Downlink Transmission and Caching Strategies for Backhaul-Limited Cloud Radio Access Networks. Binbin Dai

Transcription

1 Downlink Transmission and Caching Strategies for Backhaul-Limited Cloud Radio Access Networks by Binbin Dai A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Graduate Department of Electrical and Computer Engineering University of Toronto c Copyright 2018 by Binbin Dai

2 Abstract Downlink Transmission and Caching Strategies for Backhaul-Limited Cloud Radio Access Networks Binbin Dai Doctor of Philosophy Graduate Department of Electrical and Computer Engineering University of Toronto 2018 This thesis considers a downlink cloud radio access network (C-RAN) where all the base stations (BSs) are connected to a central processor (CP) via capacity-limited backhaul links. Two fundamental and different downlink transmission strategies are studied, namely the data-sharing strategy and the compression strategy. In the data-sharing strategy, the backhaul links connecting the CP and the BSs are used to carry user messages; each user s messages are sent to a cluster of BSs, called BS clustering, which locally form the beamforming vectors to cooperatively transmit the messages to the user. In the compression strategy, the user s messages are precoded centrally at the CP, which forwards a compressed version of the analog beamformed signals to the BSs for cooperative transmission. The first part of this thesis focuses on optimizing the data-sharing strategy and the BS clustering while explicitly accounting for the per-bs backhaul capacity limits in each time slot. We show that with the proposed static BS clustering algorithms, the data-sharing strategy can achieve most of the gain brought by the dynamic BS clustering. The second part of this thesis compares the performance of data-sharing and compression strategies from two different perspectives, maximizing the energy efficiency and maximizing the spectral efficiency of the network. From numerical simulations, we observe that although both data-sharing and compression strategies outperform traditional cellular downlink transmission strategies, their comparative performance highly depends on the backhaul capacity. In the final part of this thesis, we study a promising approach to improve the performance of the data-sharing strategy for C-RAN by augmenting the backhaul with BS caching, where the BSs pre-store contents of popular files. We consider a downlink C-RAN consisting of a single cluster of BSs and wireless backhaul channel, and study the optimal cache size allocation strategy among the BSs and the optimal beamforming transmission strategy at the CP such that the users requested messages are delivered from the CP to the BSs in the most efficient way. We show that more cache sizes should be allocated to BSs with weaker channels and that it is in general not optimal to entirely cache the most popular files first. Numerical results show considerable performance improvement of the optimized cache allocation scheme over the uniform allocation and other heuristic schemes. ii

3 To my family iii

4 Acknowledgements This thesis would not have been possible without the tremendous support I received from many people during the past seven years in University of Toronto. First and foremost, I thank my research supervisor, who is also a mentor of my life, Prof. Wei Yu, for his guidance, patience, and devotion on me throughout my graduate studies. It is still fresh in mind when I met Prof. Wei Yu during the InfoComm conference in 2011 in Shanghai, China, for the interview of my graduate school application. I was impressed by his unique perspective and deep understanding of communication networks just from the interview questions. It is my great privilege to have the opportunity to work with him. I have learnt a great deal from the interactions with him. His remarkable intuition and insight have often led me to consider the problems from different perspectives. I want to thank him for sending me to Qualcomm, San Diego, for an internship in the summer of 2013, which was my first industry experience, and also for agreeing me to take about one year off in 2017 to try different things and think about my future career. I greatly appreciate his advice offered on every stage of my research and understandings for every decision that I made. I thank my thesis defense committee members, Prof. Ravi Adve, Prof. Ben Liang, Prof. Stark Draper from University of Toronto, Prof. Vicent Wong from University of British Columbia for taking time to read my thesis and providing valuable comments, and Prof. Jacob Tsimerman and Prof. J. Stewart Aitchison for chairing my defenses. Part of this thesis is inspired from the discussions with some of my colleagues. I would like to thank Dr. Gokul Sridharan for his generosity of spending a lot of hours discussing my problems as well as offering me advice on choosing research topics and career path. Part of Chapter 2 in this thesis was inspired by our discussions in Globecom Part of Chapter 3 of this thesis was collaborated with Pratik Patil. I want to thank him for the joyful discussions on only not the research problems but also various interesting math puzzles. I benefit a great deal from the countless discussions with Prof. Yafeng Liu from the Chinese Academy of Sciences, whose solid and thorough knowledge on optimization theory have greatly improved the quality of our joint work presented in Chapter 4 of this thesis. My life in Toronto has been filled with many unforgettable moments with my dear friends. In particular, I thank Dr. Yuhan Zhou, Dr. Yicheng Lin, Dr. Lei Zhou, and Dr. Wei Bao for their kind help to both my research and personal life during the first a few years of my graduate studies. I thank Dr. Siyu Liu for his endless efforts to drag me out of the office to enjoy varieties of other indoor and outdoor activities. Many thanks to my dear friend Soroush Tabatabaei, who is always willing to help whenever I iv

5 am in need. I thank my friends in Communications Group, Zhilin Chen, Kaiming Shen, Arvin Ayoughi, Kaveh Mahdaviani, Louis Tan, Caiyi Zhu, Weiwei Li, etc., for all the joys we had together. To my mother and brother, for their unconditional love and support. To them I dedicate this thesis. Last but not least, I express my heartfelt gratitude to my wife, Dan Fang, for every minute that we spent together filling up our lives with wonderful memories. It is my great fortune to have her company and support for all these years. I am looking forward to every stage of our journey in the future after completing this milestone of my life. v

6 Contents 1 Introduction Backhaul-Limited Downlink C-RAN Data-Sharing Strategy Compression Strategy Thesis Overview Network Utility Maximization for Data-Sharing Strategy Performance Comparison of Data-Sharing and Compression Strategies Improving Backhaul Efficiency via BS Caching and Multicasting Publications Related to this Thesis Notations Network Utility Maximization for Data-Sharing Strategy Introduction Related Work Main Contributions Network Utility Maximization with Fixed BS Clustering System Model and Problem Formulation WMMSE Based Algorithm BCD Based Algorithm User Scheduling Further Improvement via Power Minimization Static Clustering Algorithms Maximum Loading Based Static Clustering Biased Signal Strength Based Static Clustering Simulation Results vi

7 2.4.1 Static Clustering versus Dynamic Clustering Algorithm 2.1 versus Algorithm Conclusion Performance Comparison of Data-Sharing and Compression Strategies Introduction Related Work Main Contributions System Model Energy Efficiency Comparison Power Consumption Model Energy Efficiency Maximization Energy Efficiency Maximization for Data-Sharing Strategy Energy Efficiency Maximization for Compression Strategy Numerical Evaluation of Energy Efficiency Spectral Efficiency Comparison Conclusion Improving Backhaul Efficiency via BS Caching and Multicasting Introduction Related Work Main Contributions System Model Broadcast Channel with Receiver Caching Separate Cache-Channel Coding Joint Cache-Channel Coding Two-Stage Caching and Beamforming Design Cache Allocation Optimization Across the BSs Minimizing Expected Downloading Time Maximizing Expected Downloading Rate Cache Allocation Optimization Across the Files Simulation Results Cache Allocation for BSs with Varying Channel Strengths Cache Allocation for Files of Varying Popularity vii

8 4.8 Conclusion Conclusion Future Work Appendices 90 A MIMO and Beamforming 90 B Proof for Theorem C Proof for Theorem D Alternating Direction Method of Multipliers (ADMM) 97 E The ADMM Approach to Solve Problem (4.17) 99 F The ADMM Approach to Solve Problem (4.25) 102 Bibliography 103 viii

9 List of Tables 2.1 Simulation Parameters for Data-Sharing Strategy with Static Clustering Simulation Parameters for Comparing Data-Sharing and Compression Strategies Simulation Parameters for Cache Allocation File Downloading Time (ms/mb) Comparison File Downloading Rate (bps/hz) Comparison Optimized Cache Allocation for a 2-File Case with Different File Popularities under C = ix

10 List of Figures 1.1 Downlink C-RAN system model. The CP is assumed to have access to the user messages s 1,s 2 requested by the users 1 and 2 respectively Downlink C-RAN with data-sharing transmission strategy. In this illustrative example, the CP transmits user 1 s message s 1 to BSs 1 and 2, and user 2 s message s 2 to BSs 2 and 3. The BS cluster (1, 2) then cooperatively serves user 1 and the BS cluster (2, 3) cooperatively serves user 2 through joint beamforming Downlink C-RAN with compression transmission strategy. In this illustrative example, the CP centrally precodes both users messages s 1 and s 2 to ˆx l,l =1, 2, 3, and forwards the compressed precoded signals x l,l =1, 2, 3, to each of the BSs. Each BS transmits the compressed beamformed signal received from the CP to both users Thesis overview Downlink C-RAN with limited per-bs backhaul capacity, in which each user is cooperatively served by a fixed subset of BSs Block diagram of the optimization framework which further improves the solutions obtained from Algorithms 2.1 and cell wrapped around two-tier heterogeneous network Cumulative distribution function of user data rate comparison with backhaul constraint (C macro,c pico ) = (690, 107) Mbps under proportionally fair scheduling Convergence behavior of Algorithm 2.2 under round-robin user scheduling and α k =1, k CDF of user data rates comparison between WMMSE based Algorithm 2.1 and BCD based Algorithm 2.2 with α k updated according to proportional fairness criterion A cellular topology with 7 cells and 4 RRHs each cell, where each dot represents a RRH Trajectories of number of active BSs under r k = 20 Mbps target rate for each user Convergence behavior of proposed algorithms under r k = 20 Mbps target rate for each user. 56 x

11 3.4 Total power consumption comparison between different schemes. Missing points indicate that the corresponding scheme is infeasible. For instance, Single BS Association is feasible only for the first three points in (a), and is only feasible for the very first point in (b), and is infeasible in (c). For Per-Cell CoMP scheme in (c), it is only feasible at 10 Mbps target rate Power consumptions of BSs and backhaul links with 2 users each cell Comparison of average fraction of active BSs. Note that the Per-Cell CoMP scheme considered in Fig. 3.4 corresponds to 100% of active BSs, while the percentage of active BSs for Single BS Association scheme depends on the number of users in each cell, which are 25%, 50% and 75% respectively for 1, 2 and 3 users per cell, although only those few points corresponding to Fig. 3.4 are feasible Cumulative distribution of user rates for the data-sharing and compression strategies Downlink C-RAN with BS caching, where each BS is equipped with a local storage unit that caches some contents of user s requested files A downlink C-RAN setup with 5 BSs. The distances from the CP to the 5 BSs are (398, 278, 473, 286, 267) meters, respectively Cache allocation for different schemes under normalized total cache size C = CDF of downloading time under different caching schemes CDF of downloading rates under different caching schemes Average downloading time for different Zipf file distributions under the same number of files K = 4 and the total normalized cache size C = xi

12 Chapter 1 Introduction The fifth-generation (5G) wireless system is expected to support an ever-increasing number of mobile devices with ubiquitous service access, leading to a growing demand for high system capacity. From the physical-layer point of view, wireless system capacity can be roughly summarized as the following expression: C = NW log (1 + SNR) (1.1) where C in bits/second (bps) denotes the system capacity, N is the number of spatial degrees of freedom representing the number of simultaneously supported interference-free transmission links, W in Hertz (Hz) is the system bandwidth, and SNR is the signal-to-noise ratio at the receiver side. Several key technologies have been proposed to meet the 5G vision and can be deduced from the above expression. For example, using millimeter wave (mmwave) frequencies for future wireless communication [1 3] can provide significantly additional spectrum W for data transmission. The mmwave technology also makes it possible to deploy massive number of antenna arrays at the base station (BS) [4 6] to increase the spatial degrees of freedom N. The small cell technology [7,8] brings the serving BS closer to the users so that the received SNR can be enhanced at the users. However, as the neighboring BSs are also located closer in distance, the users are exposed to more inter-cell interference, which limits the performance of the cellular network. Cloud radio access network (C-RAN) is an emerging network architecture that is capable of dealing with this inter-cell interference issue. C-RAN refers to a new wireless network architecture in which most of the network functionalities of traditional BSs, except for radio frequency operations and analog-digital conversions, are migrated to a central processor (CP). This concept was first proposed in [9] and described in detail in [10], and has the potential to significantly reduce the CAPital EXpenditure (CAPEX) and OPerating EXpenditure 1

13 Chapter 1. Introduction 2 Central Processor s 1,s 2 BS 1 BS 2 BS 3 User 1 User 2 Figure 1.1: Downlink C-RAN system model. The CP is assumed to have access to the user messages s 1,s 2 requested by the users 1 and 2 respectively. (OPEX) in wireless networks. In C-RAN, all the BSs are connected to the CP via backhaul links. The CP jointly processes the user messages and forwards them to the BSs, which in turn form the radio frequency signals to be transmitted to the users. The benefits of the C-RAN architecture are that it can better manage inter-cell interference, better balance traffic load, enhance energy efficiency, and improve the overall network throughput [11]. The C-RAN architecture can also be thought of as a platform for the practical implementation of network multiple-input multiple-output (MIMO) and coordinated multi-point (CoMP) transmission concepts [12]. 1.1 Backhaul-Limited Downlink C-RAN An illustration of the downlink C-RAN architecture is plotted in Fig. 1.1, in which all the BSs are connected to a central cloud. Throughout the thesis, we term the links between the CP and the BSs as backhaul, which is appropriate if the links are used to carry digital data. These links are sometimes referred to as fronthaul in the C-RAN literature, especially when they carry compressed signals. In C- RAN, all the user messages are first centrally processed in the cloud, then delivered to the BSs through the backhaul links. The BSs act as relays between the user terminals and the cloud. In this sense, the downlink C-RAN can be modeled as a broadcast-relay channel. If the backhaul links between the CP and the BSs have infinite capacities, the information theoretical capacity analysis for this setting is

14 Chapter 1. Introduction 3 straightforward, as the downlink C-RAN becomes a vector broadcast channel and the standard network information theoretic results apply [13]. However, the limitations on the practical implementation of the C-RAN architecture put constraints on the backhaul links to have finite capacities. In this more realistic case, both the theoretical analysis and the optimal practical system design become much more difficult. In [14], two important relaying strategies for the classical three-node relay channel are introduced: decode-and-forward and compress-and-forward. In the first strategy, the relay first decodes the message transmitted from the source, then re-encodes the message and transmits the encoded message to the end user. In the second strategy, the relay first compresses the signal received from the source, then directly forwards it to the end user. The optimality of decode-and-forward strategy and the compress-and-forward strategy is still an open question. This thesis studies two practical downlink transmission strategies for the setup in Fig. 1.1, which are analogous to the traditional decode-and-forward and compress-andforward relaying strategies. In the first strategy, the CP simply routes each scheduled user s intended message to a cluster of BSs over the backhaul links; the cluster of BSs then cooperatively serve that user through joint beamforming 1. Note that in order to make sure each BS successfully receives the clean messages from the cloud, the sum rate of the user messages delivered from the cloud to each BS has to be within the capacity limit of the backhaul link. This strategy is termed as data-sharing strategy and is analogous to the decode-and-forward relaying strategy. In the alternative strategy, the joint precoding of user messages is done at the CP and the precoded analog signals are compressed and forwarded to the corresponding BSs over the finite-capacity fronthaul/backhaul links for direct transmission by the BS antennas. This strategy is called compression strategy and is akin to the compress-and-forward relaying strategy. Note that in both the considered data-sharing and compression strategies, we restrict the encoding function of the user messages to be linear. Although this may not be the best option to achieve the system capacity, it is low-complexity and easy to implement in practice. Details of the data-sharing and compression strategies are described in the next two subsections. A general coding strategy for the broadcast-relay network is proposed in [17] based on a combination of Marton coding for the general broadcast channel [18] and a coding scheme for deterministic linear relay networks [19]. However, unlike in the uplink of the C-RAN, which is an instance of a multiple-access-relay channel, where compress-and-forward strategies such as quantize-map-forward scheme of [19] or more generally noisy network coding [20] are known to be approximately optimal (in the sense of constant gap to the cutset outer bound), there are no approximation results known on the capacity region for the downlink C-RAN setup. The main difficulty lies in the need for careful coordination among the 1 Beamforming is a low-complexity linear precoding technique done at the transmitter to cancel the inter-user interference at the receivers [15, 16]. A short tutorial on MIMO and beamforming is provided in Appendix A.

15 Chapter 1. Introduction 4 codewords for multiple user messages at the CP. In the uplink, there is no such need as the CP decodes all the compressed signals and the original user messages jointly. In the downlink, the CP can induce coordination among different codewords and the BSs potentially need to decode carefully chosen parts of the messages. Recently a new coding scheme that combines Marton coding for single-hop broadcast channels [18] and partial decode-forward for relay channels [14], called distributed decode-forward (DDF), is proposed for broadcasting multiple messages over a general relay network in [21]. However, the DDF scheme involves auxiliary random variables that are difficult to set when specialized to the downlink C-RAN setup. 1.2 Data-Sharing Strategy This thesis focuses on the practical system designs for the downlink C-RAN with finite-capacity backhaul links. Ideally, the backhaul links connecting the BSs to the cloud are implemented using high-capacity fibers. However, larger the centralization scale, more fibers are needed, which is unaffordable to most operators due to the high cost of fibers [22]. Several alternative schemes have been proposed such as various compression techniques, wavelength division multiplexing, optical transport networks, microwave backhaul and so on [10, 22, 23]. One way to utilize the capacity-limited backhaul links in C-RAN is to share each scheduled user s intended message from the cloud to a carefully selected set of BSs, called a BS cluster, as illustrated in Fig The BS cluster is individually selected for each user and may be overlapping among different users. For the illustrative example in Fig. 1.2, user 1 s intended message s 1 is delivered to BSs 1 and 2, which form the BS cluster to cooperatively serve user 1. Likewise, user 2 s intended message s 2 is shared to BSs 2 and 3, which form another BS cluster to jointly serve user 2. In this case, the backhaul capacity consumption for BS 1 (BS 3) is user 1 s (user 2 s) message rate R 1 (R 2 ), while the backhaul consumption for BS 2 is the sum rate of R 1 + R 2. As we can see, in data-sharing strategy, the capacity of the backhaul link limits the number of user messages that can be shared with the BS: larger backhaul capacity, the more user messages can be delivered to the BSs, leading to a larger size of BS cluster to cooperatively serve the user. After receiving the user message from the cloud, each BS in the BS cluster locally forms the beamformed signal to serve the user. It is worth noting that the beamforming coefficients, i.e. the w 11,w 21,w 22,w 32 in Fig. 1.2, are also computed in the CP and delivered to the BSs through the backhaul links, hence also occupy certain amount of backhaul capacity. However, comparing to the backhaul consumption due to data sharing, the backhaul capacity needed to deliver the beamforming coefficients is negligible and is ignored in this thesis. The system level design variables for the data-sharing strat-

16 Chapter 1. Introduction 5 Central Processor s 1,s 2 s1 R 1 s 1 R 1 + R 2 s 2 R 2 s 2 x 1 = w 11 s 1 x 2 = w 21 s 1 +w 22 s 2 x 3 = w 32 s 2 BS 1 BS 2 BS 3 User 1 User 2 Figure 1.2: Downlink C-RAN with data-sharing transmission strategy. In this illustrative example, the CP transmits user 1 s message s 1 to BSs 1 and 2, and user 2 s message s 2 to BSs 2 and 3. The BS cluster (1, 2) then cooperatively serves user 1 and the BS cluster (2, 3) cooperatively serves user 2 through joint beamforming. Central Processor ˆx l = w l1 s 1 + w l2 s 2 l =1, 2, 3 x 1 x 2 x 3 x 1 =ˆx 1 + e 1 x 2 =ˆx 2 + e 2 x 3 =ˆx 3 + e 3 BS 1 BS 2 BS 3 User 1 User 2 Figure 1.3: Downlink C-RAN with compression transmission strategy. In this illustrative example, the CP centrally precodes both users messages s 1 and s 2 to ˆx l,l =1, 2, 3, and forwards the compressed precoded signals x l,l =1, 2, 3, to each of the BSs. Each BS transmits the compressed beamformed signal received from the CP to both users. egy include BS clustering, beamforming coefficients, and user scheduling, which jointly determine the backhaul capacity consumption for the downlink C-RAN. This thesis provides several different design perspectives for these three variables under different performance metrics.

17 Chapter 1. Introduction Compression Strategy Another dominant downlink transmission strategy in backhaul-limited C-RAN is called the compression strategy, which is illustrated in Fig In compression strategy, all the scheduled users messages are first centrally precoded in the CP, then compressed and delivered to the BSs. For the illustrative example in Fig. 1.3, both of the user messages s 1 and s 2 arefirstprecodedinthecpasˆx l = w l1 s 1 + w l2 s 2,l= 1, 2, 3, where ˆx l denotes the precoded signal needed for BS l to do interference cancellation among the users. However, since the beamforming coefficients w l1 and w l2 are in general complex numbers, the precoded signal ˆx l is analog in nature, hence needs to be compressed and quantized into finite bits in order to fit in the capacity-limited backhaul links. The compressed version of the precoded signals are denoted as x l, l =1, 2, 3, in Fig. 1.3, which are related to ˆx l as x l = ˆx l + e l with e l being the quantization noise. As we can see, in the compression strategy, the backhaul capacity determines the fidelity of the compressed signals: higher backhaul capacity, the less quantization noises are introduced in the compressed signals. After receiving the compressed version of the beamformed signals from the cloud, the BSs simply do an up-conversion to the radio frequency and transmit to the end users. The system level design variables for the compression strategy are quantization noise level, beamforming coefficients, and user scheduling, where the main difficulty is to determine the quantization noise level. Generally speaking, the optimal quantization noises are correlated among the antennas since the signals to be compressed are also correlated. However, this will introduce significant complexity in the system design and also may not be easy to implement in practice [24]. In this thesis, we assume independent quantization noise structure across the antennas and jointly design the quantization noise level, beamforming, and user scheduling under different performance metrics. With both data-sharing and compression strategies being introduced so far, a common question is which one performs better in backhaul-limited downlink C-RAN? This thesis aims to answer this question from an optimization perspective. It is worth noting that the data-sharing and compression strategies described above are not the only possibilities for the downlink of C-RAN. There is a potential to combine these two strategies by sending directly the messages of only the strong users to the BSs and compressing the rest [25]. Also, reverse compute-and-forward strategy that accounts for the lattice nature of the transmitted message is also possible [26]. However, such strategy is difficult to optimize because of the need in choosing the right integer zero-forcing precoding coefficients at the CP so that the effective noise, caused by the non-integer penalty due to practical channels, at each user is minimized.

18 Chapter 1. Introduction 7 Figure 1.4: Thesis overview. 1.4 Thesis Overview This thesis focuses on the practical system designs for the downlink C-RAN and specifically investigates the effect of backhaul capacity limits on the performance of the data-sharing and compression strategies. As an extension to my Master s thesis [27], Chapter 2 of this thesis considers the design of the datasharing strategy under static BS clustering, as opposed to the dynamic BS clustering considered in [27]. The design of the compression strategy is considered in Chapter 3, where two different performance metrics are considered, i.e. maximizing the energy efficiency and maximizing the spectral efficiency. We also compare the performance between the optimized compression and data-sharing strategies in Chapter 3 through numerical simulations. One of the conclusions drawn from Chapter 3 is that although both the data-sharing and compression strategies in C-RAN outperform the conventional transmission strategies in cellular network, the data-sharing strategy typically consumes more backhaul capacity than the compression strategy. To reduce the backhaul demand for the data-sharing strategy, in Chapter 4, we investigate the potential of caching popular contents at the BSs and multicasting to improve the efficiency of the backhaul communication in C-RAN. An overview of the three chapters in this thesis is summarized in Fig In the following, we elaborate further on the three chapters and highlight some of the important contributions Network Utility Maximization for Data-Sharing Strategy The first part of this thesis studies the design of the data-sharing strategy from the network utility maximization perspective. Differing from the previous works [28 33], we explicitly formulate the per- BS backhaul capacity constraints in the optimization problem. As is revealed earlier, there are three factors determining the backhaul capacity consumption for data-sharing strategy, i.e. BS clustering, user scheduling and beamforming. In my Master s thesis [27], a joint design of these three variables is considered, where the BS cluster dynamically changes in each time-frequency slot depending on the other two variables. Dynamic clustering may introduce significant signal overhead as the user-bs association

19 Chapter 1. Introduction 8 needs to be continuously updated. In Chapter 2, we consider static clustering and propose a two-stage optimization framework. In the first stage, the BS cluster is designed on a large time scale, which only needs to be updated when user location is changed substantially. In the second stage, the BS cluster is assumed to be fixed, and only user scheduling and beamforming are designed on a small time scale to account for the backhaul limits. The network utility maximization problem for data-sharing strategy under fixed BS clustering is nonconvex and difficult to achieve the global optimality. We first realize that the reweighted l 1 -norm technique adopted in [27] for designing the dynamic clustering can also be adapted to solve the network utility maximization problem with fixed BS clustering. However, such algorithm has no theoretical convergence guarantee even though it is observed to converge numerically. We then propose a second algorithm which introduces two additional variables to the original problem and solves the transformed problem using the block coordinate descent (BCD) method [34]. The BCD based algorithm has guaranteed convergence behavior. To solve the high computational complexity issue in the BCD-based algorithm, we propose to reduce the user scheduling pool through the weighted minimum mean square error (WMMSE) approach [35,36]. Numerical results show that the BCD-based algorithm with improved user pool slightly outperforms the reweighted l 1 -norm-based algorithm with comparable complexity. In Chapter 2, we also propose two heuristic BS clustering algorithms that only depend on the relative distance between the BSs and the users and do not change as the user scheduling and beamforming. The key aspect in designing BS clustering is to balance between the BS loading (number of users associated with the BS) and the received signal strength at the user. The first proposed BS clustering algorithm tries to achieve such balance by setting a limit on the maximum number of associated users at each BS side and a candidate serving BS cluster at each user side. The second proposed algorithm is based on the biased signal strength method originated from [37], where we extend the idea to the case where each user can be associated with multiple BSs. Comparing to the dynamic clustering algorithm, both of the proposed heuristic static clustering algorithms can achieve the majority of the performance gain brought by the dynamic clustering algorithm proposed in [38] Performance Comparison of Data-Sharing and Compression Strategies The second part of this thesis focuses on comparing the optimized performance of the data-sharing strategy and the compression strategy. We first compare the energy efficiency of these two downlink transmission strategies in C-RAN. The energy saving benefits of C-RAN come from several aspects. The first-order energy saving aspect of C-RAN is due to the fact of most of the functionalities of traditional

20 Chapter 1. Introduction 9 BSs are now migrated to the CP so that the conventional high-power high-cost BSs can be replaced by low-power low-cost remote radio heads (RRHs). From the signal processing perspective, C-RAN is energy efficient because it can better manage inter-cell interference. With less interference generated, less transmission power is needed to achieve quality of service for the users. Moreover, C-RAN can do centralized resource allocation to achieve high utilization of BS resources and put those idle BSs into low-power sleep mode for energy saving purpose. However, all the above-mentioned benefits of C-RAN in energy saving come at the cost of additional backhaul links required to connect the BSs with the CP. A full characterization of the energy saving perspective for C-RAN needs to take into account the additional power consumption due to backhaul communications. In Chapter 3, we first derive a network power consumption model for the downlink C-RAN, which includes power consumption due to both the BSs and the backhaul links. The BS power consumption model considers two different modes: an active mode that models the power consumption as a linear function of the BS transmit power plus a fixed activation power, and a sleep mode that models the power consumption as a fixed constant that is less than the activation power. The backhaul link power consumption is modeled as a linear function of the backhaul rate. Based on this network power consumption model, we formulate the energy efficiency maximization problem for downlink C-RAN equivalently as minimizing the total network power consumption subject to given user rates constraints for the data-sharing strategy and the compression strategy, respectively. Both problems are nonconvex and we use the reweighted l 1 -norm approximation method and the successive convex approximation technique to find the local optimal solutions. Note that in order to get a fair comparison, we fix the user scheduling and the target rates for the scheduled users in the power minimization problems considered in this chapter, and investigate the amount of total power required for the data-sharing and compression strategies respectively in order to achieve the same target rates for the scheduled users. We compare the optimized energy efficiency of the data-sharing and the compression strategies through numerical simulations. It is found that as the user target rates increase, the power consumption due to backhaul communications dominates over the BS power consumption, and that the backhaul power consumption for data-sharing strategy increases faster than that for compression strategy, which makes compression strategy superior to data-sharing strategy at high user rate regimes. The data-sharing and compressions strategies are also compared in terms of spectral efficiency in Chapter 3. We first formulate the spectral efficiency maximization problems for both strategies as of maximizing the network utility function of user rates subject to per-bs power and per-bs backhaul constraints. For the considered utility maximization problems, we fix the transmission power budget and the backhaul capacity limit at each BS, and compare the optimized network utilities between the

21 Chapter 1. Introduction 10 data-sharing and compression strategies by optimizing over the user scheduling and beamformers. We then use the WMMSE approach to solve both problems and conduct system level simulation to evaluate the spectral efficiency of both strategies. It is observed that the comparative performance of datasharing and compression strategies share the same flavor as in the energy efficiency comparison: when the backhaul capacity is low, data-sharing outperforms compression; when the backhaul capacity is moderately high, compression strategy is superior to data-sharing strategy Improving Backhaul Efficiency via BS Caching and Multicasting From Chapter 3, we see that the performance of downlink C-RAN largely depends on the capacity limits of the backhaul links and that in most cases the data-sharing strategy requires more backhaul capacity in order to match the performance of the compression strategy. In Chapter 4, we study the potential of BS caching and multicasting to improve the efficiency of backhaul communication in data-sharing strategy. The idea of BS caching and multicasting comes from several aspects. First, as the storage unit becomes cheaper and cheaper, it is relatively much easier to deploy low-cost hard drives into BSs than to add more backhaul links to BSs. Second, as video traffic becomes the majority of the data traffic in future wireless network and a small number of videos may have high popularities, it is promising to reduce the peak-time traffic by pre-storing some of the popular files during off-peak traffic time. Third, when the backhaul links are implemented using wireless technology (e.g. mmwave), there is an opportunity for multicasting if the same file is needed at multiple BSs, which is much helpful for data-sharing strategy in C-RAN because each user s message needs to be delivered to a cluster of BSs for cooperative beamforming. Note that BS caching might not be so useful for compression strategy because in compression strategy the signals to be sent over the backhaul network are compressed version of analog beamformed signals, which change dynamically according to the channel conditions, hence can not be cached beforehand. In Chapter 4, we consider a downlink C-RAN model with single BS cluster for data-sharing strategy, where all the BSs are connected to the CP through wireless backhaul links, and focus on optimizing the efficiency of the wireless backhaul communication from the cloud to the BSs. Specifically, we study the optimal cache size allocation among the BSs subject to the total cache size constraint, and the optimal transmission strategy at the cloud subject to transmission power constraint, such that the users requested messages are delivered from the CP to the BSs in the most efficient way. We show that in general it is not optimal to allocate the cache sizes uniformly among the BSs and not optimal to entirely cache the most popular file first. Instead, the optimal cache size allocation should take into account

22 Chapter 1. Introduction 11 the disparities of the channel strength from the cloud to the BSs and distribute more cache sizes to the weaker BSs. Also, the optimal caching strategy among the files depends on the file popularity and requires to solve an optimization problem. We formulate a two-stage optimization framework for the wireless backhaul optimization. In the first stage, BS cache size allocation is optimized assuming only long-term channel statistical information by minimizing the expected file downloading time or maximizing the expected file downloading rate as the objective function. In the second stage, the multicasting beamforming at the cloud is optimized assuming fixed caching at the BSs and instantaneous channel information. The cache size allocation problem in the first stage is solved by leveraging sample approximation method as well as the alternating direction method of multipliers (ADMM) 2 approach [39]. The multicast transmit beamforming problem in the second stage is solved by semidefinite relaxation method. Numerical results show that the optimized caching strategy outperforms naive caching strategies. 1.5 Publications Related to this Thesis The results in Chapter 2 are published in [40] and [41]. Chapter 3 is composed of the published works [42] and [43]. Part of the results in Chapter 4 are to be presented in [44] and the full version has been submitted for possible publication [45]. 1.6 Notations Throughout this thesis, lower-case letters (e.g. x) denote scalars, lower-case bold letters (e.g. w) denote vectors, and upper-case bold letters (e.g. H) denote matrices. We use R and C to denote real and complex domain, respectively. The matrix inverse, conjugate transpose and l p -norm of a vector are denoted as ( ) 1, ( ) H and p respectively. The complex Gaussian distribution is represented by CN(, ) while Re{ } stands for the real part of a scalar. The expectation of a random variable is denoted as E [ ]. Calligraphy letters are used to denote sets while stands for either the size of a set or the absolute value of a real scalar, depending on the context. 2 A brief introduction to ADMM algorithm is provided in Appendix D.

23 Chapter 2 Network Utility Maximization for Data-Sharing Strategy 2.1 Introduction This chapter studies the optimization of the data-sharing strategy for C-RAN focusing on the effect of finite-capacity backhaul links on the overall network capacity. The performance of the data-sharing strategy depends crucially on the choice of BS cooperation cluster for each user: the larger cluster size provides the higher cooperation gain, but also leads to higher backhaul consumption. Broadly speaking, there are two types of BS clustering schemes: disjoint clustering and user-centric clustering. In disjoint clustering scheme, the entire network is divided into non-overlapping clusters and the BSs in each cluster jointly serve all the users within the coverage area [46]. Although disjoint clustering scheme has already been shown to be effective in mitigating the inter-cell interference [47, 48], users at the cluster edge still suffer from considerable inter-cluster interference. Differently, in user-centric clustering, each user is served by an individually selected subset of neighboring BSs and different clusters for different users may overlap. The benefit of user-centric clustering is that there exists no explicit cluster edge. Furthermore, there are two different implementations of user-centric clustering depending on whether BS clustering is dynamic or static over the different user scheduling time slots. In dynamic clustering, the BS cluster for each user can change over time, allowing for more freedom to fully utilize the backhaul resources. However, dynamic clustering scheme also requires more signaling overhead as new BS-user associations need to be established continuously. In static clustering, the BS-user association is fixed over time and may only need to be updated as the user location changes substantially. 12

24 Chapter 2. Network Utility Maximization for Data-Sharing Strategy 13 The first part of this chapter focuses on optimizing the data-sharing strategy under fixed usercentric BS clustering. We study the optimization of beamforming strategy and user scheduling policy to control the instantaneous backhaul consumption while maximize the network utility at the same time. Two algorithms are proposed: the first one adapts the reweighted l 1 -norm technique and the WMMSE approach used in [38] for designing dynamic clustering to solve the considered network utility maximization problem with fixed clustering in this chapter; the second one relies on the BCD method to solve the problem. To resolve the high complexity issue in the BCD-based algorithm, we further propose to reduce the number of potential users to be considered in the BCD algorithm through the WMMSE approach. We also show that the performances of both proposed algorithms can be further improved by iterating with an additional power minimization step. The second part of this chapter focuses on the static user-centric BS cluster design, which only relies on the long term system information and does not change over time as opposed to the dynamic clustering. We propose two heuristic static clustering design algorithms, both of which can achieve a substantial portion of the performance gain brought by the dynamic clustering scheme [38] Related Work The information-theoretical capacity of the C-RAN model has been considered extensively in the literature. However, most of the theoretical analysis on C-RAN is restricted to simplified channel models [49 52]. Specifically, the achievable rate regions derived in [51, 52] are based on a two-bs-two-user channel model, while [49] and [50] consider Wyner-like channel models and report the achievable rates and capacity bounds, respectively. In [53,54], large-system analysis of network MIMO system is carried out. Although based on simplified models, these previous information-theoretical results already reveal the benefits of C-RAN in significantly improving the system performance. This thesis focuses on the system design for the downlink C-RAN, which has been considered in the literature under various performance metrics. For instance, under the signal-to-interference-and-noise ratio (SINR) constraints at the receivers, [55] considers backhaul minimization while [56, 57] consider network power minimization as the objective. Furthermore, the optimal tradeoff between the backhaul capacity and transmit power is investigated in [58 60], while several other performance measures like mean square error (MSE) and energy efficiency (bits/joule delivered to the users) are considered in [61,62] and [63, 64], respectively. In this chapter, we consider the network utility as the performance measure for the downlink C-RAN data-sharing strategy. Differing from the network utility maximization problems in conventional wireless

25 Chapter 2. Network Utility Maximization for Data-Sharing Strategy 14 networks with only transmit power constraints, the additional backhaul constraints for the data-sharing strategy in C-RAN make the problem more challenging as the backhaul consumption at a particular BS is a function of not only the (continuous) user rates but also the (discrete) number of associated users. To tackle this mixed continuous and discrete optimization problem, existing literature mostly take the limited backhaul capacities into account implicitly either by fixing the BS clusters [28 30] or by adding the backhaul as a penalized term into the objective function [31 33]. Specifically, [28] considers sum rate maximization under fixed and disjoint clustering scheme while [29] and [30] maximize a more general utility function under user-centric but predetermined BS clusters. Dynamic user-centric clustering design is considered in [31] by penalizing the objective function with an l 2 -norm approximation of the cluster size. Alternatively, [32] and [33] choose the backhaul rate as the penalized term but solve the problem heuristically. For fixed clustering scheme assumed in [28 30], the backhaul consumption is only known afterwards by evaluating the rates of user messages delivered in each backhaul link. For dynamic clustering designs considered in [31 33], one has to optimally choose the price associated with each penalized term to ensure that the overall backhaul stays within the budget, which is not easy. In contrast to all the above existing works in network utility maximization for the downlink C- RAN, we explicitly formulate the per-bs backhaul constraints in the optimization framework. With explicit per-bs backhaul constraints, we have shown in [38] that the backhaul resources can be more efficiently utilized and that the network utility can be significantly improved. This chapter differs from our previous work [38] in that fixed clustering is considered, instead of dynamic clustering as in [38], and instantaneous backhaul capacity consumption is controlled through joint beamforming and user scheduling. Nevertheless, we show that the reweighted l 1 -norm technique proposed in [38] can still be applied to resolve the nonconvexity difficulty of the problem. After reweighted l 1 -norm approximation, the approximated problem can be solved through the WMMSE approach [36]. This is in contrast to [29], which uses the first-order Taylor expansion to approximate the nonconvex rate expression. Although the WMMSE approach has been applied to the C-RAN setup in the past [30,31], these previous works do not explicitly take the backhaul constraints into consideration. As related work, the WMMSE approach has also been adapted to solve the max-min fairness problem for MIMO interfering broadcast channel [65], a link flow rate control problem for the radio access network [66] and a power minimization problem under time-averaged user rate constraints for the CoMP architecture [67]. Recently, the WMMSE technique is generalized in [68] to a wider class of network setups using the successive convex approximation idea. Finally, we mention that the WMMSE is a numerical approach for solving for a stationary point to the weighted sum rate (WSR) maximization problem over the beamformers, which is known to be a challenging problem. Recent progress for finding globally optimal solution to the WSR maximization