Energy Efficient Resource Allocation for Phantom Cellular Networks. Thesis by Amr Mohamed Abdelaziz Abdelhady

Transcription

1 Energy Efficient Resource Allocation for Phantom Cellular Networks Thesis by Amr Mohamed Abdelaziz Abdelhady In Partial Fulfillment of the Requirements For the Degree of Master of Science King Abdullah University of Science and Technology, Thuwal, Kingdom of Saudi Arabia April 2016 Amr Mohamed Abdelaziz Abdelhady All Rights Reserved

2 2 The thesis of Amr Mohamed Abdelaziz Abdelhady is approved by the examination committee Committee Chairperson: Mohamed-Slim Alouini Committee Member: Basem Shihada Committee Member: Marc Genton

3 3 ABSTRACT Energy Efficient Resource Allocation for Phantom Cellular Networks Amr Mohamed Abdelaziz Abdelhady Multi-tier heterogeneous networks have become an essential constituent for next generation cellular networks. Meanwhile, energy efficiency (EE) has been considered a critical design criterion along with the traditional spectral efficiency (SE) metric. In this context, we study power and spectrum allocation for the recently proposed two-tier network architecture known as phantom cellular networks. The optimization framework includes both EE and SE. First, we consider sparsely deployed cells experiencing negligible interference and assume perfect channel state information (CSI). For this setting, we propose an algorithm that finds the SE and EE resource allocation strategies. Then, we compare the performance of both design strategies versus number of users, and phantom cells share of the total available resource units (RUs). We aim to investigate the effect of some system parameters to achieve improved SE performance at a non-significant loss in EE performance, or vice versa. It is found that increasing phantom cells share of RUs decreases the SE performance loss due to EE optimization when compared with the optimized SE performance. Second, we consider the densely deployed phantom cellular networks and model the EE optimization problem having into consideration the inevitable interference and imperfect channel estimation. To this end, we propose three resource allocation strategies aiming at

4 4 optimizing the EE performance metric of this network. Furthermore, we investigate the effect of changing some of the system parameters on the performance of the proposed strategies, such as phantom cells share of RUs, number of deployed phantom cells within a macro cell coverage, number of pilots and the maximum power available for transmission by the phantom cells BSs. It is found that increasing the number of pilots deteriorates the EE performance of the whole setup, while increasing maximum power available for phantom cells transmissions reduces the EE of the whole setup in a less severe way than increasing the number of pilots. It is found also that increasing phantom cells share increases the EE metric in the dense deployment case. Thus, it is always useful to allocate most of the network RUs to the phantom cells tier. Keywords: Energy efficiency, Spectral efficiency, Resource allocation, Phantom cells, Small-cell networks, Fractional programming, DC programming.

5 5 ACKNOWLEDGEMENTS Praise be to Allah through whose mercy (and favors) all good things are accomplished. Firstly, I would like to heartily thank my supervisor Prof. Mohamed-Slim Alouini for his encouragement and support throughout my Masters studies. I would like to express my greatest gratitude to Dr. Osama Amin who played a vital role in guiding me through this research and has always been a persistent source for technical support. Also, I want to express my gratitude to Dr. Anas Chaaban and Prof. Hayssam Dahrouj for the good work, we are currently working on. In addition, I would like to thank my professors who taught me the required courses for the masters degree, specially Prof. Ahmed Sultan who had been and will always be a source of inspiration and knowledge for his students, as well as my undergraduate professors, if it weren t for their efforts I wouldn t have reached this point. Furthermore, I want to thank all my colleagues at King Abdullah University of Science and Technology, whom I shared with the hard and the bright moments throughout my masters, and I wish them all the best of luck in all their future endeavors. I want also to thank the research computing team, and in particular Dr. Matthijs Van Waveren for his great support when I found difficulties with jobs submission to the cluster. Finally, I would like to thank my parents and my brother to whom I dedicate this work, I would like to really thank them for their continuous support and sacrifice.

6 6 TABLE OF CONTENTS Examination Committee Approval 2 Abstract 3 Acknowledgements 5 List of Figures 10 List of Tables 11 1 Introduction Background EE metrics and trade-offs EE and the cellular network hierarchy Resource allocation problem in cellular networks Literature review Outline of the thesis Notations System model 21 3 Sparsely deployed phantom cellular network EE resource allocation problem Simulation Results Conclusion Densely deployed phantom cellular networks with non-perfect CSIT Optimization Problem Formulation Power Allocation with Fixed Resource Units Assignment (PAFRUA) strategy Joint Power and Resource Units Allocation (JPRUA) strategy... 46

7 7 4.4 Joint Power and Resource Units Allocation assuming Fixed Average Interference (JPRUAFAI) strategy Simulation Results Conclusion Conclusion Future Research Work References 69 Appendices 73

8 8 LIST OF ABBREVIATIONS BS CNR CSI CSIT DAS DC EE KKT LTE MIMO MMSE OFDMA OFDM PSD RU RB SCA SE SINR UE Base Station Channel gain to Noise Ratio Channel State Information Channel State Information available at the Transmitter side Distributed Antenna System Difference of two Convex/Concave Energy efficiency Karush-Kuhn-Tucker Long Term Evolution Multiple Input Multiple Output Minimum Mean Square Error Orthogonal Frequency Division Multiple Access Orthogonal Frequency Division Multiplexing Positive Semidefinite Resource Unit Resource Block Successive Convex Approximation Spectral Efficiency Signal to Interference plus Noise Ratio User Equipment

9 9 LIST OF SYMBOLS h x y,z γ x y,z ˆγ x y,z β y,z C Ph σ 2 n α p α c α p,c G y,z κ M κ Ph P M,cr P Ph,cr P M P Ph σ 2 h x,u p pilot y s x y,z p x y,z Channel gain of the link between base station y, user z using RU x CNR of the link between base station y, user z using RU x Estimated CNR of the link between base station y, user z using RU x Channel estimation quality reciprocal of the link between base station y and user z The number of phantom cells within the macro cells coverage Thermal noise variance The fraction of time allocated for pilots transmission The fraction of time allocated for control signaling The fraction of time allocated for pilots and control signaling The shadowing - pathloss product of the link between base station y and user z Reciprocal of power amplifier efficiency of the macro cell Reciprocal of power amplifier efficiency of phantom cells The power used in signal processing and circuits operation at the macro cell The power used in signal processing and circuits operation at phantom cells Total power available for transmission by the macro cell Total power available for transmission by the phantom cell The variance of channel estimation error for the link between base station x and user u The power used for pilot transmission by cell y The RU allocation binary variable that controls whether RU x of cell y is assigned to user z or not The power by which BS of cell y communicates with user z using RU x

10 10 LIST OF FIGURES 1.1 EE and SE trade-off Phantom cellular network system model RU general structure Macro cell and phantom cell RU structure respectively from left to right EE and SE versus number of users per sector for N = EE and SE versus the ratio of phantom cells RUs to the total number of RUs, N = Densely deployed phantom cells within a macro cell η SE vs ηse lb Discrepancy between η SE and ηse lb Cells layout and users locations Energy efficiency vs number of active phantom cells Energy efficiency vs phantom cells maximum power Energy efficiency vs number of pilots used Energy efficiency vs number of pilots used

11 11 LIST OF TABLES 3.1 Simulation parameters Fixed parameters values Activated cells in the first simulation

12 To my parents Mohamed Abdelhady and Abeer Sleem, and my brother Waleed Abdelhady

13 13 Chapter 1 Introduction 1.1 Background Since its inception, cellular communication networks have passed through numerous stages of evolution in terms of number of subscribers, services provided, mobile equipment technology, and network architecture. This fast-going evolution has led to unprecedented growth of data traffic volumes within these networks [1, 2]. Consequently, the researchers efforts have been guided to maximize the overall network capacity. This objective has always been there to support the continuously growing required communication data rates, generated by the expanding number of users and services. Due to the scarcity of available spectrum, the spectral efficiency (SE) performance metric became the main concern of research in wireless cellular networks for a long time to get the maximum throughput using the available spectrum or achieving the same throughput using less amount of spectrum resources. Recently, it has been observed that the massive typical data traffic flow in the current cellular networks, which is expected to grow rapidly, causes a huge energy consumption which has the direct consequence of increasing the CO 2 footprint [3,4] due to the dependency of large number of base stations (BSs) on diesel operated generators as their power source, and the cellular networks operating expenditures. The previously mentioned consequences have shaded the light on the importance of introducing the energy efficiency

14 14 (EE) performance metric which measures the data throughput achievable using 1 Hz of bandwidth while spending 1 Joule of energy [5]. 1.2 EE metrics and trade-offs 1.5 Energy Efficiency vs Spectral Efficiency 3 ηee(bit/j/s/hz) ηse(bit/s/hz) P Figure 1.1: EE and SE trade-off EE of cellular networks can be measured through several metrics, and each metric provides different insights about the performance of the studied network. These definitions include: global EE metric which is used throughout this thesis, and is defined as the SE of the whole system divided by the total power required for transmission. Another definition is the weighted arithmetic mean of the EEs which is defined as the weighted sum of the EE of all the network links. Moreover, The weighted geometric mean of the EEs is defined as the weighted product of the EE of all the network links. The weighted minimum EE which is defined as the minimum EE of all the links [6,7]. These definitions vary in significance for describing the global system performance and the worst case performance so, some of them indicate EE fairness among all the

15 15 links whilst others measure the system performance from an EE perspective. It was observed that there are two fundamental trade-offs where EE performance is involved. For instance, it was found that increasing of EE metric of a given network comes at the cost of reduced SE and vice-versa, this can be observed from Fig. 1.1 in which the EE and SE of a single point to point link is considered where P is the transmitted power[8, 9]. It is clear that the global maximum of EE is different from that of the SE, so optimizing one of them will cause deterioration of the other if the maximum power available for transmission is greater than the global maximizer of the EE. Also another trade-off has been witnessed which involves EE and deployment efficiency where deployment efficiency is defined as a measure of throughput per unit of deployment cost as per [10]. Many initiatives and projects have been taken to cut down the cellular networks energy consumption such as Energy Aware Radio and network technologies project (EARTH), also many standardization organizations have shifted its attention towards energy efficient communications as mentioned in [11]. 1.3 EE and the cellular network hierarchy Currently EE is receiving a great attention in research activities and in the cellular communications industry [11]. These initiatives are approaching the intended EE performance improvements through exploiting the available degrees of freedom (design parameters) offered by the three hierarchical levels of cellular networks(component level, link level, and network level). Firstly, on the component level, it was found that the power amplifier efficiency has a great impact on the system EE as a whole. As such, there has been many efforts to improve power amplifier efficiency. Moreover, many strategies have been developed in order to manage the activity of the components as sometimes it is more efficient to deactivate subset of the components.

16 16 In addition, many BS architectures have been investigated and tuned to reach novel green BS architecture designs where the layout of components is optimized to minimize power losses. Moreover, using smart antennas/adaptive antennas has been considered for EE improvement purposes. On the network link level, two main allocation and resources scheduling schemes have been addressed in the literature; operational strategies as sleeping modes for BSs, and deployment strategies as heterogeneous networks deployment with multi-tier architectures, where density of the BSs of each tier can be tuned to maximize EE performance. 1.4 Resource allocation problem in cellular networks The resource allocation problem in cellular networks is of the same age of cellular communications. It has always received lots of attention in research studies from the early beginnings of cellular networks, and this kind of problems is still maintaining its potential till now. As cellular networks evolved, many versions of this problem with a multitude of objectives and degrees of freedom have been addressed. These versions include, but are not limited to, maximizing sum rate subject to maximum/total power constraints, or minimizing power consumption subject to quality of service constraints. The degrees of freedom being utilized to achieve these objectives included: power allocation, user-channel associations, user-cell associations, number of active relays, number of active antennas in a massive multiple input mutliple output (MIMO) system and antennas selection and associations. The proposed algorithms in this area of research varied significantly in their degree of optimality, complexity, efficiency and centralization. The tools used to tackle these problems, include but are not limited to, solving Karush-Kuhn-Tucker (KKT) systems, game theory, and graph theory, where graph theory provides powerful tools for optimization problems involv-

17 17 ing discrete optimization variables, game theoretic approaches are very appreciated when distributed optimization strategies are of interest, and solving KKT systems is very good when the non-linearity of the system is tractable and closed forms can be reached for the optimizing values, otherwise using numerical methods as gradient descent, Newton s method, interior point method becomes inevitable. 1.5 Literature review Different energy-aware strategies have been investigated to introduce ubiquitous high data rate services with minimal energy consumption [7, 12 17]. Coordinated multipoint transmission strategy involves the cooperation of the BSs to improve the EE by inter-cell interference coordination, which can be done via scheduling, beamforming and joint processing [12]. Relaying strategy is used to extend the coverage and improve the performance, where the same communication quality is obtained at a reduced energy cost, and thus EE can be enhanced for both uplink and downlink [7, 13]. Optimizing base BS density is important to enhance the EE and can be achieved through either deployment strategies or operational strategies. Deployment strategies include extremely dense multi-tier small cell networks and distributed antenna systems (DAS). On the other hand, operational strategies include BS sleeping modes [15], cell zooming strategies [16], and adaptive networks. For sleeping modes based strategies, some of the cells are switched off when they experience very low traffic demand. In cell zooming, the coverage of the BSs is controlled based on the traffic load status. Finally for adaptive networks, the transmitter adapts its codebook or its pilots density, and the power it spends on their transmission based on the channels to maximize EE. Energy efficiency aware design framework for heterogeneous networks has been considered in [17]. Also efforts towards green cellular networks extended to investigate

18 18 EE performance of device to device networks, MIMO based networks and even massive MIMO setups have been studied where the number of active antennas was tuned to optimize the EE performance. It was shown in [18] that using massive MIMO setups is the way to go if EE is our target. EE performance of fractional frequency reuse based architectures was investigated [19]. The efforts done to achieve energy efficient cellular communications even included network coding and cognitive radio setups. Phantom cellular network is a two-tier network architecture that was proposed recently in [20]. The covered geographical region is divided into a set of macro cells, which represent the first tier in the hierarchy, and within each macro cell a number of phantom cells are deployed representing the second tier in the network. Phantom cells operate on a different frequency band from the one used by the macro cells. The macro cells BSs are responsible for control signaling beside handling users data traffic. On the other hand, phantom cells are responsible for handling the data traffic of users under their coverage based on their hosting macro cell BS control signals, this organization is known as control plane (C-plane) - user plane (U-plane) splitting. Phantom cells don t declare their identities to users, and hence the nomenclature phantom. Connections between users and phantom cells are initiated by the supervising macro cell. Recently, phantom cellular networks have received a lot of attention from stochastic geometry perspective [21 23]. In [21], Mukherjee and Ishii derived expressions for the average spatial SE and the corresponding EE of the phantom cellular networks. In addition, they provided a comparison between the phantom cells and co-channel small cells, in which there is no separation between C-plane and U-plane where both tiers utilize the same spectrum band. In [22], Ibrahim et al. studied the gains acquired by deploying the phantom architecture in terms of coverage probability, average throughput per-user, and average rate. In [23], Chen et. al optimized the BSs density, number of antennas and spectrum to minimize the average spatial energy

19 19 consumption. To the best of our knowledge, the resource allocation problem of the phantom cellular networks has not been considered before in the literature. The resource allocation problem has been extensively investigated in the cellular communications literature for many systems due to its importance in many occasions. To name but a few, in [6], Venturino et al. considered an OFDMA system where a cluster of cells can cooperate together to optimize the power allocation and resources scheduling jointly. In their work, the authors provided algorithms to optimize three different EE figures of merit under subcarrier power constraints and total Bs power constraint. They have provided optimal solutions for the optimization problems in the asymptotic regime, where the system becomes noise limited. In [24], Kha has used difference of convex/concave (DC) programming to solve the power allocation problem in an interference-limited wireless network to maximize the weighted throughput and the minimum achievable rate. The DC optimization results in [24] were very promising in terms of convergence speed and closeness to optimal values. In [25], Tang et al. considered heterogeneous cellular network system with MISO setup where the beamforming vectors and power allocation are jointly considered to optimize the global EE of the system subject to real-time and real-time users rate constraints coming from the different services required by users. In [18], Hoydis et al. considered the uplink and downlink of a TDD cellular network and studied optimizing number of antennas to maximize EE.In [26], Qian et al. developed the MAPEL algorithm that achieves global power allocation solution for the sum rate maximization problem in an interference-limited wireless cellular network which serves as a performance benchmark for all other lower complexity algorithms developed to solve the same problem. In [27], Douik et al. modeled the joint resource allocation, user association and power allocation problem using graph theory to obtain optimal resource allocation algorithm that employs MAPEL algorithm internally. This algorithm can serve as a reference to compare lower complexity algorithms with.

20 Outline of the thesis In this thesis, we propose different resource allocation techniques for phantom cellular networks where power allocation and spectrum association parameters are tuned to maximize the EE. We show in the proposed algorithms that the SE optimization is done as a part of the EE optimization process. In chapter 2, we provide the mathematical framework of the considered phantom cellular network. In chapter 3, we focus on the sparse deployment scenario where the system becomes noise-limited, whilst assuming available perfect CSI at both transmitter and receiver sides. In chapter4, we provide three algorithms for maximizing the EE of the densely deployed phantom cellular system considering the interference effect with imperfect CSI. Finally, in chapter 5 we summarize the main findings of this work and suggest the plans for future work. 1.7 Notations This thesis is edited according to the following notations : E (x) denotes the expectation of the random variable x, we use boldfaced capital letters to refer to sets of variables and boldfaced small letters to indicate vectors. In addition, we use italic font to denote variables and roman font for constants and labels. Moreover, we use [.] + equivalently as max (., 0). Finally, we use x to denote the absolute value of x.

21 N Ph N Ph N Ph 21 Chapter 2 System model Backhaul Link Active Link 1 S 2,5 RB 1... RB N Ph Macro cell BS Phantom cell BS 5 S 2,7 6 C2 7 1 S 1,1 1 S 0,2 2 RB 1 RB 2... RB N M S 0,3 S 3,8 1 C1 RB 1... RB N Ph 1 S 1, C3 RB 1... RB N Ph S 3,9 9 C0 1 S 4,4 RB 1... RB N Ph 4 C4 Figure 2.1: Phantom cellular network system model. In this thesis, we consider a system consisting of one macro cell that covers a certain region within which C Ph phantom cells are deployed to serve a total of K users as shown in Fig The indexing of users in this thesis is global and unique in the sense that user number 1 in the system will be always referred to in any indexed variables that will appear further by the index 1. The total power available for transmission at the macro BS is P M, with reciprocal power amplifier efficiency κ M, while the total

22 22 power available for transmission at the phantom BS is P Ph, with reciprocal power amplifier efficiency κ Ph. We account for the macro BS and the phantom BS static circuits power consumption, backhaul links power losses, and signal processing by P M,cr and P Ph,cr, respectively. We define a resource unit (RU) as the time concatenation of N r Long Term Evolution (LTE)- defined resource blocks (RBs) [28]. The RU spans 7 N r Orthogonal Frequency Division Multiplexing (OFDM) symbol durations, and 12 subcarriers each of which occupies 15 Khz of bandwidth as shown in Fig The indexing of RUs in this thesis is localized for each cell, such that the first RU in phantom cell 1 occupies exactly the same portion of spectrum which the first RU of Phantom cell 2 occupies. RB 1 RB Nr Resource Block (RB) Resource Unit Figure 2.2: RU general structure The available RUs for the whole setup are divided between the macro cell and the phantom cells, where each phantom cell uses the same set of RUs. The total number of RUs in the proposed system is N, with N Ph reserved RUs for phantom cells usage, while N M are reserved for macro cell usage. In contrary to the user indexing convention, Phantom RUs follow local cell indexing, such that we have phantom RU number 1 of cell 1 and phantom RU 1 of cell 2 but both of them use the same spectrum portion. For this configuration, we have a total of K (N Ph C Ph + N M ) possible logical data links between the users and BSs, while the actual number of

23 23 physical links is less, because of the localization constraints of the phantom cells, where each phantom cell can only provide service to its local users. Furthermore, each RU can not be assigned to more than one user (time sharing is not allowed for RUs). We represent the spectrum allocation on a certain link by two sets of variables s n c,u and s m 0,u where c {1, 2..., C Ph }, u {1, 2..., K}, n {1, 2..., N Ph }, and m {1, 2..., N M }. We denote allocating the z-th RU of cell x to user y by setting s z x,y = 1. The macro cell is referred to by cell index 0, while phantom cells take cell indices varying from 1 to C Ph as shown in Fig We assume that any user in a given phantom cell can be served by this phantom cell, or the covering macro cell, or both of them. For example, Fig. 2.1 shows that user number 2 is assigned RU N Ph of cell 1 and RU 1 of the macro cell. We use the indexed set U c to represent the users connected to phantom cell c. Thus, for each cell c, s n c,x = 0, x U c. Similarly, we use p n c,u and p m 0,u as power allocation variables for phantom cells and macro cell, respectively. The set of all power allocation variables is denoted by P, while the set of all spectrum allocation variables is denoted by S. Pilot symbols Control symbols Pilot symbols Data symbols Data symbols Figure 2.3: Macro cell and phantom cell RU structure respectively from left to right In this setup, the macro cell and the phantom cells experience different kinds of

24 24 overheads, this is reflected in the structure of the macro cell RUs and their phantom cell counterparts as illustrated in Fig We assume that both the phantom cells and the macro cell reserve N p OFDM symbols for pilots transmission. However, in the macro cell case C Ph N c more OFDM symbols are reserved for control signaling where N c represents the control signaling overhead per phantom cell. We define α p as the pilots overhead portion in each RU and α c as the control signaling overhead portion of RU. Consequently, the total overhead part of a phantom cell RU is α p, whilst the total overhead part of the macro cell RU is α p,c = α p + α c, where α p = Np 7N r, and α c = (C Ph+1) N c 7N r. All channel impairments in terms of fading, shadowing, path loss affecting a link, along with the receiver thermal noise are integrated together into channel-to-noise terms: γ n c,u for phantom cell links and γ m 0,u for macro cell links. The general channelto-noise term γ x y,z is expressed as γ x y,z = h x y,z 2 Gy,z, σ 2 n (2.1) where h x y,z is the frequency domain channel of the link between the BS of the y-th cell and the z-th user using the x-th RU, G y,z encapsulates the path loss and shadowing effects between the BS of the y-th cell and z-th user using any RU and σn 2 is the additive white Gaussian noise (AWGN) variance. In the case of the imperfect CSI at the transmitters, h x y,z becomes ĥx y,z and γy,z x becomes ˆγ y,z. x The impact of the nonperfect CSI estimation on achievable rate and EE performance loss will be shown in the next chapters. We account for non-perfect CSI effects for a given link between the y-th BS and the z-th user, through the variance of the channel estimation error σ h 2 y,z. Under the assumption of AWGN with zero mean and variance σn 2 and L-tap power delay channel

25 model, σ 2 h y,z is expressed as [29], 25 σ 2 h y,z = L i=1 σ 2 g i y,z σ2 n σ 2 n + σ 2 g i y,z G y,z p pilot y, (2.2) where p pilot 0 = N p P M, p pilot c = N p P Ph and σ 2 g i y,z is the i-th tap channel variance of hx y,z x. The received signal by user z is given by N Ph C Ph K y z = h n c,zd n c,u + N M n=1 c=1 u=1 m=1 u=1 K h m 0,zd m 0,u + n z, (2.3) where d x y,z is the transmitted symbol by the BS of the y-th cell to its z-th user using the x-th RU multiplied by s x y,z, and n z is the AWGN with zero mean and variance σn. 2

26 26 Chapter 3 Sparsely deployed phantom cellular network In this chapter, we investigate the resource allocation problem in the downlink of a sparse deployment setting of phantom cells, where users are assumed to be concentrated in traffic hot-spots around the phantom cells. Furthermore, we assume that the distances separating the phantom cells are large enough to neglect the interference between them. We assume in this chapter that CSI is perfectly known at the transmitters. Firstly, we formulate our energy aware resource allocation optimization problem, then we use Dinkelbach s algorithm which is a well known fractional programming technique, and provide closed-form expressions for the primary variables in terms of the dual variables of the inner-loop optimization problem that will appear later in the chapter. We indicate that our algorithm is capable of getting the optimized SE solution. After that, we study the effects of some network parameters on the EE and SE performance of both resource allocation strategies. 3.1 EE resource allocation problem In this section, we formulate the EE resource allocation optimization problem for the downlink of a sparsely deployed phantom cellular network. Throughout the following

27 27 analysis, we use the global EE metric, which is defined as η EE = η SE P tot, (3.1) where η SE is spectral efficiency of the considered system and can be expressed as: η SE = 1 N ( CPh K N Ph ( s n c,ulog γ n c,u pc,u) n + (1 αc ) c=1 u=1 n=1 K N M u=1 m=1 s m 0,ulog 2 ( 1 + γ n 0,u p m 0,u) ), (3.2) where the first term represents the SE contribution of the phantom cells and the second term represents the SE contribution of the macro cell, and P tot is the total power used to deliver the data in the proposed system and is expressed as C Ph P tot = κ Ph K N Ph s n c,up n c,u + C Ph P Ph,cr + (1 α c ) κ M c=1 u=1 n=1 K N M u=1 m=1 s m 0,up m 0,u + α c κ M P M + P M,cr. (3.3)

28 28 The EE optimization is formulated as follows (P1) max P,S η EE subject to C1 : C2 : C3 : C4 : K N M u=1 m=1 s m 0,up m 0,u P M K N Ph s n c,up n c,u P Ph, c u U c u=1 n=1 K s n c,u 1, c, n u=1 K s m 0,u 1, m u=1 C5 : s n c,u {0, 1}, c, u, n C6 : s m 0,u {0, 1}, u, m C7 : p m c,u 0, c, u, n C8 : p m 0,u 0, u, m, where, we use C1 and C2 power constraints to guarantee that the total allocated transmission power of any BS does not exceed the available power budget. As for the RUs, we use C3 and C4 to indicate that the available RUs at every BS must be allocated to at most one user under the cell coverage, and both C5 and C6 constraints impose the fact that time sharing of RUs is prohibited in the proposed system. The optimization problem (P1) is classified as a mixed integer nonlinear programming problem. Thus, the optimal solution can be found by the branch and bound method which is a computationally very expensive approach. Such kind of problems can be solved by relaxing the constraints on s n c,u and s m 0,u to be continuous in the interval [0, 1] [7, 13, 30, 31]. Although relaxing the constraints results in a different solution, solving the dual problem of the relaxed version of (P1) leads to near optimal solution for large number of subcarriers [30]. Furthermore, simulation

29 29 results show that 8 subcarriers are used in [31] and 4 subcarriers are used in [7] and achieved a close to optimal performance. We define the two new sets of variables p n c,u = s n c,up n c,u and p m 0,u = s m 0,up m 0,u and reformulate our optimization problem in terms of them. Since the numerator of the objective function of the relaxed optimization problem is concave and its denominator is affine, then the objective function is quasiconcave [32]. To solve this nonconvex fractional nonlinear programming problem, we use the Dinkelbach iterative approach [33]. First, we convert our optimization problem from the fractional form to the parametric form using the concave objective function F (q, P, S) (please check Appendix A for proof), where it is defined as F (q, P, S) = η SE qp tot. (3.4) Dinkelbach method states that if the EE optimal solution is ( P EE, S EE), then the following condition holds [33] F ( q, P EE, S EE ) = ηse ( P EE, S EE ) ( qptot P EE, EE) S = 0, (3.5) where q is the optimal EE, i.e., q = η EE ( P EE, S EE). Thus, the equivalent optimization problem is written as (P2) max P,S subject to F (q, P, S) C1, C2, C3, C4, C7, C8 s n c,u [0, 1], c, u, n s m 0,u [0, 1], u, m.

30 30 The Lagrangian formulation of (P2) is written as L EE = 1 N ( q C Ph K N Ph s n c,ulog 2 (1 + γc,u n c=1 u=1 n=1 κ Ph C Ph c=1 u=1 n=1 C Ph + λ c (P Ph c=1 p n c,u s n c,u ) + (1 α c ) 1 N K N Ph p n c,u + C Ph P Ph,cr + (1 α c ) κ M K N Ph u=1 n=1 p n c,u ). K N M u=1 m=1 K N M u=1 m=1 s m 0,ulog 2 (1 + γ m 0,u p m 0,u s m 0,u ) p m 0,u + α c κ M P M + P M,cr ) (3.6) where λ 0 represents the Lagrange multiplier associated with the power budget constraint of the macro cell, and λ c represents the Lagrange multiplier associated with the power budget constraint of the phantom cell c. Then, we express the dual problem of (P2) as (P3) min max λ 0 P,S L EE (λ, P, S, q). By applying the KKT conditions, it can be shown that the optimal power allocations is expressed as [ p n c,u 1 = N ln(2)(qκ Ph + λ c ) 1 ] +, (3.7) γc,u n [ p m 0,u 1 α c = N ln(2)((1 α c ) qκ Ph + λ 0 ) 1 ] +. (3.8) γ0,u m where [x] + = max(0, x), and x is the optimized value. Using the same argument in

31 [30, 34], we allocate them using 31 1 if L EE = max S 0,u m s = m 0,u j 0 otherwise. 1 if L EE = max S c,u n s = n c,u j 0 otherwise. L EE, j {1 : K} and L s m EE 0,j s m 0,u L EE, j U s n c and L EE c,j s n c,u 0 0 (3.9), (3.10) where L EE s m 0,u and L EE s n c,u are computed, respectively, from are the first order derivatives with respect to s m 0,u and s n c,u which L EE s m 0,u = 1 α c N ( ( log γ m 0,u p ) m 0,u γm 0,up m 0,u ) γ0,up m m 0,u ln(2) (3.11) L EE s n c,u = 1 N ( ( log γ n c,u p ) n c,u γn c,up n c,u ) γc,up n n c,u ln(2) (3.12) It is worth noting that the aforementioned solution of S satisfies the constraints C3 and C4. Now, we have the solution of max P,S L SE(λ, s n c,u, p n c,u) for a certain value of λ, where λ is the vector consisting of λ 0, λ 1,..., λ CPh. To find the power allocation solution from (3.7), (3.8), we need to know λ and q, which can be found iteratively using Algorithm I. Throughout Algorithm I, we use the following notations to deal easily with both types of cells, the macro cell and the phantom cells. The generalized number of users per cell is defined as N l = N M if l = 0, (3.13) otherwise N Ph

32 32 and the power budget per cell is defined as p l max = P M if l = 0. (3.14) otherwise P Ph Algorithm I 1: Input user assignments to phantom cells, ɛ outer : maximum tolerable error for Dinkelbach s algorithm, ɛ inner : maximum error tolerated in the complementary slackness of KKT condition. 2: Set q error =, i = 0 and q i = 0 3: while q error > ɛ outer do 4: Choose λ such that we get a feasible power, and RUs allocation using (3.7), (3.8), (3.9) and (3.10). 5: Set l = 0 6: while l C Ph do 7: Set CompSlack error =. 8: while CompSlack error > ɛ inner do 9: Compute (P, S) from (3.7),(3.8), (3.9) and (3.10) 10: Compute descent direction 11: λl = pl max K N l s r l,u log 2(1+γl,u r pr l,u) u=1 r=1 p l max K N l s r l,u log 2(1+γl,u r pr l,u) u=1 r=1 12: Compute the descent step size λ step 13: Update λ l λ l + λ step λl 14: Compute ( CompSlack error as: 15: λ l p l max K N l s r l,u log ( γ r l,u pl,u) ) r u=1 r=1 16: l l : if i = 1 then 18: Set P SE = P, S SE = S 19: else 20: Set P EE = P, S EE = S 21: Compute q error = F (P, S, q i ) 22: i i : Compute q i = η SE P tot, using (3.2) and(3.3). 24: Output P EE, S EE, P SE, and S SE. Algorithm I consists of three nested loops to iteratively allocate the resources. The central part computes (P, S) for a given value of q and λ l within a cell l as seen

33 33 in step 9. The first inner loop from step 8 to step 16 is responsible for solving the dual optimization problem (P4) using the gradient descent method to find λ l for a given q and a cell l. The second inner loop from step 6 to step 18 is to switch between different cells. Finally, the outer loop from steps 3 to 27 is responsible for updating q based on Dinkelbach s method. Algorithm I starts with a zero initial value of q, which yields the optimized SE solution. Thus, Algorithm I can provide the resource allocation strategies for both EE and SE optimization problems. 3.2 Simulation Results In this section, we study the average EE and SE performance for the two resource allocation strategies previously mentioned, i.e., optimizing EE and optimizing SE. The simulation setup consists of a macro cell containing four phantom cells as shown in Fig.2.1. The phantom cells are equally loaded with users, and the number of users outside phantom cells coverage is the same as the number of users in any of the phantom cells. We considered here that α c is very small and can be neglected as the number of cells is not large, and P Ph is also small so the control overhead effect will not be fundamental. The average EE and average SE are computed over different channel realizations and users locations. The adopted large scale channel model is similar to the one used in [20] where, the macro cell links experience zeromean log-normal shadowing with 8 db standard deviation and the phantom cells links experience also a zero-mean log-normal shadowing but with 10 db standard deviation [35]. The path loss for macro cell links is described by [20] L M = log 10 (d u ) db (3.15)

34 34 Table 3.1: Simulation parameters. P M = 46 dbm P Ph = 20 dbm κ M = 2.6 P M,c = 60 W P Ph,cr = 20 W κ Ph = 5 N 0 = 174 dbm/hz f c = 3500 MHz h UT = 1.5 m C Ph = 4 W = 20 m h = h BS = 20 m where d u is the distance between the BS and user u in meters. On the other hand, the path loss for the links in the phantom cells is described by [20, 36] L Ph = log 10 (W ) log 10 (h) (3.16) ( (h/h BS ) 2) log 10 (h BS ) + ( log 10 (h BS ))(log 10 (d) 3) + 20 log 10 (f c ) (3.2(log 10 (11.75h UT )) ) where W is the street width in meters, h BS is the BS height in meters, h is average building height in meters, h UT is the average user height in meters, f c is the carrier frequency in MHz, and d is the distance between the BS and the user in meters. The small scale fading is modeled as multipath fading with a six-ray typical urban model as described in [35] with 3 Km/hr speed. We provide the values of the simulation parameters in Table 3.1. In the first simulation scenario, we study the effect of number of users on both EE and SE performance metrics for both EE and SE resource allocation strategies. To this end, Fig. 3.1 plots the four relationships existing between both EE and SE performance metrics and the two resource allocation strategies against the number of users per sector. We observe that as the number of users per cell increases, both SE and EE performance metrics increase as shown in Fig 3.1. This goes back to the fact that increasing the number of users per sector increases the degrees of freedom in distributing each RU (increase in the ratio of the number of users to the number of RUs) which implies that the system will have better chances of distributing the

35 Optimized EE EE for Optimized SE Optimized SE SE for optimized EE 30 ηee(bit/j/s/hz) ηse(bit/s/hz) Number of users per sector Figure 3.1: EE and SE versus number of users per sector for N = 50. resources among a set of users experiencing better channels. The second simulation scenario explores the importance of proper division of RUs between the macro cell and the phantom cell tiers. To this end, we study the EE and SE performance against the phantom cells RUs share (N Ph /N) as shown in Fig First, we find that both SE and EE improves for both strategies with increasing N Ph /N. This effect owes back to the fact that phantom cells users experience less path loss than macro cell users according to the considered models (3.15), (3.16). Second, we observe that optimizing EE performance comes at the cost of degrading the SE performance and vice versa. However, the SE performance loss due to adopting EE optimization strategy is less significant than the EE performance loss due to adopting SE optimization strategy. Interestingly, the degradation of SE performance when adopting EE optimization strategy diminishes and asymptotically vanishes as

36 Optimized EE EE for Optimized SE Optimized SE SE for optimized EE 50 ηee(bit/j/s/hz) ηse(bit/s/hz) Figure 3.2: EE and SE versus the ratio of phantom cells RUs to the total number of RUs, N = 50. N Ph N phantom cells tend to use all data RUs. This observation is due to the different energy consumption behavior of SE and EE optimization strategy. The former consumes the available budget, which is not necessary the same for the latter. A clear and effective example for this behavior is the power allocation of the macro cell. In this case, the SE optimization strategy pushes the macro BS to use its total power budget, on the other hand, the EE optimization strategy prefers not to use that much power which provides a non-significant SE increase.

37 3.3 Conclusion 37 In this chapter, we formulated the joint power and spectrum allocation problem to maximize the EE and SE for a sparse phantom cellular network with perfectly known CSI severally. To solve the optimization problem, we used Dinkelbach s approach that converts the quasi concave function into a concave function, and provides optimal solution iteratively. For sparsely deployed phantom cells, simulation results showed that increasing the number of users per cell improves the EE and SE performance. In addition, optimizing EE strategy provides a comparable SE performance with the SE optimization strategy as the phantom cells share of RUs increases.

38 38 Chapter 4 Densely deployed phantom cellular networks with non-perfect CSIT In this chapter, we consider the dense deployment of phantom cells where their intercell interference becomes non-negligible. Furthermore, we assume non-perfect CSI available at the BSs transmitters. We provide three different sub-optimal approaches to solve the EE and SE optimization resource allocation problems. 4.1 Optimization Problem Formulation We study the resource allocation problem for optimizing the global EE performance metric of the phantom cellular network downlink, where the EE of the adopted system is defined as η EE = η SE P tot, (4.1)

39 39 Macro cell BS Phantom cell BS C 6 C 10 C 2 C 5 C 9 C 12 C 1 C 0 C 3 C 4 C 8 C 11 C 7 Figure 4.1: Densely deployed phantom cells within a macro cell where η SE is the spectral efficiency of the considered system, expressed as 1 η SE = N ln (2) (1 α N Ph C Ph p) + 1 N ln (2) (1 α N M p,c) K n=1 c=1 u=1 K m=1 u=1 s n c,uln s m 0,uln 1 + ( 1 + ˆγ m 0,up m 0,u β 0,u G 0,u p m 0,u + 1 ˆγ n c,up n c,u s n c,u ˆγ c n,u pn c,u + β c,u G c,u p n c,u + 1 c c,u ), (4.2) where the first term represents the SE contribution of the phantom cells and the second term represents the SE contribution of the macro cell, β y,z = σ2 hy,z, and P σn 2 tot

40 40 is the total power spent by the system expressed as N Ph C Ph K P tot = (1 α p ) κ Ph s n c,up n c,u + α p κ Ph P Ph + C Ph P Ph,cr (4.3) + (1 α p,c ) κ M N M n=1 c=1 u=1 m=1 u=1 K s m 0,up m 0,u + α p,c κ M P M + P M,cr In this model for SE and total power delivered, we can see that the SE contribution of phantom cells is scaled by (1 α p ) to exclude the portion of signaling rate used for pilots transmission. Similarly, the SE contribution of the macro cell is scaled by (1 α p,c ) to exclude the pilots and control transmission overheads. In a similar fashion, we scale power terms that originate from phantom cells data transmission by (1 α p ), also we scale the power terms coming from macro cell transmission by (1 α p,c ). The terms representing power spent on phantom cells pilots transmission are scaled by α p, and the terms representing power expenses of the macro cell control signaling and pilots transmission is scaled by α p. The effect of non-perfect CSI on the achievable rate and consequently on the EE metric appears in two terms ˆγ y,z x and β y,z. We would like to emphasize that as β y,z increases the achievable rate decreases, which is expected since β y,z will increase if the variance of the estimation error increased. This may happen if, either the total power spent on pilots transmission decreased, or their number decreased. Moreover, the effect of imperfect channel estimation becomes more severe when the transmission on this ill-estimated channel is done at high power levels.

41 41 We are interested in the following optimization problem: (P1) max P,S η EE subject to C1 : C2 : C3 : C4 : K N M u=1 m=1 s m 0,up m 0,u P M K N Ph s n c,up n c,u P Ph, c u U c u=1 n=1 K s n c,u 1, c, n u=1 K s m 0,u 1, m u=1 C5 : s n c,u {0, 1}, c, u, n C6 : s m 0,u {0, 1}, u, m C7 : p m c,u 0, c, u, n C8 : p m 0,u 0, u, m, where, we use C1 and C2 power constraints to guarantee that the total allocated transmission power of any BS does not exceed the available power budget. As for the resource units, we use C3 and C4 to indicate that the available RUs at every BS must be allocated to at most one user under the cell coverage, and both C5 and C6 constraints impose the fact that time sharing of RUs is prohibited in the proposed system. This optimization problem has the same structure of (P1) presented previously in chapter 3, with the difference that the objective function in this case captures the effects of interference and non-perfect CSI. In similarity to the general fractional programming framework employed in chapter 3, we solve this optimization problem using Dinkelbach s algorithm.

42 Power Allocation with Fixed Resource Units Assignment (PAFRUA) strategy The PAFRUA strategy assigns the RUs within each phantom cell to the users experiencing the best SINR assuming that the other cells (interferers) equally distribute their power budget on their owned RUs. Moreover, average interference channel gains are assumed. In this way, the optimization problem reduces to the following one: (P2) max P η EE subject to C1, C2, C7, C8. The fractional form of the objective function of (P2), promotes reformulating it to its equivalent parametric form as in [33]. However, to guarantee the convergence of Dinkelbach s algorithm to a global optimal value, the numerator function must be concave, the denominator must be convex, and the constraints must form a compact and connected set[33]. Yet, this is a sufficient but not necessary condition, hence if we can find the global optimal solution of the inner loop non-convex optimization problem within Dinkelbach s algorithm, we can use Dinkelbach s algorithm to get a global solution for the original fractional programming problem. However, we are going to use successive convex approximation (SCA) in order to solve the inner loop optimization problem. This guarantees only a local optimal solution for that DC optimization problem, and as a result, we have a suboptimal solution for the original fractional program.

43 43 In fact, η SE is a difference of two concave functions of P variables: η SE = f (P) g (P), f (P) = 1 α N Ph p N ln (2) + 1 α p,c N ln (2) C Ph K n=1 c=1 u=1 N M K m=1 u=1 g (P) = 1 α N Ph p N ln (2) C Ph s m 0,uln K n=1 c=1 u=1 s n c,uln ( ( 1 + s n c,uln 1 + ˆγ n c,up n c,u + ˆγ m 0,up m 0,u β 0,u G 0,u p m 0,u + 1 ( 1 + s n c,u ˆγn c,up n c,u + β c,ug c,u p n c,u c c,u ) c c,u s n c,u ˆγn c,up n c,u + β c,ug c,u p n c,u ) ), (4.4) First, we use the equivalent parametric programming problem formulation where the function F (q, P) is used to solve the optimization problem, where it is defined as F (q, P) = η SE qp tot. (4.5) Dinkelbach method states that if the EE optimal solution is P EE, then the following condition holds [33] F ( q, P EE ) = ηse ( P EE ) ( qptot P EE) = 0, (4.6) where q is the optimal EE, i.e. q = η EE ( P EE). In each of Dinkelbach algorithm iterations, we need to solve the DC optimization problem whose objective function is F ( q, P EE) subject to the same set of constraints. We solve this DC problem by SCA, such that in each iteration of solving the DC program, the following convex optimization problem is solved: (P3) max P f (P) g P (P) qp tot subject to C1, C2, C7, C8.