. It also describes the dynamic property of the transmitted signal (S(n)). PAPR, expressed in units of dB (decibel), is given by (5.7), where Pavg is the average power of the transmitted signal [50].

max{|S(n)|2} P AP RdB = 10 log10( ) (5.7) Pavg

Variations in operating average power aﬀect the behavior of the PA, even for less than

1 dB [88].

71 5.5.2 ACPR

As shown in Figure 5.3 in the frequency domain, the ACPR is the ratio of the integrated power in the adjacent channel (adj.ch.) with the largest amount of power over power in the main input channel band (ch.) expressed in units of dBc (dB below the main carrier power).

The ACPR is given by [89,90]: R adj.ch. Φ(f) df ACP R = R (5.8) ch. Φ(f) df where Φ(f) is the power spectral density of the ampliﬁed signal. This parameter characterizes mostly the out-of band distortion and the likelihood of providing interference for neighboring radio channel for a given system. Since the ACPR indicates the amount of spectral regrowth

occurring in adjacent channels, it is desired to be as low as possible.

ACPR_lower

ACPR_upper

(dBm) (dBm)

Power Spectral Density Density Density Spectral Spectral Power Power

Frequency (Hz)

Figure 5.3: Graphical deﬁnition of the ACPR.

5.5.3 EVM

In order to compare and quantify the nonlinear distortion of the PAs, the EVM is measured for OFDM and FBMC signals. As depicted in Figure 5.4, in the constellation domain, the

EVM is the deviation between the original undistorted constellation point (reference) and the distorted one. EVM is expressed in dB (EVMdB) or percentage, given by the following

72 formula in dB [91]:

PE EVMdB = 10 log10( ) (5.9) PR where PE and PR denote the mean power of error vector and the mean reference power, respectively.

Reference constellation point

Measured constellation point

Figure 5.4: Graphical deﬁnition of the error vector.

5.6 Signal Generation

The generation of OFDM and FBMC waveforms was accomplished using Keysight Sys- temVue software [92], using its provided example ”5G-FBMC-Source”. Figure 5.5 shows the schematic for narrow band FBMC waveform in SystemVue where the random bits go into a constellation mapper that map QPSK/64-QAM signals to the FBMC transmitter block that generates FBMC baseband signal (proposed in [16,41,93]) with one transmit antenna port.

The FBMC signal produced by the FBMC transmitter block includes preamble symbols and data symbols but the pilot could be inserted or not. It also performs extended IFFT or PPN

IFFT, and generates FBMC signal with diﬀerent overlap, in the range from one to four.

Then, the complex signal converts to real (I) and imaginary (Q) value by CxToRect block and saves I/Q signal to the text ﬁle by Sink block.

73 The signals generated at 20 MHz bandwidth and sampling frequency of 160 Msps and

80 Msps for Class AB and Doherty PA, respectively. They have 128 active subcarriers with

20 data symbols, 6 preamble symbols and ﬁlter overlap factor whose value is selected in the

range from one to four. The extended inverse fast Fourier transform (IFFT) ﬁlter bank is

used with PHYDAS prototype ﬁlter [41] while applying both QPSK and 64-QAM modulation

techniques. The OFDM signal generated has similar characteristics to the FBMC signals

generated in terms of occupied subcarriers and subcarrier frequency spacing. However, a

1 cyclic preﬁx of 4 T s has been added, in addition to a windowing function to reduce OOB

emissions.

Figure 5.5: Narrow band FBMC

5.7 Power Ampliﬁer Characterization Setup

A moderately linear (Class AB) and a nonlinear (Doherty) PAs are used to study and com-

pare OFDM and FBMC signals’ characteristics regarding ACPR and EVM. The Class AB

PA uses a 10 W Cree CGH40010 device, designed for low to medium power base stations.

The laterally diﬀused metal oxide semiconductor (LDMOS–based) Doherty power ampliﬁer operating at 2.14 GHz, is a high power PA (with an output power of 300 W ) with strong non-

linearity and memory eﬀect. Firstly, in order to have a better comparison between OFDM

and FBMC signals, the Class AB PA is used to avoid the impact of high PA distortion

on EVM and ACPR (as in Doherty PA). Secondly, to study in-depth the emerging FBMC

waveform characteristics on the PA’s behavioral model, a more challenging PA with high

74 nonlinearity and memory eﬀect (Doherty) is used. Figures 5.6 and 5.7 present the measure-

ment setup for Class AB and Doherty PA, respectively, where the generation of OFDM and

FBMC waveform signals was accomplished using Keysight SystemVue software. The gener-

ated signals were downloaded into a Keysight E4438C Vector Signal Generator (VSG) or NI

PXIe-5646R transceiver to convert the digital baseband data to analog, and up-converted

to the RF band. Then the signal is applied to the PAs (Class AB/Doherty), to study the

impact of OFDM and FBMC signals’ characteristics on the PA’s behavioral model. The PA

output signal is captured by a Keysight E4440A Vector Signal Analyzer (VSA) or NI PXIe-

5646R transceiver which down converts the PA output signal. A general purpose interface

bus (GPIB) or PXI backplane with an NI 8135 embedded PC controller connects VSG and

VSA to the PC. A trigger pulse is used to synchronize the analyzer with the beginning of

the waveform.

5.8 Experimental Results and Discussion

Multicarrier signals comprise N sets of independent data which are transmitted over N orthogonal subcarriers. According to the central limit theorem, for a high value of N, the superposition of these data makes OFDM and FBMC complex Gaussian signals. As a result, both OFDM and FBMC exhibit high PAPR and high sensitivity to nonlinearity caused by the high power ampliﬁer of the transmitters [51].

Figure 5.8 shows the complementary cumulative distribution function (CCDF) of the original OFDM and FBMC signals generated by Keysight SystemVue for both QPSK and

64-QAM modulation schemes. The CCDF indicates the probability of the instantaneous envelope being higher than the mean power of the signal. In this case, as seen from the

ﬁg., both OFDM and FBMC waveforms have a high PAPR regardless of the modulation schemes. However, FBMC with an overlap 4 has a higher PAPR than its OFDM counterpart i.e. 2.57 dB for QPSK and 0.87 dB for 64-QAM modulation, respectively. The reason for

75 Transmitter\Feedback

NI PXIe-5646R PA transceiver

PXI PC backplane (a)

(b)

Figure 5.6: a) block diagram of the measurement setup for Class AB PA, b) Class AB measurement setup. high PAPR is due to the fact that FBMC being multicarrier in nature exhibits Gaussian characteristics [51].

This Section studies and compares OFDM and FBMC signals’ characteristics in terms of EVM and ACPR, before and after applying DPD techniques for Class AB and Doherty

PA.

5.8.1 EVM and ACPR Results before applying DPD

In order to recommend minimum acceptable IPBO of the FBMC and OFDM signals regarding EVM, the impact of Class AB and Doherty PAs’ IPBO on EVM is studied in this

Section. Applying same setup as in Figures 5.6, and 5.7, Figure 5.9 shows the sensitivity of

EVM (in dB) to the IPBO power of intended signals of Class AB and Doherty PA. It also

76 Transmitter

Keysight E4438C VSG PA Trigger

Keysight E4440A VSA PC GPIB Feedback (a)

(b)

Figure 5.7: a) block diagram of the measurement setup for Doherty PA, b) Doherty PA measurement setup.

includes AM-AM characteristics of Class AB and Doherty PA which measured sensitivity

to bandwidth under FBMC overlap 4. The IPBO is varied from 0 dB to -27.5 dB for Class

AB PA and is varied from 0 dB to -22.5 dB for Doherty PA with step size equals to 2.5 dB. The EVM is calculated in Keysight SystemVue using ﬁxed data pattern for input and output signals. There are three main ﬁndings from Figure 5.9. First, a higher IPBO results in better EVM due to reaching the linear region of PA. This can also be corroborated from

Figure 5.1. However, increasing IPBO leads to reduced efficiency as the PA operates in the linear region, which is undesirable. Second, regardless of the modulation scheme, the FBMC overlap 4 has a better EVM than OFDM signal. Because FBMC has better OOB due to efficient filtering [17] leading to lesser distortion and lower degradation in EVM. Finally, it is observed that except for overlap 1 which has no filtering, other FBMC signals (overlaps 2–4)

77 Figure 5.8: the PAPR CCDF of original signals in dB for both 64-QAM and QPSK modulation schemes. show the same behavior regarding EVM due to ﬁltering and they all are good at linearity.

5.8.2 EVM and ACPR results with DPD

Applying the same setup as in Figures. 5.6, and 5.7 the predistorted OFDM and FBMC signals are measured by Class AB and Doherty PAs. The LUT algorithm and memory polynomial algorithm with memory depth 3 and polynomial order 13 are applied to the signals described earlier in the signal generation Section. The Bussgang theorem claims that the noise power level of PA is independent of constellation type or size but it only depends on PA input power which is same for both QPSK and 64-QAM under the case study. Thus,

QPSK and 64-QAM should have the same level of the mean power of error vector that results in the same EVM using (5.9). In Figure 5.9, consistent with the Bussgang theorem, the EVM performance of QPSK and 64-QAM are similar. Hence, 64-QAM will be used in the following experiments.

The performance evaluation of the PA is done by calculating ACPR and EVM of the PA output signals. Results are generated for three scenarios enumerated as follows:

• Measuring the output of the transmitter when applying the peak of the input signal

at the saturation point of the PA (No DPD).

78 • Measuring the output of the transmitter after applying the LUT model (LUT).

• Measuring the output of the transmitter after applying the MP model (MP).

(a) ClassAB PA

-0 FBMC Overlap 1 (64-QAM) FBMC Overlap 2 (64-QAM) FBMC Overlap 3 (64-QAM) FBMC Overlap 4 (64-QAM) -5 FBMC Overlap 1 (QPSK) FBMC Overlap 2 (QPSK) FBMC Overlap 3 (QPSK) FBMC Overlap 4 (QPSK) -10

FBMC_O4 AM-AM Characteristics 65 -15

EVM (dB) EVM 60

-20

55 Gain(dB)

50 -25 -20 -15 -10 -5 0 P (dBm) in

-30 -20 -15 -10 -5 0 IPBO (dB) (b) Doherty PA

Figure 5.9: The EVM of the OFDM and FBMC signals versus IPBO including AM-AM characteristics; a) measured by Class AB PA, b) measured by Doherty PA.

79 Figures 5.10(a) and 5.10(b) compare the frequency spectra of the output signals of the

FBMC overlap 4, before and after applying DPD with the Class AB and Doherty PA in a nonlinear mode of operation. The FBMC overlap 4 is chosen as an example to show the impact of LUT and MP on the performance of the intended signals. As expected, the nonlinear output of PA (No DPD) produces signiﬁcant out of band distortion resulting in unwanted interference in the adjacent channels. As demonstrated in Figure 5.10, the main ﬁnding is that both predistorters, being the inverse models of the PA characteristics, can reduce the spectral regrowth caused by driving the PA in nonlinearity. But, comparing Figure 5.10(a)

with 5.10(b) MP can mitigate spectral regrowth more than LUT measuring with Class AB

PA than Doherty PA which results in the same level of performance for both LUT and MP.

The reason is, Doherty PA with strong nonlinearity and memory eﬀect has a high level of

distortion that affects memory effect. Whereas, a linear PA with memory effect with the

lower level of distortions shows a better performance concerning using memory–based DPD

(MP) than memoryless one (LUT).

In Figure. 5.11(a), the ACPRs and EVMs of OFDM and FBMC signals (overlaps 1–4)

are illustrated under Class AB PA. The ACPRs are measured for two lower, and upper

adjacent channels under DPD where each of them has 19 MHz bandwidth with frequency

oﬀset 20 MHz. For each adjacent channel, the average of ACPR values in lower and upper

channel is considered. There are ﬁve main ﬁndings from ACPR results in Figure. 5.11(a).

The ACPR improves as adjacent channel index increases (ch1 to ch2), as expected from the

signal’s characteristics, consistent with the results in Figure 5.10. Secondly, FBMC overlap 3

and overlap 4 provide almost the same ACPR performance as OFDM due to good out of band

(OOB) emission in FBMC overlap 3 and overlap 4. The third signiﬁcant ﬁnding is that FBMC

overlap 3 and overlap 4 present up to 22 dBc and 5 dBc ACPR improvement than FBMC

overlap 1 and overlap 2 caused by having a better OOB. The fourth ﬁnding is FBMC overlap 3

and overlap 4 show almost same ACPR, because they provide equivalent OOB emission.

80 Finally, it is interesting to observe that both MP and LUT present apparently similar ACPRs for OFDM and FBMC overlap 1 and overlap 2, due to the level of ﬁltering in FBMC overlap 1 and overlap 2 that brings a high level of distortion that cannot be overcome by using more accurate DPD model (MP). Whereas MP in FBMC overlap 3 and overlap 4 provide about

7 dBc and 2–3 dBc ACPR improvement than LUT for ch1 and ch2, respectively. The reason is good ﬁltering in FBMC overlap 3 and overlap 4 that results in signiﬁcant reduction in OOB emission, thus less distortion and better performance.

Moreover, Figure. 5.11(a) also presents the EVMs under DPD algorithms and original input signals for Class AB PA. FBMC overlap 4 improves performance (regarding EVM) 2 dB and 5.5 dB higher than OFDM when applying MP on 64-QAM and QPSK signals, respectively. This shows that FBMC outperforms OFDM. Moreover, FBMC overlap 3 provides the same EVM as OFDM. Comparing Figure. 5.11(a) EVM results with Figure 5.9 shows DPD provides a signiﬁcant improvement in EVM using either LUT or MP algorithm. Using DPD provides up to 20 dB and 25 dB enhancement in EVM using LUT and MP, respectively, over that of the corresponding scenario without DPD. It can be observed that MP provides signiﬁcant improvement about 8 dB and 6 dB for FBMC overlap 2 and overlap 4 in EVM over LUT. Finally, it is interesting to observe that FBMC overlap 2 provides better EVM than FBMC overlap 3, and is consistent with the EVM of original signals which are due to signals’ characteristics.

81 10 FBMC_Overlap 4: No_DPD FBMC_Overlap 4: LUT 0 FBMC_Overlap 4: MP

-10

-20

-30

-40

-50

Normalized Power Spectral Density (dBm) Density Spectral Power Normalized -60

-70 2.325 2.335 2.345 2.355 2.365 2.375 2.385 2.395 2.405 2.415 2.425 2.435 2.445 2.455 2.465 2.475 2.485 2.495 2.505 2.515 2.525 Frequency (GHz)

(a) ClassAB PA

(b) Doherty PA

Figure 5.10: The frequency spectra of FBMC overlap 4; a) measured by Class AB PA, b) measured by Doherty PA.

82 (a)

(b)

Figure 5.11: The EVM and ACPR of the OFDM and FBMC signals after applying predistortion. a) measured by Class AB PA, b) measured by Doherty PA.

Finally, Figure. 5.11(b) depicts the ACPRs and EVMs of FBMC signals (overlaps 1–4) using very nonlinear PA (Doherty) to study more in-depth their characteristics on the PA’s behavioral model. The average of ACPR values in lower and upper adjacent channels are considered while applying DPD algorithms. Due to reducing OOB emission, FBMC overlaps 2–4 provide a signiﬁcant improvement in ACPR than FBMC overlap 1. Secondly,

FBMC overlap 3 presents up to 5 dBc ACPR improvement than FBMC overlap 2 caused by having a better OOB, whereas, same ACPR enhancement in overlap 3 and overlap 4 due to

83 same OOB emission. Thirdly, as expected, both MP and LUT improves ACPRs and EVMs

oversignals without DPD. MP improves ACPR roughly 1 dBc more than LUT in best case

scenario, consistent with results for Doherty as a very nonlinear PA in Fig. 2(b).

Taken together, it is observed that to have same or better performance as OFDM concerning ACPR and EVM, at least FBMC with overlap factor of 3 is needed. Compensating for memory eﬀect is important for FBMC, but not for OFDM, which led to signiﬁcant enhancement (up to 7 dBc in ACPR and up to 5.5 dB in EVM). Besides, FBMC is superior to

OFDM regarding SE [16], but it suﬀers from implementation and computational complexity as compared to OFDM.

5.9 Summary

In this chapter, an examination of the performance enhancement of wireless transmitters driven by OFDM and FBMC signals using digital predistortion technique is carried out, supported by extensive measurements performed on two cases of a typical base station transmitter (e.g. RRH). LUT and MP algorithms are used to investigate the ability to enhance performance via OFDM and FBMC waveform along with DPD. Measurement results reveal that DPD provides a boost in ACPR and EVM when operating in PA nonlinearity region, leading to an increase in the PA eﬃciency. Moreover, experimental results show that FBMC outperforms OFDM by up to 5.5 dB concerning EVM and up to 7 dBc regarding ACPR.

The significance of the findings is that it is imperative to improve PA efficiency by at least using FBMC overlap 3 while applying DPD to get the most performance enhancement. The explanation is based on experimental results: FBMC overlap 3 and overlap 4 present almost similar performance due to providing equivalent OOB emission, thus overlap 3 is favorable for having less computational complexity.

84 Chapter 6

Conclusions

6.1 Major Research Findings

This thesis has accomplished its objectives of developing a comprehensive framework that

characterizes the SE and EE performance of cloud-RAN to provide support for high consumer

data traﬃc and maintaining high system eﬃciency for 5G. In this regard, the SE and EE

performance are determined as a function of the achievable average rate in the network. The

research ﬁndings reported in this thesis are summarized in the following relevant categories.

• EE/SE of cloud-RAN incorporating cooperative transmission:

The centralized processing along with cooperative transmission in cloud-RAN architecture

analyzed in chapter 3 by using stochastic geometry framework shows EE and SE perfor-

mance improvement. The received signal power enhancement and interference mitigation

along with power consumption alleviation due to cooperative transmission and centralized

processing improves achievable network rate and thus increases EE and SE. It shows that

up to two-fold increase in SE and good improvement in EE is feasible via cooperation in

cloud-RAN. Moreover, accounting for the cluster radius and transmit power reveals the

optimal number of cooperating RRHs that maximize the EE.

• EE of cloud-RAN incorporating distance-based fractional power control:

Tuning transmit power based on distance combined with centralized processing in cloud-

RAN can potentially oﬀer the much sought after relief in energy consumption by reducing

interference and increasing achievable network rate as analyzed by the stochastic geom-

etry tools in chapter 3. The use of fractional distance-based power control on coverage

probability, achievable average rate, and thus EE reveals up to a seven-fold increase in the

85 EE of cloud-RAN without power control by minimizing network power consumption and

network interference power when the control factor is set at 0.5.

• EE/SE of cloud-RAN incorporating distance-based fractional power control

along with cooperative transmission:

The impact of taking into account both cooperation among the RRHs within a cluster and

control of the transmit power of the RRHs in the cloud-RAN performance is investigated

in chapter 4 to analyze the throughput reliability, per-user achievable average rate, EE,

and SE performance of cloud-RAN. Using the stochastic geometry analysis framework, the

throughput reliability is studied ﬁrst, which then serves as the foundation for cloud-RAN

SE and EE performance analysis. Thanks to D-FPC that enables power savings achieve-

ment along with interference mitigation and cooperative transmission that provides an

improvement in the aggregate received signal power, which both result in an increase in

the achievable network average rate and, hence, both SE and EE improvement. The key

ﬁnding from the analysis is that by carefully tuning the RRH transmit power and coop-

eration parameter (cluster radius), it is possible to realize up to a three-fold improvement

in the EE along with 108% enhancement in the SE of cloud-RANs. Moreover, it is fea-

sible to utilize an optimal RRH density for not only maximizing EE and SE but also for

minimizing the network’s capital and operational expenditure.

• 5G signaling/evaluation by FBMC waveform:

The performance evaluation of wireless transmitters with FBMC waveform considering

diﬀerent values of the overlapping factor, selected in the range one to four, and OFDM

waveform while using DPD technique for two cases of a typical base station transmitter,

carried out in chapter 5. The extensive measurements with Doherty and ClassAB PAs

performed to evaluate FBMC as compared to OFDM comprising memoryless and memory

polynomial DPD to achieve highly eﬃcient PA. The peak to average power ratio (PAPR),

adjacent channel power ratio (ACPR), and error vector magnitude (EVM) are considered

86 as performance metrics. While both FBMC and OFDM show high PAPR, DPD improves

ACPR and EVM when operating in PA nonlinearity in both waveforms that results in

an increase in the PA eﬃciency. Results show that FBMC outperforms OFDM regarding

EVM (up to 5.5 dB) and ACPR (up to 7 dBc). Moreover, due to CP requirement in

OFDM as compared to FBMC, it is imperative to double data rate, and hence SE by

using FBMC instead of traditional OFDM.

6.2 Thesis Conclusions

Currently, cloud-RAN is a developing network architecture which requires more in-depth investigations to fully understand its capabilities and limitations. While a majority of the recent works are on the performance of heterogeneous and homogeneous cellular networks, cloud-RANs require more indepth study. This thesis analyzes the performance improvement achievable via cooperative transmission, distance-based power control and the combination of them, using stochastic geometry, based on which new insights into mitigating interference, and improving SE/EE are obtained. Moreover, wireless transmitters driven by OFDM and

FBMC signals are evaluated while using DPD, with the view of performance enhancement regarding ACPR and EVM. Extensive experiment results reveal that FBMC outperforms

OFDM, and at least FBMC overlap 3 is needed to get PA eﬃciency improvement.

6.3 Engineering Signiﬁcance of the Thesis Findings and Conclusions

On the one hand, the exponential growth of mobile data traffic with no prospect for additional spectrum to satisfy the increasing users’ demands stresses the need for installing more BSs. On the other hand, the destructive environmental aspect of adding new network equipment underscores the need for adopting an innovative technology like cloud-RAN that can potentially fulfill the goal of achieving green (i.e. energy-efficient) and spectral efficient communications in 5G networks. While the current spectrum availability is limited and ex-

87 pensive, it is still ineﬃciently utilized and has lots of opportunities to be further improved.

Collectively, the ﬁndings from this research promise to increase the SE/EE performance in

cloud-RANs to address the high traﬃc demand issues facing current and future cellular net-

works. The research shows that the cooperative transmission provides SE improvement by

improving received signal power due to joint transmission by all the RRHs in a cluster to the

desired user. It also shows that by carefully tuning the transmit power, it is feasible to en-

hance EE due to mitigating interference. Rigorous analysis conducted in this research shows

the combination of power control and cooperation along with centralized processing boost

both SE and EE. Moreover, the proposed research makes use of the FBMC waveform as an

innovative approach that ensures high data rate, unlike the existing works which are mostly

OFDM-based. Experimental results show how FBMC is a viable alternative for increasing

the system efficiency. The significance of this finding lies in showing that at least FBMC

overlap 3 with applying DPD is needed to get the most performance enhancement concern-

ing PA eﬃciency. The research also recommends minimum acceptable IPBO for FBMC and

OFDM signals for which further decrease in power results in no further gain in PA eﬃciency.

6.4 Thesis Limitations and Future Directions

The present thesis has accomplished its goal of cloud-RAN performance improvement regard-

ing high data rate and high system eﬃciency by developing a comprehensive mathematical/ experimental framework. However, in this thesis, a range of assumptions and system models are presented that leave some of the nontrivial aspects unaddressed in the system. For instance, the cloud-RAN system analyzed in chapter 3 and 4 has not dealt with the spatial interaction between users as the network nodes and considered users are distributed as

PPP [94]. Besides, the eﬀect of incorporating RRH with a sleeping strategy on EE has also not been addressed. Thus, the following directions can be undertaken to extend the work reported in this thesis:

88 • EE and SE of cloud-RAN with partially overlapped channelization technique

Recently, there has been a surge of interest in using partially overlapped channelization

(POC) technique which deliberately overlaps adjacent subchannels for communications

in wireless networks, particularly in cellular networks, wireless sensor networks and mesh

networks [95–104]. While overlapping subchannels exacerbates the interference level, it

also increases usage of the available bandwidth, thereby giving higher opportunity to en-

hance the system capacity. To highlight the signiﬁcance of the POC technique, consider

S the Shannon capacity formula provided by C = B log2(1 + N+I ) which indicates that the capacity C increases linearly with the bandwidth B while it decreases logarithmically

with the sum of interference I and background noise N. This implies that the increase in

available bandwidth has greater impact on the capacity enhancement than the increase in

interference. Speciﬁcally, the increase in the data rate achieved by increasing the band-

width is higher than the decrease in the data rate due to the reduced SINR caused by

the increase in interference resulting from channel overlap. In this case, due to the direct

proportionality of both the SE and EE with the capacity, the POC technique makes a

compelling strategy for its use in the cloud-RAN architecture. Furthermore, to ensure

that the users QoS requirements are satisﬁed at all times, it is pertinent to quantify the

tradeoﬀ between interference and spectrum utilization. As a future direction, determining

the optimal overlapping channel allocation strategy that jointly maximizes the SE and EE

of cloud-RANs in interference limited environment can be considered.

• Heterogeneous Cellular Networks Combined with cloud-RAN

Heterogeneous networks (HetNets) and cloud-RAN are two potential 5G network archi-

tectures. However, both architectures have their limitations. The fronthaul constraint

and the limited capacity of BBU pool limit the performance of cloud-RAN. HetNets are

plagued with severe inter-tier interference which also limits their performance. To over-

come the challenges in both cloud-RAN and HetNets, a hybrid wireless network architec-

89 ture consisting of the existing heterogeneous network (macrocells overlaid with multiple

tiers of small cells e.g. picocells and femtocells) with cloud-RAN is considered to provide

greater beneﬁts to improving the network performance [105–108].The greater beneﬁts arise

because the centralized processing at the BBU pool for heterogeneous cloud-RAN (H-C-

RAN) makes the interference coordination and joint processing more feasible than that for

heterogeneous networks. The proposal for the H-C-RAN network for use in 5G networks

is still in its infancy, and many issues are still open, speciﬁcally, theoretical performance

analysis of H-C-RAN still lacks in the literature. This research can extend by developing

a general performance evaluation framework based on stochastic geometry to determine

SE and EE metrics and also study how they can be maximized with and without QoS

constraints. H-C-RAN is expected to oﬀer improved performance over the cloud-RAN due

to mobility enhancement (i.e. ability to maintain a call as a UE moves between cloud-

RAN and heterogeneous network). Speciﬁcally, determining the optimal network design

parameters (e.g. small cell BS density, macrocell BS density, RRH density, transmit power

of small cell BS, macrocell BS, and RRH) that maximize the SE and EE in H-C-RAN can

be considered as an interesting future direction.

• EE of cloud-RAN with RRHs equipped with sleeping strategy

The eﬀect of incorporating RRH with a sleeping strategy on the network power consump-

tion and interference by dynamically turning oﬀ the RRHs when users become inactive in

their coverage areas can be studied. Thus, incorporating a sleeping strategy that keeps

RRHs at very low power consumption in idle times, with the view of increasing EE more

eﬃciently, can be considered as a future direction.

• Incorporating diﬀerent spatial models

Since the present thesis only considered PPP for user distribution, it is feasible to present

more accurate framework by incorporating diﬀerent spatial models like Cox Process and

Gibbs Process [21,24] at the expense of losing tractability and adding to the complexity.

90 • EE and SE of cloud-RAN for uplink transmission

This thesis studied downlink transmissions (i.e. from RRHs to users), hence, as a future

direction transmissions in the uplink (i.e. from users to RRHs) can be considered, to

satisfy the expected high uplink traﬃc in the future 5G networks.

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http://www.math.uah.edu/stat/expect/Integral.html Appendix A3

Appendices to Chapter 3

A3.1 Derivation of Average Achievable Rate (General Case)

Appendix A3.1 calculates the per user average achievable rate denoted by R¯ as follows.

Z ¯ (a) R = E (ϕ, h) [b ln(1 + SINR)] fr(r) dr r>0 P −α (b) Z 2 Pihir = b e−πλr [ln(1 + Ai∈{A1,...,AK } i )] 2πλr dr (A3.1.1) E (ϕ, h) P P h R−α + N r>0 Aj ∈ ϕ\{A1,...,AK } j j j

where the label (a) follows from the Shannon capacity law, using probability density function

(pdf) of user distance to its nearest RRH fr(r). The label (b) deﬁnes SINR when having cooperation.

Z ∞ −xN e X −α X −α E (ϕ, h)[ exp(−x PjhjRj )(1 − exp(−x Pihiri )) dx] x>0 x Aj ∈ ϕ\{A1,...,AK } Ai∈ {A1,...,AK } (A3.1.2)

R ∞ e−u −xu By invoking the identity [109]: ln(1 + x) = u=0 u (1 − e ) du, employing a change of

u a+b a b variables: x = P −α and simplifying by using e = e e . pj hj R +N Aj ∈ ϕ\{A1,...,AK } j

Z ∞ −xN (c) e Y X −α = Eϕ( Eh(exp(−x PjhjRj ))) x>0 x Aj ∈ ϕ\{A1,...,AK } Aj ∈ ϕ\{A1,...,AK }

Y X −α (1 − Eϕ( Eh(exp(−x Pihiri )))) dx (A3.1.3)

Ai ∈ {A1,...,AK } Ai∈ {A1,...,AK } where (c) follows from interchanging the expectation and integration operators applying

Fubinis theorem [110], E(ϕ, h) = Eϕ Eh follows from independency of fading channels h and RRH location ϕ, and independent and identical distribution (iid) of fading channels.

(d) X −α 1 = Eh(exp(−x PjhjRj )) = −α (A3.1.4) xPjRj + 1 Aj ∈ ϕ\{A1,...,AK }

106 Z ∞ −xN (e) e Y −α −1 Y −α −1 = Eϕ( (xPjRj + 1) )(1 − Eϕ( (xPiri + 1) )) dx x>0 x Aj ∈ ϕ\{A1,...,AK } Ai ∈ {A1,...,AK } (A3.1.5)

where (d) and (e) follow from Radio Channel Model assumption: Rayleigh fading and hj ∼

exp(1), and hi ∼ exp(1).

∞ −xN ∞ Rc (f) Z e Z 1 Z 1 = exp(−2πλ (1− −α )R dR)(1−exp(−2πλ (1− −α )rdr))dx x>0 x R=Rc xPjRj + 1 r=0 xPiri + 1 (A3.1.6)

where (f) uses Probability Generality Functional of PPP(ϕ) with density λ.

Z Z ∞ −xN Z ∞ ¯ (g) −πλr2 e 2/α du R = b e exp(−(xPj) πλ α/2 ) x Rc 2 1 + u r>0 x>0 u=( 1/α ) (xPj ) Rc 2 Z ( 1/α ) 2/α (xPi) dv (1 − exp(−(xPi) πλ α/2 ))dx 2πλrdr (A3.1.7) v=0 1 + v

R 2 r 2 where (g) uses the change of variables u = ( 1/α ) , v = ( 1/α ) , and substituting (xPj ) (xPi) (A3.1.6) to (A3.1.1).

Z Z ∞ −xN ¯ (h) −πλr2 e 2/α 2/α R = b e exp(−(xPi) πλς)(1 − exp(−(xPi) πλ(t − ς)))dx 2πλrdr r>0 x>0 x (A3.1.8) R y R ∞ R ∞ where (h) uses the fact u=0 f(u)du = u=0 f(u)du − u=y f(u)du and Mathematica for R ∞ du R y dv 2y1−α/2 2 2 −α/2 solving u=y 1+uα/2 and v=0 1+vα/2 . Here, ς = α−2 2F1 1, 1 − α ; 2 − α ; −y and t =

2π csc(2π/α) Rc 2 , y = ( 1/α ) , and 2F1 (., .; .; .) is the Gauss hypergeometric function. α (xPj )

A3.2 Derivation of Average Achievable Rate (Special Case)

Appendix A3.2 follows from solving (3.2) for the case (N = 0, ﬁxed transmit power=pmax, and α = 4).

∞ ∞ (a) Z 2 Z √ √ c dx Z √ dx R¯ = b e−πλr ( exp(−(γ x + β x arctan(√ ))) − exp(−γ x) ) 2πλrdr r>0 x=0 x x x=0 x (A3.2.1)

107 √ √ R2 where γ = p π2λ/2, β = − p πλ, c = √ c . The label (a) follows from using max max pmax Mathematica to solve the inner integrations of (3.2).

∞ (b) Z 2 Z √ dx R¯ = 2 b πλ(eβc − 1) e−πλr ( exp(−a x) ) rdr (A3.2.2) r>0 x=0 x

2 where (b) uses the approximation arctan(θ) ' θ and follows from independency of βc = πλRc from x and r. Lastly, by using Mathematica (3.3) will result.

A3.3 Derivation of Optimal RRH Density (Special Case)

∂EE Appendix A3.3 derives the optimal RRH density λopt that maximizes the EE, solving ∂λ = 0

for the case (N = 0, ﬁxed transmit power=pmax, and α = 4).

0.5 2 2 ∂EE (a) 1 2 bλ Γ(0, p π λ/2)(exp(πλR ) − 1) = × ∂ u max c = 0 (A3.3.1) ∂λ ∂λ λ(NTRX p0 + ∆ Pout)

$2λ2 µ2λ2 (b) 1 2 bλ (K − ln(λ) + $λ − )(µλ + ) = × ∂ u 4 2 = 0 (A3.3.2) ∂λ λ(NTRX p0 + ∆ Pout)

0.5 2 2 where $ = 0.5 pmax π , g = −(0.577216 + ln($)), µ = πRc . The label (a) uses (3.7). The label (b) follows from estimating the incomplete Gamma and exponential functions with the

ﬁrst 3 terms of their Taylor series expansion as follows: $2x2 Γ(0, $x) ≈ −(0.577216 + ln($)) − ln(x) + $x − (A3.3.3a) 4 µ2x2 exp(µx) ≈ 1 + µx + (A3.3.3b) 2 Rewriting (A3.3.2) based on λ we have:

2 2 2 2 (g−ln(λ)+$λ− $ λ )(µλ+ µ λ ) ∂EE ∂{ξ × 4 2 } = λ = 0 (A3.3.4) ∂λ ∂λ

where ξ = 2 b λu . After simpliﬁcation we have: λ(NT RX p0+∆ Pout) µ 3µ$2 $2 µ λ3( − ) − λ2(µ + − $µ) + λ( (g + 1) + $) − 1 = 0 4 √8 2 2 3 2 2 (c) 2 4 c c − 12c c + 3c + 4c 2 4 √ 1 3 4 2 λopt = 3 6 4 c1c4

108 here, the label (c) provides the solution to the third degree polynomial equation obtained

µ 3µ$2 $2 µ using Mathematica, where c1 = 4 − 8 , c2 = µ + 2 − $µ, c3 = 2 (g + 1) + $, c4 =

2 3 p 2 3 2 3 2 1/3 (27c1 + 2c2 − 9c1c2c3 + 4(−c2 + 3c1c3) + (27c1 + 2c2 − 9c1c2c3) ) .

A3.4 Coverage Probability Derivation

Appendix A3.4 derives the result for the conditional coverage probability. Mathematically,

let

−α (a) p1h1r Pr[ P −α > T |r] = Pr[h1 > s(I + N)|r] (A3.4.1) pj hj R +N j∈φ\{A1} j

(b) −sN Pcov = e LI (s) (A3.4.2)

T rα P −α The label (a) sets s = , I = pjhjR , after rearrangement. The label p1 j∈φ\{A1} j

(b) invokes the assumption h1 ∼ exp(1), where LI (s) is the Laplace transform of aggregate interference. The (A3.4.2) consists of two parts which are solved separately.

(c) X −α LI (s) = Eφ[exp(−s pjhjRj )] (A3.4.3) j∈φ\{A1} (d) Y 1 = Eφ[ −α ] (A3.4.4) 1 + spjRj j∈φ\{A1} ∞ (e) Z 1 = exp(−2πλ R dR) (A3.4.5) R r α+2 1/α α Rcell 1 + ( ( ) ) r Rcell 2T 2 (f) 2πλR ω 2 2 = exp(− cell F (1, 1 − ; 2 − ; −ω)) (A3.4.6) (α − 2) 2 1 α α

where (c) invokes the Laplace transform deﬁnition. The label (d) follows from the fact ec(a+b) = ecaecb and recalls the small-scale Rayleigh fading assumption and independence of the hj’s. (e) uses the Probability Generating Functional (PGFL) for PPP [21] and replaces

0 0 pj by pj. pj is the transmit power of the RRH j to its own user (located inside the RRH R Rα j’s coverage area). p0 is given by p0 = R cell p f (x) dx = 2p ( pmin ) cell , where x is the j j x=0 j xj max pmax α+2 j distance between interfering RRH j and its own user. p = p ( pmin )rα is the assumed 1 max pmax

109 D-FPC scheme. Knowing that the PPP distribution becomes the uniform distribution for a

2x bounded area [37], probability density function of xj is deﬁned as fxj (x) = 2 . The label Rcell R r α+2 1/α 2 Rcell 2 r α+2 1/α 2 (f) applies a change of variable v = ( ( ) ) and sets β = ( ) ( ( ) ) , r Rcell 2T r Rcell 2T then uses Mathematica where ω = 2T ρα(1−), ρ = r . Next, solving e−sN : α+2 Rcell

α pmax (g) T Nr ( ) e−sN = exp(− pmin ) = e−ηN (A3.4.7) pmax

T rα where (g) substitutes (s = ), and p1, the transmit power of RRH 1, by using the p1

α(1−) pmax assumed D-FPC scheme. It also sets η = T r ( ) /pmax for notation simplicity. pmin Next, substituting (A3.4.6) and (A3.4.7) into (A3.4.2), the conditional coverage probability results.

110 Appendix A4

Appendices to Chapter 4

A4.1 PROOF of Proposition 4.1

Appendix A4.1 derives the result for the conditional throughput reliability, deﬁned as the

probability that the achievable throughput exceeds a certain threshold θ, given the desired user is at a distance r from its closest RRH, denoted Pr(T hr > θ |r). Starting from (4.1) in

the text, discounting the (1/ ln 2) factor and making SINR explicitly a function of distance

r, we have:

(a) Pr(T hr > θ |r) = Pr[ ln(1 + SINR(r)) > θ ] (A4.1.1)

−α K −α (b) p h r + P p h r = Pr[ 1 1 i=2 i i i > (eθ − 1)] (A4.1.2) P p h R−α + N j∈ϕ\{A1,...,AK } j j j θ K (c) e − 1 X −α 1 X −α = Pr[h1 > −α ( pjhjRj + N − θ pihiri )] p1r e − 1 j∈ϕ\{A1,...,AK } i=2

where r is the distance between the desired user and its nearest RRH. The label (a) fol-

lows from the Shannon capacity law, where ln(1 + SINR(r)) is the achieved data rate

in nats/sec/Hz by the desired user. Label (b) substitutes SINR(r) deﬁnition under the

general case of having both RRH power control and RRH cooperation, and (c) rearranges

T θ P −α (A4.1.2). For notational simplicity, set s = −α ,T = e − 1,I = pjhjR , p1r j∈ϕ\{A1,...,AK } j PK −α w = i=2 pihiri . Recall from Section 4.2.2 of text that h1 ∼ exp(1). The conditional throughput reliability is then expressed as:

(d) −sN Pr(T hr > θ |r) = e LI (s)Lw(−s/T ) (A4.1.3)

where (d) follows from the fact that h1 ∼ exp(1), and LI (s) and Lw(−s/T ) denote the Laplace transform of aggregate inter-cluster interference and aggregate received signal power

111 from the cooperating RRHs, respectively.

Now,

(e) X −α LI (s) = Eϕ[exp(−s pjhjRj )] (A4.1.4)

j∈ϕ\{A1,...,AK }

(f) Y −α = Eϕ[ Ehj [exp(−spjhjRj )] (A4.1.5)

j∈ϕ\{A1,...,AK } (g) Y 1 = Eϕ[ −α ] (A4.1.6) 1 + spjRj j∈ϕ\{A1,...,AK } ∞ (h) Z 1 = exp(−2πλ 1 − R dR) (A4.1.7) 1 + T rα p0 R−α Rc p1 j ∞ (i) Z 1 = exp(−2πλ R dR) (A4.1.8) r r α+2 1/α α Rc 1 + ( ( ) ) R Rcell 2T Z ∞ (j) 1− 2T 1/α 2 du = exp(−πλ (r Rcell( ) ) α/2 ) (A4.1.9) α + 2 u=β 1 + u 2 (k) 2πλR ξ 2 2 = exp(− c F (1, 1 − ; 2 − ; −ξ)) (A4.1.10) (α − 2) 2 1 α α

where (e) follows from the deﬁnition of the Laplace transform, (f) uses the fact ec(a+b) =

ca cb e e , (g) follows from the independence of the hj’s and Laplace transform of the exponential function. (h) follows from the Probability Generating Functional (PGFL) for PPP [21] and

0 replacing pj by pj as the RRH j transmit power to its own user where the user is located anywhere inside the RRH j’s coverage area. The label (i) substitutes distance-based FPC

R Rα scheme p = p ( pmin )rα and p0 = R cell p f (x) dx = 2p ( pmin ) cell by considering 1 max pmax j x=0 j xj max pmax α+2 2x probability density function of xj as fxj (x) = 2 , assuming uniformly distributed users Rcell in light of the fact that PPP distribution becomes uniform distribution when the area is

R r α+2 1/α 2 bounded [37]. The label (j) employs a change of variable u = ( ( ) ) and sets r Rcell 2T Rc 2 r α+2 1/α 2 β = ( ) ( ( ) ) , (k) applies some simpliﬁcations by using Mathematica where r Rcell 2T 2T rRcell α ξ = ( ) . α+2 r Rc Next, the Laplace transform of the aggregate received signal from the cooperating RRHs is

determined as follows:

112 K K (l) s X (m) Y s L (−s/T ) = [ews/T ] = [exp( p h r−α)] = [ [exp( p h r−α)]] w Ew EK T i i i EK Ehi T i i i i=2 i=2 K r (n) Y 1 (o) Z c 1 = [ ] = exp(−2πλ 1 − w dw) (A4.1.11) EK s −α 1 0 −α 1 − pir 1 − −α p w i=2 T i w=r p1r i R (p) Z c 1 = exp(−2πλ w dw) (A4.1.12) 1 + (− w ( r )( α+2 )1/α)α w=r r Rcell 2 Z Vul (q) 1− 2 1/α 2 dV = exp(−πλ(r Rcell( ) ) α/2 ) (A4.1.13) α + 2 V =Vll 1 + V

2 (r) 2πλr ϑ 2 2 2 2 = exp(− ( F (1, 1 − ; 2 − ; −ϑ) − ρ(α−2) F (1, 1 − ; 2 − ; −ϑρα))) (A4.1.14) (α − 2) 2 1 α α 2 1 α α where (l), (m), (n), (o), and (p) use the same reasoning as (e), (f), (g), (h), and (i), respec-

w r α+2 1/α 2 tively. The label (q) employs a change of variable V = (− ( ) ( ) ) where Vul = r Rcell 2

Rc r α+2 1/α 2 r α+2 1/α 2 (− ( ) ( ) ) and Vll = (( ) ( ) ) . The label (r) applies some simpliﬁca- r Rcell 2 Rcell 2 R b R ∞ R ∞ tions by using Mathematica, recalling the fact that x=a f(x) dx = x=a f(x) dx− x=b f(x) dx α r 2Rcell where ρ = , ϑ = α . Rc (α+2)r Finally, α pmax (u) T Nr ( ) e−sN = exp(− pmin ) = e−Nδ (A4.1.15) pmax

−sN T where (u) simpliﬁes e in (A4.1.3) by substituting (s = −α ) and p1 and setting δ = p1r

α(1−) pmax −T r ( ) /pmax. Next, substituting (A4.1.10), (A4.1.14) and (A4.1.15) into (A4.1.3), pmin the conditional throughput reliability is determined as follows

−Nδ −πλτ −πλκr2 T hrReliab(θ, λ, Rc, |r) = e e e (A4.1.16)

α 2 2 2 r 2Rcell θ where τ = (2R ξ/(α − 2)) F (1, 1 − ; 2 − ; −ξ), ρ = , ϑ = α , T = e − 1, c 2 1 α α Rc (α+2)r 2 2 (α−2) 2 2 α κ = (2ϑ/(α − 2)) × (2F1(1, 1 − α ; 2 − α ; −ϑ) − ρ 2F1(1, 1 − α ; 2 − α ; −ϑρ )), δ = α pmax 2T rRcell α −T r ( ) /pmax, ξ = ( ) , and 2F1(a, b; c; d) is the Gauss-hypergeometric func- pmin α+2 r Rc tion. Clearly, (A4.1.16) is the same as (4.4) in Section 4.3 of the chapter, thus completing the Proof.

113 A4.2 PROOF of Proposition 4.4

Appendix A4.2 derives the result for the unconditional throughput reliability under inter-

ference limited (i.e. N = 0) condition and cloud-RAN operational scenario of RRH transmit

power control but no cooperation. Setting N = 0 and Rc = r in (4.5) gives:

−α (a) Z p h r 2 T hrReliab(θ, λ, α) = Pr[ 1 1 > (eθ − 1)]e−πλr 2πλr dr (A4.2.1) P p h R−α r>0 j∈ϕ\{A0} j j j Z (b) −πλr2 T hrReliab(θ, λ, α) = e LI (s)2πλr dr (A4.2.2) r>0 where (a) substitutes SIR deﬁnition for the case of having power control with no cooperation, and (b) follows the same analysis as (A4.1.3) by setting I = P p h R−α, r = r ,T = j∈ϕ\{A0} j j j 1

θ T e − 1, s = r−α , p = p1, and h1 ∼ exp(1).

∞ (c) Y 1 (d) Z 1 L (s) = [ ] = exp(−2πλ R dR) (A4.2.3) I Eϕ α −α Rpr−α 1 + T r pjRj Rcell 1 + j∈ϕ\{A0} T p´j ∞ (e) Z 1 = exp(−2πλ R dR) (A4.2.4) R r α+2 1/α α R 1 + ( ( ) ( ) ) cell r Rcell 2T 2 (f) 2πληR 2 2 = exp(− cell F (1, 1 − ; 2 − ; −η)) (A4.2.5) (α − 2) 2 1 α α

where (c) arises from the similar reasoning as in (A4.1.4), (A4.1.5) and (A4.1.6), and (d), (e),

and (f) use the same analysis as (A4.1.8), (A4.1.9) and (A4.1.10) where η = 2T ( r )α(1−). α+2 Rcell Substituting (A4.2.5) into (A4.2.2), (4.7) gets deduced.

114