Copyright Statement

Millimeter Wave Systems for

Wireless Cellular Communications

Lou Zhao

A thesis submitted to the Graduate Research School of

The University of New South Wales

in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

School of Electrical Engineering and Telecommunications

Faculty of Engineering

The University of New South Wales

August 2018

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I hereby declare that this submission is my own work and to the best of my knowledge it contains no material previously published or written by another person, or substantial portions of material which have been accepted for the award of any other degree or diploma at UNSW or any other educational institute, except where due acknowledgment is made in the thesis. Any contribution made to the research by others, with whom I have worked at UNSW or elsewhere, is explicitly acknowledged in the thesis. I also declare that the intellectual content of this thesis is the product of my own work, except to the extent that assistance from others in the project’s design and conception or in style, presentation and linguistic expression is acknowledged.

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Dedicated to my parents, my wife, and my son.

Abstract

This thesis considers channel estimation and multiuser (MU) data transmission for time division duplex (TDD) massive multiple-input multiple-output (MIMO) systems with fully digital/hybrid structures in millimeter wave (mmWave) channels. The work reported in this thesis contains novel mmWave transmission schemes and performance analysis, which provides insights into the design of hybrid mmWave networks. It contains three main contributions.

In this thesis, we first propose a tone-based linear search algorithm to facilitate the estimation of angle-of-arrivals (AoAs) of the strongest line-of-sight channel components as well as scattering components of the users at the base station (BS) with fully digital structure. Our results show that the proposed maximum-ratio transmission (MRT) based on the strongest components can achieve a higher data rate than that of the conventional MRT, under the same mean squared errors (MSE) of channel estimation. In addition, we quantify the achievable rate degradation due to phase quantization errors and propose an angular domain user scheduling algorithm for mmWave systems to improve the users’ receive signal-to-interference-plus-noise ratio (SINR).

Second, we develop a low-complexity channel estimation and beamformer
/precoder design scheme for hybrid mmWave systems, which utilizes tone signals and orthogonal pilots for the design of analog beamforming matrices and digital precoding matrices, respectively. In addition, the proposed scheme applies to both non-sparse and sparse mmWave channel environments. We then leverage the proposed scheme to investigate the downlink achievable rate performance. The results show that the proposed scheme obtains a considerable achievable rate of fully digital systems. Taking into account the effect of various types of errors, we investigate the achievable rate performance degradation of the considered scheme.

Third, we extend our proposed scheme to a multi-cell MU mmWave MIMO network. We derive the closed-form approximation of the normalized MSE of channel estimation under pilot contamination over Rician fading channels. Furthermore, we derive a tight closed-form approximation and the scaling law of the average achievable rate. Our results unveil that channel estimation errors, the intra-cell interference, and the inter-cell interference caused by pilot contamination over Rician fading channels can be efficiently mitigated by simply increasing the number of antennas equipped at the desired BS.

Acknowledgments

This work would not have been done without the encouragement and the support from some people I have met during my fascinating Ph.D. journey.

First and foremost, I would like to thank my supervisor Professor Jinhong Yuan with my deepest gratitude for offering me a Ph.D. opportunity three and half years ago and having faith in me ever since. He guides me throughout this work with patience, technical and personal support, and encouragement. He tolerates my shortcomings and helps me to overcome my weakness. Besides, he is passionate about new technologies and exciting ideas. I feel fortunate to pursue my Ph.D. degree under his supervision.

Second, I would like to thank my co-supervisor, Dr. Derrick Wing Kwan Ng, for his guidance, constructive suggestions, and help on my research. Derrick is talented, extremely self-disciplined, and very hard-working. I will regard him as the role model of my academic career.

I would also like to thank Dr. Giovanni Geraci and Dr. Tao Yang for the first step of my research. Many thanks to Dr. Lei Yang, Dr. Yixuan Xie, Dr. Tao Huang, Dr. Mengyu Huang, Dr. Chenxi Liu, Dr. Shuang Tian, Dr. Nan Yang, Dr. Shihan Yan, Dr. Yansha Deng, Dr. Yeqing Hu, and others for having a lot of discussions with me. Special thanks to my colleagues and friends at the University of New South Wales, you guys make the Ph.D. journey funny and interesting. I will always hold dear the days and nights spent in the office.

Finally, my deepest appreciation goes to my beloved family for everything they have done for me. I would like to dedicate this thesis to my parents, my wife, and my son. To my son, you make my life brighter.

List of Publications

Journal Articles:

  1. L. Zhao, D. W. K. Ng, and J. Yuan, “Multi-user precoding and channel estimation for hybrid millimeter wave systems,” IEEE J. Sel. Areas Commun., vol. 35, no. 7, pp. 1576–1590, Jul. 2017.

  2. L. Zhao, G. Geraci, T. Yang, D. W. K. Ng, and J. Yuan, “A tone-based AoA estimation and multiuser precoding for millimeter wave massive MIMO,” IEEE Trans. Commun., vol. 65, no. 12, pp. 5209–5225, Dec. 2017.

  3. L. Zhao, Z. Wei, D. W. K. Ng, J. Yuan, and M. C. Reed, “Multi-cell hybrid millimeter wave systems: Pilot contamination and interference mitigation,” IEEE Trans. Commun., vol. 66, no. 11, pp. 5740-5755, Nov. 2018.

  4. Z. Wei, L. Zhao, J. Guo, D. W. K. Ng, and J. Yuan, “Multi-Beam NOMA for Hybrid mmWave Systems,” accepted, IEEE Trans. Commun., Nov. 2018.

Conference Articles:

  1. L. Zhao, T. Yang and G. Geraci and J. Yuan “Downlink multiuser massive MIMO in Rician channels under pilot contamination” in Proc. IEEE Intern. Commun. Conf. (ICC), Kuala Lumpur, May 2016, pp. 1–6.

  2. L. Zhao, D. W. K. Ng, and J. Yuan, “Multiuser precoding and channel estimation for hybrid millimeter wave MIMO systems,” in Proc. IEEE Intern. Commun. Conf. (ICC), Paris, May 2017, pp. 1–7.

  3. L. Zhao, Z. Wei, D. W. K. Ng, J. Yuan and M. C. Reed, “Mitigating pilot contamination in multi-cell hybrid millimeter Wave Systems,” in Proc. IEEE Intern. Commun. Conf. (ICC), Kansas City, May 2018.

  4. Z. Wei, L. Zhao, J. Guo, D. W. K. Ng, and J. Yuan, “A multi-beam NOMA framework for hybrid mmWave systems,” in Proc. IEEE Intern. Commun. Conf. (ICC), Kansas City, May 2018 (ICC best paper awards).

Abbreviations

3-D Three-dimensional
5G Fifth-generation
AoA Angle-of-arrival
AoD Angle-of-departure
ADC/DAC Analog-to-digital converter/Digital-to-analog converter
AWGN Additive white Gaussian noise
BS Base station
CSI Channel state information
CW Continuous wave
CRLB Cramér Rao lower bound
dB Decibel
DS Delay spread
D2D Device-to-device
DPC Dirty paper coding
FDD Frequency division duplex
HPBW Half-power beam width
i.i.d. Independent and identically distributed
ISI Inter-symbol interference
I/Q In-phase/Quadrature
IoT Internet-of-things
LOS Line-of-sight
LO Local oscillator
LS Least squares
MU Multi-user
mmWave Millimeter wave
MIMO Multiple-input multiple-output
MMSE Minimum mean square error
MRC Maximal-ratio combining
MRT Maximal-ratio transmission
MSE Mean squared error
NMSE Normalized mean squared error
NLOS Non line-of-sight
NOMA Non-orthogonal multiple access
OLB Open-loop beamforming
PA Power amplifier
PDP Power delay profile
PAC Pilot-aided-CSI
PESA Passive electronically scanned array
QoS Quality-of-service
RA Random angle
RF Radio frequency
RCS Radar cross-section
RACH Random access channel
r.m.s. Root mean square
SS Synchronization signals
SLOS Strongest LOS
SLPS SLOS-plus-scattering components
SNR Signal-to-noise ratio
SINR Signal-to-interference-plus-noise ratio
SVD Singular value decomposition
TDD Time division duplex
UMi Urban micro-cell
UPA Uniform panel array
ULA Uniform linear array
US User scheduling
WLAN Wireless local area networks
ZF Zero-forcing

List of Notations

Boldface upper-case letters denote matrices, boldface lower-case letters denote vectors, and italics denote scalars.

Transpose of
Complex conjugate of
Conjugate transpose of
Inverse of
The element in the row and the column of
Determinant of
Trace of
Absolute value (modulus) of the a complex scalar
The space of all matrices with complex entries
Frobenius norm of a vector or a matrix
Zero matrix. A subscript can be used to indicate the dimension
dimension identity matrix
Imaginary unit
Statistical expectation with respect to random variable
Complex Gaussian distribution
Natural logarithm
Logarithm in base two
The -th maximum eigenvalue of a matrix
A diagonal matrix with the entries of on its diagonal
Limit
Sinc function with input
Maximization
Minimization
Subject to
Contents
List of Figures

Chapter 1 Introduction

The significantly increased data rate requirement and quality-of-service (QoS) triggered by the proliferation of smartphones and tablets cannot be satisfied by current communication networks. In particular, the tremendous number of devices and appliances are expected to connect wirelessly to the Internet, e.g.
device-to-device (D2D) communications and internet-of-things (IoT) applications, the required capacity exceeds the limit of existing networks. To address the aforementioned requirements, the fifth generation (G), the true revolution of technologies in both the radio access network and the mobile core network, is expected to support times higher system capacity than current the fourth generation (G) systems and have attracted tremendous interests from both academia and industry, e.g. [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]. For example, G should support Gb/s peak data rate, Mb/s guaranteed data rate, Tb/s/km mobile data volume, less than ms end-to-end latency, million/km number of devices, higher than reliability, and less than meter outdoor terminal location accuracy. As a result, denser network, larger bandwidth, and higher spectral efficiency are necessary to satisfy these demands. To meet the stringent spectral efficiency requirement, massive multiple-input multiple-output (MIMO) technology is introduced by using hundreds of antennas equipped at the base station (BS) to serve tens of users simultaneously [28, 27, 31, 32]. It is proved that, by adopting low computational complexity linear precoding schemes, such as maximal-ratio transmission (MRT) and zero-forcing (ZF), massive MIMO systems can significantly improve the spectral efficiency and fully explore a large amount of available spatial degrees of freedom [28, 14, 33, 34, 35, 15]. Besides, to overcome the bandwidth limitation in licensed band, millimeter wave (mmWave) systems that migrate from sub- GHz to higher frequencies in unlicensed band can inevitably offer a huge trunk of a bandwidth of the order of gigahertz, e.g. an unlicensed spectrum ranging from GHz to GHz, to achieve ultra-high data rate communication [3, 36, 37, 2, 18, 19, 20, 21, 33, 38, 17, 5, 39]. In practice, mmWave and massive MIMO can complement each other to overcome some drawbacks in each technology. For example, due to the short wavelength of mmWave frequencies, mmWave technology can shrink the physical size of antenna arrays of massive MIMO systems. Therefore, the antenna array of mmWave massive MIMO is small which enables flexible and practical deployment. On the other hand, massive MIMO, equipping a BS with hundreds of antennas, can provide significant antenna array gains to help mmWave communication systems to compensate the inherent high propagation path loss, low penetration coefficients, and high signal attenuation caused by raindrop absorption [40, 29]. Thus, the combination of mmWave communication systems with massive MIMO systems is considered as one of the promising candidate technologies for 5G communication systems with many potential opportunities for research [3, 41, 37, 18, 33].

1.1 Background

In this section, we will briefly introduce the concepts of massive MIMO and the characteristics of mmWave channels.

1.1.1 The Concepts of Massive MIMO

Massive MIMO technology is one of the key technologies for G. Compared with the conventional multi-user (MU) MIMO systems, massive MIMO is a special form of MIMO systems with hundreds of antennas equipped at the BS to simultaneously serve tens of users in their cells [42]. In general, a large amount of experimental and theoretical research shows that several favorable properties can be obtained when the number of antennas equipped at the BS is significantly larger than the number of users.

There are several main advantages when the number of antennas is sufficiently large: (1) the effects of small-scaling fading vanish (also known as channel hardening); (2) simple linear signal processing algorithms can achieve considerable rate performance compared to optimal algorithms, e.g. dirty paper coding (DPC); (3) higher spectral efficiency and higher energy efficiency [28, 43, 44, 45, 46, 47]. The more antennas the transmitter/receiver are equipped with, the better performance in terms of data rate and link reliability the system can achieve. However, the cost, the energy consumption, and the complexity of hardware (power amplifier (PA) and analog-to-digital converter/digital-to-analog converter (ADC/DAC)) increase with the increasing number of antennas [21, 37, 27, 14, 48].

Key Aspects of Massive MIMO:

A lot of efforts have been dedicated to the investigation of massive MIMO from different aspects, e.g. architecture aspects [49, 43, 50, 16, 51], capacity and fundamental aspects [28, 52, 44, 45, 46, 53, 54], channel state information (CSI) acquisition [55, 56, 57, 58, 59, 60, 61, 2, 62, 63], detection algorithms [64, 65, 66, 67, 36], downlink precoding design [68, 69, 70, 3, 20, 71, 72, 73], channel measurements and modeling [74, 51, 75], resource allocation [15, 76, 42, 77, 78, 79, 80], hardware impairments [80, 81, 1, 82, 83], beamforming and precoding [84, 85, 86, 87, 88, 89] and performance analysis [90, 91, 92, 93, 94, 95, 96, 97, 76, 42]. These aspects of massive MIMO had been well studied and interested readers may refer to these works for details.

1.1.2 MmWave Channels Statistics

The study of mmWave channels can be dated back to decades ago [98, 99]. Due to the high propagation path loss, mmWave technology has not been widely adopted for cellular application in the past.

Nowadays, the spectral resource below GHz becomes tense while sufficiently large bandwidth is still available at the mmWave band. Thus, large efforts have been devoted to the research of mmWave communication and there are some practical communication systems utilizing the mmWave band, e.g. mmWave wireless local area networks (WLAN) IEEE ad. However, these frequencies have not been well-explored for cellular applications. As mmWave technology is considered as a key feature for G, the features of mmWave channels must be considered carefully for system design.

Path Loss:

According to the free space propagation path loss model provided by the Friis transmission formula, the received power can be expressed as [100]

(1.0)

where is wavelength, is the transmission distance between the desired BS and the user, is the path loss exponent, and is the transmit power. In addition, and are the antenna gains of the transmitter and receiver, respectively.

We can rewrite Equation (1.1.2) in the form of path loss. The commonly adopted empirical propagation path loss model is considered as a function of distance and carrier frequency, which is given by

(1.0)

where in a log-log plot of the path loss curve, slope and intercept are estimated by least squares (LS) linear regression over the measured data [101, 102]. For different scenarios, and may have different values, e.g. line-of-sight (LOS) environment and non line-of-sight (NLOS) environment. In addition, the propagation path loss model should also take into account the impacts of rain attenuation, atmospheric absorption, and shadowing [101, 29, 102, 103, 18].

Generally speaking, the severe path loss of mmWave channels is one of the key technical challenges in preventing mmWave technology to be implemented in conventional cellular communication systems [101, 29, 102, 104]. Nowadays, there are two methods to overcome such a challenge, e.g. increasing antenna array gain and decreasing the propagation distance. In fact, it is expected that small cell will serve as a core structure of future cellular systems [49, 105]. Hence, applying mmWave technology to small-cell urban mobile networks becomes a new trend [106]. In particular, it can significantly reduce the requirement of transmit power of mmWave systems. In addition, the high antenna array gain can be enabled by adopting the massive numbers of antennas.

Power Delay Profile and Delay Spread:

The power delay profile gives the intensity of a signal received through a multi-path channel as a function of time delay. The shape of power delay profile (PDP) in mmWave channel measurements is a superposition of multiple exponentially decaying spectrums. The delay spread (DS) is usually quantified through root mean square (r.m.s.) and considered as a collection of the multi-path containing significant energy which spread over the PDP. Besides, the DS of the channel is an important metric to understand the required system overhead to facilitate communication [107]. To provide sufficient channel characteristics information for the system design (concerning the length of cyclic prefix for a multi-carrier design), it is necessary to proceed the PDP estimation in mmWave channel measurements, which is called channel sounding.

Channel sounding for the estimation of PDP and calculating DS can be performed with both omni-directional antenna as well as directional antenna array/horn antennas. The basic procedure of channel sounding with directional horn antennas is listed as follows [108, 107, 109]:

  • Perform an azimuthal scan and produce number of slices (the beamwidth of main lobe of directional horn antenna can cover degrees)

  • Mark the absolute propagation times for different sounding slices

  • Synthesize the equivalent omni-directional PDP over an absolute propagation time axis

The PDP sounding and DS calculation for the indoor environment can be conducted via omni-directional antennas due to the short propagation distance. The results illustrate that for most indoor scenarios the DS estimated via directional antennas as well as omni-directional antennas are small, e.g. ns indoor office and ns indoor shopping mall [108, 107, 109]. However, the outdoor PDP environment sounding should be conducted via directional horn antennas with large antenna-gain to compensate the severe propagation path loss. Then, by synthesizing the estimated PDP via directional antennas over an absolute propagation time axis, we can obtain the equivalent omni-directional PDP. For the equivalent omni-directional PDP, there are different outdoor scenarios where a significantly large DS have been observed, e.g. ns for street canyon settings and even up to ns for open square settings [108, 107, 109]. In addition, the simulation results conducted by adopting ray tracing demonstrate that scattering and reflections from small objects affect the mmWave propagation channel [110, 102, 108]. These simulation and experiment results for outdoor scenarios can be explained with radar cross-section (RCS) effect, where small objects that do not participate in electromagnetic propagation at low frequencies show up at higher frequencies [108, 107, 102]. According to the simulation and experiment results as mentioned earlier, the sparse scattering assumption of mmWave channels holds for most indoor scenarios. The omni-directional delay spread is comparable with after-beamforming delay spread. However, for non-sparse mmWave channels, the omni-directional delay spread is significantly larger than that of after-beamforming delay spread. Thus, how to support these extremes without incurring a high amount of signaling overhead is an important unsolved problem. Fortunately, field test results showed that the after-beamforming delay spread could be significantly smaller than the omni-directional delay spread [108, 107, 109]. Furthermore, the blocking capability” improves with the increasing number of antennas equipped at the BS/horn antenna gains [111, 1]. Specifically, the beamwidth of the main lobe becomes narrower and the magnitude of sidelobes becomes lower when the number of antennas becomes larger [111, 102, 1]. Thus, the non-sparse scattering environment and the analog beamforming technology should be taken into account in the design of future mmWave systems, e.g. channel estimation and frequency selectivity [108, 107, 109, 101, 29, 102].

1.2 Challenges and Motivations

There are plenty of implementation challenges for mmWave massive MIMO communication systems, such as efficient hardware structures, low-cost hardware elements, hybrid precoding strategies, and channel estimation algorithms. In this thesis, channel estimation for mmWave hybrid systems as well as the impact of hardware impairments on rate performance are the primary focus of this thesis.

1.2.1 Hardware Constraint: Fully Digital vs Hybrid Structure

From the literature, it is certain that conventional fully digital MIMO systems, in which each antenna connects with a dedicated radio frequency (RF) chain, are impractical for mmWave systems due to the prohibitively high cost, e.g. tremendous energy consumption of high-resolution ADC/DAC and PAs [112, 113, 114, 17].

Figure 1.1: Illustration of different hybrid structures.

As a result, several mmWave hybrid systems were proposed as compromised solutions which strike a balance between hardware complexity and system performance [3, 115, 116, 117, 20, 118, 37, 18, 33], such as fully access hybrid structure, subarray hybrid structure and lens-based hybrid structure [113, 17, 112, 36], as shown in Figure 1.1. In particular, the trade-offs between system performance, hardware complexity111The hardware includes PA, ADC/DAC, phase shifters, and antenna array., and energy consumption are still unclear [17, 112].

In the hybrid structure, data streams are first through the baseband digital precoding, and then the output is through the RF chains. After the RF analog beamforming, the RF signals are outputted to the antennas. With , the number of RF chains can be significantly reduced for practical implementation. Specifically, the use of a large number of antennas, connected with only a small number of independent RF chains at transceivers, is adopted to exploit the large array gain to compensate the inherent high path loss in mmWave channels [29, 102]. In the fully access structure shown in Figure 1.1(a), an RF chain is connected to all the antennas through the network of analog phase shifters. In the subarray structure shown in Figure 1.1(b), the array is divided into sub-arrays, and each sub-array is fed by its RF chain. The lens antenna array structure shown in Figure 1.1(c), which is formed by an electromagnetic lens with energy focusing capability and a matching antenna array with elements located on the focal surface, can simultaneously realize signal-emitting and phase-shifting. In general, the hybrid system imposes a restriction on the number of RF chains which introduces a paradigm shift in the design of both resource allocation algorithms, transceiver signal processing, and channel estimation algorithms.

1.2.2 Hybrid Precoding: Basic Concepts

For a hybrid mmWave system, the utmost important issues should be developing channel estimation algorithms and hybrid precoding algorithms [18].

To address the importance in designing hybrid precoding algorithms, we take a MU hybrid mmWave system with the fully access structure as an example, which consists of one -antenna BS with RF chains and single-RF-chain users with -antenna.

During the downlink transmission, the signal received at user is given by

(1.0)

where is the downlink mmWave channel between the BS and user , is the analog beamformer at the BS, is the digital precoder at the BS, is the analog beamformer at user , , is the transmitted symbols, , is the total transmit power, is an additive white Gaussian noise (AWGN) vector, , and is the noise variance at each antenna equipped at a user. The achievable system sum rate is given by [3, 18]

(1.0)

In Equation (1.2.2), is the rate achieved by user and can be expressed as

(1.0)

where is the -th column of .

The optimal joint digital precoder and analog beamformer design is to maximize the achievable sum rate. Thus, the optimal precoders design can be found by solving the following optimization problem [3, 20, 36, 47, 18, 103]:

(1.0)

where and are the hardware constraint for the design of analog beamformers and the total power constraint is enforced by normalizing in .

The problem in Equation (1.2.2) is a non-convex optimization problem. In particular, the digital precoder design is under the constraint of the number of RF chains and the designed analog beamformers. Thus, the optimal solution to the hybrid precoding design is not known in general and only suboptimal iterative solutions exist [116, 3, 70, 119, 112].

In order to avoid the exhaustive search for the optimal analog beamforming and digital precoding design, Ref. [3] proposed a two-stage algorithm which designs analog beamformer and digital precoder separately. In the first-stage, for each user , , the BS and user select their analog beamformers respectively to solve

(1.0)

In fact, the main idea of the first-stage is to jointly design analog beamformers at the user and the BS to maximize the desired signal power of each user. For the analog beamformer design, Equation (1.0) is widely adopted in many works [112, 120]. It is true that the power of the received signal before analog beamforming is typically low due to high mmWave path losses, additional blockage, and penetration losses. Thus, it is reasonable that the proposed analog beamformer design tries to maximize the received power of the desired signal. However, it neglects the resulting interference among different users [47, 107, 1]. Actually, the MU inter-user interference due to the analog beamformers may cause severe impacts and should be taken into account. Thus, we should consider the trade offs between the received power of the desired signal and the MU interference for the joint analog beamformer design [106, 107, 121, 109, 108, 118]. Then, a novel low-complexity practical algorithm for the design of analog beamformers is highly desirable.

In the second-stage of the hybrid precoding design, all the users feed back the downlink equivalent CSI to the BS based on the jointly designed analog beamformers:

(1.0)

where , . The digital precoder of the BS based on the feedback of equivalent channel to manage the MU interference

(1.0)

However, explicit CSI feedback from users is still required for estimating these channel. In practice, CSI feedback may cause high complexity and extra signallings overhead. In addition, there will be a system rate performance degradation due to the limited amount of the feedback and the limited resolution of CSI quantization.

Therefore, a low computational complexity mmWave channel estimation algorithm, which does not require explicit CSI feedback, is necessary to unlock the potential of hybrid mmWave systems.

1.2.3 Combination of MmWave Systems and A Small-cell Scenario

To further improve the network spectral efficiency, the small-cell scenario has been proposed to cooperate with mmWave systems [22, 37, 119]. In fact, the combination of hybrid mmWave systems and a small-cell scenario is still unexplored and possesses many exciting research opportunities [37]. For example, cell shrinking/small-cell scenario can bring numerous benefits for hybrid mmWave systems. In particular, it facilitates the reuse of the same piece of spectrum across a large geographic area for achieving a high network spectral efficiency [122] and reducing of the severe large-scale propagation path loss by shortening the distances between transceivers [22, 119]. For the multi-small-cell mmWave network, the interference received at the desired user originates from two sources, as illustrated in Figure of [119]: interference among different BSs and interference within the desired cell. It is mentioned in [22] that, mmWave beams are highly directional, which completely changes the interference behavior as well as the sensitivity to beams misalignment. In particular, the interference adopts an on/off behavior where strong interference occurs intermittently [22]. With a shrinking cell radius, distances from neighbouring BSs to the desired user decrease, which may lead to severe inter-cell interference to the desired user. Recently, it is also mentioned in work [123] that the received interference significantly increases when directional transmission is simultaneously adopted in both transceivers for the same amount of total emitted energy. Besides, due to the impact of imperfect CSI on the design of downlink precoder, the desired BS will cause severe intra-cell interference on the desired user. Thus, for the multi-small-cell mmWave downlink transmission with imperfect CSI and a large number of antennas, the desired user may suffer severe intra-cell and inter-cell interference. Hence, it is necessary to study the performance in the multi-small-cell hybrid mmWave network.

1.2.4 MmWave Channel Estimation

Several channel estimation algorithms are widely adopted in different works, such as multi-resolution hierarchical codebook algorithms, compress sensing algorithms, open-loop beamforming algorithms, and pilot-aided algorithms, cf. [24, 124, 125, 126, 59, 127, 26, 128, 129, 130, 131, 132, 133, 134, 135, 112, 5, 60, 57, 37, 136]. Some of the algorithms mentioned above are based on the assumption of sparse mmWave channels, which may not hold true for some scenarios as shown recent field measurements. The field test results show that both strong LOS components and non-negligible scattering components may exist in mmWave propagation channels, especially in urban areas, e.g. building valley environment [108, 107, 109, 101, 29, 102]. Therefore, we introduce two widely adopted algorithms which do not rely on the assumption of sparse mmWave channels.

Pilot-aided Channel Estimation and Pilot Contamination:

Pilot-aided channel estimation, which relies on orthogonal pilot symbols, is widely adopted by MIMO systems and is suitable for sparse or non-sparse environments. The majority of contributions in the literature considered that massive MIMO systems rely on pilot sequences to estimate CSI [21, 53, 44, 28, 96]. Due to the limited orthogonal pilot resources, they must be reused across different cells. Thus, the reuse of orthogonal pilot sequences causes interference during channel estimation, which is known as pilot contamination [53, 28]. As a result, the downlink transmission based on the CSI obtained via contaminated pilots causes severe intra-cell and inter-cell interference in the desired cell. In fact, pilot contamination is considered as a fundamental performance bottleneck of the conventional multi-cell MU massive MIMO systems, since the resulting channel estimation errors do not vanish even if the number of antennas is sufficiently large, cf. [28, 86, 53, 137, 35, 46, 138, 139].

Recently, various algorithms [53, 60, 140, 141, 142, 143, 58, 63, 144] have been proposed to alleviate the impact of pilot contamination, e.g. data-aided iterative channel estimation algorithms, pilot design algorithms, multi-cell minimum mean square error (MMSE) based precoding algorithm, and so forth. However, some algorithms, e.g. multi-cell MMSE algorithm, are mostly based on the assumption that the desired BS can have perfect knowledge of covariance matrices of pilot-sharing users in neighbouring cells, which is overly optimistic. Besides, the condition that the desired BS has the perfect knowledge of covariance matrices is a necessary but not sufficient condition for pilot contamination mitigation, cf. [58, 63, 144]. The algorithm proposed in [58] requires that covariance matrices of pilot-sharing users in neighbouring cells are orthogonal, which is unlikely in practice [144]. Also, the requirement of [63] for completely eliminating pilot contamination is that the number of antennas equipped at the BS and the size of a coherence time block jointly go to infinity. In the literature, most of existing multi-cell massive MU-MIMO works for pilot contamination [28, 53, 22, 60, 86] assumed that cross-cell channels from pilot-sharing users in neighbouring cells to the desired BS are Rayleigh fading channels with zero means. However, as discussed in Section IV of [145], it is probably not accurate for modeling the inter-cell interference as a Gaussian random variable with a small-cell setting. In fact, recent field measurements have confirmed that the strongest angle-of-arrival/angle-of-departure (AoA/AoD) components always exist in the inter-cell mmWave channels in small-cell systems [101, 29, 102, 146]. Besides, the mean values of cross-cell channels are not zero and different from each other. In other words, the distribution of cross-cell mmWave channels is different from that of the sub- GHz channels. Thus, the results obtained in works mentioned above for pilot contamination mitigation and performance analysis, e.g. [28, 53, 22, 60, 144, 37], cannot be applied directly. Furthermore, a thorough study on the impact of pilot contamination in such a practical network system with small cell radius has not been reported yet.

Open-Loop Beamforming Channel Estimation:

Channel estimation of practical mmWave systems may rely on AoA estimation in mmWave channels [37, 33, 32]. As a result, for mmWave channel estimation, the open-loop beamforming (OLB) channel estimation has been widely adopted. Generally, the OLB algorithm is widely used in analog beamforming and hybrid precoding. In particular, the BS transmits beamforming vectors to its users. Then, each user reports the index of a beam with the largest gain in the beams via a feedback link with numbers of bits. However, due to the limited amount of feedback bits, the OLB algorithm does not allow the BS to accurately estimate the channel responses of a large number of users. Interestingly, fully digital systems, which can be considered as a subcase of hybrid systems, can also adopt the OLB algorithm for AoAs estimation [37, 147]. Thus, the fully digital system, which contains more RF chains than analog and hybrid structures, can simultaneously transmit predesigned beams in all estimation directions., e.g. [148, 135, 149, 114, 29]. For the OLB channel estimation, the required number of beams depends on the required resolutions and is predesigned by the codebook. The number of beams for AoA estimation does not necessarily scale up with the number of transmit antennas. However, to serve an area with an increasing user density, it is expected that the BS should increase the spatial resolution. For example, if the system requires an half-power beam width (HPBW) coverage for the OLB training, that the required number of beams should be [111], where is the number of antennas equipped at the BS. In this case, the required number of beams for the OLB training scales with an increasing number of antennas, which may not be suitable for mmWave systems employing massive MIMO technology. In fact, it is expected that the required coherence time resources of channel estimation for mmWave massive MIMO systems shall neither scale up with the number of users nor with the number of antennas [37, 41, 33]. Therefore, a simple AoA channel estimation algorithm with low overhead is highly desirable for hybrid mmWave system design.

1.2.5 TDD or FDD Feedback?

In practice, the conventional fully digital systems and the hybrid systems are designed based on different hardware architectures. Hence, intuitively, the channel estimation algorithms for hybrid mmWave systems are different from that for fully digital systems. Currently, the majority of contributions in the literature focus on the development of CSI feedback based channel estimation methods for frequency division duplex (FDD) hybrid mmWave systems, e.g. [3, 32, 150, 96, 118, 10]. This is motivated by the assumption of the sparsity of mmWave channels that the numbers of resolvable AoA/AoD paths are finite and limited. Thus, the CSI acquisition via feedbacks only leads to a small amount of signaling overhead compared to non-sparse CSI acquisition. Generally, due to the high propagation path loss, the sparsity may only exist in outdoor long distance propagation mmWave channels [102]. In some scenarios, the assumption of the sparsity of mmWave channel may not hold anymore. For example, for practical urban micro-cell (UMi) scenarios, such as the city center, the number of scattering clusters increases significantly and the channels are expected to be non-sparse. In [101, 29, 102], recent field test results, as well as ray-tracing simulation results, have shown that reflections from street signs, lamp posts, parked vehicles, passing people, etc., could reach a receiver from all possible directions in urban micro-cell (UMi) scenarios. In other words, the AoAs of scattering components between the users and the BS are uniformly distributed between . In [151], the authors revealed that the presence of significant amount of scatterers in propagation environment has a non-negligible impact on the achievable rate performance of FDD systems when the conventional CSI feedback algorithms are adopted. Besides, the required amount of feedback signalling overhead increases tremendously with the number of scattering components, consuming a significant portion of system resources [3]. Moreover, recent field test results have also verified that, for both fully digital and hybrid massive MIMO systems in different channel environments, time division duplex (TDD) based beamforming exploiting channel reciprocity for channel estimation can outperform the FDD based beamforming scheme utilizing CSI feedback in terms of achievable sum-rate [151, 107]. To overcome the aforementioned common drawbacks of conventional CSI feedback based FDD mmWave channel estimation algorithms, a TDD-based beamforming channel estimation algorithm for mmWave channels is strongly welcomed. However, time synchronization and calibration issues between the forward and reverse links need to be taken into account [18].

1.2.6 Hardware Impairments

In practice, considering the high cost and the high complexity of hardware for high frequency bands, it is likely to build mmWave systems with low-cost components that are prone to hardware imperfection. Thus, constraints due to non-ideal hardware should be taken account in the designs of mmWave MIMO systems. In practice, hardware components may have various types of impairments that may degrade the achievable rate performance. For example, practical transceiver hardware is impaired by phase noise, limited phase shifters resolution, non-linear power amplifiers, in-phase/quadrature (I/Q) imbalance, and limited ADC/DAC resolution [152, 83, 153, 154, 136, 114, 88].

Generally, three different hardware impairments are considered in the literatures, e.g. additive distortions, incorporate multiplicative phase-drifts, and quantization loss caused by low-resolution ADC/DAC. The authors of [152] proved that for a fully digital massive MIMO system, the additive distortion caused by hardware impairments creates finite ceilings on the channel estimation accuracy and on the uplink/downlink capacity. In other words, the system performance cannot be improved by increasing the number of antennas equipped at the BS as well as the signal-to-noise ratio (SNR). In addition, the work in [153] concluded that the impact of phase error on hybrid beamforming has a further reduction on the potential gain brought by mmWave systems. In fact, the achievable rate degradation caused by phase errors can be compensated by simply employing more transmit antennas, e.g. phase errors in phase shifters induced by thermal noise, transceiver RF beamforming errors caused by AoA estimation errors, and channel estimation errors affected by independent additive distortion noises [152, 83, 153]. However, the rate performance degradation caused by joint hardware imperfections, i.e., random phase errors, transceiver analog beamforming errors, and channel estimation errors, has not been thoroughly discussed.

1.3 Thesis Outline and Contributions

The main contributions and the outline of the thesis are summarized as follows.

In Chapter , we investigate channel estimation and MU downlink transmission of a TDD massive MIMO system in mmWave channels. We propose a tone-based linear search algorithm to facilitate the estimation of AoAs of the strongest LOS (SLOS) channel component as well as scattering components of the users at the BS. Based on the estimated AoAs, we reconstruct the SLOS component and scattering components of the users for downlink transmission. We then derive the achievable rates of MRT and ZF precoding based on the SLOS component and the SLOS-plus-scattering components (SLPS), respectively. Taking into account the impact of pilot contamination, our analysis and simulation results show that the SLOS-based MRT can achieve a higher data rate than that of the traditional Pilot-aided-CSI based (PAC-based) MRT, under the same mean squared error (MSE) of channel estimation. As for ZF precoding, the achievable rates of the SLPS-based and the PAC-based are identical. Furthermore, we quantify the achievable rate degradation of the SLOS-based MRT precoding caused by phase quantization errors in the large number of antennas regime. We show that the impact of phase quantization errors on the considered systems cannot be mitigated by increasing the number of antennas and therefore the resolutions of RF phase shifters is critical for the design of efficient mmWave massive MIMO systems.

The results in Chapter 2 have been presented in the following publications:

  • L. Zhao, G. Geraci, T. Yang, D. W. K. Ng, and J. Yuan, “A tone-based AoA estimation and multiuser precoding for millimeter wave massive MIMO,” IEEE Trans. Commun., vol. 65, no. 12, pp. 5209–5225, Dec. 2017.

  • L. Zhao, T. Yang and G. Geraci and J. Yuan “Downlink multiuser massive MIMO in Rician channels under pilot contamination” in Proc. IEEE Intern. Commun. Conf. (ICC), Kuala Lumpur, May 2016, pp. 1–6.

In Chapter 3, we develop a low-complexity channel estimation for hybrid mmWave systems, where the number of RF chains is much lower than the number of antennas equipped at each transceiver. The proposed mmWave channel estimation algorithm first exploits multiple frequency tones to estimate the strongest AoAs at both BS and user sides for the design of analog beamforming matrices. Then all the users transmit orthogonal pilot symbols to the BS along the directions of the estimated strongest AoAs in order to estimate the channel. The estimated channel will be adopted to design the digital ZF precoder at the BS for the multi-user downlink transmission. The proposed channel estimation algorithm is applicable to both non-sparse and sparse mmWave channel environments. Furthermore, we derive a tight achievable rate upper bound of the digital ZF precoding with the proposed channel estimation algorithm scheme. Our analytical and simulation results show that the proposed scheme obtains a considerable achievable rate of fully digital systems, where the number of RF chains equipped at each transceiver is equal to the number of antennas. Besides, by taking into account the effect of various types of errors, i.e., random phase errors, transceiver analog beamforming errors, and equivalent channel estimation errors, we derive a closed-form approximation for the achievable rate of the considered scheme. We illustrate the robustness of the proposed channel estimation and multi-user downlink precoding scheme against the system imperfection.

The results in Chapter 3 have been presented in the following publications:

  • L. Zhao, D. W. K. Ng, and J. Yuan, “Multi-user precoding and channel estimation for hybrid millimeter wave systems,” IEEE J. Sel. Areas Commun., vol. 35, no. 7, pp. 1576–1590, Jul. 2017.

  • L. Zhao, D. W. K. Ng, and J. Yuan, “Multiuser precoding and channel estimation for hybrid millimeter wave MIMO systems,” in Proc. IEEE Intern. Commun. Conf. (ICC), Paris, May 2017, pp. 1–7.

In Chapter 4, we investigate the system performance of a multi-cell MU hybrid mmWave MIMO network. Due to the simultaneous reuse of pilot symbols among different cells, the performance of channel estimation is expected to be degraded by pilot contamination, which is considered as a fundamental performance bottleneck of conventional multi-cell MU massive MIMO networks. To analyze the impact of pilot contamination to the system performance, we first derive the closed-form approximation expression of the normalized MSE of the channel estimation algorithm proposed in [1] over Rician fading channels. Our analytical and simulation results show that the channel estimation error incurred by the impact of pilot contamination and noise vanishes asymptotically with an increasing number of antennas equipped at each RF chain at the desired BS. Furthermore, by adopting ZF precoding in each cell for downlink transmission, we derive a tight closed-form approximation of the average achievable rate per user. Our results unveil that the intra-cell interference and inter-cell interference caused by pilot contamination over Rician fading channels can be mitigated effectively by simply increasing the number of antennas equipped at the desired BS.

The results in Chapter 4 have been accepted to appear in the following publications:

  • L. Zhao, Z. Wei, D. W. K. Ng, J. Yuan, and M. C. Reed, “Multi-cell hybrid millimeter wave systems: Pilot contamination and interference mitigation,” IEEE Trans. Commun., vol. 66, no. 11, pp. 5740-5755, Nov. 2018.

  • L. Zhao, Z. Wei, D. W. K. Ng, J. Yuan and M. C. Reed, “Mitigating pilot contamination in multi-cell hybrid millimeter Wave Systems,” in Proc. IEEE Intern. Commun. Conf. (ICC), Kansas City, May 2018.

In Chapter 5, future works and conclusions are presented.

Chapter 2 Fully Digital mmWave MIMO Systems: A Tone-based Channel Estimation Strategy

2.1 Introduction

In this chapter, we consider a mmWave MU massive MIMO system. First, we propose a novel and simple channel estimation algorithm, which is inspired by the signal processing of radar and sonar systems. We illustrate the proposed channel estimation for mmWave channels via analysis and simulation results. In addition, we analyze the rates achieved by utilizing MRT and ZF precoding, which are based on the estimated components of mmWave channels. Furthermore, we discuss some hardware constraints that may affect the achievable rate performance, e.g. the limited resolutions of digital RF phase shifters. Our main contributions are summarized as follows:

  • We propose a novel MU channel estimation scheme via tone-based AoA estimation. By introducing multiple frequency tones, the proposed scheme can simultaneously and efficiently estimate all users’ AoAs. More importantly the accuracy of the proposed channel estimation algorithm increases with the number of antennas available at the BS. Compared to existing the pilot-aided channel estimation and the OLB channel estimation methods, our proposed AoA estimation over Rician fading channles neither causes pilot contamination nor requires a channel estimation overhead which increases with the numbers of users and antennas equipped at the BS.

  • Based on various components of the estimated CSI, we derive the achievable rates of the MRT and the ZF precodings. In particular, the SLOS is adopted for the SLOS-based MRT. In addition, the combination of multiple AoAs from the users to the BS are utilized for the SLPS-based ZF downlink transmissions. We also derive closed-form approximations for the achievable rates of the MRT and the ZF precoding strategies in mmWave channels when the traditional PAC estimation is adopted. We analytically show that the achievable rates per user for the SLPS-based and the PAC-based ZF precoding strategies are identical, if the MSEs of CSI are the same. Also, it is interesting to note that the achievable rate per user of the SLOS-based MRT is better than that of the PAC-based MRT.

  • To obtain system design insights, we perform an asymptotic analysis on achievable rates of the MRT and ZF precoding strategies. The analysis and simulation results verify that the mmWave massive MIMO can achieve a high sum rate performance even with dense users population. On the other hand, we show that the resolutions of RF phase shifters is critical for mmWave massive MIMO design. In fact, the negative impact of limited resolutions of shifters on the system rate performance cannot be mitigated by increasing the number of antennas.

The rest of the chapter is organized as follows. Section 2.2 describes the system model considered in the chapter. In Section 2.3, we detail the proposed channel estimation algorithm. In Section 2.4, we derive the downlink achievable rate performance based on the CSI estimated by the proposed algorithm. In Section 2.5, we compare rate performance between the conventional algorithms and that investigated in Section 2.4. The impact of imperfect hardware are discussed in Section 2.6. Finally, Section 2.7 summarizes the chapter.

2.2 System Model

Figure 2.1: Fully digital massive MIMO architecture.

In this chapter, an mmWave massive MU MIMO system is considered, which is shown in Figure 2.1. The system consists of neighboring cells and there are users per cell. The BS in each cell is equipped with antennas to serve the single-antenna users simultaneously, . Due to the significant propagation attenuation at mmWave, the system is dedicated to cover a small area, e.g. with a cell radius of approximately m. The channels from the BS to the users in the same cell are modeled by Rician fading and with large K-factors ( dB) [29, 155, 156]. We assume that the users and the BSs in all cells are fully synchronized in time and that the uplink and downlink in each cell adopt TDD [28, 53].

Let be the uplink channel matrix between the users and the BS in the desired cell. We assume that is a narrowband slow time-varying block fading Rician fading channel, i.e., the channel is constant in a time slot but varies slowly from one time slot to another. Each time slot is divided into three phases: channel estimation phase, uplink transmission phase, and downlink transmission phase. We denote the -th column vector of as representing the channel vector between the BS and user in the desired cell. According to the field measurement of mmWave channels [29], a strong LOS component is expected and other propagation paths can be considered as scattering components. We assume that the large scale path loss can be compensated by using automatic gain control (AGC). Thus, the channel vector of user can be expressed as a combination of a deterministic strongest LOS channel vector and a multiple-path scattered channel vector , i.e.,

(2.0)

where is the Rician K-factor of user , which denotes the ratio between the power of the SLOS component and the power of the scattering components. In general, we can re-express Equation (2.0) as

(2.0)

where , . In addition, we have , and . We adopt uniform linear array (ULA) as in [135, 157]. Here, is the -th column vector of the SLOS matrix and it can be expressed as

(2.0)

where is the distance between the neighboring antennas at the BS, is the wavelength of the carrier frequency, and is the AoA of the SLOS component from user to the BS in the desired cell. For convenience, we set for the rest of the chapter which is an assumption commonly adopted in the literature [158, 159]. The scattering component is the -th column vector of the scattering matrix and can be expressed as

(2.0)

where denotes the number of propagation paths, is the complex path gain and is the AoA associated to the -th propagation path [117], and is the -th propagation path of user given by

(2.0)

We assume that all the users have various AoAs which are uniformly distributed over and they are separated by at least hundreds of wavelengths[28, 160]. To facilitate the investigation of channel estimation and downlink transmission, we assume that perfect long-term power control is performed to compensate for path loss and shadowing between the desired BS and the desired users and that equal power allocation is used among different data streams of the users [3, 115, 46].

2.3 Channel Estimation and Downlink Transmission

In this section, we first propose a novel MU mmWave channel estimation algorithm based on various single carrier frequency tones, which is inspired by signal processing of radar and sonar systems [147, 161]. Based on the estimated SLOS component and scattering components, we propose the SLOS-based MRT and the SLPS-based ZF precoders for MU downlink precoding. In addition, the achievable rate performance of these two precoders are derived and used for comparison in the following section.

2.3.1 MU MmWave Channel Estimation

We note that the channel estimation of mmWave channels is equivalent to the AoA estimation of the SLOS and scattering components. In this section, we propose to use the frequency tone resources to simultaneously estimate the AoAs of the users without causing collision among different cells. The details are discussed in the following paragraphs.

At the beginning of a coherence time block, all the users register at the desired BS and transmit unique tones separated in frequency. This initialization can be done during the time synchronization in the handshaking between the desired BS and the users. The frequency tone of user for the AoA estimation is a single carrier continuous wave (CW) signal, , where is the carrier frequency for user and is the time variable of the tone signal. We also denote that is the system carrier frequency, is the total available bandwidth for all tone frequencies, and is at the very center of the total bandwidth.

For the channel estimation, we choose to transmit tone signals from the users to the BS via one of the omni-directional antennas equipped at the users.

The reasons are three:

  • The utilizing of only one omni-directional antenna at the user to transmit the tone signal is to sound mmWave channels in every direction;

  • In practice, the number of antennas equipped at the users is much smaller than the number of antennas equipped at the BS, . As long as a sufficiently large number of antennas, , is equipped at the BS, the power gain loss can be compensated;

  • For the AoA estimation, tone signal is robust to the background noise. It is known that the thermal noise power is determined by the signal bandwidth and the noise spectral density level. Due to the extreme narrow bandwidth of the tone signal, the receive thermal noise power is low. Thus, it is easy to detect the tone signal even with a slightly low receive signal power [147].

Figure 2.2: Tone-based AoA channel estimation.

For any two different frequency tones and , , in the , if the frequency tones satisfy the following condition,

(2.0)

the AoA estimation performance by using ULA with any tones in is identical111The difference of different carrier wavelengths is less than micrometers for a carrier frequency of GHz.. The condition also can be re-expressed as [111]. For example, if the system operates at a carrier frequency of GHz, then is MHz. Any frequency tones in the frequency range of have an identical performance in the AoA estimation. However, the frequency tones will be affected due to users’ doppler frequency shift .

In addition, to overcome the collisions caused by users’ doppler frequency shift between neighboring frequency tones, a frequency protectional gap need to satisfy

(2.0)

For example, if the system operates at GHz and the maximum speed of users is km/h, then the minimum frequency protection gap is kHz. In practice, a single carrier frequency CW signal can be easily generated by a commercial GHz signal generator[162], which has a narrow bandwidth of Hz. Therefore, for a bandwidth of MHz we can generate single carrier CW signals, which can estimate users’ AoAs simultaneously. For mmWave massive MIMO systems, according to the 3GPP medium user density standard [163], the number of users in each cell ranges from to . Therefore, the frequency resources can support at least three cells without causing any collision in the AoA estimation among different cells.

The basic idea of utilizing frequency tone signal for the AoA estimation is borrowed from single-carrier monopulse radar systems [147]. The key idea is that the narrow-band single-carrier frequency CW signal can be performed for the AoA estimation. Therefore, orthogonal pilot symbols are no longer required for the AoA estimation of mmWave channels. In addition, different users can be distinguished at the BS via different carrier frequencies. At the beginning of a coherence time block, all the users register at the desired BS. At the same time, the desired BS instructs all the users’ unique tone carrier frequencies. At the user’s side, according to the allocated tone carrier frequencies, a single-carrier frequency CW pass-band signal is created in the user’s RF chain and broadcasted via one of its antennas. For example, the frequency tone of user for the AoA estimation is , where is the carrier frequency for user and is the time variable of the tone signal. The pass-band received signal of user at the BS is given by

(2.0)

where is the AWGN vector at the BS antennas, whose entries follow independent and identically distributed (i.i.d.) and is the noise variance at each antenna of the BS. At the BS, different frequency tones will be generated as the reference signals for the down-conversion of received signals, as shown in Figure 2.2. Take user for example, the reference signal is at the BS and the received signal after down-conversion is given by

(2.0)

Then the mixed signal will pass through different narrow low pass filters with an appropriate filter bandwidth to remove high frequency components [147]. After the high frequency components are filtered and removed, the received base-band signal which contains the AoA information can be expressed as

(2.0)

To facilitate the estimation of AoAs, we perform a linear search in the angular domain ranged from to with an angle search step size of , where is the maximum number of search steps. The AoA detection matrix for all users is , where is a column vector of matrix given by

(2.0)

where , , stands for a potential AoA of user at the BS. We note here, the coefficient appears in Equations (2.11) is the normalization factor. The size of matrix represents the computational complexity of AoA estimation. We then utilize different AoA detection vectors, e.g. to obtain detection output of user . Specifically, for ,

(2.0)

Now we obtain the detection outputs . The potential AoA of the SLOS, which leads to the maximum value among the observation directions, i.e.,

(2.0)

is considered as the SLOS component of user . If the number of search steps is sufficiently large, we accurately approximate the channel of user , , by using AoAs from the strongest detection outputs. We first sort the detection outputs in descending order and obtain the ordered detection output vector as , where . Then, we can obtain the estimated channel as

(2.0)

where is the -th strong AoA given by

(2.0)

and the Rician K-factor is given by

(2.0)

We note that the exact number of combined AoAs is hard to obtain in practice. As a result, the number of combined AoAs is set as a reasonable value for practical implementation. In the sequel, we set as for simplicity [102]. In fact, the tone-based AoA channel estimation error is mainly caused by the uncertainty of .

Utilizing the estimated SLOS component as the estimated channel, the MSE of the proposed algorithm in the high SNR regime is given by

(2.0)

We demonstrate and validate the accuracy of the proposed AoA estimation via simulation in Figures 2.3(a), 2.3(b), 2.3(c), and 2.3(d). The accuracy of the AoA estimation is determined by the number of search steps as well as the number of strongest AoAs .

(a) Illustration of AoAs estimation.
(b) Illustration of AoAs estimation.
(c) Successful rate of SLOS estimation.
(d) Normalized MSE versus Rician K-factor.
Figure 2.3: (a) Illustration of AoA estimation for the SLOS component and scattering components for and ; (b) Illustration of AoA estimation for the SLOS component and scattering components for and ; (c) Successful rate of the SLOS estimation versus the Rician K-factor for various number of antennas; (d) Normalized MSEs of channel estimation versus the Rician K-factor for various number of antennas. For (a), (b), (c), and (d), we set the number of combination AoAs as and the number of search steps as .

Searching for can be processed via baseband digital signal processing. More details on the Cramér-Rao lower-bound of the ULA AoA estimation can be found in [161]. In practice, larger number of antennas means higher spatial resolution for AoAs estimation.

In Figures 2.3(a) and 2.3(b), we illustrate the proposed AoA estimation for different . The SNR of tone signal adopted in the simulations for Figures 2.3(a) and 2.3(b) is dB.

With a large , the impact of noise on the AoA estimation is mitigated, as shown in Figures 2.3(a) and 2.3(b). These figures indicate that the proposed algorithm is robust to the AWGN when the BS is equipped with a sufficiently large number of antennas. If the norm of the angle difference between the estimated SLOS component and the actual SLOS component is less than , we denote the estimation of the SLOS component as successful.

Figure 2.3(c) shows the successful rate of the AoA estimation achieved by the proposed algorithm versus the Rician K-factor for different number of antennas . It is clear that the successful rate increases with the number of antennas as well as with the Rician K-factor. In addition, we also see that the successful rates of the SLOS estimation for dB with are almost the same as those for dB with . Figure 2.3(d) shows the normalized MSEs of channel estimation versus the Rician K-factor for different number of antennas . It shows that the SLPS algorithm has better MSE performance than the SLOS algorithm. In Figure 2.3(d), the correctness of Equation (2.0) is also verified. In Figures 2.3(c) and 2.3(d), we also observe that the improvement in MSE is saturated for a large number of antennas. Compared to conventional orthogonal pilot-aided and the OLB algorithm approaches for channel estimation [28, 53, 37], the proposed tone-based AoA estimation scheme is simpler and the required coherence time resources will neither increase with the number of users nor the number of antennas. In addition, the proposed channel estimation relies on the antenna array gain for AoA estimation and the tone-based AoA estimation can be extended to hybrid systems by following a similar approach as in [1]. Literally, the more antennas used, the more antenna array gain can be obtained. Therefore, it is expected that the required power of the transmitted tone is low in the considered massive MIMO mmWave system. More importantly, the proposed tone-based AoA estimation algorithm can avoid the system performance degradation due to pilot contamination. With a sufficiently large number of antennas, the proposed algorithm can accurately estimate the SLOS component as well as scattering components.

Figure 2.4: Illustration of the practical 5G NR CSI acquisition/initial access procedure.

In mmWave systems, channel estimation is important for unlocking the potential of the system performance. Majority of contributions in the literature focus on the development of CSI feedback based channel estimation methods for hybrid mmWave systems, e.g. [3, 32, 150, 96, 118, 10]. In practice, the 5G NR specification includes a set of basic beam-related procedures for the above 6 GHz CSI acquisition [164]. The beam management of 5G NR mmWave systems consists of four different operations which are shown in Figure 2.4, i.e., beam sweeping, beam measurement, beam determination, and beam reporting. Taking a single antenna user in 5G NR stand-alone (SA) downlink scheme for example, the BS sequentially transmits synchronization signals (SS) and CSI reference signals (CSI-RSs) to the users by using a predefined codebook of directions. Then, the users search and track their optimal beams by measuring the collected CSI-RSs. At the end of CSI acquisition phase, beam reporting, the users feed back the determined beam information (beam quality and beam decision) and the random access channel (RACH) preamble to the BS.

Figure 2.5: Illustration of the overhead signalling difference between the practical 5G NR CSI acquisition procedure and the proposed algorithm.

Mainly, the difference between the channel estimation algorithm adopted in practical mmWave systems and the proposed tone-based algorithm is the overhead signalling consumed for the channel estimation phase. Figure 2.5 illustrates the overhead signalling difference between our proposed tone-based algorithm and the practical 5G NR mmWave channel estimation protocol. It shows that utilizing tone signals can significantly save the overhead signalling resource. In addition, the MSE performance of aforementioned algorithms are the same. The reason is simple and straightforward. The antenna array adopted in these two algorithms to facilitate the channel estimation is same and has the same Cramér Rao lower bound (CRLB).

In the following sections, we analyze the system rate performance of downlink transmission based on the estimated CSI via the proposed tone-based AoA estimation scheme.

2.4 Performance Analysis

For the downlink transmission performance analysis, we first discuss the adopted assumptions. In reference [101], which is based on recent field test results, the authors suggested that the angles between the users and the BS are uniformly distributed between . In addition, reference [102] adopted ray-tracing model to characterize the AoAs of users at different locations. The ray-tracing simulation results are verified and supported by field test results (Figure 5 of [102]). It is shown that reflections from street signs, lamp posts, parked cars, passing people, etc., could reach the receiver from all directions. Based on these field test results, it is clear that the AoAs between the BS and the users are caused by many clusters in the propagation directions. In fact, the clusters around different separated users are different with high probability in the urban areas as shown in Figure 2 of [102]. Although some users may share part of the clusters [150], to simplify the average achievable rate performance analysis, we assume that the set of AoAs of multi-path between different users will be different with high probability [165] in the large number of antennas regime. In other words, the scattering components of different users are assumed not highly correlated due to the random clusters in the urban scenario in the considered system. Specifically, in the large number of antennas regime, for , it is expected that

(2.0)

We assume that given the random location of the scatters, the set of AoAs of multi-path between different users will be different with high probability [165]. Therefore, for , we have the following result:

(2.0)

2.4.1 SLOS-based MRT Precoding

MRT is considered as the simplest precoding strategy, due to its low computational complexity. In [159], the authors proved that single-user massive MIMO systems are more suitable to exploit strong LOS components of Rician fading channels by comparison with pure Rayleigh fading environments. In this section, we study the rate performance of the considered MU mmWave systems when MRT downlink transmission is employed and designed based on the estimated SLOS component. To facilitate the following study, we assume that the perfect SLOS component is available222It was verified by simulation that, for the proposed SLOS estimation with a sufficiently large number of antennas at the BS, e.g. antennas, our proposed SLOS estimation algorithm is highly accurate. The simulation results are shown in Figure 2.3(c). and the downlink MRT precoder is given by . The rate performance achieved by using the MRT precoder can be considered as the system performance benchmark. We then express the received signal of user as

(2.0)

where is the power normalization factor, is the transmitted signal from the BS to user in the desired cell, , and is the transmit power. We then present the signal-to-interference-plus-noise ratio (SINR) expression of user as

(2.0)

where represents the transmit SNR. In the large number of antennas and high receive SNR regime, the approximated average achievable rate of the MRT precoding can be expressed as

(2.0)

where in Equation (2.0) is considered as the interference to the desired user caused by SLOS components of different users. In addition, decreases significantly with an increasing number of antennas . in Equation (2.0) is considered as the interference caused by the scattering parts, which is determined by the Rician K-factor and the number of users to the number of antennas ratio.

2.4.2 SLPS-based ZF Precoding

ZF precoding is widely adopted for MU systems due to its capability in interference suppression. It was verified by simulation that the estimated SLPS can achieve a better MSE performance in channel estimation than the estimated SLOS, which is shown in Figure 2.3(d). While the estimated SLPS is adopted for the design of ZF precoder, the achievable rate of the SLPS-based ZF can be considered as the rate performance benchmark. Based on the estimated SLPS-based uplink channel , the downlink precoder is expressed as

(2.0)

The received signal at user in the desired cell is given by

(2.0)

where the variable is the number of neighbouring cells, is the -th column vector of and is the normalization factor. For the ZF precoder under the perfect CSI, the precoder matrix is given by . Let denote the -th column vector of , and . We re-express Equation (2.0) as

(2.0)

where denotes the -th column vector of the ZF precoder error matrix , and denotes the transmitted signal vector. We then express the SINR of user as

(2.0)

Now we summarize the achievable rate per user in the large number of antennas and high SNR regime in the following theorem.

Theorem 2.1.

For a large receive SNR and large number of antennas, the average achievable rate of the ZF precoding based on the estimated CSI can be approximated by

(2.0)

where , represents the -th diagonal element of , and is the normalized MSE of proposed channel estimation algorithm.

Proof: Please refer to Appendix A.

Observing Equation (2.0), the approximated average achievable rate of the ZF precoding is bounded by above. The finite achievable rate ceiling is mainly determined by the normalized MSE of the estimated SLPS.

2.5 Comparison with PAC-based Precoding

In this section, we analyze the achievable rates performance of the MRT and the ZF precoders in multi-cell mmWave systems via pilot-aided estimated CSI. The adopted CSI for the design of these precoders is under the impact of pilot contamination, which is caused by the reuse of orthogonal pilot symbols among different cells. The analytical results obtained in this section will be used as a performance reference in the subsequent sections. In particular, our analysis quantifies the connection between rate performance and the MSE of channel estimation.

2.5.1 PAC-MRT and PAC-ZF Precoding under Pilot Contamination

Here we study the performance of the MRT precoding based on pilot-aided CSI in the presence of pilot contamination in mmWave channels. The pilot contamination leads to two types of interference in the considered system: intra-cell interference and inter-cell interference [28, 53]. For the uplink channel estimation, we denote the received pilot sequences at the BS in the desired cell as

(2.0)

where stands for the reused orthogonal pilot sequences matrix and is the cross-cell path loss attenuation coefficient. In Equation (2.0), is the channel matrix from the users in the -th neighboring cell to the BS in the desired cell. According to the field test, the probability of existing LOS component decreases significantly with increasing propagation distance [29]. In this case, we model the entries of cross-cell channels as i.i.d. random variable .

Conventionally, the MMSE channel estimation, which requires the prior channel information, can achieve a better channel estimation performance than LS channel estimation. However, the prior information of mmWave channels, e.g. the Rician K-factor, is hard to obtain. Therefore, we adopt the LS algorithm for channel estimation instead of the MMSE algorithm, the estimated channel can be expressed as