Propagation Characteristics and Performance Evaluations for Millimeter Wave Transmissions

Muyang Li

A thesis in fulfilment of the requirements for the degree of

Master by Research

School of Electrical Engineering and Telecommunications

Faculty of Engineering

January 2018

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Date ……………………………………………...... Abstract

The fourth generation (4G) mobile communication systems are widely used in these years. However, with the increasing mobile data demands, there is still a gap between the users’ requirements and what can be offered now. In order to meet the users’ growth demands and to achieve a faster data transmission speed for future wireless systems, millimeter wave is considered to be a key technology in the fifth generation (5G) cellular networks.

This thesis first reviews the propagation characteristics of millimeter wave and compares it with traditional microwave systems. We discuss the details of the millimeter wave spectrum, oxygen and rain attenuation, penetrability, reflection, path loss exponents, delay spreads, Doppler shift and outage probability of millimeter wave.

We then estimate the path loss, outage probability and channel capacity of the millimeter wave system in order to study how the propagation characteristics affect the performance of the wireless communication systems. We evaluate the path loss with shadow fading and outage probability of the four typical frequencies at 28 GHz, 38 GHz, 60 GHz and 73 GHz; as well as the channel capacity of single-input-single-output (SISO), multiple-input-single-output (MISO), single-input-multiple-output (SIMO) and multiple-input-multiple-output (MIMO) channels at these frequencies. We notice that the path losses for 28 GHz and 38 GHz are not very large and the channels with these two carrier frequencies can support the signal transmission for a longer distance for about 400 meters with the standard transmit power. However, 60 GHz performs not very well because of the huge atmosphere and rain attenuation and it can only support 50 meters reliable signal transmission by using multiple antennas with similar transmit power.

We then set up a single-cell multi-user system model and a 19-cell multi-user system model to evaluate how millimeter wave perform communications in a multiple active

1 user scenario. In the evaluation, we calculate the interference from other users in the same cell as well as in neighboring cells. In addition, we exam the effect of the number of active users, transmit antennas and carrier frequencies on the sum-rate performance in both single cell model and 19-cell model. The cumulative distribution function (CDF) of the sum-rate is used to show the behavior of the sum-rate distributions and the 10th percentile of user rate is used to measure the performance of cell-edge users. It is shown that while all the frequencies perform better in the single-cell system than in the multi-cell system, the influence from the inter-cell interference is largest for 28 GHz among all the bands and its sum-rate decreases by 11.73%.

We also review the signal processing techniques for millimeter wave systems and evaluate the hybrid transceiver architecture. We set up a 7-cell multi-user MIMO hybrid system to compare the power efficiency of the full digital, full access hybrid and subarray hybrid architecture. The results show that although the full digital array has the best performance in a high power region, it is very costly and impractical because of the space limitation. If the total power for the system is small, the full access hybrid can achieve a higher sum-rate for the system than the full digital array. As for subarray hybrid architecture, although the achievable sum-rate is not the best, there is only a small gap between it and the full digital architecture at a very low power. Thus, subarray hybrid architecture is still considered as a very useful approach in practical wireless communication systems with very limited transmit power since it offers the simplest circuit design and fewer losses compared to fully access architecture.

Acknowledgement

I would like to express my appreciation to all the people who helped and supported me during my study at the University of New South Wales these years.

Above all, I would like to express my special thanks to my supervisor Prof. Jinhong Yuan, who gave me the opportunity to study here and do this wonderful project on wireless and telecommunications. During the research, he supports me a lot not only on the research project itself but also teach me how to study well. This work would not have been possible without his guidance. In these years, I learnt so many new things in my research area and I am really thankful to him.

Secondly, I would like to thank Dr. Derrick for his help on my research project, and also the advice from him for my future career. I would also like to express my appreciation to my parents who encourage me to study at UNSW, although they are not staying with me in Australia these years. In addition, thanks to all my colleagues Lou, Jiajia, Sissi, Sunny, Zhiqiang, KP and Min for giving me such a wonderful research environment and the precious days we have spent together. Especially for Lou and Jiajia, who gave me so many helps on my project as well as on programming. Also, thanks Sunny and KP for organizing a lot of interesting activities.

Last, I would like to express my appreciation to the friends I met in Australia, especially the girls in my dance group. They encouraged me when I feel tired and upset and cheer me up. Thanks for all of the help, support and encouragement from these friendly people.

Contents

Abbreviations

List of Figures

List of Tables

Chapter 1. Introduction ...... 1

1.1. Contribution of Thesis ...... 2

1.2. Organization of Thesis ...... 4

Chapter 2. Introduction of Millimeter Wave Propagation ...... 6

2.1. Introduction of Millimeter Wave ...... 6

2.2. Millimeter Wave Spectrum ...... 7

2.3. Propagation Characteristics for Millimeter Wave ...... 12

2.3.1. Free Space Propagation Model ...... 13

2.3.2. Simplified Path Loss Model ...... 15

2.3.3. Atmosphere Gaseous Losses ...... 16

2.3.4. Rain Attenuation ...... 20

2.3.5. Penetrability ...... 22

2.3.6. Reflection Coefficients ...... 26

2.3.7. Path Loss Exponents...... 27

2.3.8. Root Mean Square (RMS) Delay Spreads ...... 30

2.3.9. Doppler Shift ...... 31

2.3.10. Outage Probability ...... 32

2.4. Millimeter Wave Wireless Applications ...... 33

2.4.1 Small Cell and Cellular Access ...... 33

2.4.2 Wireless Backhaul System ...... 34

2.5. Summary ...... 37

Chapter 3. Outage Probability and Channel Capacity of Millimeter

Wave Channels ...... 38

3.1. Path Loss and Shadowing Effect for Various Frequency Bands ...... 38

3.2. Outage Probability ...... 48

3.3. Rayleigh Fading and Rician Fading Channel ...... 52

3.4. Channel Capacity ...... 54

3.4.1. Additive White Gaussian Noise (AWGN) Channel Capacity ...... 54

3.4.2. Capacity of SISO System over a Rician Fading Channel ...... 55

3.4.3. Capacity with Antenna Diversity ...... 58

3.4.4. Comparison of Capacity of SIMO, MISO and MIMO Channels ...... 71

3.5. Summary ...... 73

Chapter 4. Multi-user Millimeter Wave Systems ...... 75

4.1. Interference and Signal-to-interference-plus-noise Ratio (SINR) ...... 75

4.2. Single-cell Multi-user Millimeter Wave System ...... 76

4.2.1. System Model ...... 76

4.2.2. Scheduling ...... 77

4.2.3. Beamforming...... 77

4.2.4. Zero-forcing Beamforming ...... 79

4.2.5. Multi-user Sum-rate Evaluation ...... 80

4.3. Multi-cell Multi-user Millimeter Wave System ...... 90

4.3.1. System Model ...... 90

4.3.2. System with Zero-forcing Beam forming ...... 91

4.3.3. Multi-user Sum-rate Evaluation ...... 93

4.4. Comparison of Sum-rate between Single-cell and Multi-cell System ...... 104

4.5. Summary ...... 106

Chapter 5. Hybrid Architecture for Millimeter Wave Transceivers ..... 108

5.1. Hybrid Architecture ...... 109

5.1.1. Hybrid Architecture for Millimeter Wave Systems ...... 109

5.1.2. Hybrid Analog-Digital Processing ...... 112

5.1.3. Low Resolution Receiver ...... 115

5.1.4. Hybrid beamformer ...... 115

5.2. Power Consumption Evaluation ...... 117

5.3. Summary ...... 125

Chapter 6. Summary and Future Works ...... 127

6.1. Summary ...... 127

6.2. Future Works ...... 129

6.2.1. Optimal Cell Radius and Small Cell Density ...... 129

6.2.2. Multiple Access Design in Millimeter Wave Communications ...... 133

6.2.3. Angle-of-arrival (AoA) and Angle-of departure (AoD) of Millimeter

Wave ...... 134

6.2.4. Phase-shifting Beamformers for Millimeter Wave ...... 135

Reference

Abbreviations

4G Fourth Generation

5G Fifth generation

AWGN Additive white Gaussian noise

CDF Cumulative distribution function

CDMA Code division multiple access

CSI Channel statement information

D2D Device-to-device

EES Earth Exploration-Satellite

FDD Frequency division duplex

FDE Frequency-domain equalization

FDMA Frequency division multiple access

HCN Heterogeneous cellular network

ICI Inter-carrier interference

IMT-Advanced International Mobile Telecommunications-Advanced

ITU International Telecommunication Union

LNA Low noise amplifier

LOS Line-of-sight

LTE Long Term Evolution

M2M Machine-to-machine

MIMO Multiple-input-multiple-output

MISO Multiple-input-single-output

MRC Maximum-ratio combining

MU-MIMO Multi-user MIMO

NLOS Non-line-of-sight

NOMA Non-orthogonal multiple access

OFDMA Orthogonal frequency-division multiple access

PA Power amplifier

PPP Poisson point process

RF Radio frequency

RMS Root mean square

SDMA Space-division multiple access

SIC Successive interference cancellation

SIMO Single-input-multiple-output

SINR Signal to interference and noise ratio

SISO Single-input-single-output

SNR Signal to noise ratio

TDD Time division duplex

TDMA Time division multiple access

ZF Zero-forcing

List of Figures

Figure 2.1. Traditional microwave bands and millimeter wave bands [11] ...... 6

Figure 2.2. Millimeter wave spectrum [14] ...... 8

Figure 2.3. Millimeter wave band allocation in the United States 2003 [21] ...... 11

Figure 2.4. Free space propagation model ...... 13

Figure 2.5. Specific attenuation due to atmospheric gases (Pressure: 1013 hPa,

Temperature: 15 ȭ, Water Vapor Density: 7.5 g/m^2) [18] ...... 1 7

Figure 2.6. Attenuation by oxygen and water vapour [13] ...... 18

Figure 2.7. Rain attenuation according to frequency [31] ...... 22

Figure 2.8. Illustration of measurement of penetration at 28 GHz in New York City ...... 23

Figure 2.9. Single gateway node backhaul model ...... 35

Figure 2.10. Multiple gateway node backhaul model ...... 36

Figure 3.1. Path loss and shadowing of 28 GHz ...... 42

Figure 3.2. Path loss and shadowing of 38 GHz ...... 43

Figure 3.3. Path loss and shadowing of 60 GHz ...... 45

Figure 3.4. Path loss and shadowing of 73 GHz ...... 46

Figure 3.5. Path loss and shadowing of 2.4GHz ...... 47

Figure 3.6. Path loss comparison between 2.4, 28, 38, 60 and 73 GHz ...... 48

Figure 3.7. Outage probability comparison between 28, 38, 60, 73 GHz ...... 51

Figure 3.8. Diagram of fading channel model ...... 54

Figure 3.9. SISO channel capacity of 28, 38, 60, 73 GHz with Rician fading channel

...... 57

Figure 3.10. SIMO channel capacity of 28 GHz with Rician fading channel ...... 60

Figure 3.11. SIMO channel capacity of 38 GHz with Rician fading channel ...... 61

Figure 3.12. SIMO channel capacity of 60 GHz with Rician fading channel ...... 61

Figure 3.13. SIMO channel capacity of 73 GHz with Rician fading channel ...... 62

Figure 3.14. SIMO channel capacity of 28, 38, 60, 73 GHz with Rician fading channel when N=5 ...... 63

Figure 3.15. SIMO channel capacity of 28, 38, 60, 73 GHz with Rician fading channel when N=20 ...... 64

Figure 3.16. SIMO channel capacity of 28, 38, 60, 73 GHz with Rician fading channel when D=100m ...... 65

Figure 3.17. SIMO channel capacity of 28, 38, 60, 73 GHz with Rician fading channel when D=200m ...... 66

Figure 3.18. V-BLAST architecture [62] ...... 67

Figure 3.19. MIMO channel capacity of 28 GHz with Rician fading channel ...... 69

Figure 3.20. MIMO channel capacity of 38 GHz with Rician fading channel ...... 70

Figure 3.21. MIMO channel capacity of 60 GHz with Rician fading channel ...... 70

Figure 3.22. MIMO channel capacity of 73 GHz with Rician fading channel ...... 71

Figure 3.23. Comparison of SIMO, MISO and MIMO channel capacity of 73 GHz with Rician fading channel when M=N=5 ...... 72

Figure 3.24. Comparison of Channel Capacity of 73GHz with Rician fading channel when M=N=10 ...... 73

Figure 4.1. MIMO downlink system with scheduler and zero-forcing beamforming (L transmit antennas and K users) [66] ...... 79

Figure 4.2. Single cell system model ...... 82

Figure 4.3. CDF of 28 GHz with 10 transmit antennas ...... 83

Figure 4.4. CDF of 28 GHz with 20 transmit antennas ...... 83

Figure 4.5. CDF of 38 GHz with 10 transmit antennas ...... 84

Figure 4.6. CDF of 38 GHz with 20 transmit antennas ...... 84

Figure 4.7. CDF of 60 GHz with 10 transmit antennas ...... 85

Figure 4.8. CDF of 60 GHz with 20 transmit antennas ...... 85

Figure 4.9. CDF of 73 GHz with 10 transmit antennas ...... 86

Figure 4.10. CDF of 73 GHz with 20 transmit antennas ...... 86

Figure 4.11. CDF of 28 GHz with 2 scheduled users ...... 87

Figure 4.12. CDF of 38 GHz with 2 scheduled users ...... 87

Figure 4.13. CDF of 60 GHz with 2 scheduled users ...... 87

Figure 4.14. CDF of 73 GHz with 2 scheduled users ...... 88

Figure 4.15. CDF of different frequencies with 10 receive antennas and 2 scheduled users...... 89

Figure 4.16. CDF of different frequencies with 10 receive antennas and 10 scheduled users...... 89

Figure 4.17. 19-cell system model ...... 95

Figure 4.18. CDF of 28 GHz with 10 transmit antennas ...... 96

Figure 4.19. CDF of 28 GHz with 20 transmit antennas ...... 97

Figure 4.20. CDF of 38 GHz with 10 transmit antennas ...... 97

Figure 4.21. CDF of 38 GHz with 20 transmit antennas ...... 98

Figure 4.22. CDF of 60 GHz with 10 transmit antennas ...... 98

Figure 4.23. CDF of 60 GHz with 20 transmit antennas ...... 99

Figure 4.24. CDF of 73 GHz with 10 transmit antennas ...... 99

Figure 4.25. CDF of 73 GHz with 20 transmit antennas ...... 100

Figure 4.26. CDF of 28 GHz with 2 scheduled users ...... 101

Figure 4.27. CDF of 38 GHz with 2 scheduled users ...... 101

Figure 4.28. CDF of 60 GHz with 2 scheduled users ...... 102

Figure 4.29. CDF of 73 GHz with 2 scheduled users ...... 102

Figure 4.30. CDF of different frequencies with 10 receive antennas and 2 scheduled users...... 103

Figure 4.31. CDF of different frequencies with 10 receive antennas and 10 scheduled users...... 103

Figure 4.32. Comparison of the rate at 28 GHz of single cell model and multi-cell model ...... 105

Figure 4.33. Comparison of the rate at 38 GHz of single cell system model and multi-cell system model ...... 105

Figure 5.1. MIMO architecture of sub-6GHz [67] ...... 109

Figure 5.2. MIMO hybrid architecture at high frequencies (millimeter wave) [67] ...... 111

Figure 5.3. Two types of phase shifter for analog processing [67] ...... 113

Figure 5.4 Two types of switches for analog processing [67] ...... 114

Figure 5.5. 1-bit ADC receiver [67] ...... 115

Figure 5.6. Sum-rate vs. power consumption at 28 GHz ...... 120

Figure 5.7. Sum-rate vs. power consumption at 38 GHz ...... 121

Figure 5.8. Sum-rate vs. power consumption at 60 GHz ...... 122

Figure 5.9. Sum-rate vs. power consumption at 73 GHz ...... 123

Figure 5.10. Sum-rate vs. power consumption of full access hybrid at 28, 38, 60 and 73 GHz ...... 124

Figure 5.11. Sum-rate vs. power consumption of subarray hybrid at 28, 38, 60 and 73 GHz ...... 125

List of Tables

Table 2.1. Millimeter wave designations for sub-100 GHz [16] ...... 9

Table 2.2. NASA Spectrum 20 GHz to 100 GHz [22] ...... 12

Table 2.3. Atmosphere attenuation for different millimeter wave frequencies [24] ...... 19

Table 2.4. Signal Loss through atmosphere at 70 GHz [29] ...... 20

Table 2.5. Signal Loss due to rain at 70GHz [29] ...... 21

Table 2.6. Rain attenuation for 28 GHz, 38 GHz, 60 GHz and 73 GHz at 200 m [13] ...... 21

Table 2.7. Penetration measurement result at 28 GHz in New York City [32] ...... 24

Table 2.8. Attenuation for some common materials [33] [34] ...... 25

Table 2.9. Reflection coefficient for millimeter wave at 28 GHz [32] ...... 26

Table 2.10. Typical path loss exponent at 900 MHz and 1.9GHz [35] ...... 28

Table 2.11. LOS path loss exponent [36] [37] ...... 28

Table 2.12. Path loss in New York City and Austin for NLOS propagation [38] ..... 29

Table 2.13. LOS and NLOS path loss exponent for 28 GHz, 38 GHz, 60 GHz and 73 GHz [13] [39] ...... 30

Table 2.14. RMS delay spreads [38] ...... 31

Table 2.15. Outage probability for 38 GHz at Austin within 400 m [39] ...... 33

Table 2.16. Applications on millimeter wave communications ...... 37

Table 4.1. Simulation parameters for sing-cell system ...... 82

Table 4.2. Simulation parameters for multi-cell system ...... 95

Table 5.1. General power consumption for different devices [67] ...... 110

Table 5.2. Simulation parameters ...... 119

Chapter 1. Introduction

The fourth generation (4G) mobile communication systems are widely used in these years. In the 4G, mobile communications and technologies are mainly based on the spectrum ranging from 300 MHz to 3 GHz which is usually called microwaves. According to Rappaport et al [1]., there is total less than 780 MHz of all global spectrum bandwidth has allocated for cellular technologies. The International Telecommunication Union (ITU) defined a standard for 4G mobile communications technologies called International Mobile Telecommunications-Advanced (IMT-Advanced) [1], which stated that the peak data rates for 4G service for high mobility communication is 100 megabits per second (Mbit/s) and for low mobility communication is 1 gigabit per second (Gbit/s) [2]. Long Term Evolution (LTE) radio access technology is also developed to support 4G mobile communications since 2009 [3]. Orthogonal frequency-division multiple access (OFDMA) multi-carrier transmission and other frequency-domain equalization (FDE) schemes are used in 4G to achieve higher data rates [4]. Multiple-input multiple-output (MIMO) is also an important technology in 4G that allows multi-stream to be transmitted for improving efficiency. The utilization of large-scale antenna arrays at the base station is considered as a good method to achieve a higher supported data rate as well [5], for example, Massive MIMO and multi-user MIMO (MU-MIMO).

However, with the increasing of traffic data demand, the sub-3 GHz spectrum has become very crowded and there is still a gap between the users’ requirements and what can be offered by 4G technologies now. In order to provide much higher data rates, the fifth generation (5G) was developed and a new standard IMT-2020 was defined by ITU in 2012 [6]. Many countries and companies have started a lot of researches on 5G in order to use 5G in commercial service by 2020 [7]. In addition, it is expected to have a technical revolution of wireless communication styles by 5G technologies [7], which is the thing-centralized communication, for example,

1 device-to-device (D2D) [8] and machine-to-machine (M2M) [9].

According to these researches, there are mainly three key technologies were used in 5G communications [10]. The first one is the usage of large-scale antenna arrays which is similar to the strategy we used in 4G communications. The second one is to reduce the size of cellular cells so that there would be more cells in the same area than now and a larger data rate density is able to achieve. The third method is the usage of higher carrier frequencies, such as millimeter wave bands. The huge bandwidth that can be used in the millimeter wave band ranges from 30 GHz to 300 GHz, and it is now considered to for 5G cellular networks in order to meet the users’ growth and to achieve a faster data transmission speed. According to Niu, Y. et al [13], it is expected to provide multi-gigabits communication services if the millimeter wave frequency spectrum is utilized well. Compared to the traditional wireless communications, millimeter wave suffers from higher attenuation loss and is sensitive to blockage. However, taking good use of these millimeter wave propagation characteristics can also make opportunities and develop new technologies for future 5G networks.

1.1. Contribution of Thesis

In the thesis, we review the propagation characteristics and evaluate the channel performance of millimeter wave transmissions in order to understand the feasibilities of various millimeter frequency sub-bands for 5G cellular networks. The contribution of this thesis is listed as follows:

1. The path loss, outage probability and channel capacity of the millimeter wave communications are evaluated in order to study how the propagation characteristics affect the performance of the wireless communication systems. Software simulations are used to evaluate these figures of merits. By the simulation results, we know the reasonable signal transmission distance of millimeter wave bands at 28 GHz, 38 GHz, 2

60 GHz and 73 GHz in Rician fading channels. Compared to 60GHz and 73 GHz, the path loss of 28 GHz and 38 GHz is not very large. With the standard transmit power, the channels with these two carrier frequencies (28 GHz and 38 GHz) are able to support the signal transmission for a longer distance for about 400 meters and also able to provide a very large channel capacity if the distance between transmitter and receiver is smaller than 100 meters. However, 60 GHz does not perform very well because of the huge path loss caused by the atmosphere and rain attenuation. The channel with this frequency is very difficult to support 50 meters reliable transmission with the standard transmit power.

2. We compare the intra-cell interference from other users in the same cell and the inter-cell interference from neighboring cells by comparing the sum-rate performance in both single-cell system and multi-cell system. We use the cumulative distribution function (CDF) of the long-term average sum-rate to evaluate the channel performance and the 10th percentile user rate was used to illustrate the performance of cell-edge users. We know that all the frequencies we evaluated have a higher sum-rate performance in the single-cell system than in the multi-cell system, especially the 28 GHz provides the largest sum-rate if other factors are the same for both system models. However, the influence from the inter-cell interference is also the largest at 28 GHz among all the bands, whose cell-edge users’ sum-rate of multi-cell system decreases by 11.73% compared to single-cell system. As for 38 GHz, 60 GHz and 73 GHz, the difference of the cell-edge users’ sum-rate between the two system models is 7.89%, 0.95% and 1.92%, respectively.

3. We investigate various hybrid transceiver architectures for millimeter wave communications, including full access hybrid and subarray hybrid. In particular, we study the achievable sum-rate and compare the power efficiency of these architectures. We show that if the total power for the system is smaller than 90 Watts, the full access hybrid can achieve a much higher sum-rate for the system than full digital array and subarray hybrid under our assumptions. Compared with full digital array, the sum-rate at 28 GHz at 50 Watts is increased by 18.9% by using a full

3 access hybrid. As for 38 GHz, 60 GHz and 73 GHz, the difference of the sum-rate between the full access hybrid and the full digital is 25.2%, 38.8% and 34.6%, respectively. In addition, there is only 2-4 bits/Hz/s difference of achievable sum-rate between the subarray hybrid architecture and full digital architecture at 50 Watts. This would be an important advantage of the subarray hybrid as it offers the simplest circuit design, but only few losses compared to full digital and fully access architecture.

1.2. Organization of Thesis

The thesis is organized as follows:

In Chapter 2, the propagation properties of millimeter waves are reviewed and then compared to the lower frequencies microwave bands. We discuss the details of the millimeter wave spectrum, free space propagation, simplified path loss model, oxygen and rain attenuation, penetrability, reflection, path loss exponents, RMS delay spreads, Doppler shift and outage probability. Some of the popular applications of millimeter waves, such as small cell access and backhaul architecture are introduced as well.

In Chapter 3, path loss, outage probability and capacity are evaluated. We pay attention on the link and the distance between one transmitter and one receiver. We simulate the path loss with shadow fading and outage probability of the channel frequencies at 28 GHz, 38 GHz, 60 GHz and 73 GHz and compared them with the main Wi-Fi used microwave frequency at 2.4 GHz. In addition, the channel capacity of single-input-single-output (SISO), multiple-input-single-output (MISO), single-input-multiple-output (SIMO) and multiple-input-multiple-output (MIMO) channels at those high frequencies are evaluated as well.

In Chapter 4, a single-cell multi-user model and a 19-cell multi-user model are set up

4 to evaluate how millimeter wave performs in a more complex system. The achievable sum-rate is evaluated in these two channel models and then we discuss how the number of active users, transmit antennas and carrier frequencies influence the sum-rate in the multi-user cellular systems.

In Chapter 5, the signal processing techniques and the hybrid transceiver architecture for millimeter wave systems are reviewed and discussed including full access hybrid and subarray hybrid. A 7-cell multi-user MIMO hybrid system is set up to evaluate the achievable sum-rate and compare the power efficiency of the full digital array, full access hybrid and subarray hybrid architectures.

In Chapter 6, a summary of the works in the previous chapters is provided and then the potential future research works are discussed.

Chapter 2. Introduction of Millimeter Wave Propagation

In this chapter, we are going to introduce the characteristics of millimeter waves. There are many differences between this high frequency band and the traditional microwave especially the propagation properties. In the following, we will discuss the details of the spectrum, propagation characteristics including free space propagation, simplified path loss model, oxygen and rain attenuation, penetrability, reflection, path loss exponents, delay spreads, Doppler shift and outage probability. Some of the popular applications of millimeter waves, such as small cell access and backhaul architecture will be introduced as well.

2.1. Introduction of Millimeter Wave

Almost all mobile communication systems today use spectrum in the range of 300 MHz and 3 GHz. However, with the increasing of traffic demand and rapid exploitation, this sub-3 GHz spectrum has become very crowded. The explosion of big data transmission and requirements are facing challenges. In order to meet the users’ growth and to achieve a faster data transmission speed, the usage of millimeter wave is considered to be an outstanding resolution.

Figure 2.1. Traditional microwave bands and millimeter wave bands [11]

Usually, as shown in Figure 2.1, the spectrum in the 3 GHz to 30 GHz is called super high frequency, while the frequency ranges from 30 GHz to 300 GHz in which the wavelength between 10 mm to 1 mm is referred to as extremely high frequency or millimeter wave [12]. Because the propagation characteristics between super high frequency and extremely high frequency are similar to each other, for example, both of them propagate mainly by line-of-sight (LOS); they are not reflected by the ionosphere and the ground waves also do not occur [13]. Generally, these two bands are combined and referred to as millimeter wave with wavelength ranges from 1 mm to 100 mm. Compared to the current commercial radio communications such as GPS, AM/FM radio and Wi-Fi which are contained in a narrow band of the radio frequency (RF) spectrum in 300 MHz to 3 GHz, there are many benefits to use millimeter wave frequencies in radio communications. Intuitively, the bandwidth in the millimeter wave spectrum is much wider than what we have now and the most part of the spectrum is still undeveloped. What’s more, because of the high attenuation in free space, the same frequency can be reused in a short distance, which can increase the channel capacity directly. According to Pi, Z. et al [14], it is expected that the gains of network capacity can be obtained up to 10 times than current if the millimeter wave frequency spectrum is utilized well. In addition, there are many propagation characteristics of millimeter wave that the traditional microwave does not have. For example, because of the very high carrier frequency, millimeter wave communication suffers from larger propagation attenuation than microwaves. Also, millimeter wave is inherently directional, so that beamforming antenna is an essential technique. Thus, it is worth to do more researches on millimeter wave to develop these useful resources.

2.2. Millimeter Wave Spectrum

For wireless communication, the main carrier frequency spectrum used in the public

7 domain today is microwave spectrum ranging from 700 MHz to 2.6 GHz. However, as shown in Figure 2.2, there are much more resources are undeveloped at high frequency spectrum between 30 GHz and 300 GHz with the wavelength between 10 mm to 1 mm, which is called millimeter wave frequency spectrum. According to research, there are totally up to 252 GHz are considered can be used for mobile broadband [4] if millimeter wave frequency bands are utilized. Due to the absorption by Oxygen and water vapour in the atmosphere, the transmission in some bands is experiencing high attenuation so that the propagation is limited. Excluding these bandwidths and other parts which are not suitable for mobile communication, about 100 GHz millimeter wave spectrum is left and these available frequency resources are mainly at around 28 GHz, 38 GHz, 45 GHz, 60 GHz and 94 GHz [15].

Figure 2.2. Millimeter wave spectrum [14]

Based on the wavelength and the usage of it, the millimeter wave spectrum is generally divided into several bands for easier to memorize. Since the available frequency resources now are mainly laid on the spectrum below 100 GHz, only parts of the bands are discussed here. Band designations and its frequency ranges are shown in the Table 2.1 below.

Band Designation Frequency Range (GHz) Wavelength (mm)

Q 30-50 10.00 - 6.00

V 50-75 6.00 - 4.00

E 60-90 5.00 - 3.33

W 75-110 4.00 - 2.73

Table 2.1. Millimeter wave designations for sub-100 GHz [16]

The Q band is a range of frequencies contained in both microwave region and millimeter wave region of the electromagnetic spectrum. Commonly, it ranges from 30 GHz to 50 GHz, but may different depending on the source using the term [17]. It is mainly used for satellite communications, terrestrial microwave communications and also for radio astronomy studies. In addition, it is used in automotive radar and in radar investigating the properties of the Earth's surface as well.

For the bandwidth between 50 GHz to 75 GHz, the most useful frequency ranges from 59 GHz and 64 GHz, which usually called as 60 GHz band or V-band, is not heavily used nowadays for commercial communications. However, it is mainly used for millimeter wave radio research or other many kinds of academic researches. In the United States, this band is used for some unlicensed applications in industrial, science and medical. Also, they allocated a part of this band from 57 GHz to 71 GHz for unlicensed wireless communication systems [17]. Since there is a significant absorption by Oxygen which can result in a large attenuation about 15 dB/km, this band can be used for very short range but high-speed and high capacity links point to point transmission applications. One interesting thing is that this band at 60GHz is the first crosslink communication between satellites in a constellation all around the world, for the U.S. Milstar 1 and Milstar 2 military satellites [19].

The E-band is contained in 60 GHz to 90 GHz, mainly focuses on three parts of bands, 9 which the frequencies at 71 GHz to 76 GHz, 81 GHz to 86 GHz and 92 GHz to 95 GHz. These total 12.9 GHz is allocated for ultra-high-speed data point to point wireless links and high-density fixed wireless services in the United States, licensed by the Federal Communications Commission in October, 2003. For the whole millimeter wave spectrum, V band and E band are the most important and useful frequency bands since they have clear technological and economic advantages [17] [18]. These bands allow multi-Gigabit per second capacities as well as lowing the cost of wireless backhaul.

The W band is partly overlapped with E band. It ranges from 75 GHz to 110 GHz; wavelength 2.73 mm to 4 mm. Similar to the Q band, W band also can be used for satellite communications and millimeter wave radar research. But except these non-military applications, it can be used in military radar targeting and tracking applications as well [18]. Especially at 94 GHz, which is an atmospheric radio window, is used for imaging millimeter wave radar applications in astronomy, defence, and security applications in the United Stated Air Force. As for millimeter wave wireless communication, W band also can provide a high data rate throughput when used at high altitudes and in space. No commercial use is applied in this band now. However, it is thought to be used for commercial satellite operators by the International Telecommunication Union.

There is also a 7 GHz bandwidth from 22 GHz to 29 GHz, which is called 24 GHz band, is allocated for automotive radar. 24 GHz band is suitable for short range (<100 m) radar since the large bandwidth offers sufficient small distance resolution. Similar to this, the 77 GHz band between 76 GHz and 77GHz is used for automotive radar as well. However, it is used for long range (>100 m) radar because the high carrier frequency allows modest-size antennas to have a small beamwidth and therefore a better angular resolution [20].

Actually, in the United States, some bands of millimeter wave have already

10 requisitioned by NASA for their space research and data tracking, while other parts are open for commercial communications or academic research until now, which shows in Figure 2.3 and Table 2.2.

Figure 2.3. Millimeter wave band allocation in the United States 2003 [21]

Frequency (GHz) Usage

22.55-23.55 Passive Tracking Data Relay Satellite (TDRS) Return

25.25-27.5 Tracking Data Relay Satellite (TDRS) Return

25.5-27 Earth Exploration Satellite (EES)

31.8-32.3 Deep Space

34.2-34.7 Deep Space

35.5-36.0 Active

37.0-38.0 Lunar Martian

40.0-40.5 Lunar Martian

42.5-43.5 Radio Astronomy

65.0-66.0 Earth Exploration Satellite (EES)/Space Research Services (SRS)

74.0-84.0 Very Long Baseline Interferometry (VLBI)

Table 2.2. NASA Spectrum 20 GHz to 100 GHz [22]

In Australia, the millimeter wave frequencies are also used in many places. The 60 GHz band has allocated to fixed and mobile service, inter-satellite service and radiolocation service. Within this band, the frequencies from 58.2 GHz to 59 GHz and 59 GHz to 59.3 GHz are used for primary the Earth Exploration-Satellite (EES), Space Research services as well as radio astronomy service [23]. The main parts of E-band from 71 GHz to 76 GHz and 81 GHz to 86 GHz have allocations for fixed and mobile service, space-to-earth fixed-satellite service by the Australia Communications and Media Authority. 74 GHz to 76 GHz band is also used for broadcasting [24].

2.3. Propagation Characteristics for Millimeter Wave

Since the range of different frequency bands has different propagation characteristics, we cannot directly apply the traditional wireless communication model and

12 technologies of microwave bands to the millimeter wave communications. Thus, it is important to learn the characteristics of millimeter wave and its propagation.

2.3.1. Free Space Propagation Model

Figure 2.4. Free space propagation model

As mentioned in the paper before, since the propagation of non-line-of-sight (NLOS) suffers from huge attenuation, the millimeter wave transmission is mainly focused on line-of-sight (LOS) channel. Thus, we consider a free space model for the signal transmission first.

Free space propagation model is an ideal model which assumes that the transmitter and the receiver are located in an empty environment and there is only one clear LOS path between them. The influence of the obstruction, atmosphere effects and earth’s surface are assumed to be entirely absent. This model only characterized the ability of propagation. The path loss under these conditions is called free space path loss. H. T. Friis [25] presented the method to calculate the received signal power in free space in his paper. Assume the distance between the transmit antenna and the receive antenna is (in meters), the power density in a round area with the radius from the transmitter is:

= (2.1) 4 where the transmit power is and the transmit antenna gain is .

If we set the receive antenna gain is , and = is the wavelength (in meters), =3×10 m/s, the effective area A of the transmit antenna is:

A= (2.2) 4

Then, the received power as a function of distance can be calculated as:

∙A () = = (2.3) (4) where ( ≥ 1) is the system loss factor.

Commonly, we set = ==1 in the simulations for easier calculation.

From the Equation (2.3), it is easy to see that the received signal power falls off inversely proportional to the square of the distance between the transmit antenna and receive antenna. Also, it is proportional to the square of the signal wavelength , which means with the increase of the carrier frequency, received power would decrease very fast.

The free space path loss equation is the ratio of the received power to the transmit power. And then, the free space path loss as a function of distance can be calculated as:

() PL() = = (2.4) 4

There is a more convenient way to express the path loss Equation (2.4) is in terms of dB in communication systems:

PL(dB) =10log =−10log (2.5) (4)

In this situation, the large-scale fading F() can be expressed as follow:

F() =PL() + 10log − (2.6) where is called reference distance, PL() means the path loss at , is the path loss exponent and representing the shadow fading which is a Gauss

distribution random variable with mean zero and variance .

2.3.2. Simplified Path Loss Model

In a real propagation environment, signals may be reflected by buildings or other reflecting surface which would result in that a number of different paths of signal could be received. Depending on the relative phases of these signals, they may add or subtract from each other [26]. The complexity of the propagation paths makes it difficult to calculation received power in different environments. Thus, there is a simplified path loss model which is an approximation to the real channel. It only considers the wavelength of the carrier frequency and the distance between transmitter and receiver, which is usually used to estimate the channel or system design.

In this model, the received power at distance can be expressed as:

() = (2.7) in term of dB:

(dBm) =(dBm) +(dB) − 10log (2.8)

15 where is the reference distance and it is usually assumed to be 1 m to 10 m for indoor environment and 10 m to 100 m for outdoor environment, is the path loss exponent which depends on the surroundings. The value K is sometimes set to be the free space path loss at distance , which can be calculated as:

4 (dB) = −20 (2.9)

2.3.3. Atmosphere Gaseous Losses

Similar to other microwave wireless communication systems, millimeter wave communications also suffer from a large propagation loss. However, compared with the one using lower carrier frequencies, millimeter wave propagation is facing more challenges. Two most severe attenuations for millimeter wave propagation are atmosphere gaseous losses and precipitation attenuation, which are hardly ever occurring in low frequency wave bands [27].

Figure 2.5. Specific attenuation due to atmospheric gases (Pressure: 1013 hPa, Temperature: 15 ć, Water Vapor Density: 7.5 g/m^2) [18]

According to the measurements shown in Figure 2.5, both water vapour and dry air (Oxygen) have influences on the propagation of high frequency bands. The atmosphere attenuation of millimeter wave frequency is from 0.01 dB/km to 40 dB/km, while by using the traditional transmission method with the frequency lower 17 than 3 GHz, the atmosphere attenuation is between 0.001 dB/km and 35 dB/km. Although the worst situation is almost the same, the lowest loss for millimeter wave is 10 times larger than the loss for traditional bandwidths that are used now.

Figure 2.6. Attenuation by oxygen and water vapour [13]

Figure 2.6 illustrates a simplified conclusion of the millimeter wave attenuation by both oxygen and water vapour. The detailed information for different frequency is listed in Table 2.3. From Figure 2.6 and Table 2.3, we can see there are three obvious large attenuations at 60GHz, 183GHz and 325GHz, respectively; and two small peaks at around 23GHz and 120GHz. These oxygen and water absorption bands are called atmospheric attenuation windows, which have a huge influence on the propagation of millimeter wave as mentioned before.

Frequency (GHz) Atmosphere Attenuation (dB/km)

3 0.0075106

23 0.19488

31 0.10003

60 15.17285

78 0.35743

119 2.04379

127 0.86255

183 28.36202

214 2.72848

325 38.59649

341 9.87251

Table 2.3. Atmosphere attenuation for different millimeter wave frequencies [24]

Since the atmospheres depend primarily on atmospheric oxygen, humidity, fog and rain, some researchers made lots of experiments on how and how much these factors can affect the attenuation. Based on the research by Adhikari P et al. [29], they measured the signal loss at around 70 GHz frequency band under different atmosphere environment. According to their experiments, the signal loss due to atmospheric oxygen is less than 0.2 dB/km. The effect of water vapour, which is tested by varying the absolute humidity, is between 0 and 3 dB/km. The attenuation is also influenced by the temperature. The higher temperature and humidity is, the more signal loss occurs. The effect of fog or cloud is similar to the loss due to humidity. The numerical results show as below in Table 2.4 [29].

Effect Comments Signal Loss (dB/km)

Oxygen Sea level 0.22

Humidity 100% at 30°C 1.8

Fog 10°C, 1 gm/m3 3.2

(50m visibility)

Rain 25 mm/hour rain 10.7

Table 2.4. Signal Loss through atmosphere at 70 GHz [29]

2.3.4. Rain Attenuation

From the Table 2.4 in previous section, it is obvious that rain causes a significant attenuation and it affects the most. It is because that the wavelength of millimeter wave is too small and even has the same size with the raindrop. When the transmitted millimeter wave crushes with a rain drop, there will be a large scattering and then the radio signal is lost. The amount of signal loss due to rain depends on the rate of rainfall. The heavier rain falls, the larger signal loss occurs. Experimental results of rain attenuation at 70 GHz frequency band are listed below in Table 2.5 [29]. Their data shows that in a light rain situation with rain rate at 1 mm per hour, the signal loss is about 0.9 dB per kilometer. As the rain rate gets larger at 50 mm per hour, the signal loss increases to 18.4 dB per kilometer.

Description Rain Rate Signal Loss (dB/km)

Light Rain 1 mm/hour 0.9

Moderate Rain 4 mm/hour 2.6

Heavy Rain 25 mm/hour 10.7

Intense Rain 50 mm/hour 18.4

Table 2.5. Signal Loss due to rain at 70GHz [29]

In addition, different frequency bands suffer from different values of rain influence. Niu Y. et al. [13] concluded the rain attenuation for 28 GHz, 38 GHz, 60 GHz and 73 GHz at 200 m, which is illustrated in Table 2.6. From the data, it is obvious that higher frequency suffers larger rain attenuation at the same rain rate. Shrestha S. et al. [30] also made a rain attenuation statistics experiment in South Korea and analyzed all the data from 2013 until 2015. They recorded the signal loss in 3.2 km experimental link of 38 GHz and 0.1 km link at 75 GHz. The result shows at the rain rate about 50 mm/h, attenuation values are 20.89 dB and 28.55 dB, respectively.

Frequency (GHz) Rain Attenuation at 200m

5mm/hour 25mm/hour

28 0.18 dB 0.9 dB

38 0.26 dB 1.4 dB

60 0.44 dB 2.0 dB

73 0.6 dB 2.4 dB

Table 2.6. Rain attenuation for 28 GHz, 38 GHz, 60 GHz and 73 GHz at 200 m [13]

Figure 2.7. Rain attenuation according to frequency [31]

We can see from Figure 2.7, at the same rain rate, for the frequency less than 100 GHz, the rain attenuation grows with the frequency. However, the attenuation gradually trends to be a horizontal level and even get a little lower when the frequency goes up to 1000 GHz.

Comparing this characteristic of millimeter wave to the traditional wireless system using lower frequency bands with only 0 to 0.001 dB/km rain attenuation, we can say that the rain attenuation is a very important problem that needs to be concerned.

However, the recent research shows that with small cells which cell sizes on the order of 200 m, there is no significant additional path loss causes by atmosphere and rain attenuation. Thus, millimeter wave communications are now usually used in indoor environment or with the small cell size at around 200 m.

2.3.5. Penetrability

Another special characteristic of millimeter wave is the penetrability. Different from low frequency waves, millimeter wave signal cannot penetrate most solid materials very well. This makes the millimeter wave be easily obstructed by walls and buildings even humans, which may confine the signal transmission from outdoor base station to indoor receiver or the signal transmission in densely built areas. In some special situation, the mobile users should also be considered in the communication system designs.

To measure the penetrability of millimeter wave, a lot of experiments have done by researchers. Zhao H. et al. [32] measured penetration at 28 GHz in New York City in the summer of 2012. In their paper [32], the bandwidth of measurements is not mentioned. The experiment locations were at the MetroTech Center in Brooklyn, the Othmer Residence Hall in Brooklyn and the Warren Weaver Hall in Manhattan. The transmitter and the receiver were set on each side of tested materials including several common materials in buildings at 5 m distance which is shown in Figure 2.8.

Figure 2.8. Illustration of measurement of penetration at 28 GHz in New York City

The measurements were taken in both indoor and outdoor environments. The following Table 2.7 lists the result of their experiment. As shown in Table 2.7, it is obvious that there is more penetration loss in outdoor environments. The highest 23 penetration loss is 40.1 dB and 28.3 dB for 3.8 cm tinted glass and 185.4 cm bricks, respectively, both in outdoor environments. And clear glass has the lowest penetration loss at 3.6 dB and 3.9 dB in indoor environments. This result also proves that millimeter wave is not easy to be used in outdoor transmission, especially there are many buildings blocking the way.

Environment Location Material Thickness (cm) Penetration Loss (dB)

Outdoor Othmer Tinted Glass 3.8 40.1 Residence Hall

Warren Brick 185.4 28.3 Weaver Hall

Indoor MetroTech Clear Glass <1.3 3.9 Center

Warren Tinted Glass <1.3 24.5 Weaver Hall Clear Glass <1.3 3.6

Wall 38.1 6.8

Table 2.7. Penetration measurement result at 28 GHz in New York City [32]

Table 2.8 below shows more data of the attenuation for some common materials, measured by Anderson C. R. et al. [33] and Alejos A. et al [34]. As we can see from Table 2.8, for a 1.9 cm whiteboard, there is 9.6 dB loss at 60 GHz while 0.5 dB at 2.5 GHz. As for a 10 cm concrete, the attenuation at 40 GHz is almost 10 times larger than that at 2.5 GHz. Although there are some of the materials listed in the table have similar influence on the tested frequency, it still can be seen that the higher

24 frequency bands are more impressionable. In addition, there is no obvious relationship between the thickness of the material and the attenuation, which means that the most influential factor of the attenuation at the same frequency is the material itself.

Material Thickness (cm) Attenuation (dB)

2.5 GHz 40 GHz 60 GHz

Drywall 2.5 5.4 - 6.0

Whiteboard 1.9 0.5 - 9.6

Clear glass 0.3 6.4 2.5 3.6

Mesh glass 0.3 7.7 - 10.2

Chipwood 1.6 - 0.6 -

Wood 0.7 5.4 3.5 -

Plasterboard 1.5 - 2.9 -

Mortar 10 - 160 -

Brick wall 10 - 178 -

Concrete 10 17.7 175 -

Table 2.8. Attenuation for some common materials [33] [34]

However, the low penetrability may not be a weakness in millimeter wave wireless communication. As mentioned before, millimeter wave propagation suffers from huge attenuation, thus, it has difficulty in being used for long distance signal transmission. With the characteristic of low penetrability, millimeter wave is more

25 suitable for indoor short distance signal transmission, and it can provide a better inherent security and privacy to users.

2.3.6. Reflection Coefficients

In physics and electrical engineering, the reflection coefficient is a parameter that describes how much of an electromagnetic wave is reflected by an impedance discontinuity in the transmission medium. A millimeter wave measurement for reflection in New York City done by Zhao H. et al. [32] gave us a clear description of the reflection coefficients at 28 GHz. The reflection was measured through several materials such as glass and concrete in both indoor (at MetroTech Center) and outdoor (at Othmer Residence Hall) environments. The following Table 2.9 shows the reflection coefficients results.

Environment Location Material Angle (°) Reflection Coefficient

Outdoor Othmer Tinted Glass 10 0.896 Residence Concrete 10 0.815 Hall 45 0.623

Indoor MetroTech Clear Glass 10 0.740 Center Drywall 10 0.704

45 0.628

Table 2.9. Reflection coefficient for millimeter wave at 28 GHz [32]

The reflection coefficients are up to 0.896 for tinted glass in outdoor propagation and 0.740 for clear glass in indoor propagation. If looking at the coefficients of the same

26 material such as concrete outdoor or drywall indoor, it is easy to find that with the increase of angle of incidence, the reflection coefficient would decrease. For example, the reflection coefficient of the concrete is 0.623 if the angle is 45° while it is 0.815 if the angle is 10°. In addition, we can see that the reflection coefficient of a similar material in outdoor environment is larger than that in indoor environment. It is most likely due to outdoor building materials containing thick and dense metal layers.

2.3.7. Path Loss Exponents

Path loss (or path attenuation) is the reduction in power density (attenuation) of an electromagnetic wave as it propagates through space. It is normally represented by the path loss exponent. For low frequency or microwave communication, path loss exponent usually ranges from 2 to 4, where 2 is transmitted in free space model while 4 is for flat earth model which means it is transmitted with full specular reflection from the earth surface [13]. In some cases, the path loss exponent may go up to 6 such as in buildings or in very complex environment. Detailed typical path loss exponent of 900 MHz and 1.9 GHz are showed in Table 2.10 [35].

Environment Path Loss Exponent Range

Urban macro-cells 3.7-6.5

Urban micro-cells 2.7-3.5

Office Building (same floor) 1.6-3.5

Office Building (multiple floors) 2-6

Store 1.8-2.2

Factory 1.6-3.3

Home 3

Table 2.10. Typical path loss exponent at 900 MHz and 1.9GHz [35]

Generally speaking, path loss exponent tends to be higher when the frequency increases [35]. Thus, for millimeter wave, the path loss exponent is slightly higher than traditional wireless communications at the same propagation environment and get much higher at some special frequencies. Table 2.11 lists the LOS path loss exponent range at frequency 28 GHz, 38 GHz and 60 GHz

Frequency (GHz) LOS Path Loss Exponent Range

28 2.55

38 2.0

60 2.23

Table 2.11. LOS path loss exponent [36] [37]

According to George R et al. [38], they did an experiment to measure the path loss in New York City and Austin for both line-of–sight (LOS) and non-line-of-sight (NLOS) propagation. However, since the path loss exponent of LOS is similar to that in free space, they only recorded NLOS data. The main result is listed in Table 2.12 below.

Close-in Reference Floating Intercept Model Model (d =5m) 0 (30m

Frequency 28GHz 38GHz 28GHz 38GHz

TX height - - 7m 17m 8m 36m

Path Loss Exponent 5.76 3.88 3.73 4.51 1.28 0.45 28

(dB) 9.02 14.6 8.36 8.52 7.59 6.77

Table 2.12. Path loss in New York City and Austin for NLOS propagation [38]

In this table, the millimeter wave frequency at 28 GHz was measured in New York City while 38 GHz data was measured in Austin. The researchers found that in Austin, measurement data set was much smaller than the New York City data set, and was recorded in a much less scatter-rich environment than New York City, which contributed to the lower path loss exponent values computed for Austin. This result shows that the millimeter wave channels would have less path loss and work better in urban environment.

Rappaport et al. [37] also measured the path loss at 28 GHz in New York City urban area. Their results show that the average path loss exponent for the LOS and NLOS are 2.55 and 5.76, respectively, which is similar to the experiment data discussed in the Table 2.11 and Table 2.12.

Another research group Niu Y et al. [13] gave a conclusion for both LOS and NLOS path loss exponent for four representative frequency bands in their paper. The result shows in the following Table 2.13. For LOS, the path loss exponent is around 2 with small fluctuations for all the frequency, while for NLOS, it fluctuates a lot which changes from 2.5 to 4.6. There is no clear linear relationship between the frequency and the path loss exponent, because the path loss is influenced by a lot of factors. Especially we can see from the table, for LOS propagation, path loss exponent for 60 GHz is higher than other bands and for NLOS propagation, path loss exponent for 28 GHz is the highest amount the four bands. If we look at the section 2.3.3, it can be found that these two bands both suffer from huge atmosphere attenuation. As a result, their path loss exponents are higher than others.

Frequency (GHz) Path Loss Exponent

LOS NLOS

28 1.8-1.9 4.5-4.6

38 1.9-2.0 2.7-3.8

60 2.23 4.19

73 2.0 2.45-2.69

Table 2.13. LOS and NLOS path loss exponent for 28 GHz, 38 GHz, 60 GHz and 73 GHz [13] [39]

2.3.8. Root Mean Square (RMS) Delay Spreads

In telecommunications, the delay spread is a measure of the multipath richness of a communications channel [35]. In general, it can be seen as the arrival time difference between the earliest multipath component and the latest multipath component. The root mean square (RMS) delay spread is the most common used one for measuring the delay time. The RMS delay spread can be expressed as [40]:

( ) ( ) ∫ −̅ = (2.10) ( ) ∫ where () is the power delay profile of the channel, ̅ is the average delay of the channel which is [40]:

∫ () ̅ = (2.11) ( ) ∫

The RMS delay spread for millimeter wave shows in Table 2.14 below. In this table, the millimeter wave frequency at 28 GHz was measured in New York City while the data at 38 GHz was measured in Austin [38]. As we can see from Table 2.14, the RMS delay spread of LOS is usually around 0.8 but it changes a little when the frequency is

38 GHz. For NLOS, it decreases fast when the frequency goes up. The reason is that the number of receivable multipath components decreases due to propagation loss when the frequency is getting higher, thus causing fewer detectable multipath components and a smaller RMS delay spread.

Frequency (GHz) RMS Delay Spread (us)

LOS NLOS

28 0.878 47.2

38 1.2 23.6

60 0.8 7.4

Table 2.14. RMS delay spreads [38]

2.3.9. Doppler Shift

The Doppler of a wireless channel depends on the carrier frequency and mobility. In a mobile environment, the received frequency can be expressed as [78]:

+ = (2.12) +

In Equation (2.12), is emitted frequency, is observed frequency, is the speed of the wave, is the velocity of the receiver relative to the medium and is the velocity of the source relative to the medium.

The Doppler frequency is shown by [62]:

= − (2.13)

If we set =0, we have:

= (2.14) c

According to Equation (2.14) and experiments, the Doppler shift for carrier frequency at 60 GHz with mobility of 3km/h to 60 km/h can range from 60 Hz to 3 kHz. Assuming there is a rich scattering environment and omnidirectional antennas, Doppler spread will occur when the Doppler shift values of incoming waves on different angles at the receiver are different [41].

2.3.10. Outage Probability

The outage probability is defined as the probability that the signal to interference and noise ratio (SINR) at μ falls below a given threshold δ. In this case, the receiver cannot receive signals from the transmission side. This probability can be expressed as the cumulative distribution function (CDF) of the SINR:

=( < δ) (2.15)

An experiment done by Murdock J. N. et al. [42] measured the outage probability for millimeter wave at 38 GHz with measurements made within approximately 400 m around the transmitter locations at the University of Texas at Austin campus. Transmitter 1 was set on the roof of the Engineering Science Building (ENS) and the location of transmitter 2 was the roof of W.R. Woolrich Laboratories (WRW). Measurements from two transmitter locations provided outage probability for base stations of different heights. The results show in table 2.15.

Tx Location Height (m) Outage (%) for <160dB Outage (%) for <150dB path loss path loss

Tx1 ENS 36 18.9% < 400 m 52.8% < 400 m

0% < 200 m 27.3 < 200 m

TX2 WRW 18 39.6% <400 m 52.8% < 400 m

0% < 200 m 10% < 200 m

Table 2.15. Outage probability for 38 GHz at Austin within 400 m [39]

Research data shows that if the path loss is less than 160dB, the outage probability for both 36 m height transmitter and 18 m height transmitter is 0% within 200m. This outage study also indicates that within 200 m from the transmitter, a lower transmitter experienced fewer outages since it is able to use more reflectors in the environment to cover all locations. However, a higher transmitter can get smaller outage probability because of the diffraction of signals around lower buildings if the distance is over 200 m [42]. This work suggests that millimeter wave cellular systems may work better in dense urban environments with microcell deployments of cell radius less than 200 m.

2.4. Millimeter Wave Wireless Applications

2.4.1 Small Cell and Cellular Access

To meet the high mobile traffic demand, the large bandwidth of millimeter wave provides a huge resource and it is considered to be one of the main technologies in the 5G cellular network. With the small cells get massive densification, we can achieve a huge increase in network capacity in a decade [13]. These undeveloped millimeter wave resources can offer multi-gigabit rates and high-speed data transfer between users. As stated in [13], it is very efficient to apply millimeter wave communication in cellular access at 28 GHz and 38 GHz with the small cell sized at the order of 200m. It is predicted that the capacity could be 20 times larger than the

4G system which we are using now and it can be further increase when directional antennas are equipped.

2.4.2 Wireless Backhaul System

In communication systems, the backhaul portion of the network comprises the intermediate links between the core network, or backbone network and the small sub-networks at the "edge" of the entire hierarchical network [43]. With the utilization of small cells growths densely, wireless backhaul is more effective compared to the old fiber based wired backhaul system. It costs less, but more flexible and can create efficient large coverage areas easily. In addition, it can reach a larger capacity and higher gain. By using the millimeter wave bands at E band and 60 GHz, the wireless backhaul system could provide a much higher transmit data rates between the gateway and small cell base stations.

Utilizing the backhaul system for millimeter wave, there are mainly two types of topology design [44]. First one is called single gateway node model which is shown as Figure 2.9. In this scenario, the small base stations not only handle their own traffic, but also accumulate traffic for the other small base stations further along the branches of the tree. For more efficiency, point to point links that are closer to the gateway node require higher capacity. The frequency bands used in each connection must be considered carefully in order to meet the capacity requirement and also minimize the interference [45].

Figure 2.9. Single Gateway Node backhaul Model

The second system design is multiple gateway nodes model. Different from single gateway, there are some small base stations are connected to multiple gateway nodes and leading to a multi-root tree topology [44]. Sometimes small base stations can even become a gateway node for each other. Comparing to a single gateway node, multiple gateway nodes usually can improve the overall throughput. However, it is much more complex than the single gateway node because it not only needs to consider the frequency used, but also needs to have a plan on geographical locations of the gateways [44].

Figure 2.10. Multiple Gateway Node backhaul Model

These years, there are many researchers are working on millimeter wave backhaul systems. The following Table 2.16 lists the typical works on millimeter wave backhaul according to the frequency band, the scenario, and the main application. From this table, we can see that the most used frequency band is at 60 GHz and there are many works related to indoor environments communications.

Researcher Frequency used Scenario Application (GHz)

Singh et al. [46] 60 Indoor Internet access

Son et al. [47] 60 WPAN Transmission between devices

Chen et al. [48] 60 WLAN Uplink channel access

Wu et al. [49] 60 and 70 indoor multimedia

Niu et al. [50] 60 Small cell in HetNets Backhaul, D2D

Singh et al. [51] 60 WPAN HD video

Ghosh et al. [52] 28,38,71-76,81-86 Urban Backhaul

Taori et al. [55] 28 Outdoor cellular Backhaul

Table 2.16. Applications on millimeter wave communications

2.5. Summary

In this chapter, we discuss the peculiar propagation characteristics of millimeter wave communications. Compared to the traditional wireless communications, millimeter wave suffers from higher attenuation loss and is sensitive to blockage. These problems bring challenges to the application of millimeter wave communication systems. However, taking good use of these characteristics can also make opportunities and developing new technologies for future 5G networks.

Chapter 3. Outage Probability and Channel Capacity of Millimeter

Wave Channels

In the previous chapter, we discussed the basic characteristics of millimeter wave and the main difference between it and traditional microwave. In this chapter, we are going to discuss details of the propagation properties of millimeter wave in order to study how it affects the performance of the wireless communication systems and investigate the restriction of it. Three main properties are introduced here including path loss and shadow fading, outage probability and channel capacity. To make the calculation results intuitively, simulations are used to evaluate these figures of merits in this chapter. In particular, we simulate the path loss with shadow fading and outage probability of the channel frequencies at 28 GHz, 38 GHz, 60 GHz and 73 GHz; as well as the channel capacity of SISO, MISO, SIMO and MIMO channels at these frequencies.

3.1. Path Loss and Shadowing Effect for Various Frequency Bands

In wireless communications, transmitted signal suffers from big challenges due to fading, noise, interference and other channel impediments. Most of the impediments are hard to predict since they are changing over time partially because of the receivers’ movement. However, path loss and shadowing can be predicted since these variations in received signal power are mainly caused by transmission distance.

Generally speaking, path loss mainly refers to the propagation losses caused by dissipation of the power radiated over transmitted distance. In a path loss model, it always assumes that the path loss does not change at a given fixed transmit-receive distance, which means this model does not include the shadowing effect. The variation due to path loss occurs over very large distances, for example 100 to 1000

38 meters. As for shadowing, it is mainly caused by large obstructions obscure the main signal path between the transmitter and the receiver and absorb the power. Different from path loss, shadowing effect varies over small distance, for example 10 meters in outdoor environments and even much smaller in indoor situations, which may change within 10 cm.

In a practical system, the transmitted signals will encounter multiple objects which result in a multipath caused by reflection or diffraction, producing distortion in the received signal. If we assume all the locations and dielectric properties are known, it is possible to solve the details of the multipath propagation. However, the computational complexity is very high that make it impractical as a general modelling tool [62].

In order to simplify the calculation and simulation, here, we use the simplified path loss model to estimate the path loss of the channel [53] for our millimeter wave wireless communication systems.

In this model, the received power can be expressed as [35]:

= (3.1)

In term of dB:

(dBm) = (dBm) +(dB) − 10log (3.2)

The constant in Equation (3.2) is the reference distance which is usually assumed to be 1 m to 10 m for indoor environment and 10 m to 100 m for outdoor environment. In simulations, it is usually set to be 1 meter for convenience, is the path loss exponent, is set to be the free space path loss at distance , which can be calculated as:

4 (dB) = −20 (3.3)

where = is the wavelength (in meters) of the carrier frequency and = 3×10 m/s is the speed of light which equals to the transmitted speed of the wave.

Then, the path loss can be expressed as:

PL(dB) =10 = 10γ − (3.4)

In addition to path loss, we set up the shadowing model. Usually, shadowing is considered as a random variable due to the blockage in the signal path. Since it is hard to know the location, size of the blocking objects as well as the reflection surface and scattering exponent that cause the small power attenuation, statistical models are very suitable to be used here. The most common model for this additional attenuation is log-normal shadowing model [35] for both microwave and millimeter wave systems.

In this model, the path loss is assumed random as a log-normal distribution given by [35]:

(10log− ) PL() = exp − , > 0 (3.5) 2 √2π

Where = , μ is the mean of = 10log in dB and is the standard deviation of , also in dB. The linear average path loss, which is the mean of , can be expressed as:

=[] =exp + (3.6) 2

The conversion from the linear mean (in dB) to the log mean (in dB) is derived from Equation (3.6) as:

10log = + (3.7) 2

From the Equation (3.7) we can see that the distribution of follows the Gaussian 40 distribution with the mean and standard deviation . In practical

communications, usually ranges from 3 to 10 [35].

Then we combine path loss and shadow fading together. Total path loss with shadowing can be calculated as:

PL(dB) =10 = 10γ −+ (3.8)

Put into the equation, the path loss finally is described as:

4 PL(dB) = 10γ + 20 + (3.9)

In this model, the propagation path is captured by the path loss model and shadow fading representing as fluctuation.

From Equation (3.9), we can see that the path loss is mainly affected by the wavelength , the average path loss exponent γ and the distance between the transmitter and receiver.

Next, we evaluate the effect of path loss and shadowing on the signal propagation for the typical millimeter wave frequency bands at 28 GHz, 38 GHz, 60 GHz and 73 GHz as well as the main Wi-Fi used microwave frequency at 2.4 GHz. In the simulation, we assume that the signals are transmitted in an urban microcell environment with potential LOS propagation. The reference distance is assumed to be 1 meter and the distance between transmitter and receiver is from 1 m to 200 m. For the path loss exponent γ, we will use the actual measurement results of γ from previous researches which means the influence by those oxygen absorption and rain attenuation of different frequency bands has already be considered in the

path loss exponent γ and shadowing effect standard deviation .

In our simulation, the first carrier frequency is the frequency band at 28 GHz (27.5 – 29.5 GHz). This band is designated for use by fixed point-to-point links in Australia [44]. In 2015, Samsung mentioned in a 3GPP 5G RAN workshop that 28 GHz band is a 41 possible millimeter wave band for 5G communication in small cells and they have already made some 5G test at several locations until now [55].

According to Niu Y et al. [13], the average path loss exponent is γ=1.85 and

shadowing effect standard deviation is =8.0 dB. The simulation result of the path loss and shadowing at this frequency band is shown in Figure 3.1.

Figure 3.1. Path loss and shadowing of 28 GHz

From the figure, we can see that the path loss grows fast in the first 20 meters from 62 dB to about 84 dB. After that, the path loss increases slowly and finally reaches at about 100 dB at 200 meters. On the other hand, the shadowing fluctuates a lot and even changes 25 dB in 1 meter distance.

Next, we consider the carrier frequency at 38 GHz with bands from 37 GHz to 38GHz.

This band is designated for use by short haul low-medium capacity fixed point-to-point services in Australia [56]. There are approximately 4 GHz bandwidth that can be used only for LOS point-to-point links with high power and very directive antennas. In recent research, it is shown that this band can be used for point-to-multipoint access in dense outdoor urban environment. It is also possible to provide stable signal propagation with very low outage within 200 meters by using reasonable power levels and directional antennas [57].

The average path loss exponent for this band is γ=1.95 and shadowing effect

standard deviation is =7.0 dB [13]. The simulation result of the path loss and shadowing for 38 GHz is shown in Figure 3.2.

Figure 3.2. Path loss and shadowing of 38 GHz

The figure shows that, the path loss also grows fast in the first 35 meters from 65 dB to about 90 dB. In addition, because the path loss exponent here is larger than that 43 at 28GHz, the path loss finally reaches at about 108dB at 200 meters. Also, the shadowing fluctuates a lot and changes about 25 dB in 1 meter distance.

Then the carrier frequency changes to 60 GHz. This band is one of the most important and useful frequency bands and many researches and tests were done at this band. 60 GHz band suffers from huge oxygen absorption and rain attenuation. With this characteristic, it can only transmit within a very short distance. However, it will allow a high level of frequency re-use and suitable for short-range wireless communication [23]. In addition, 60GHz is a good resource for backhaul technology. In 2004, the 58 GHz (57.2 GHz to 58.2 GHz) band is already used to support mobile backhaul links in Australia [23]. A lot of unlicensed band resources at around 60 GHz have been allocated to many countries. For example, in 1997, the Federal Communications Commission assigned the 59 GHz to 64 GHz band as an unlicensed band for radio, television, wire, satellite and cable in the United States [27]. In Europe, the 59 GHz to 66 GHz band has been allocated for mobile services by The European Conference of Postal and Telecommunication Administration. Until now, there are still parts of this frequency band that are undeveloped [23].

For 60GHz, the average path loss exponent for this band is γ=2.23 and shadowing

effect standard deviation is =7.9 dB [13]. The simulation result for the path loss and shadowing of 60 GHz is shown in Figure 3.3.

Figure 3.3. Path loss and shadowing of 60 GHz

Since the huge oxygen absorption and rain attenuation, path loss exponent of 60 GHz is much larger than that of the two frequency bands above. Thus, the path loss of 60 GHz is heavier than them. It increases rapidly within 20 meters and exceed 100 dB at about 30 meters. Then it still goes up fast and finally reaches 119 dB at 200 meters. However, the shadowing effect is similar to the previous simulation results, which changes about 23 dB in 1 meter distance.

The 73 GHz bandwidth is a part of E-band and it is a popular topic for both research and commercial areas. It is usually used in ultra-high-speed data point to point wireless links and allowed multi-Gigabit per second capacities. In 2016, Optus achieves 35 Gbps downlink speed over the 73 GHz band in 5G network trial with Huawei in Australia [58]. The Singapore mobile operator M1 Limited also achieved this high speed successfully in 2017 [59]. Huawei committed to develop this 73 GHz

45 technology and they believed that it can be an important part of 5G communication by 2020.

For the 73 GHz, the average path loss exponent for this band is γ=2.0 and

shadowing effect standard deviation is = 8.0dB [13]. The simulation result for the path loss and shadowing of 73 GHz is shown in Figure 3.4.

Figure 3.4. Path loss and shadowing of 73 GHz

Similar to the path loss of 60 GHz, it grows rapidly and exceeds 100 dB before 40 meters propagation and finally reaches 115 dB at 200 meters.

Considering the frequency bands at 2.4 GHz or below 2.4 GHz which is the most used frequency in 3G and 4G communication systems for mobile, radio and Wi-Fi in microwave in Australia, there is another equation to calculate its path loss when

46 transmitted in urban environments. From the 3GPP standard, the equation of path loss without shadowing effect of the frequency from 2 GHz to 6 GHz can be expressed as [60]:

PL(dB) =22∗+28+20() (3.10) where is the frequency unit in GHz.

The shadowing effect standard deviation is σ =6.3 dB [60]

Thus, we can know the path loss of 2.4 GHz, which is shown in Figure 3.5 below. It is clear that the path loss goes up with the distance which is similar to the path loss curve of millimeter wave and the largest path loss is 86 dB at 200 meters.

Figure 3.5. Path loss and shadowing of 2.4GHz

Figure 3.6. Path loss comparison between 2.4, 28, 38, 60 and 73 GHz

Figure 3.6 above shows the comparison of the path loss between 2.4 GHz, 28 GHz, 38 GHz, 60 GHz and 70 GHz. The path loss increases fast in the first 20 meters and then grow gently. According to the Figure 3.6, the path loss of 2.4 GHz is much smaller than that of other millimeter wave frequencies. The largest path loss at 200 meters is at 60 GHz, which is 35 dB larger than that at 2.4 GHz, 19 dB at 28 GHz and 11 dB at 38 GHz. Since the path loss is mainly influenced by the path loss exponent, it is clear that at the same distance, the carrier frequency at 60 GHz suffers the heaviest path loss. It can be understood from the physical point of view that the most serious oxygen and water absorption occurs at 60 GHz band.

3.2. Outage Probability

Outage probability means the probability that an outage will occur at a specific time. 48

In wireless communication systems, there is a target minimum received power which usually designated as . The signal will not be received if the received power is lower than this threshold. Generally speaking, the outage probability is the probability if the received power is smaller than . It is important to achieve a lower outage probability in system design to reduce the probability that the users cannot receive any signal.

In a practical millimeter wave system, the outage probability is greatly affected by the transmitted power, antenna gains as well as the propagation environment [1]. In order to simplify the calculation and the simulation, we only consider the outage caused by path loss and shadowing fading, which are the main factors that make the signal power smaller than the threshold when arriving at the receiver side. Since the path loss and shadowing fading is proportional to the transmit distance and influence by frequency, the outage probability is also related to the distance between the transmitter and receiver, the carrier frequency, the path loss exponent and shadowing standard deviation. According to [35], it can be expressed as:

(() ≤)

−( +−10log(/) =1− (3.11) σ where is the same as it in the path loss function which is:

4 (dB) = −20 (3.12)

All the variables in this equation must be in dB.

The Q function is the probability that a Gaussian random variable with zero mean and variance one is larger than :

1 Q() ≜p(>) = (3.13) √2

Next, the simulation results will show the outage probability for the typical millimeter wave frequency bands at 28 GHz, 38 GHz, 60 GHz and 73 GHz. Assuming that the distance between transmitter and receiver is from 1 meter to 1000 meters since the millimeter wave is not suitable for very long distance propagation. We also assume the reference distance is 1 meter. According to the 3GPP document [60], the for users’ equipment varies in different bands and receive antenna. We choose the E-UTRA Band 1 for the channel bandwidth 20 MHz with only one receive antenna. In that case, the can be considered as -94 dBm.

The typical transmit power can be found in ETSI TR 102 243-1 V1.2.1 (2013) [61]. Maximum transmit power is expressed in dBm and concluded in Table 3.1 below.

Power parameters Typical transmitter highest power for real equipment (dBm)

23 GHz, 26 GHz,28 GHz Systems +25

31 GHz, 32 GHz, 38 GHz and 42 GHz +23 Systems

50 GHz, 52GHz, 55GHz Systems +15

57 GHz to 66 GHz Band +15

71 GHz to 86 GHz Band +18

Table 3.1. Maximum transmit power for different frequency bands [61]

From the above Table 3.1, the maximum transmit power for 28 GHz is 25 dBm at the transmit antenna with the path loss exponent γ = 1.85 and shadowing effect

standard deviation σ =8.0 dB. For 38 GHz, the maximum transmit power is 23

50 dBm at the transmit antenna and the loss exponent γ=1.95 and shadowing effect

standard deviation σ =7.0 dB. For 60 GHz, the maximum transmit power is

15dBm at the transmit antenna and the path loss exponent γ = 2.23 and

shadowing effect standard deviation σ =7.9 dB. For 73 GHz, the maximum transmit power is 18 dBm at the transmit antenna and the path loss exponent γ=

2.0 and shadowing effect standard deviation σ =8.0 dB. The simulation result of outage probability according to distance is shown in Figure 3.7.

Figure 3.7. Outage Probability comparison between 28, 38, 60, 73 GHz

From Figure 3.7 we can see the outage probability for these four carrier frequency bands as well as the differences among them. For 28 GHz, the outage probability is close to zero in the first 50 meters and then the curve growth slightly from 100 meters to 1000 meters. At about 750 meters distance, the outage probability goes

51 over 50% and reaches 62% at the farthest distance. The trend of the curve of 38 GHz is similar to 28 GHz. At the first 50 meters, the outage probability is almost zero and the increases gradually. It exceeds 50% at about 500 meters which is nearer 1/3 of that of 28 GHz and finally ends in 78% at 1000 meters. According to the simulation result, these two frequency bands performed very well when the distance between transmitter and the receiver is smaller than 200 meters. In addition, they can provide a stable communication with 300 meters where the outage probability is less than 25%.

However, compared with these two lower frequency bands, the carrier frequency at 60 GHz and 73 GHz is facing big challenges. For 60 GHz, since the path loss exponent is the largest among all tested bands, it suffers from highest attenuation. The outage probability curve grows dramatically from 20 meters and even reaches 90% within 200 meters. That means when transmitting signals with this frequency band, there is a very high probability the signals cannot be received beyond 200 meters. It only performs very well in the first 25 meters and could be used for communication if the distance between transmitter and receiver is smaller than 50 meters for the given threshold. The outage probability curve for 73 GHz shows a similar trend as that of 60 GHz. However, it is a bit better than 60GHz since it can be used within 75 meters and gets 90% outage probability at about 400 meters for the given threshold.

In conclusion, millimeter wave frequency now is not suitable for a long distance transmission over 400 meters. For an outdoor environment with the distance between the base station and the users is smaller than 200 meters, both 28 GHz and 38 GHz can offer good performance. However, higher frequency bands at 60 GHz and 73 GHz are more appropriate for indoor short distance communications within 50 or 75 meters.

3.3. Rayleigh Fading and Rician Fading Channel

Besides the path loss and shadowing effect, the transmitted signal in wireless communications also suffers from other fading. Two typical fading models are Rayleigh fading and Rician fading.

The Rayleigh fading model is a statistic model in wireless communication. It assumes that the magnitude of a signal that has passed through such a transmission medium will vary randomly, or fade, according to a Rayleigh distribution [62], which is the sum of many uncorrelated multipath random variables. Rayleigh fading model is mainly caused by multipath reception. We assume that the phase for each path is uniformly distributed between 0 and 2π and the phases of different paths are independent to each other. The envelope of the channel response will therefore be Rayleigh distributed. In wireless communications, Rayleigh fading model is widely used since there are usually many objects which can reflect or scatter the transmitted signal before it can be received.

Another widely used fading model is Rician fading model. Rician fading is similar to Rayleigh fading which is also caused by signal scattering. However, it occurs when one of the paths, typically a line of sight signal, is much stronger than the others [62]. Thus, it can be considered as the sum of two parts: the LOS signal plus ground reflections which could be seen as independent signals. There are two key parameters to describe a Rician fading channel: K and Ω. K is the ratio of the energy in the specular path to the energy in the scattered paths which is usually from 4 to 10 depends on the environment and Ω is the total power from both paths [63]. Consider a wireless communication and its signal is transmitted in millimeter wave. It is mainly assumed that there is a LOS propagation. Thus, we can assume that the received signal follows the Rician fading model.

In the Rician fading model, the channel can be described as:

= + (3.14) where y, h, x and n are all complex random variables, y is the channel output, h is the channel gain, x is the channel input and n means the additive Gaussian noise. The h 53 in this case can be expressed as:

1 = + (3.15) 1+ 1+

where is the Rician factor as mentioned before and >0. is a normalized constant representing the line of sight component and is the specular component which is a circularly symmetric complex Gaussian random variable with zero mean and unit variance.

The channel model can be also described as a figure in Figure 3.8:

Figure 3.8. Diagram of the fading channel model

3.4. Channel Capacity

3.4.1. Additive White Gaussian Noise (AWGN) Channel Capacity

Channel capacity is the maximum rate that the information can be reliably transmitted over a communication channel [62]. With the growth of traffic demand, it is important to know the capacity of the channels and improve it. The channel capacity is first developed by Claude E. Shannon in the 1940s during World War II. He defines the notion of channel capacity and provides a mathematical model to 54 compute it. As the result of his experiment, we can calculate the channel capacity of a continuous-time additive white Gaussian noise (AWGN) channel by his equation [62]:

C=Wlog(1+SNR) bits/ sec (3.16) where the W is the channel bandwidth, SNR is the signal-to-noise radio. The unit bits/sec can be abbreviated to bps. In wireless communications, this equation is usually used to calculate the upper bound capacity of the channel. We can also express the capacity of the AWGN channel with power constraint and noise variance after applying a capacity-achieving AWGN codes which is [62]:

1 C = log 1 + bits/sec (3.17) 2

Because the Gaussian noise is independent in the I and Q components, which means it can be seen as two independent AWGN channel combined together, the power

constraint per real symbol is and the noise variance per real symbol is . Thus, the capacity of a continuous-time AWGN channel united in bits per real dimension and bits per complex dimension (or degree of freedom) are:

1 C = log 1 + (3.18) 2 W and

P C =log 1 + (3.19) W respectively.

3.4.2. Capacity of SISO System over a Rician Fading Channel

Next, we are going to discuss the capacity of a basic SISO link with Rician fading.

A SISO channel can be expressed as:

[m] =h[m][m] +[m] (3.20) where [m] is the channel output at time m, h[m] means the Rician fading channel gain, [m] is the channel input at time m and [m] means the complex baseband additive Gaussian noise.

This channel can be seen as an AWGN channel with the received SNR being related to the received power , noise power and fading h. According to [62], the capacity of this Rician fading with receiver channel statement information (CSI) only can be expressed as [52]:

C[m] = log (1+SNR) =log 1 + |h[m]| bps/Hz (3.21) where h[m] follows the Rician fading,

k 1 h= h + h (3.22) 1+k 1+k and,

(dB) = −−− (3.23) where is transmitted power, is path loss fading, is shadow fading and

is the background noise at the receiver side which is usually from -90 dBm to -103 dBm [51] depending on the receive facility.

Since h[m] is a random variable, the result of capacity Equation (3.21) is also a random variable. Therefore, in mathematic model, the ergodic capacity is usually used to describe the channel capacity which is defined as the statistical average of the mutual information, where the expectation is taken over |h[m]|. Thus, the average capacity of the fading channel can be rewritten as:

P C=log 1 + |h[m]| bps/Hz (3.24) σ where [] represents the expectation.

In the following, we evaluate the average capacity of the SISO link between transmitter and receiver with the carrier frequencies at 28 GHz, 38 GHz, 60 GHz and

73 GHz respectively by simulation. In this case, h is a constant since there is only one LOS propagation in the channel. In the simulation, h is set to be 1 and the

Rician factor K is 5. In addition, the background noise N0 is set to be the average number which is -97 dBm. As for path loss fading and shadow fading, we use the data in the previous section. To compare the capacity of these bands in a Rician fading channel, simulation results are shown in the Figure 3.9.

Figure 3.9. SISO channel capacity of 28, 38, 60, 73 GHz with Rician fading channel

According to the Equation (3.21), the capacity depends on the fading channel and received SNR. Since the Rician fading channel is assumed to be same in the simulation, the main factor to affect the capacity is the received SNR which is related to the distance between transmitter and receiver. Because the path loss is going up with the distance increase, the received SNR will reduce. Therefore, the capacity will also decrease with the distance increase. From the figure, we can easily find that the capacity of 28 GHz is the largest, which is still 4 bps/Hz at 400 meters, because it has the smallest path loss. For 38 GHz, the capacity is 2 bps/Hz at 400 meters which is only a half of that at 28 GHz. However, for 60 GHz and 73 GHz, the capacity is less than 1 bps/Hz over 200 meters and even decrease to almost 0 at 400 meters. The result of SISO fading channel capacity shows that high frequency millimeter wave is not suitable for long distance propagation; especially 60 GHz and 73 GHz may only be able to be used within 50 meters and 100 meters, respectively.

3.4.3. Capacity with Antenna Diversity

In wireless communication systems, if the propagation path suffers from deep fading and other attenuation, it will be very likely to receive wrong information. To reduce the error probability, diversity schemes are introduced [62]. Generally, diversity is a method to dramatically improve the reliability of communications by using multiple signal paths. There are many ways to obtain diversity in wireless communication. One directly method is antenna diversity or spatial diversity which is by placing two or more antennas at transmitter side or/ and receiver side. Thus, there are three kinds of antenna diversity: receive diversity, which is using multiple antenna at the receiver side usually called single input multiple output or SIMO channels; transmit diversity, which is using multiple antenna at the transmitter side usually called multiple input single output or MISO channels; and the last one is multiple input multiple output or MIMO channels. In this method, as long as one signal path is strong enough to the receiver, the communication is reliable. It is also possible to increase the channel capacity by using multiple antennas. 58

3.4.3.1. Capacity of SIMO System over a Rician Fading Channel

Let us consider a SIMO channel with one transmit antenna and N receive antennas. The channel can be expressed as:

[m] =ℎ[m] +[m] n = 1, … , N (3.25) where ℎ is the channel gain from the transmit antenna to the th receive antenna, which we assume a Rician fading channel here, is the additive Gaussian noise following (0, σ) and independent to each other across antennas. To detect

[m] from [m] =[[m],…,[m]] by using maximum-ratio combining (MRC) method:

[m] =∗[m] = ‖‖x[m] +∗[m] (3.26)

∗ In this equation, =[ℎ,…,ℎ] and [m] =[[m], … , [m]] , where represents the conjugate of and [ ] represents transpose.

This channel can be seen as an AWGN channel with the received SNR= ||, where is the average received energy and noise power . Thus, the capacity of the SIMO fading channel with receiver CSI only is [62]:

C=log (1+SNR) =log 1 + ‖‖ bps/Hz (3.27)

The advantage of multiple antennas is to increase the effective SNR by providing more power or diversity gain for the channel. That is to say, with the more antennas at transmitter side or receiver side, there would be a larger power used for signal detection. Thus, it can provide a larger capacity.

We evaluated the SIMO link with the Rician fading and carrier frequencies at 28 GHz, 38 GHz, 60 GHz and 73 GHz respectively are shown in the following. In the simulation, the Rician fading factor K is set to be 5 and N indicates the number of receive

59 antennas. Path loss and shadow fading factors are the same as in the previous section.

A. Comparison of capacity vs. distance for different antennas

Figure 3.10. SIMO Channel Capacity of 28 GHz with Rician Fading Channel

Figure 3.11. SIMO Channel Capacity of 38 GHz with Rician Fading Channel

Figure 3.12. SIMO Channel Capacity of 60 GHz with Rician Fading Channel

Figure 3.13. SIMO Channel Capacity of 73 GHz with Rician Fading Channel

Figure 3.10 to Figure 3.13 compare how different number of receive antennas influences the channel capacity. It is obvious that when N is getting larger, the channel capacity is also getting larger if the distance between the transmitter and receiver is the same. With 20 receive antennas, the capacity of the channel with the carrier frequency at 60 GHz can exceed 2 bps/Hz at 200 meters. That means it is possible to use this frequency when there is a receive diversity. However, the capacity is not growing linearly with the N. For example, for the channel with the frequency at 38GHz, comparing N=5 and N=10, C is 4 bps/Hz and 5 bps/Hz, respectively. N increases by 5 and C goes up 1 bps/Hz here. Then comparing N=10 and N=20, we can find that C is 5bps/Hz and 6bps/Hz, respectively. This time N is increased by 10 to achieve the same growth of capacity at 1 bps/Hz. The result indicates that when applying receive diversity to improve channel capacity, we should also consider the efficiency of using the number of antennas. 62

B. Comparison of capacity vs. distance for different frequency

The next two figures (Figure 3.14 and Figure 3.15) compare the capacity of the channel with carrier frequency at 28GHz, 38GHz, 60GHz and 73GHz with a fixed number of receive antenna where N=5 and N=20.

Figure 3.14. SIMO Channel Capacity of 28, 38, 60, 73 GHz with Rician Fading Channel When N=5

Figure 3.15. SIMO Channel Capacity of 28, 38, 60, 73 GHz with Rician Fading Channel When N=20

Similar to the SISO channel capacity, the capacity of 28 GHz is the best among all these four different frequencies while the capacity of 60 GHz and 73 GHz drops very fast when the distance exceeds 100 meters. In addition, the total capacity of N=20 is obvious larger than the capacity of N=5 no matter which carrier frequency is.

C. Comparison of capacity vs. the number of antennas N for different frequency

Figure 3.16 and Figure 3.17 show the capacity of the channel with carrier frequency at 28 GHz, 38 GHz, 60 GHz and 73 GHz with a fixed distance from transmit antenna to receive antenna D=100m and D=200m.

Figure 3.16. SIMO Channel Capacity of 28, 38, 60, 73 GHz with Rician Fading Channel When D=100m

Figure 3.17. SIMO Channel Capacity of 28, 38, 60, 73 GHz with Rician Fading Channel When D=200m

From Figure 3.16 and Figure 3.17, it is obvious that the channel capacity goes up with the increasing number of receive antenna. However, the speed of growth is slowing down when N is getting larger. In addition, at the same distance and same number of receive antenna, the channel capacity of 28 GHz and 38 GHz is much larger than that of 60 GHz and 73 GHz.

3.4.3.2. Capacity of MISO System over a Rician Fading Channel

Let us consider a MISO channel with M transmit antennas and a single receive antenna. The channel can be expressed as:

[m] =∗[m] +[m] (3.28)

where =[h,…,h] and h is the channel gain from the mth transmit antennas to the receiver and [m] is the additive Gaussian noise following (0, σ).

If the channel is known at the transmitter, beam forming scheme is introduced. That is to say, for MISO channels, system would only send the message in the direction of the channel vector h, and all the signals which are sent in any orthogonal direction will be ignored. According to [62], if we set:

[m] = x[m] (3.29) ‖‖ this MISO channel can be seen as a scalar AWGN channel, that is:

y[m] = ‖‖x[m] +n[m] (3.30)

with the received SNR= ||, where is the average transmitted energy and noise 66 power is . Thus, the capacity of the MISO fading channel with the transmitter CSI is [62]:

P C=log (1+SNR) =log 1 + ‖‖ bps/Hz (3.31) σ

Comparing Equation (3.27) and Equation (3.31), we notice that the transmitter diversity and receiver diversity get the same capacity if transmit beamforming or receive beamforming is used accordingly. Therefore, we will not show the simulation results for transmit beamforming.

3.4.3.3. Capacity of MIMO system over a Rician fading channel

Let us now consider a MIMO channel with M transmit antennas and N receive antennas:

y[m] =[m][m] +[m] (3.32) where [m] is the Rician fading channel gain and [m] is the additive Gaussian noise following (0, σ). In many cases, the channel matrix H is unknown to the transmitter, thus, to calculate the capacity of a MIMO channel, we first introduce the V-BLAST architecture as shown in Figure 3.18.

Figure 3.18. V-BLAST architecture [62]

The independent data streams are multiplexed in some arbitrary coordinate systems 67 given by a unitary matrix Q and jointly decoded. By using the V-BLAST architecture, the data is not necessarily dependent on the channel matrix H. After applying a capacity-achieving AWGN code, the kth data stream will have an allocated power Pk and a rate Rk. Using a sphere-packing argument analogous, the upper bound of the total rate R is [62]:

1 R

∗ =diag{P,…,P} (3.34) is the covariance matrix of the transmitted signals .

A long-term average rate by coding over many coherence time intervals of the channel can be expressed as [62]:

1 R = log det + ∗ (3.35)

Then, by choosing we can achieve a reliable communication rate by [62]:

1 ∗ C= max log det + (3.36) :[] where Tr[ ] means the trace and P is the power constraint.

With equal power allocation, the statistic capacity of this MIMO Rician fading channel with receiver CSI then could be [62]:

C=log det + ∗ (3.37) where M is the number of transmit antennas and N is the number of receive

antennas. And received SNR= with the average received energy P and noise power .

In the following, we evaluated the capacity of the MIMO link with various number of transmit antennas and receive antennas over the Rician fading channel and carrier frequency at 28 GHz, 38 GHz, 60 GHz and 73 GHz, respectively. The Rician factor K is 5 and path loss and shadow fading factors are the same as in the previous section.

Figure 3.19. MIMO Channel Capacity of 28 GHz with Rician Fading Channel

Figure 3.20. MIMO Channel Capacity of 38 GHz with Rician Fading Channel

Figure 3.21. MIMO Channel Capacity of 60 GHz with Rician Fading Channel

Figure 3.22. MIMO Channel Capacity of 73 GHz with Rician Fading Channel

Figure 3.19 to Figure 3.22 show that the capacity of a MIMO channel is decreasing with the increase of distance between transmitter and receiver. Similar to SIMO and MISO, the capacity of 28 GHz is the best among all these four different frequencies while for 60 GHz and 73 GHz, the capacity drops rapidly when the distance exceeds 50 meters.

3.4.4. Comparison of Capacity of SIMO, MISO and MIMO Channels

In this section, we take the frequency at 73 GHz as an example to compare the capacity of SIMO, MISO and MIMO channel. Figure 3.23 is the channel capacity when the number of transmit antennas and receive antennas are both 5 and Figure 3.24 is the channel capacity when they are both 10. The Rician factor K and path loss fading are the same as in the previous section. 71

Figure 3.23. Comparison of SIMO, MISO and MIMO Channel Capacity of 73 GHz with Rician Fading Channel when M=N=5

Figure 3.24. Comparison of Channel Capacity of 73GHz with Rician Fading Channel when M=N=10

Comparing the capacity of SIMO, MISO and MIMO channels, as shown in Figure 3.23 and Figure 3.24, we can see that the capacity of SIMO and MISO channel are the same as we mentioned before. However, the capacity of MIMO channel is much larger than those two channels. For example, in Figure 3.23, the capacity of SIMO and MISO channel is 6 bps/Hz at 50 meters, while the capacity of MIMO channel is 15.5 bps/Hz which is nearly two times larger than that of a SIMO or MISO channel.

3.5. Summary

In this chapter, by evaluating the path loss, outage probability and capacity of 28 GHz, 38 GHz, 60 GHz and 73 GHz carrier frequencies, we get to know the properties of these millimeter wave bands in Rician fading channels. Since the path loss of 28 GHz 73 and 38 GHz are not very large, the channel with these two carrier frequencies can support the signal transmission for a longer distance for about 400 meters with the standard transmit power. If the distance between transmitter and receiver is smaller than 100 meters, the channel with 28 GHz and 38 GHz can provide a very large channel capacity. However, 60 GHz performs not very well because of the huge atmosphere and rain attenuation. It is very difficult to support 50 meters reliable transmission by using multiple antennas for this frequency. These conclusions can help us to design a practical millimeter wave wireless communication system.

Chapter 4. Multi-user Millimeter Wave Systems

In the previous chapter, we discussed the path loss and shadow fading, outage probability and channel capacity of millimeter wave channels and gave a brief introduce of MIMO systems. To show these characteristics directly, we only pay attention to the link between one transmitter and one receiver, which means we only consider a single base station serves a single user in one cellular cell. However, in practical wireless communications, the system cannot be constituted by only one cell and one user. There are more factors needed to be concerned as well. Thus, in this chapter, we evaluate the achievable sum-rate of a single-cell multi-user millimeter wave system as well as a multi-cell multi-user millimeter wave system and discuss how multiple base stations and users can influence the data rate in the cellular systems.

4.1. Interference and Signal-to-interference-plus-noise Ratio (SINR)

In wireless communications, when there are multiple transmitters and multiple receivers, one important factor needs to be concerned is interference. For one particular receiver, interference usually refers to the interaction of waves from the other source or because the other nearby receivers use the same frequency. It can be seen as an unwanted noise which can affect the transmitted information.

We have mentioned the signal-to-noise radio (SNR), which is the ratio of signal power to the noise power [35]:

P SNR = (4.1) N in the previous chapter to calculate the theoretical channel capacity without other effects. When computing more rigorous capacity and data rate, with the interference to be concerned, we introduce signal-to-interference-plus-noise ratio, which is 75 usually known as SINR. Similar to SNR, SINR is the ratio of signal power to the sum of interference power and noise power. It is usually expressed as:

P SINR = (4.2) I+N where I indicate the interference power. From the definition, we can easily find that if the interference power reduces to zero, then the SINR becomes the SNR.

4.2. Single-cell Multi-user Millimeter Wave System

4.2.1. System Model

In the previous chapter, we assumed that there is only one user in the cell. In this section, we extend it to a multi-user system which means that there are several users are served by one base station in one cell.

First, we consider a downlink transmission channel with one regular hexagonal cellular cell. Assume there is a single base station located in the central of the cell and supports total K users in its cell. The base station is equipped with L (L≤K) transmit antennas and each user has only one receive antenna. For simplicity, we assume that each user k (k≤K) only receives one information stream from the base station and the data stream for different users are independent from each other and identically distributed according to (0,1). Then, the signal received by user k is:

= + +, = 1,2, … , (4.3) ,

× Here ∈ ℂ is the channel gain vector to the kth user from the base station with the CSI is available at both transmitter side and receiver side. Since we are applying millimeter wave, the should follow a Rician fading given by: 76

α 1 = + (4.4) 1+α , 1+α ,

And Rician factor α is the ratio of the energy in the specular path to the energy in the scattered paths. In addition, is the desired received signal for user k, and

∑, can be seen as interference form other users, is the additive noise at the kth user with zero mean and variance.

4.2.2. Scheduling

Since we assume that the number of users is larger than the number of transmit antennas, it is obvious that not all the users can be served by the base station at the same time. In this situation, we will use scheduling to decide which user is active for transmitting signal. For simplicity in simulations, k active users out of total K users are selected randomly in the cell. It can be easily find that the number of scheduled users k should be no more than the number of transmit antennas L at the base station.

4.2.3. Beamforming

Beam forming is a signal processing technique used in antenna arrays for transmitting or receiving signals directionally [64]. It is achieved by combining elements in an antenna array with proper weighting factors, which makes some of the signals at particular angles experiencing constructive interference while others experiencing destructive interference. In beam forming scheme, user streams are separated by different beam forming directions. After applying beam forming, the transmitted signal from the base station to the kth user can be written as:

= (4.5)

× where ∈ ℂ is the network-wide beam forming vector for the transmit signal from base station to the user k. Then, with the linear transmit beam forming scheme at the base station, the received signal for user k in the cell of base station can be written as:

= + + (4.6) ,

From the equation, we can see that is the desired received signal for user k,

and ∑, can be seen as interference from other users, is the additive noise with zero mean and variance at the kth user. In addition, the equation of transmitted signal can also account for the user scheduling operation. If and only if the beamformer vector is nonzero, user k can be scheduled at base station [64]. In other words, the scheduling choice is determined by the indicator function:

1, if ‖ ‖ =0 (‖ ‖) = (4.7) 0, otherwise

In addition, we can get a beamformer matrix =[,… , ] by collecting all beamformer vectors from base station. Considering the average power constraint , should follow:

Tr[∗] ≤ (4.8) where Tr[ ] represents the trace.

Under these considerations, the achievable rate for user k can be written as [64]:

∗ ∗ R = log(1+) =log(1+ ) (4.9) where

∗ ∗ = + (4.10) ,

4.2.4. Zero-forcing Beamforming

k L Tx

users antennas

Figure 4.1. MIMO downlink system with scheduler and zero-forcing beamforming (L transmit antennas and K users) [66]

Figure 4.1 shows the diagram of a zero-forcing (ZF) beam forming downlink channel model [66]. Here, this ZF scheme is used for cancelling the intra-user interference. We assume that the capability of the base station is powerful enough to process the entire signal information. First the K users in the cell will be scheduled by a random scheduler as mentioned before. Then the channel of those chosen k users will be coded and send to the zero-forcing beamformer. In zero-forcing beam forming, beam forming vectors are selected to satisfy the zero-interference condition, which is

=0 (≠). Since we have the beamformer matrix =[,… , ] and channel matrix =[,… , ], for base station, to choose a zero-forcing beam forming vector, we first assume a corresponding submatrix () and (), where

∈{1,…,}. Then, the () that gives zero-interference is the pseudo inverse of (), which can be expressed as [66]:

() =() =()∗(()()∗) (4.11)

4.2.5. Multi-user Sum-rate Evaluation

In this section, we evaluate the achievable sum-rate for the single-cell multi-user downlink channel with the ZF beamforming scheme. The sum-rate of the system is given by:

∗ ∗ R =R =log(1+ ) (4.12) and is the same as Equation (4.10).

Since the scheduled users are chosen randomly, it makes R and R are also random and hard to calculate. In order to examining the effects of the proposed ZF beamforming scheme over a millimeter wave channel, we will use the cumulative distribution function (CDF) of the long-term average sum-rate to show the channel performance. The CDF can show the behavior of the sum rate distributions, for example, the 10th percentile user rate of the channel. The low-rate user is especially an important figure of merit to evaluate the experience of cell-edge users which received the smallest power from the base station. In this regard, the 10th percentile user rate will be used to illustrate the performance of cell-edge users.

80 point represents the base station and blue dots mean the users. According to the simulation results for these millimeter wave bands, the radius of the cell is set to be 0.25 kilometers, which is reasonable as discussed in Chapter 3. As for the fading channel, we still consider the Rician fading channel H with the factor α=5. The channel vector for user k is given by:

α 1 = + ( −PL −SF) (4.13) 1+α , 1+α ,

where , is a normalized constant representing the line of sight component for user k and , is the specular component which is a circularly symmetric complex

Gaussian random variable for user k with zero mean and unit variance, is transmitted power from the base station, PL is the path loss fading for the user k and SF is the shadow fading, which is calculated as the same in Chapter 3. The simulation parameters can be seen in Table 4.1

Figure 4.2. Single cell system model

Simulation Parameter

Frequency (GHz) 28 38 60 73

Max. Tx power (dBm) 25 23 15 18

Path loss exponent 1.85 1.95 2.23 2.0

Shadowing fading(dB) 8.0 7.0 7.9 8.0

Antenna gain (dBi) 15

Background noise (dBm) 97

Table 4.1. Simulation parameters for sing-cell system

A. Comparison of sum-rate vs. the number of scheduled users

We first examine how the number of scheduled users affects the system sum-rate.

Figure 4.3 and Figure 4.4 show the CDF of the achievable sum-rate at 28 GHz with 10 or 20 transmits antennas. From the figures, we can obviously see that for both 10 and 20 transmit antennas, the rate is larger as the number of scheduled users getting larger. For example, when there are 10 transmit antennas, the rate with 2 scheduled users is concentrated between 1.6 to 1.9 bits/s/Hz while the rate with 10 scheduled users is concentrated between 4.8 to 6.8 bits/s/Hz. In addition, as the scheduled users increase from 2 to 10, the 10th percentile sum-rate goes up from 1.66 to 5.37 bits/s/Hz, which increases the sum-rate of cell-edge users by 3.71 bits/s/Hz.

Figure 4.3. CDF of 28 GHz with 10 transmit antennas

Figure 4.4. CDF of 28 GHz with 20 transmit antennas

Figure 4.5 and Figure 4.6 show the CDF of the achievable sum-rate at 38 GHz with 10 or 20 transmit antennas. From the figures, we can see that the trend of the curves is similar to that at 28 GHz. The rate is obviously getting larger as the number of scheduled users getting larger. When there are 10 transmit antennas, the achievable rate with 2 scheduled users is concentrated between 1.55 to 1.85 bits/s/Hz, while the achievable rate with 10 scheduled users is concentrated between 4.4 to 6.5 bits/s/Hz. In addition, as the scheduled users increase from 2 to 10, the 10th percentile sum-rate goes up from 1.58 to 4.76 bits/s/Hz, which increases the sum-rate of cell-edge users by 3.18 bits/s/Hz.

Figure 4.5. CDF of 38 GHz with 10 transmit antennas

Figure 4.6. CDF of 38 GHz with 20 transmit antennas

Figure 4.7 and Figure 4.8 show the CDF of the achievable sum-rate at 60 GHz with 10 or 20 transmit antennas. From the figures, we can see that the trend of the curves is also similar to that at 28 GHz and 38 GHz. The rate is larger as the number of scheduled users getting larger. For example, when there are 10 transmit antennas, the achievable rate with 2 scheduled users is concentrated between 1.25 to 1.65 bits/s/Hz, while the achievable rate with 10 scheduled users is concentrated between 3 to 4.8 bits/s/Hz. In addition, as the scheduled users increase from 2 to 10, the 10th percentile sum-rate goes up from 1.33 to 3.13 bits/s/Hz, which increases the

84 sum-rate of cell-edge users by 1.8 bits/s/Hz.

Figure 4.7. CDF of 60 GHz with 10 transmit antennas

Figure 4.8. CDF of 60 GHz with 20 transmit antennas

Figure 4.9 and Figure 4.10 show the CDF of the achievable sum-rate at 73 GHz with 10 or 20 transmit antennas. We can see that the result does not show much difference to the previous figures. As the scheduled users increase from 2 to 10, the 10th percentile sum-rate goes up from 1.44 to 3.65 bits/s/Hz, which increases the sum-rate of cell-edge users by 2.21 bits/s/Hz. Thus, we can conclude that for both 10 and 20 transmit antennas, the rate is increasing as the number of scheduled users getting larger. That means when there are more active users, the achievable sum-rate 85 of the channel could reach a higher level as well as the sum-rate of the cell-edge users.

Figure 4.9. CDF of 73 GHz with 10 transmit antennas

Figure 4.10. CDF of 73 GHz with 20 transmit antennas

B. Comparison of sum-rate vs. the number of transmit antennas

Next, we examine how the different number of transmit antenna affects the sum-rate. Figure 4.11 to Figure 4.14 show the CDF of the achievable sum-rate with different frequency bands and various number of transmit antennas. We compare the sum-rate of 10 and 20 transmit antennas with 2 scheduled users.

Figure 4.11. CDF of 28 GHz with 2 scheduled users

Figure 4.12. CDF of 38 GHz with 2 scheduled users

Figure 4.13. CDF of 60 GHz with 2 scheduled users 87

Figure 4.14. CDF of 73 GHz with 2 scheduled users

For all of the 4 frequency bands, with the fixed number of scheduled user (we set 2 users in the simulation), the sum-rate of 20 transmit antennas is better that it with 10 transmit antennas. For example, in figure 4.11, where the carrier frequency is 28 GHz, the sum-rate of 10 transmit antennas is mainly distributed from 1.63 to 1.93 bits/s/Hz while the sum-rate of 20 transmit antennas is from 1.73 to 2.05 bits/s/Hz. As for the 10th percentile, the sum-rate goes up from 1.66 to 1.77 bits/s/Hz when then number of transmit antennas change from 10 to 20, which increases the sum-rate of cell-edge users by 0.11 bits/s/Hz.

C. Comparison of sum-rate VS. the carrier frequency

In this section, we examine how the carrier frequency band affects the sum-rate. Figure 4.15 and Figure 4.16 show the CDF of the achievable sum-rate with different frequency bands and fixed number of transmit antennas and scheduled users. We consider two situations here: 10 transmit antennas and 2 scheduled users and 10 transmit antennas and 10 scheduled users.

Figure 4.15. CDF of different frequencies with 10 receive antennas and 2 scheduled users

Figure 4.16. CDF of different frequencies with 10 receive antennas and 10 scheduled users

From Figure 4.15 and Figure 4.16 we can see that with the same number of transmit antennas and scheduled users, 28 GHz achieves the best performance among the 4 frequency bands while 60 GHz performs worst. For example, with 10 receive antennas and 2 scheduled users, the rate data of 28 GHz is distributed between 1.63 to 1.93 bits/s/Hz and the rate data of 60 GHz is distributed between 1.28 to 1.64 bits/s/Hz. The main reason is that the path loss exponent of 60 GHz band is much larger than all of other frequency bands, meanwhile the maximum transmit antennas power is the smallest from the standard [61]. This result is similar to what we have in 89 the previous chapter when examining the capacity in a SISO system. By comparing the 10th percentile sum-rate of these four bands, for example, when 10 receive antennas and 10 scheduled users, we can know that the sum-rates of cell-edge users are 5.37 bits/s/Hz, 4.76 bits/s/Hz, 3.16 bits/s/Hz and 3.65 bits/s/Hz at 28 GHz, 38 GHz, 60 GHz and 73 GHz, respectively.

4.3. Multi-cell Multi-user Millimeter Wave System

4.3.1. System Model

After discussing the achievable sum-rate in a single cell system, we next extend the evaluation and see how the achievable sum-rate performs under a multi-cell multi-user system.

We consider a downlink transmission channel with N regular hexagonal cellular cell in the system, and the distance between neighboring cells is D kilometers. Each base station b, where b is an integer and not larger than N, is located in the center of a cell. In addition, there are total K users in each cell but only k (k≤K) of them are active at the same time. To decide which user is served by the base station, we still use random scheduling to pick up the active k users randomly. Then, assuming that there are L (L≤K) transmit antennas equipped in each base station and one receive antenna for each user. For easy to set up the model, we also assume that each user k only receives one information from the base station b which is expressed as ,.

Assume the data stream , for different users are independent from each other and identically distributed according to (0,1). Then, the transmitted signal from the base station b is:

=, (4.14)

90 and the received signal for user k in the cell of base station b can be expressed as:

y, =,, +,, + ,, , , ,

+, (4.15)

× Here, , ∈ ℂ represents the channel gain vector from base station b to the user k with the CSI is available at both transmitter side and receiver side in this cell.

Since we are applying millimeter wave, the , should follow Rician fading channel:

α 1 = + (4.16) , 1+α ,, 1+α ,,

The Rician factor α is the ratio of the energy in the specular path to the energy in the scattered paths. In addition, ,, is the desired received signal from base

station b to user k, and ∑, ,, + ∑∑, , ,, can be seen as

total interference form other users. In particular, ∑, ,, represents the intra-cell interference for user k from other users in the same cell, while

∑∑, , ,, is the inter-cell interference from other users in other cell,

, is the additive noise with zero mean and variance at the kth user.

4.3.2. System with Zero-forcing Beam forming

After applying ZF beam forming to the base station transmitter, the transmitted signal from base station b can be written as:

=,, (4.17)

× where ∈ ℂ is the network-wide beam forming vector for the transmit signal from base station b to the user k. Then, with the ZF beam forming scheme, the received signal for user k in the cell of base station b can be written as [55]:

, =,,, +,,, + ,,, , , ,

+, (4.18)

Same as in Equation (4.15), ,,, is the desired received signal from base station b to user k, and other parts can be seen as interference plus noise. This equation of transmitted signal also accounts for the user scheduling operation.

Similar to the single-cell model, if and only if the beamformer vector , is nonzero, user k can be scheduled at base station b [55]. In other words, the scheduling choice is determined by the indicator function:

1, if =0 = , (4.19) , 0, otherwise

In addition, we can get a beamformer matrix =[,,… , ,] by collecting all beamformer vectors from base station b. Considering the average power constraint

, should follow:

∗ Tr() ≤ (4.20)

In the ZF beam forming, beam forming vectors are selected to satisfy the zero-interference condition, which is ,, =0 (≠). Since we have the beamformer matrix =[,,… , ,] and channel matrix =[,,… ,

,], for base station b, to choose a zero-forcing beam forming vector, we first assume a corresponding submatrix () and (), where ∈{1,…,}. Then, the () that gives zero-interference is the pseudo inverse of (), which can be expressed as [66]:

∗ ∗ () =() =() (()() ) (4.21)

Under these assumptions, the achievable rate for user k in cell b can be written as [55]:

∗ ∗ R, =log1 + ,=log1 + ,,,,, (4.22) where

∗ ∗ J, =, ,,, ,

∗ ∗ + , ,,, + σ (4.23) , ,

4.3.3. Multi-user Sum-rate Evaluation

In this section, we evaluate the achievable sum-rate for the multi-cell multi-user downlink channel with ZF beamforming scheme. The sum-rate of the system is given by:

R =R,

∗ ∗ =log1 + ,,,,, (4.24) and is the same as Equation (4.23).

We also use CDF of the long-term average sum-rate to show the behavior of the sum rate distributions, and the 10th percentile is used to illustrate the performance of 93 cell-edge users.

In the following, numerical simulations on CDF of the cellular sum-rate are conducted to show how the carrier frequencies, number of users and number of transmit antennas influence the achievable sum-rate in a multi-cell multi-user system. Similar to the previous section, we use the frequency bands at 28, 38, 60 and 73 GHz. To fully demonstrate the inter-cell interference, we consider a 19-cell model and each cell serves totally 20 users which are located in the cell randomly as shown in Figure 4.15. in Figure 4.15, the number means the base station b and the blue dots represent users. According to the results of path loss of millimeter wave in Chapter 3, the distance D between neighboring cells is 0.5 kilometers, which is reasonable. As for the fading channel, we also consider the Rician fading channel with the Rician factor α=5. The channel vector for user k from base station b is given by:

α 1 = + −PL − SF (4.25) , 1+α ,, 1+α ,, ,

where is transmitted power from base station, PL, is the path loss fading for the user k in cell b and SF is the shadow fading, which is calculated as the same in Chapter 3. The simulation parameters can be seen in Table 4.2

Figure 4.17. 19-cell system model

Simulation Parameter

Frequency (GHz) 28 38 60 73

Max. Tx power (dBm) 25 23 15 18

Path loss exponent 1.85 1.95 2.23 2.0

Shadowing fading(dB) 8.0 7.0 7.9 8.0

Antenna gain (dBi) 15

Background noise (dBm) 97

Table 4.2. Simulation parameters for multi-cell system

A. Comparison of sum-rate VS. the number of scheduled users

We first examine how the number of scheduled users affects the sum-rate.

Figure 4.18 and Figure 4.19 show the CDF of the achievable sum-rate at 28 GHz with 10 or 20 transmits antennas. From the Figure, we can obviously see that for both 10 and 20 transmit antennas, the more scheduled users there are, the larger sum-rate system can achieve. For example, when there are 10 transmit antennas, the sum-rate with 2 scheduled users is concentrated between 1.6 to 2.4 bits/s/Hz while the rate with 10 scheduled users is concentrated between 4.2 to 8.8 bits/s/Hz. In addition, as the scheduled users increase from 2 to 10, the 10th percentile sum-rate goes up from 1.65 to 4.74 bits/s/Hz, which increases the sum-rate of cell-edge users by 3.09 bits/s/Hz.

Figure 4.18. CDF of 28 GHz with 10 transmit antennas

Figure 4.19. CDF of 28 GHz with 20 transmit antennas

Figure 4.20 and Figure 4.21 show the CDF of the sum-rate at 38 GHz with 10 or 20 transmit antennas. From the figures, we can see that the trend of the curves is similar to that at 28 GHz. The sum-rate is obviously getting larger as the number of scheduled users gets large. When there are 10 transmit antennas, the sum-rate with 2 scheduled users is concentrated between 1.45 to 2.3 bits/s/Hz, while the achievable rate with 10 scheduled users is concentrated between 4 to 8.8 bits/s/Hz. In addition, as the scheduled users increase from 2 to 10, the 10th percentile sum-rate goes up from 1.52 to 4.38 bits/s/Hz, which increases the sum-rate of cell-edge users by 2.86 bits/s/Hz.

Figure 4.20. CDF of 38 GHz with 10 transmit antennas

Figure 4.21. CDF of 38 GHz with 20 transmit antennas

Figure 4.22 and Figure 4.23 show the CDF of the achievable sum-rate at 60 GHz with 10 or 20 transmit antennas. From the figures, we can see that the trend of the curves is also similar to that in the all of the previous figures. The rate is larger as the number of scheduled users getting large. In addition, as the scheduled users increase from 2 to 10, the 10th percentile sum-rate goes up from 1.12 to 3.13 bits/s/Hz, which increases the sum-rate of cell-edge users by 2.01 bits/s/Hz.

Figure 4.22. CDF of 60 GHz with 10 transmit antennas

Figure 4.23. CDF of 60 GHz with 20 transmit antennas

Figure 4.24 and Figure 4.25 show the CDF of the achievable sum-rate at 73 GHz with 10 or 20 transmit antennas. We can see that the result does not show much difference to the previous figures. As the scheduled users increase from 2 to 10, the 10th percentile sum-rate goes up from 1.35 to 3.58 bits/s/Hz, which increases the sum-rate of cell-edge users by 2.23 bits/s/Hz. Thus, we can conclude that for both 10 and 20 transmit antennas, the sum-rate is increasing as the number of scheduled users getting larger.

Figure 4.24. CDF of 73 GHz with 10 transmit antennas

Figure 4.25. CDF of 73 GHz with 20 transmit antennas

From the figures, we can observe that when there are more active users, with the same number of transmit antennas, for these four frequency bands, the sum-rate of the system could reach a higher level as well as the sum-rate of the cell-edge users. However, one interesting thing is that the sum-rate is not increasing linearly with the growing number of scheduled user. For example, form Figure 4.18, the 10th percentile CDF is 1.65 bits/s/Hz when there are 2 scheduled users, while it is 3.62 bits/s/Hz when there are 5 scheduled users. When there are 10 scheduled users, the 10th percentile CDF is 4.74 bits/s/Hz. As the scheduled users increasing 2.5 times from 2 to 5, the 10th percentile sum-rate goes up about 220%, while the scheduled users increasing 5 times from 2 to 10, the sum-rate goes up about only 287%. These indicate that although the increase number of scheduled users makes the system achieve a higher sum-rate, the base station should not serve the users as much as possible. When designing this multi-cell multi-user system, we need to consider an efficiency number of the scheduled users to make a balance between the rate and the cost.

B. Comparison of sum-rate VS. the number of transmit antennas

In this section, we examine how the different number of transmit antennas affects

100 the sum-rate. Figure 4.26 and Figure 4.27 show the CDF of the achievable sum-rate with different frequency bands and various number of transmit antennas. We compare the sum-rate of 10 and 20 transmit antennas with 2 scheduled users.

Figure 4.26. CDF of 28 GHz with 2 scheduled users

Figure 4.27. CDF of 38 GHz with 2 scheduled users

101

Figure 4.28. CDF of 60 GHz with 2 scheduled users

Figure 4.29. CDF of 73 GHz with 2 scheduled users

For all of the 4 frequency bands, with the fixed number of scheduled users (we set 2 users in the simulation), the sum-rate of 20 transmit antennas is larger than that of 10 transmit antennas. For example, in Figure 4.26, where the carrier frequency is 28 GHz, the rate of 10 transmit antennas is mainly distributed from 1.63 to 2.43 bits/s/Hz while the rate of 20 transmit antennas is from 1.72 to 2.57 bits/s/Hz. As for the 10th percentile, the sum-rate goes up from 1.65 to 1.76 bits/s/Hz when then number of transmit antennas change from 10 to 20, which increases the sum-rate of cell-edge users by 0.11 bit/s/Hz.

102

C. Comparison of sum-rate VS. the carrier frequency

In this section, we examine how the carrier frequency band affects the sum-rate. Figure 4.30 and Figure 4.31 show the CDF of the achievable sum-rate with different frequency bands and fixed number of transmit antennas and scheduled users. We consider two situations here: 10 transmit antennas and 2 scheduled users and 10 transmit antennas and 10 scheduled users.

Figure 4.30. CDF of different frequencies with 10 receive antennas and 2 scheduled users

Figure 4.31. CDF of different frequencies with 10 receive antennas and 10 scheduled users

103

From Figure 4.30 and Figure 4.31 we can see that with the same number of transmit antennas and scheduled users, 28GHz achieves the best performance among the 4 frequency bands while 60 GHz performs worst. For example, with 10 receive antennas and 2 scheduled users, the sum-rate of 28 GHz is distributed between 1.63 to 2.43 bits/s/Hz and the sum-rate of 60 GHz is distributed between 1.17 to 2.13 bits/s/Hz. The result is caused by the path loss exponent of 60 GHz band is much larger than all of other frequency bands, meanwhile the maximum transmit power is the smallest from the standard. By comparing the 10th percentile sum-rate of these four bands, for example, when 10 receive antennas and 10 scheduled users, we can know that the sum-rates of cell-edge users are 4.74, 4.38, 3.13 and 3.58 bits/s/Hz at 28 GHz, 38 GHz, 60 GHz and 73 GHz, respectively. Obviously, the sum-rate of cell-edge users at 28 GHz is also larger than that at other frequencies. The result is similar to what we have in previous sections when examining the sum-rate in the single-cell system.

However, although our simulation shows that higher frequencies perform not as good as lower frequencies since the high attenuation, in practical network systems, their antenna sizes are smaller. We can use more antennas for high frequencies propagation to compensate for their attenuation and improve their performance. In addition, although we compare their sum-rate under the same cell size, higher frequencies are usually used in smaller cell sizes systems compared to lower frequencies in practical networks. When considering the sum-rate or spectrum efficiency in practical systems, it would be better to compare them normalized by area under different cell sizes.

4.4. Comparison of Sum-rate between Single-cell and Multi-cell System

In this section, we make a general comparison between the single-cell model and multi-cell model. Take examples of 28 GHz and 38 GHz with the system that both

104 have 10 transmit antennas. We compare the sum-rate of these two models as shown in Figure 4.32 and Figure 4.33. In the figures, “S” means single-cell model and “M” means multi-cell model.

Figure 4.32. Comparison of the rate at 28 GHz of single cell model and multi-cell model

Figure 4.33. Comparison of the rate at 38 GHz of single cell system model and multi-cell system model

From these two figures, we can find that for both 5 and 10 scheduled users, the

105 sum-rate for single-cell seems slightly larger than that for multi-cell system model. Comparing these two models, the main difference is that when using the single cell model, the active users suffer from fading and intra-cell interference from the other users in the cell, while for multi-cell model, the active users are not only affected by the intra-cell interference but also the inter-cell interference from the active users from their own base stations and active users in other 18 cells. Inter-cell interference greatly reduces the sum-rate of the users in multi-cell system. Particular for cell-edge users which they received the smallest signal from their own base station but largest interference from other cells. Their sum-rate reduces significantly. For example, look at the 10th percentile of the CDF curve in Figure 4.30, where the carrier frequency is 28 GHz. The sum-rate with 5 scheduled users of single-cell system is 3.68 bits/s/Hz, while for multi-cell system is 3.62 bits/s/Hz, which decreases by 1.63%. As for 10 scheduled users, this gap becomes larger, which is 11.73%. This is mainly caused by the increasing inter-cell interference when the number of active users getting larger. As for 38 GHz, 60 GHz and 73 GHz, the difference of the sum-rate between the two system models is 7.89%, 0.95% and 1.92%, respectively. Comparing all the frequency bands, with the same number of transmit antennas and scheduled users, we can see that 28 GHz provides the largest sum-rate but also has the largest gap at the 10th percentile sum-rate between single-cell and multi-cell systems.

4.5. Summary

In this chapter, we built up a single-cell system model and a 19-cell system model to evaluate how millimeter wave performs in these two models. In the evaluation, we not only consider the path loss and fading of a particular user, but also calculate the interference from other users in the same cell as well as in neighboring cells. In addition, we exam the effect of the number of active users, transmit antennas and carrier frequencies in both single cell model and 19-cell model on the sum-rate

106 performance. Generally speaking, all the frequencies perform better in the single-cell system than in the multi-cell system, especially the 28 GHz provides the largest sum-rate if other factors are the same for both two system models. However, the influence from the inter-cell interference is also the largest at 28 GHz among all the bands, whose 10th percentile sum-rate decreases by 11.73%.

107

Chapter 5. Hybrid Architecture for Millimeter Wave Transceivers

In the previous chapters, we discussed the path loss, outage probability and capacity of four millimeter wave bands in a single-user model as well as the sum-rate of them in a multi-user model. As mentioned before, compared to the commercial spectrums below 6 GHz, millimeter wave can provide a much larger bandwidth and higher data rates with novel techniques. In this chapter, we are going to discuss the signal processing techniques for millimeter wave systems and introduce the hybrid architecture for millimeter wave transceivers.

Obviously, signal processing for millimeter wave systems is different from that for sub-6 GHz systems. There are mainly three reasons [67]. First and intuitively, the channel models are different since the smaller wavelength of millimeter wave is more easily affected by the propagation environment such as buildings, trees and human body. The difference between LOS and NLOS propagation makes the channel models and fading effects different as well. Second, larger arrays can be used in millimeter wave systems. For example, compared to lower frequencies which usually have 2 - 8 elements in an array, the array size for millimeter wave could be 32 – 256 [68]. In addition, these kinds of large array can be used in both transmitter and receiver side. The third reason is the difference on hardware architecture which is currently a hot research topic on millimeter wave [67]. The high frequency and large bandwidth make the hardware of millimeter wave faced big challenges in terms of space limitation, power consumption and high expense. To solve these problems, one signal processing technique, hybrid architecture, is developed [69]. In hybrid architecture, the signal processing is divided into two parts: analog and digital. Signal processing can be acted in both domains to reduce the number of RF chains and analog-to-digital and digital-to-analog converters.

In this chapter, we are going to review the signal processing techniques for millimeter wave systems and evaluate the hybrid transceiver architecture. We set up a 7-cell multi-user MIMO hybrid system to compare the achievable sum-rate and discuss the

108 power efficiency of the full digital array, full access hybrid and subarray hybrid architectures.

5.1. Hybrid Architecture

5.1.1. Hybrid Architecture for Millimeter Wave Systems

Let us first have a look at the MIMO architecture of sub-6 GHz as Figure 5.1 below

[67]. In Figure 5.1, M is the number of inputs and outputs, is the number of RF chains and transmit antennas at the transmitter side while is the number of RF chains and receive antennas at the receiver side.

(a) Transmitter

(b) Receiver

Figure 5.1. MIMO architecture of sub-6GHz [67]

109

For the lower frequencies MIMO architecture, all the signals are processed in the baseband which is shown as baseband precoding in the transmitter side and baseband combining in the receiver side. Each transmit antenna and receive antenna is connected with a separate RF chain and a digital-to-analog converter (DAC) or an analog-to-digital converter (ADC). Under this structure, we find that the signal processing for sub-6 GHz is acted on digital domain only. However, for the millimeter wave, it is very hard to have a separate RF chain and converter for every antenna because of the hardware constraints. As we mentioned in the previous section, first is the space limitation. Since there are more elements in an array for higher frequencies, it is difficult to pack all of the power amplifier (PA) or the low noise amplifier (LNA) and RF chain for each antenna in a very small space. Second, the high power consumption for those ADC and DACs is hard to afford, as well as the power used for signal processing itself. Table 5.1 shows the range of power consumption for several kinds of elements. Form Table 5.1 we can see that the maximum power required of ADC/ DAC is much higher than that of other devices. If we connect all the RF chains with an ADC/ DAC, the power assumption will be terribly high. The last is the high expense of hardware itself, especially ADC and DACs. It can come up to 1000 dollars for only one ADC device for millimeter wave systems. Thus, it is impossible to equip a separated RF chain and ADC/ DAC for every antenna.

Device PA LNA Phase Shifter ADC/ DAC

Power (mW) 40-250 4-86 10-110 15-795

Table 5.1. General power consumption for different devices [67]

To solve these problems, hybrid architectures are introduced to millimeter wave systems to reduce the power assumption and cost as well as keep the benefits of MIMO millimeter wave communications. The structure of a MIMO hybrid

110 architecture is shown in Figure 5.2.

(a)Transmitter

(b)Receiver

Figure 5.2. MIMO hybrid architecture at high frequencies (millimeter wave) [67]

The main difference between the architecture at lower frequencies and hybrid is the usage of RF analog precoding and RF analog combining. In hybrid architecture, the signal processing is divided into digital domain and analog domain and processing is done in both two parts. In Figure 5.2, M is the number of inputs and outputs, is the number of RF chains and is the number of transmit antennas at the transmitter side, while is the number of RF chains and is the number of

111 receive antennas at the receiver side. Usually, we have ≤ ≤ and ≥

≥ to achieve high antenna gain at a lower cost. The RF precoding and RF combining are analog processing, while the processing that the signals from baseband to DAC or from ADC to baseband is known as digital beamforming which is similar to the processing at lower frequencies. In digital beamforming, the signals are weighted by complex values in the simplest case [68]. In addition, there is a special case which is called analog beamforming when = = =1 [56].

We may treat the whole hybrid array as subarrays, where each subarray is an analog array, consisting of each RF precoding in its RF chain. In this case, the hybrid array can be classified into two types by the topology of those subarrays: interleaved and localized arrays [68]. If the antenna elements in each subarray scatter uniformly over the whole array, it is called an interleaved array. The subarray beam width of interleaved array is usually narrow, but the subarray grating lobe is large. As for a localized array, the antenna elements in each subarray are adjacent to each other. Compared with interleaved array, the subarray beam width is wide while the subarray grating lobe is small in localized array. These two different types of hybrid arrays are usually used in different applications. Usually, Interleaved array is used for pure beamforming space-division multiple access (SDMA), while localized array is more suitable for LOS-MIMO SDMA [68]. Generally speaking, the localized array is easier to be hardware implemented than the interleaved array.

5.1.2. Hybrid Analog-Digital Processing

One of the most important parts in millimeter wave hybrid architecture -- the RF precoding and combining stage, can be implemented using several analog approaches. For example, phase shifters [69] and switches [70] are commonly used.

The first method is to use a set of phase shifter. There are mainly two types of phase shifter hybrid structures which can be seen in Figure 5.3 below. In the first type, which is shown in Figure 5.3 (a), each antenna is connected with one LNA. By

112 crossing over, all the antennas can connect to each RF chain. This type is called full-access structure. The second type as shown in Figure 5.3 (b) is called subarray structure. Each antenna is also connected with one LNA, however, the antennas are divided into several groups, every antennas are connected to one RF chain [67].

(a) Full-access structure (b) Subarray structure

Figure 5.3. Two types of phase shifter for analog processing [67]

Phase shifter hybrid structures would normally use digitally controlled phase shifters with a small number of quantized phases [69]. Usually 3- or 6-bit phase shifter which provides 8 to 64 phase shifting value are required in the analog processing [68]. There are many advantages of this hybrid approach, one of that is that when the precision in the analog processing is not good, the digital (baseband) precoding or combining processing could cancel some of the interference, such as the residual multi-stream interference [71].

There is another analog processing approach which is to make use of switching networks with small losses [70] as mentioned before. The two types of structure can 113 be seen in Figure 5.4. Compared to the hybrid architecture using phase shifters, this recently proposed method can further reduce complexity and power consumption [67]. Similar to the phase shifter structure, there are mainly two types. In the first type, which is shown in Figure 5.4 (a), each RF chain can be connected to all antennas. In the second type shown in Figure 5.3 (b), the antennas are divided into several groups, and every antennas are connected to one RF chain. Compared to the phase shifter structures, the analog processing with switches is performed by a subset antenna selection algorithm instead of an optimization over all quantized phase values [67], which is the main reason that can reduce the complexity. In practical wireless systems, although there are several benefits by using switches, the main problem is that the accuracy of signal processing of this structure is lower than that of phase shifter structures if we assume the system can provide enough power for calculations. Therefore, in the following sections, our discussion will be based on the phase shifter hybrid structures.

(a) (b)

Figure 5.4. Two types of switches for analog processing [67]

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5.1.3. Low Resolution Receiver

There is a special approach for hybrid architectures that can reduce the power consumption of the ADCs at the receiver, which is to reduce the resolution. As shown in Figure 5.5, low resolution (1 to 3-bit) ADCs are used to sample the in-phase and quadrature components of the signals from the RF chains. The advantage of low resolution ADCs is that it has lower power consumption and hardware cost compared to the original ADCs and other devices under this structure [67]. The architecture also simplifies the overall complexity of the circuit. In addition, the resolution has influence on the power consumed by the high-speed interfacing cards. Thus, low resolution, especially 1-bit ADCs can reduce both of the power consumed by the receiver and by the baseband circuitry [72].

Figure 5.5. 1-bit ADC receiver [67]

5.1.4. Hybrid beamformer

In this section, we discuss the hybrid beamformer of the MIMO hybrid architecture for millimeter wave systems.

Consider the architecture shown in Figure 5.2. We assume a downlink transmission from the base station (as the transmitter side in the figure) to the user (as the

115 receiver side in the figure). Also, assume a Rician fading channel H since we are applying millimeter wave in this model. The received signal can be expressed as [73]:

=√∗ + ∗ (5.1)

In equation (5.1), is the power constraint, is the additive noise vector at the

× receiver with zero mean and variance, =, where ∈ℂ is the baseband digital beamformer which processes the M input data streams to outputs. Then the outputs are up converted to transmit antenna elements by an

× analog beamformer ∈ℂ at the transmitter. Similarly, =

× contains the baseband digital beamformer ∈ℂ and analog beamformer

× ∈ℂ at the receiver.

In practical wireless systems, it is very difficult to calculate the digital beamformer and analog beamformer even with full-instantaneous CSI at the transmitter. First, as we mentioned before, the RF (analog) precoding and RF (analog) combining are usually a set of phase shifter or switches. Thus, there would be more constraints on

and and makes the system becoming more complex. Second, the digital and analog beamformers at each link end are coupled, which makes the objective function of the non-convex optimization [74]. Although it is hard to find the optimal solution, there are still some methods to compensate these problems and achieve a near-optimal solution.

According to Ni W. et al [75], a near-optimal hybrid beamforming can be achieved by minimizing the Euclidean distance to the full digital optimum beamforming which has the same number of RF chains and number of antennas ( = and =). The objective function of this near-optimal is still non-convex but it is less complex. A evaluation of the average sum-rate of the downlink transmission of single-cell multi-user MIMO system [76] proves that at the same SNR, the performance of system with the full-access structure of the RF precoding and combining (as shown in Figure 5.3 (a)) is the same as a fully digital structure.

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5.2. Power Consumption Evaluation

As we mentioned in the previous section, one of the main reasons that applying hybrid architecture on millimeter wave systems is to reduce the power consumption and lower the cost. In this section, we will focus on the power efficiency of both full digital architecture and hybrid architectures (including full-access structure and subarray structure).

Let us consider a downlink multi-user hybrid millimeter wave channel which is in a single cellular cell with the radius at 100 m. Assume there is only one base station located in the central of the cell and there are total RF chains to supports total K users in the cell. The base station is equipped with M transmit antennas, and each user has receive antennas and connected with one single RF chain. As the definition for the hybrid architecture ≥≥, for simplicity, we assume that

=. In addition, each user k (k≤K) only receives one information stream from the base station and the data streams for different users are independent from each other and identically distributed according to (0,1).

× We assume that ∈ ℂ is the channel gain matrix from the base station to the kth user with the CSI is available at both transmitter side and receiver side. Since we employ millimeter wave, should follow a Rician fading given by:

α 1 = + (5.2) 1+α , 1+α ,

And Rician factor α is the ratio of the energy in the specular path to the energy in the scattered paths. The received signal at pass-band can be expressed as:

y = + +, = 1,2, … , (5.3) ,

where is the additive noise at the kth user with zero mean and variance. 117

Similar to Chapter 4, we apply ZF precoding to the channel and as well as the analog beamformer as Equation (5.1). Thus, the received signal at user k after beamforming can be expressed as:

̅ ̅ = + + (5.4) ,

× × where ∈ ℂ is the ZF beam forming vector for user k, ∈ℂ is the analog beamformer and is the additive noise at the kth user with zero mean and variance. We assume that =[| |] is the average transmitted symbol ̅ power for each user. The beamformer matrix is =[,… , ] and =

is the transmission power normalization factor. After applying ZF [∗] beamforming, the SINR for user k can be expressed as:

̅ = (5.5)

According to [76], in the large numbers of antennas regime, the upper bound of achievable rate per user of the hybrid system is given by:

.. 1 R log 1 + + (5.6) →∞ +1 +1

As for the full digital system, we also assume that there are M antennas equipped at base station, the number of RF chains equipped at the base station is equal to the number of antennas. Each user k is connected with one RF chain and equipped P antennas. The channel matrix with full CSI at both transmitter and receiver is ∈ ℂ×, and ZF precoder is given by:

∗ ∗ =() (5.7)

The upper bound of achievable rate per user of the fully digital system can be expressed as [76]:

118

.. R log 1 + (5.8) →∞

In the following, we evaluate the achievable sum-rate of full digital, full access hybrid and subarray architectures at the total power from 50 to 100 Watts from the base station and see how the sum-rate various. In addition, the four bands at 28 GHz, 38 GHz, 60 GHz and 73 GHz will be used to compare the influence of the carrier frequencies on the sum-rate. In three different architectures, we set the number of RF chains to be 20 for all, the number of transmit antennas for full digital and full access hybrid to be 100 while the number of antenna elements for subarray hybrid to be 40 which is practical. The power consumption is 400 mW for each ADC and for each phase shifter is 10 mW [67]. The average transmitted power is the rest power that subtracts consumption by hardware devices from the total power. In other words, there will be more power using for signal transmission if the consumption by hardware is lower. Generally speaking, the one that achieves a higher sum-rate has a better power efficiency if the transmitted power is the same. For the Rician fading factor, is the same as in previous chapter which is set to be 5, path loss exponent and other simulation parameters can be seen in Table 5.2

Simulation Parameter

Frequency (GHz) 28 38 60 73

Path loss exponent 1.85 1.95 2.23 2.0

Path loss at 100 m (dB) 98.4 103 112.6 109.7

Table 5.2. Simulation parameters

We first examine the achievable sum-rate of full digital, full access hybrid and subarray architectures at 28 GHz which is shown as Figure 5.6.

119

Figure 5.6. Sum-rate vs. power consumption at 28 GHz

It can be seen that with the increasing of total power supply, the sum-rate for all three structures is getting larger. The performances of full digital and full access hybrid are better than that of subarray hybrid. However, the sum-rate of full access hybrid is significant larger than that of full digital architecture for a low power. For example, at 50 watts, the sum-rates of full access, full digital and subarray are 97.5, 82 and 78.2 bits/s/Hz, respectively. Compared to the full digital system, the sum-rate is increased by 18.9% by using a full access hybrid. As the total power going up, the gap becomes smaller and sum-rate of the full digital array finally gets larger than that of the full access hybrid when the power exceeds 91 watts.

120

Figure 5.7. Sum-rate vs. power consumption at 38 GHz

Then, we evaluate the achievable sum-rate of full digital, full access hybrid and subarray architectures at 38 GHz which is shown in Figure 5.7.

The result is similar to 28 GHz. The performances of full digital and full access hybrid are much better than that of subarray hybrid under high power supply. However, if the total power is smaller than 92 watts, the sum-rate of full access hybrid is larger than that of full digital architecture, especially for a low power. At 50 watts, the sum-rates of full access hybrid, full digital and subarray hybrid are 70.1, 56 and 52.7 bits/s/Hz, respectively. Compared to the full digital, by using a full access hybrid, the sum-rate is increased by 25.2%.

121

Figure 5.8. Sum-rate vs. power consumption at 60 GHz

The evaluation of the achievable sum-rate of full digital, full access hybrid and subarray architectures at 60 GHz is shown as Figure 5.8.

The result is similar to 28 GHz and 38 GHz. The performances of full digital and full access hybrid are much better than that of subarray hybrid under high power supply. However, if the total power is smaller than 92 watts, the sum-rate of full access hybrid is larger than that of full digital architecture, especially for a low power. At 50 watts, the sum-rates of full access hybrid, full digital and subarray hybrid are 25.4, 18.3 and 16.6 bits/s/Hz, respectively. Compared to the full digital, the sum-rate is increased by 38.8% by using a full access hybrid.

122

Figure 5.9. Sum-rate vs. power consumption at 73 GHz

The comparison of sum-rate vs. power consumption at 73 GHz can be seen in Figure 5.9. The sum-rate of full access hybrid is also larger than that of full digital architecture if the total power is smaller than 91 Watts. At 50 watts, the sum-rates of full access hybrid, full digital and subarray hybrid are 36.2, 26.9 and 24.8 bits/s/Hz, respectively. Compared to the full digital, the sum-rate is increased by 34.6% by using a full access hybrid.

Interestingly, the results show that for all carrier frequencies, the sum-rate of full access hybrid is larger than that of full digital architecture, especially for a low power which is smaller than 90 Watts. That means that when the total power is not high enough, the full access hybrid has a better power efficiency than full digital structure. As for subarray hybrid architecture, although the achievable sum-rate is not the best, the gap between it and full digital architecture is not very large at 50 Watts total 123 power.

Figure 5.10. Sum-rate vs. power consumption of full access hybrid at 28, 38, 60 and 73 GHz

124

Figure 5.11. Sum-rate vs. power consumption of subarray hybrid at 28, 38, 60 and 73 GHz

We also make a comparison on the sum-rate between four carrier frequencies to show the influence of the frequencies. In Figure 5.10 and Figure 5.11, the sum-rates of full access hybrid and subarray hybrid architecture at 28 GHz, 38 GHz, 60 GHz and 73 GHz are shown. It is obvious that the system at 28 GHz has the best performance among all in both two architectures. However, one interesting thing is that as we calculated in the previous section, compared to the full digital architecture, the sum-rate increasing by using full access hybrid are 18.9%, 25.2%, 38.8% and 34.6% for the four bands, respectively. The best performed frequency 28 GHz in sum-rate gets the least growth while 60 GHz gets the largest increase.

5.3. Summary 125

In this chapter, we discussed the signal processing and the hybrid architecture transceivers for millimeter wave including full access hybrid and subarray hybrid. Theoretically, the full digital array is the best if there is enough power supply since it provides full capacity and flexibility. However, it is very costly and impractical because of the space limitation [67]. Our result shows that if the total power for the system is small, the full access hybrid can achieve a higher sum-rate for the system which means it has the best power efficiency among these three structures. As for subarray hybrid architecture, although the achievable sum-rate is not the best, there is only a small gap between it and full digital architecture at a very low power. In practical wireless communication systems, one of the advantages of the subarray hybrid is that it offers the simplest circuit design and fewer losses compared to fully access architecture. Thus, subarray hybrid architecture is still considered as a very useful approach, especially when total power and antenna space are limited.

126

Chapter 6. Summary and Future Works

In this chapter, we are going to provide a summary of the works in the previous chapters and discuss the potential future research works.

6.1. Summary

In Chapter 2, we reviewed the characteristics of millimeter waves. There are many differences between millimeter wave bands and the lower frequencies microwave bands. Compared to the traditional wireless communications, millimeter wave suffers from higher rain and atmosphere attenuation and is more sensitive to blockage. We discussed the millimeter wave spectrum, free space propagation, simplified path loss model, oxygen and rain attenuation, penetrability, reflection, path loss exponents, RMS delay spreads, Doppler shift and outage probability. Heavier propagation loss brings challenges to the application of millimeter wave communication systems. However, it also makes opportunities and develops new technologies for future 5G networks. Some of the popular applications of millimeter waves, such as small cell access and backhaul architecture were introduced in this chapter as well.

In Chapter 3, we discussed details of the propagation properties of millimeter wave, including path loss and shadow fading, outage probability and channel capacity. To make the calculation results intuitively, simulations are used to evaluate these figures of merits in this chapter. We simulated the path loss with shadow fading and outage probability of the channel frequencies at 28 GHz, 38 GHz, 60 GHz and 73 GHz. In addition, the channel capacity of SISO, MISO, SIMO and MIMO channels at these frequencies are evaluated as well. By evaluating these propagation characteristics, we illustrate the properties of these millimeter wave bands in Rician fading channels. The results show that the path loss of 28 GHz and 38 GHz are not very large and the channel with these two carrier frequencies are able to support the signal transmission for a longer distance for about 400 meters with the standard transmit 127 power. Moreover, if the distance between transmitter and receiver is smaller than 100 meters, the channel with 28 GHz and 38 GHz are able to provide a very large channel capacity. However, 60 GHz does not perform very well because of the huge atmosphere and rain attenuation. It is very difficult to support 50 meters reliable transmission by using multiple antennas for this frequency with the standard transmit power. These results are helpful when designing a practical millimeter wave wireless communication system.

In Chapter 4, a single-cell multi-user model and a 19-cell multi-user model were set up to evaluate how millimeter wave performs in a more complex system. We considered the interference from other users in the same cell as well as in neighboring cells. The achievable sum-rate was evaluated in these two models and how the number of active users, transmit antennas and carrier frequencies influence the data rate in the cellular systems were discussed. We used CDF of the long-term average sum-rate to evaluate the channel performance and the 10th percentile user rate was used to indicate the performance of cell-edge users. The results show that all the frequencies perform better in the single-cell system than in the multi-cell system, especially the 28 GHz provides the largest sum-rate if other factors are the same for both system models. However, the influence from the inter-cell interference is also the largest at 28 GHz among all the bands, whose 10th percentile sum-rate decreases by 11.73%. As for 38 GHz, 60 GHz and 73 GHz, the difference of the 10th sum-rate between the two system models is 7.89%, 0.95% and 1.92%, respectively.

In Chapter 5, we reviewed the signal processing techniques and evaluate the hybrid transceiver architecture for millimeter wave systems including full access hybrid and subarray hybrid. A 7-cell multi-user MIMO hybrid system was set up to compare the achievable sum-rate and the power efficiency of the full digital array, full access hybrid and subarray hybrid architectures were discussed. Theoretically, the full digital array is the best if there is enough power supply since it provides full capacity and flexibility. However, our result shows that if the total power for the system is small, for example, from 50 Watts to 90 Watts, the full access hybrid can achieve a much

128 higher sum-rate for the system which means it has the best power efficiency among these three structures. In addition, although the achievable sum-rate of subarray hybrid architecture is not the best, there is only a small gap between it and full digital architecture at a very low power. In practical wireless communication systems, one of the advantages of the subarray hybrid is that it offers the simplest circuit design and fewer losses compared to fully access architecture. Thus, subarray hybrid architecture is still considered as a very useful approach, especially when total power and antenna space are limited.

6.2. Future Works

6.2.1. Optimal Cell Radius and Small Cell Density

Recently, massive antennas and dense deployments of access points are usually proposed to significantly improve the cellular throughput for 5G systems. These two methods lead to the Massive MIMO and small cell techniques in cellular networks [79] [80] [81].

Massive MIMO, which can be seen as very large MIMO systems, uses a very large number of antenna elements (usually hundreds even thousands) at the base station that are operated fully coherently and adaptively [82]. It can serve many users simultaneously at the same time-frequency resource. Intuitively, the large number of transmit antennas increases the capacity through excessive spatial dimensions. It can provide sharp beamforming and average out the effect of fast channel fading as well [82] [83]. The advantages of Massive MIMO also include the extensive use of inexpensive low-power components, which reduce the transmit power and cost. Massive MIMO was originally envisioned for time division duplex (TDD) operation, but can potentially be applied also in frequency division duplex (FDD) operation [82].

According to Jose J. et al. [84], the performance of Massive MIMO is mainly limited

129 by pilot contamination. In their paper, they described an uplink TDD system model in multi-cell and characterize the impact of corrupted channel estimates caused by pilot contamination. As they state, pilot contamination should be used in Cooperative MIMO. To create distributed arrays, clusters of base stations are wired together [84]. They proposed a multi-cell MMSE-based precoding method for the general setting with multiple users in every cell. In their method, the coordination between base stations is not a necessity which means that there is no exchange of CSI among the base stations. They also provided an equation to calculate achievable rates using by using their MMSE-based precoding method. However, to apply this MMES-based precoder, the base stations need to share the channel covariance matrix, which is very difficult to implement in practical wireless communication systems. In addition, their evaluation is more focus on the uplink training and data transmission which is not suitable for our assumption of the system model.

The other approach is the small cell techniques. The small cell radius usually ranges from 10 meters to a few hundred meters, which is much smaller than a mobile macro-cell. By reducing the radius of the cell, the distance between transmitter and receiver can be significantly reduced which decreases the path loss of the transmitted signal and increases the rate gains [85]. Small cell improves the system capacity by densely deploying low-power access points into the traditional high-power macro-cells [79] [86]. However, the performance of small cell is affected by the large inter-cell interference since the distance between the receivers to other base stations and users in neighboring cells is smaller which results in a larger inter-cell interference.

There have been a lot of experiments and analyses to compare the system performance of Massive MIMO and small cell technologies. According to Zhang Q. et al [86], a heterogeneous cellular network (HCN) containing different types of multi-antenna and randomly located base stations are required when comparing these two methods. To analyze the performance, stochastic geometry is a useful tool that describes the spatial distribution of base station sites [86]. It is a mathematical

130 model to study the random spatial patterns and widely used in wireless network, for example, to model the coverage and connectivity constructed from randomly sized round areas at random locations [86]. By using the stochastic geometry, many works are done on HCN with Poisson point process (PPP) distributed base stations [87].

The research did by Zhang Q. et al. [86] derived tight approximation of achievable rate in a downlink HCN to compare the performance between Massive MIMO and small cells including both LOS and NLOS transmissions. They also compare the system performance between increasing small cells density and expanding the number of base station antennas. In their paper, they found that reducing the cell radius, which means increasing the small cell density is a useful method to improve the achievable rate and the improvement by adding small cells into networks is even much faster than increasing the number of antenna arrays at the base station. They also found that there is a threshold for the small cell density. The system capacity will not increase anymore and even reduce if the cell density is larger than the threshold. Based on these, they estimated an optimal density that maximizes the achievable downlink rate [86]. However, in their research, they also used MMSE estimation method at base station and did not give a direct relationship between the small cell radius and achievable rate.

Therefore, in the future works, we can consider a simpler and more general multi-cell MIMO hybrid model with ZF beamforming to evaluate and directly show the optimal cell radius or small cell density.

In this case, we consider a downlink transmission channel with N cells in the system, and the cell radius is D meters. Each base station b, where b is an integer and not larger than N, is located in the center of a cell. In addition, there are total K users in each cell and L=K is the number of RF chains at each base station. Then, assuming that there are M transmit antennas equipped in each base station and P receive antennas for each user. Assume , is the transmitted signal from base station b to user k and the data streams , for different users are independent from each other and identically distributed according to (0,1). 131

× We assume that , ∈ ℂ represents the channel gain from base station b to the user k with the CSI is available at both transmitter side and receiver side in this cell. Since we employ millimeter wave, , should follow Rician fading channel:

α 1 = + (6.1) , 1+α ,, 1+α ,,

The Rician factor α is the ratio of the energy in the specular path to the energy in the scattered paths.

After applying ZF beamforming and analog beamforming, the received signal at user k from base station b can be expressed as [88]:

̅ ̅ , =,,,, +,,,, ,

̅ + ,,,, +, (6.2) , ,

× × where , ∈ ℂ is the ZF beamforming vector for user k, , ∈ℂ is the analog beamforming of base station b and , is the additive noise at the kth user with zero mean and variance. We have the ZF beamforming matrix = ̅ [,,… , ,] and = ∗ is the transmission power normalization [ ] ̅ factor in the cell of the base station b. In the equation, ,,,, is the

̅ desired signal, ∑, ,,,, represents the intra-cell interference

̅ from other users in the same cell, while ∑∑, , ,,,, is the inter-cell interference from other users in other cells. We assume that =

[, ] is the average transmitted symbol power for each user.

As we use ZF beamforming, with the enough capability of the base station to process the entire signal information, the intra-cell interference can be cancelled. Then the 132 average SINR for user k can be expressed as [88]:

̅ ,= (6.3) ∑∑ ̅ , , , ,,,, +

For a large number of antennas and high received SNR, the average achievable rate per user can be approximated as [88]:

, = 1 + , (6.4)

Under these assumptions, we can know that , is a function of inter-cell interference. If we set a fixed N, K, M, P, then the inter-cell interference would vary mainly based on cell radius D and the distance between active users and base stations. Thus, we can get achievable sum-rates according to different cell radius D, and find the optimal cell radius D that achieves the largest sum-rate.

In addition, we may investigate the optimal small cell density to achieve the maximum network throughput by using the stochastic geometry with Poisson point process (PPP) distributed base stations for millimeter wave cellular communications.

6.2.2. Multiple Access Design in Millimeter Wave Communications

Multiple access design is necessary and significant for supporting multi-users in cellular networks, which is widely investigated in the lower frequency bands now. Various multiple access technologies have been utilized in previous generation wireless networks, such as frequency division multiple access (FDMA), time division multiple access (TDMA), code division multiple access (CDMA) and orthogonal frequency division multiple access (OFDMA) [89] [90]. However, it is not easy to apply multiple access schemes on millimeter wave, because the propagation properties of millimeter wave are very different from the lower frequency

133 communications. In particular, since the doppler shift scales linearly with the carrier frequency, FDMA and OFDMA suffer from higher inter-carrier interference (ICI) in millimeter wave cellular networks, despite the sufficient bandwidth in the millimeter wave bands [91] [92]. As for CDMA, it is limited by the near-far effects and its performance relies more on power control [62]. TDMA might be a good choice for millimeter wave, where users share the spectrum in different time slots. However, the challenge of applying TDMA on millimeter wave is the time synchronization since millimeter wave provides a high symbol rate. More importantly, the shorter wavelength and the highly directional propagation in millimeter wave band enable spatial multiplexing [93]. Therefore, spatial division multiple access (SDMA) is potential to be used in millimeter wave. In SDMA, the precoding design for full digital millimeter wave systems and the hybrid precoding design for hybrid millimeter wave systems are interesting problems. Moreover, due to the limitation of RF chains in hybrid millimeter wave systems, non-orthogonal multiple access (NOMA), which exploits power domain multiplexing and successive interference cancellation (SIC), is considered as a good method to improve spectral efficiency [94] [95] [96]. Therefore, the use of NOMA in millimeter wave communications will be a research direction in the future.

6.2.3. Angle-of-arrival (AoA) and Angle-of departure (AoD) of Millimeter Waves

Recent research shows that the power consumption and energy efficient of wireless devices are more concerned in 5G networks. Localization and beamforming techniques are considered as very useful techniques especially in millimeter wave communications with multiple antennas to direct energy towards optimal directions. The conventional methods to estimate the position of the signal source and optimal directions are to measure the AoA and AoD. The study of AoA and AoD of millimeter wave signals in MIMO system should be considered in the future works.

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6.2.4. Phase-shifting Beamformers for Millimeter Wave

For simplifying the calculation and simulation, ZF beamforming is considered for our millimeter wave system in the previous chapters. However, there is another beamformer method to achieve coherency among the received signals which is phase-shifting beamformer. According to Zalawadia, K. et al [97], phase-shifting beamformer is a special case of the discrete Fourier transform beamformer and it is only used in narrow band signals. We assume that the amplitude and phase of the received signal have a constant frequency and maximum amplitude during the proper delay time in a phase-shifting beamformer. Then, the received signals are phase-shifted by an amount equal to the proper time delay multiplied by the assumed frequency of the incoming signal, which can be expressed as [97]:

/ () =() (6.5)

Where 0≤k≤N−1.

Since the millimeter wave signal is mainly based on line-of-sight propagation and there are not so many scattering components, phase-shifting beamformers may work better in millimeter wave systems. More experiments and simulations are worthy to be done in the future.

135

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