Title Page

Abstract

Contents

Chapter 1. Introduction 15

1.1. Background 15

1.2. Motivation 16

1.3. Related Work 19

1.4. Outline and Contributions 23

Chapter 2. Overview on Stochastic Geometry Analysis 27

2.1. Mathematical Background on Stochastic Processes 27

2.2. Coverage Analysis for Simple Downlink Cellular Net-works 31

2.2.1. Reference System Model 31

2.2.2. Performance Metric 32

2.2.3. Coverage Probability Analysis 34

Chapter 3. Coverage and Rate Analysis under Nakagami & Log-normal Composite Fading Channel for Downlink Cellular Networks 36

3.1. Introduction 36

3.2. System Model 37

3.3. Coverage Probability Analysis 39

3.4. Average Rate Analysis 46

3.5. Numerical Result 47

Chapter 4. Low-Complexity Coverage Analysis of Downlink Cellular Network Under Combined LOS and NLOS Propagation 50

4.1. Introduction 50

4.2. System Model 52

4.2.1. Blockage Model 52

4.2.2. Network Model 53

4.2.3. Channel Model 56

4.2.4. Association Model 56

4.3. Coverage Probability 57

4.4. Interference Approximation 58

4.5. Numerical Result 61

4.6. Appendix 65

4.6.1. Proof of Lemma 4.1 65

4.6.2. Proof of Lemma 4.2 68

4.6.3. Proof of Lemma 4.3 69

Chapter 5. Low-Complexity Coverage Analysis of Downlink Cellular Network with Bidirectional Beamforming 77

5.1. Introduction 77

5.2. System Model 79

5.3. Coverage Probability Analysis 83

5.3.1. Interference for Multi-cosine Beam Pattern 84

5.3.2. Interference for Multi-level Beam Pattern 87

5.4. Numerical Result 90

5.4.1. Perfect Beam Alignment 90

5.4.2. Imperfect Beam Alignment 92

Chapter 6. Conclusion 98

Bibliography 100

List of Tables

Table 1.1: Comparison of system models for the related works 22

Table 1.2: Comparison of system models (chapter) 24

Table 4.1: Intensity Measure of the Distance Process 55

Table 4.2: Radii of LOS- and NLOS-ball, RL and RN(이미지참조) 60

Table 5.1: Mainlobe beam gain coefficient (k＝0) 81

Table 5.2: Sidelobe beam gain coefficient (k ∈ {1,2,...,K}) 82

Table 5.3: Default system parameters 91

List of Figures

Figure 1.1: A 40 x 40 ㎞ view of a current base station deployment by a major service... 17

Figure 1.2: Poisson distributed base stations and mobiles, with each mobile associated... 18

Figure 1.3: Outline of the thesis 23

Figure 2.1: Illustrative example of MS and BS; the MS is located at origin and BSs are... 32

Figure 3.1: Nakagami-lognormal distribution as varying the number of GHQ samples... 40

Figure 3.2: Mean Square Error of the approximation 41

Figure 3.3: Coverage probability as varying the number of GHQ samples (σSF＝6㏈...(이미지참조) 48

Figure 3.4: Coverage probability for various Nakagami-m fading parameters 49

Figure 4.1: Comparison of LOS probability distributions for the various blockage models 54

Figure 4.2: Illustrative example of the special case of association 56

Figure 4.3: Concept of proposed interference approximation method 59

Figure 4.4: Comparison of coverage probabilities for the various blockage models 62

Figure 4.5: Comparison of average interference for the various blockage models 63

Figure 4.6: Comparison of average interference for two different PLEs 64

Figure 4.7: Coverage probability with different blockage conditions by varying the average... 65

Figure 5.1: Illustration of the discrete model for beam pattern: N＝16 82

Figure 5.2: Coverage probability as varying the number of quantization samples 92

Figure 5.3: Coverage probability for varying the number of receive antennas with the fixed... 93

Figure 5.4: Coverage probability for varying the number of transmit antennas with Nr＝4(이미지참조) 94

Figure 5.5: Comparison of coverage performance with the fixed number of antennas Nt＝...(이미지참조) 95

Figure 5.6: Comparison of coverage performance with the fixed number of antennas Nt＝...(이미지참조) 96

Figure 5.7: Coverage performance as varying the beam misalignment ratio for spatial AoD... 97

 Due to the ever-growing number of mobile devices, increased trend in the usage of applications, and more data hungry applications, there is a constant need for increased data rates in the cellular network. It is predicted that there will be a thousand-fold increase in mobile traffic by the next decade. To meet the required data rates, researchers have started investigating new 5G techniques. Due to the limited bandwidth in the current mobile communication systems, hundreds of megahertz potential bandwidth in millimeter-wave (mmW) band has been considered for access link in 5G cellular system. It is concerned with taking advantage of the vast amount of spectrum available in the range of 30 to 300 GHz, which offers great potential in achieving the 100x data rate increase. Moreover, the very short wavelength makes it possible to adopt relatively large antenna arrays in mobile terminals. Unlike the conventional sub-6 GHz systems, mmW-band signals have been confirmed to have some unique propagation characteristics, such as the huge propagation losses and the susceptibility to blockages. Thus, beamforming is generally employed to achieve substantial array gains and synthesize highly directional beams.

An extensive performance analysis is required before manufacturing and testing actual base stations and terminals to see how changes in various system parameters affect actual 5G mobile network with different characteristics from traditional cellular networks. A field of mathematics called stochastic geometry turned out to be one of the useful tools to analyze the system performance in cellular networks. The set of analytical techniques used to study HetNets that is described in this book comes from a field of mathematics called stochastic geometry. The key idea is to model the locations of base stations and user terminals in a cellular network as realizations of a class of random mathematical objects called point process on the Euclidian plain. Then, some important performance measures, including the coverage or outage probability, can be derived in a simple form, e.g., a closed-form expression for some special cases. As the cellular network analysis that takes various system models into account using stochastic geometry has been made, however, the problem of computational complexity has been gradually increased. Considering the blockage model, classified as line-of-sight (LOS) and non-line-of-sight (NLOS) links, for accurate 5G system performance analysis, the base station is divided into LOS- and NLOS-BS with inhomogeneous PPP and then, computational complexity for the underlying coverage analysis is dramatically increased. Furthermore, additional computational complexity is required as it reflects the beam pattern generated by the base station and the terminal using multiple antennas, so as to deal with propagation characteristics in mmW communication, such as the huge propagation losses and the susceptibility to blockages. The main purpose of this thesis is to provide a low-complexity analysis while reflecting the generalized system model that can be best fitted to practical 5G communication system and ensuring the analytical tractability of the analysis.

An approximation method has been proposed for the various system components that the 5G network should consider, while ensuring the tractability of the analysis. In particular, the system's coverage performance can be calculated with low computational complexity. In order to deal with various aspects of channel characteristics in the different environments, a generalized channel model is introduced for accurate analysis. Integrated shadow fading and multi-path fading channel are modeled by a Nakagami-lognormal distribution, which cannot be expressed in a closed form. We first approximate a gamma-lognormal distribution, which characterizes power of composite fading, as a weighted sum of gamma distributions by the Gauss-Hermite quadrature (GHQ) for analytical tractability. Meanwhile, since there is a significant difference in the signal strength between the LOS and the NLOS links, they must be distinguished in the course of analyzing the coverage performance. For example, the longer link is less likely to be a LOS link. As the base stations are either in LOS or NLOS situation, their distribution is modeled as an inhomogeneous PPP, which complicating the coverage analysis. Therefore, another approximation has been proposed to compute the interference experienced by a MS while approximating BSs simply with a homogeneous PPP. As a cellular network is operating in a mmW-band with a short wavelength, a base station and a terminal can hold a plurality of antennas, which allows for enhancing the coverage with a powerful beamforming technique. Since a distribution of the interference experienced by the UE varies upon the use of the beamforming technique, an accurate antenna model is critically required for the coverage analysis. In order to deal with the computation complexity associated with the actual beam pattern, another level of approximation is finally proposed for a beam pattern, establishing a mathematical framework for accurate yet tractable coverage analysis.

We propose an approximation method for wireless channel, propagation, and beam pattern, and provide a low-complexity coverage analysis framework that can remove three integral signs compared to the existing studies. We also verify the accuracy of the coverage probability distribution with approximation through simulation. As communication technology develops, coverage analysis that reflects new system characteristics will be needed, and the framework with low complexity will be useful.