DEGREE PROGRAMME IN WIRELESS COMMUNICATIONS ENGINEERING MASTER S THESIS

Transcription

1 DEGREE PROGRAMME IN WIRELESS COMMUNICATIONS ENGINEERING MASTER S THESIS COORDINATED BEAMFORMING AND POWER CONTROL FOR NETWORK CONTROLLED DEVICE-TO-DEVICE (D2D) COMMUNICATION Author Supervisor Second Examiner Technical Advisor Amin Ghazanfari Docent Antti Tölli Doctor Petri Komulainen Harri Pennanen January, 2014

2 Ghazanfari A. (2014) Coordinated Beamforming and Power Control for Network Controlled Device-to-Device (D2D) Communication. University of Oulu, Department of Communications Engineering, Master s Degree Program in Wireless Communications Engineering. Master s thesis, 51 p. ABSTRACT Since the integration of data services into cellular communications, cellular operators are struggling to harness the overwhelming data traffic on their networks. Underlay Device-to-Device (D2D) communication is a new and promising paradigm which allows proximate mobile users to have direct communication over the cellular spectrum that may be reused by other cellular users in the same cell. This new paradigm is proposed to assist the cellular operators to deal with the booming demand of mobile users. Recent studies have shown that underlay D2D communication significantly increases the cellular network capacity, and enables cellular operators to support rich multimedia services. However, reusing cellular resources for both D2D and cellular communication introduces interference issues. In such systems, interference management is of utmost importance because improper interference coordination may lead to a self-destructive network. Power control and beamforming appears to be viable techniques for interference management which can also be used to enhance the energy efficiency of the system. Network coordinated sum power optimization schemes for D2D communications underlaying uplink and downlink cellular spectrum is considered in this thesis. In particular, the system optimization target is to minimize the sum transmission power while guaranteeing the user specific rate constraints. Novel algorithms are proposed to solve the power minimization problem optimally. For the uplink, the problem is solved using joint transmit power control and receive beamforming algorithm. The downlink problem is reformulated as a second-order cone program (SOCP), and thus, it can be solved efficiently via standard SOCP solvers. Moreover, a decentralized algorithm is proposed that reduces the amount of control information exchange in comparison to the centralized approach. The performance of the proposed algorithms is compared with the conventional cellular scheme. Simulation results demonstrate that the proposed underlay D2D communication approach is capable of achieving significant performance gains over the conventional cellular scheme. Results also illustrate that the power consumption of the system is highly affected by the location of the interfering cellular user and whether the resources are shared in uplink or downlink. Therefore, four different resource sharing areas are defined for D2D communications. These areas specify the type of resources (i.e., downlink and uplink) suitable for D2D communication. Keywords: Device-to-Device communication, coordinated beamforming, power minimization.

3 TABLE OF CONTENTS ABSTRACT TABLE OF CONTENTS PREFACE LIST OF SYMBOLS AND ABBREVIATIONS 1. INTRODUCTION 7 2. D2D COMMUNICATIONS IN CELLULAR NETWORKS Definition and Taxonomy of D2D Communications Advantages and Challenges of D2D Communications Use Cases Overview of D2D Approaches Summary and Discussion COORDINATED BEAMFORMING IN CELLULAR NETWORKS Motivation and Background Multi-cell Multi-user SIMO Uplink Joint Transmit Power Control and Receive Beamforming Multi-cell Multi-user MISO Downlink Coordinated Beamforming via Uplink-Downlink Duality Coordinated Beamforming via Dual Decomposition POWER MINIMIZATION FOR NETWORK COORDINATED D2D COM- MUNICATIONS System Model and Problem Formulation Solution for Uplink Communications Solutions for Downlink Communications Centralized SOCP-based Algorithm Decentralized Dual Decomposition-based Algorithm Practical Considerations NUMERICAL EVALUATION Simulation Model and Parameters Impact of Distance between D2D Users Impact of Distance between Cellular User and D2D Pair Impact of SINR Targets DISCUSSION SUMMARY REFERENCES 46

4 PREFACE This Master thesis has been carried out as part of the CRUCIAL project in the Department of Communications Engineering and Centre for Wireless Communications (CWC) at the University of Oulu, Finland. I would like to gratefully acknowledge the Finnish Funding Agency for Technology and Innovation (Tekes), Nokia Solution Networks (NSN), Electrobit and Anite plc for supporting this project. I would like to express my deepest appreciation to my supervisor Docent Antti Tölli whose guidance and support helped me to overcome the obstacles of this research. I would also like to thank Dr. Petri Komulainen for his review. My special thanks goes to M.Sc. (Tech.) Harri Penannen for his invaluable guidance during this thesis. I would also like to thank my friends Nastaran and Arash for their support throughout the thesis. Last but not least, I would like to thank my parents for their unconditional love and encouragement during my studies.

5 LIST OF SYMBOLS AND ABBREVIATIONS B set of BSs d cu data symbol of cellular user ˆd cu estimated data symbol of cellular user d dtx data symbol from D2D transmitter ˆd drx estimated data symbol of D2D transmitter in uplink d j data symbol of user j ˆd j estimated data symbol of user j g dtx,drx channel response between D2D transmitter and D2D receiver g cu,drx channel response between cellular user and D2D receiver h b,j channel vector from user j to BS b h H b,j hermitian transpose of channel vector from user j to BS b h cu channel response between cellular user and BS h dtx channel vector from D2D transmitter to BS h drx channel vector from BS to D2D receiver I identity matrix J number of single antenna users L dtx,drx distance between D2D transmitter and receiver l 0 far field reference distance m j transmit beamformer vector towards user j m cu downlink transmit beamforming vector for cellular user n b additive white Gaussian noise vector at BS b n bs additive white Gaussian noise at BS n drx additive white Gaussian noise sample at receiver of D2D pair n j complex white Gaussian noise sample at user j N 0 noise spectral density p cu transmit power of cellular user p dtx transmit power of D2D transmitter in uplink p dtx transmit power of D2D transmitter in downlink p j transmit power of jth user r 0 far field reference distance R b cell radius of cellular BS R cu minimum rate target for cellular user R drx minimum rate target for D2D pair T number of transmit antenna at BS U set of all active users U b set of users that are served by BS b. w cu uplink receive beamforming vector for cellular user w j receive beamforming vector for user j wj H hermitian transpose of receive beamforming vector for user j y j received downlink signal of user j y drx received signal at D2D receiver y bs received signal vector at BS downlink received signal at cellular user ỹ cu

6 y b β cu β dtx,drx uplink received signal vector at BS b complex scalar channel of cellular user without pathloss i.i.d complex scalar channel α pathloss exponent λ j transmit power for user j in dual uplink σ j scaling factor for user j ψ b,j inter-cell interference from BS b to user j ψb b,j local copy of inter-cell interference term at BS b γ j target SINR of user j γ cu fixed SINR target of cellular user γ drx fixed SINR target of D2D receiver µ b vector of the dual variables associated with ψ (b) ω the step-size in subgradient method ADMM BS CSI CR D2D DL DEA DL-EA ICI ISM LTE LTE-A MIMO MISO MMSE MVDR OFDMA OSA QoS SINR SIMO SOC SOCP TDD UL UL-EA UMTS WLAN WiMAX WSR ZF alternating direction method of multipliers base station channel state information cognitive radio device to device downlink D2D-exclusive-area downlink-exclusive-area inter-cell interference industrial, scientific and medical long-term evolution long-term evolution-advanced multiple-input multiple-output multiple input single output minimum mean square error minimum variance dimensionless response orthogonal frequency-division multiple access open-sharing-area quality of service signal to interference plus noise ratio single input multiple output second-order cone second-order cone programming time-division duplexing uplink uplink-exclusive-area universal mobile telecommunications system wireless local area networks worldwide interoperability for Microwave Access weighted sum rate zero-forcing

7 7 1. INTRODUCTION Satisfying the basic demands of cellular users, such as voice calls and text messages, is not sufficient anymore. The cellular network operators face greater and greater challenges in dealing with the emerging mobile applications developed for the new generation of cellular devices, such as smartphones and tablets. These new cellular devices allow users to enjoy services with high Quality of Service (QoS) requirements such as video/audio streaming, online gaming, video calls and social networking. The rapid penetration of the smartphones has been so fast that the operators have struggled to adapt the existing infrastructure to support these new applications. Although the third and fourth generations of cellular technologies (e.g., UMTS [1] and LTE [2]) are designed to accommodate high speed data services, the operators are still struggling with the increasing bandwidth demand of cellular users. These limitations highlight the need of a new communication paradigm that revolutionizes the existing cellular architecture. Device-to-device (D2D) communications is one of such paradigms that has been introduced to harness these increasing bandwidth requirements. D2D communication in cellular networks is capable of direct communication between two cellular devices located in vicinity of each other. One of the main functionalities of cellular base station (BS) in conventional cellular networks is to relay traffic between cellular users. In D2D communication, the data bypasses the BS and it is instead sent using a direct communication link between the users. Bypassing the BS allows D2D communications to significantly increase the spectral efficiency of the dense cellular network. Furthermore, D2D communications can improve the throughput, power efficiency and cell coverage [3 12]. D2D users can either reuse the cellular network resources in the licensed spectrum (i.e., inband D2D) or use the resources from the unlicensed spectrum (i.e., outband D2D). Outband D2D communication can be seen as an attractive choice because there is no need to assign cellular network resources for D2D users. However, the service providers have no control over license-exempt spectrum, and thus, they cannot guarantee minimum QoS for D2D users. Majority of the papers on D2D communications in cellular networks exploit the cellular spectrum for D2D communications. Inband D2D communications can be classified into underlay and overlay. In underlay D2D communication, the cellular resources can be reused for D2D communications. In overlay communication, D2D users transmit on cellular resources which are specifically dedicated to D2D communications. Since allocating dedicated resources for D2D communications decreases the gains of spectral efficiency, underlay communications schemes are preferable. However, inband D2D communication introduces extra interference to cellular users which calls for advanced interference and power management schemes. Indeed, there are plenty of solutions to mitigate the interference from D2D transmitter to cellular users by mode selection (e.g., cellular or D2D mode), power allocation, and scheduling techniques [9, 13, 14]. However, there is a lack of beamforming schemes for the interference mitigation purposes in D2D communications. The aim of this thesis is to propose novel power control and beamforming schemes with interference coordination for the network-assisted D2D communication underlaying both uplink and downlink cellular resources. The considered single-cell system

8 consists of a multi-antenna BS communicating with a cellular user, and an underlaying D2D user pair, which exploits the same radio resources. The optimization objective is to minimize the total transmission power of the system while satisfying the predefined per user rate targets. In the uplink resource sharing case, a joint uplink power control and receive beamforming algorithm is proposed to solve the power minimization problem. The optimal uplink powers for the users are obtained via fixed-point iterations, whereas the optimal receive beamforming at the BS is achieved by using the linear MMSE receiver. In the downlink resource sharing case, a centralized algorithm is proposed to solve the sum power optimization problem by reformulating it as a secondorder cone program (SOCP), and solving it efficiently via standard SOCP solvers. As a result, the optimal transmit power for the D2D user and the optimal transmit beamformer for the cellular user are obtained. This centralized algorithm performs all the computations at the BS side. Thus, it is required that the BS has the knowledge of all the channels in the system. In this respect, a distributed algorithm is also proposed which potentially reduces the amount of exchanged control information between the BS and D2D transmitter. This algorithm utilizes standard dual decomposition method to turn the original centralized optimization into two levels of optimizations, which can be then solved in a decentralized manner. The sum power performance of the proposed algorithms are numerically evaluated and compared with the conventional cellular system via Matlab-based simulations. The organization of this thesis is as follows. Chapter 2 provides an overview of D2D communications in cellular networks. In Chapter 3, coordinated beamforming in cellular networks is considered. In Chapter 4, sum power minimization problem is introduced for underlying D2D communication, and centralized and decentralized algorithms are proposed to solve it. In Chapter 5, the proposed algorithms are numerically evaluated via Matlab-based simulations. Chapters 6 and 7 are dedicated to discussion and summary of this thesis. 8

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11 11 In D2D communication, users are expected to be in each other s vicinity, and thus, it is generally expected to use lower transmission power in comparison to a cellular transmission. Therefore, D2D communication potentially prolongs the battery life of mobiles which is an existing challenge for smartphone producers, see e.g., [6,7,17,19, 37]. This feature makes D2D communication specifically attractive for green mobile communications [4,7,8,17,38]. In addition to energy efficiency, D2D communications can lead to improved throughput and reduced delay for the same reasons (i.e., user proximity and direct communication link) [3, 8, 11, 12, 39]. The above mentioned merits are easier to achieve using inband D2D rather than outband D2D. For instance, outband D2D may lower the energy efficiency of the device. That happens because the mobile device should maintain a secondary wireless interface under outband D2D. Therefore, it is easier to improve the energy efficiency in inband D2D due to the use of a single wireless interface. Moreover, using two wireless interfaces with different technologies introduces extra complexity in terms of intertechnology compatibility issues such as vertical handover, acknowledgments and so on. In addition, the majority of candidate technologies for outband D2D (e.g., Bluetooth [30] and WiFi Direct [40]) require manual connection establishment and device association which is an inconvenience for transparent D2D communications [13, 41]. Outband D2D implementation also faces challenges such as providing operator-level security, guaranteed QoS [41], effective D2D pairs management, and interference management over ISM spectrum [6,17]. The main advantage of outband D2D over inband D2D is the lack of interference between D2D and cellular communication. Actually, this interference issue is the main challenge of the inband D2D communication. In order to efficiently handle the extra interference, proper interference management algorithms need to be applied. However, designing efficient interference management algorithms is challenging. In general, if the interference can be properly managed, inband D2D can provide better performance than outband D2D Use Cases In order to acquire insight about the emergence of using D2D communication in the future generations of the cellular networks, this section provides some examples about the practical use cases of D2D communication. After evaluating the merits and disadvantages of each D2D approaches, inband underlay D2D communication appears to be the most promising solution. In fact, majority of the literature focus on cellular network with underlaying D2D communication. D2D communication is attracting more and more attention not only due to the general performance gain, but also because of its practical use cases. For example [42] and [43] use D2D communications for multicasting purposes. Multicasting in D2D communication works such that the user with high channel quality is responsible to retransmit the received data from the BS to the users with weak channel quality, the retransmission of the data is through D2D links. It is shown that D2D communication enhances the multicasting performance of cellular network. Multicasting is specifically useful in densely populated cells such as cells covering stadiums and venues meant for festivals and conferences in which majority of the crowd share the same interest.

12 12 Data disseminations is another use case of D2D communication [26, 44]. For instance consider the case where a server is installed in sport complex, and the fans can download promotional materials or join the poll to select the best player of the match, etc. In this case, the cellular network BS supports phone calls. The cellular BS directs requests for aforesaid services to the server. The direct links between the server and users are used for D2D communication [6, 24, 44, 45]. Furthermore, peer-to-peer communication and machine-to-machine has been discussed in [41] and [46] as other practical use cases of D2D communication Overview of D2D Approaches In this section, the state-of-the-art approaches of D2D communications underlaying cellular networks are reviewed. Amongst the various research objectives considered in the related literature to underlay D2D communication, spectral efficiency improvement [3, 6, 9, 16, 19, 47 51] and energy efficiency enhancement [7, 8, 11, 14, 31] have been studied more than others. In the literature with focus on spectral efficiency improvement, variety of techniques are used, such as; interference management [19, 47 50], resource allocation [16, 51], and mode selection [3, 6, 9]. These techniques are used when D2D communication occurs on uplink and downlink resources. Energy efficiency is another major objective in underlay D2D. The proposed solutions for achieving better energy efficiency are power allocation, mode selection, and D2D specific scheduling algorithms. Some authors have proposed hybrid schemes that use a joint combination of the aforementioned techniques. These approaches can be categorized according to the optimization objectives, direction of the shared resources, and whether they operate in a centralized or decentralized manner. The authors of [7, 8, 11, 14, 31] aim to improve the energy efficiency of D2D communication underlaying cellular networks. The authors of [8] and [31] assume joint mode selection and power control optimization in a single-cell scenario. Both papers considered the uplink resource sharing. A distributed heuristic algorithm is presented in [8] and the proposed algorithm of [31] is based on exhaustive search. Sum rate maximization with total transmit power constraint and power optimization with rate constraint is studied in [11]. In that work, both uplink and downlink resource sharing in a single-cell system is considered. The authors proposed a heuristic centralized algorithm to solve the optimization problem. In [14] and [7], the authors consider an optimization problem of sum power minimization in OFDMA cellular networks with D2D communications underlaying downlink resources. The authors of [14] proposed a heuristic algorithm in order to solve the optimization problem which is constrained with per-user data rates. The heuristic algorithm solves the optimization problem using a joint resource allocation and mode selection approach. In [7], a distributed algorithm for finding optimal sum power in uplink sharing is proposed. The optimization problem is constrained based on the sum rate. The algorithm searches for the SINR target iteratively and it continues the search until it converges to the predefined sum rate value. Both SIMO and MIMO settings are studied.

13 Summary and Discussion Previous sections provided a detailed introduction to D2D communications in cellular networks. Considering all the aforementioned pros and cons for inband and outband D2D communications, inband D2D appears to be a more promising option. Hence, the focus of this thesis is on inband communication. In addition, considering the aforementioned merits of underlay inband D2D communications, this thesis focuses on D2D communications underlaying cellular network. Underlay D2D communication appears to be the most promising candidate for implementation in future generation cellular networks to improve spectrum and energy efficiency as well as to provide higher data rates and better QoS.

14 14 3. COORDINATED BEAMFORMING IN CELLULAR NETWORKS This chapter provides a brief overview of coordinated beamforming in cellular networks. First, the background and motivation of the coordinated beamforming are discussed. Then, the main algorithms for sum power minimization in uplink and downlink are considered. The ideas behind these algorithms are exploited in the context of network assisted underlaying D2D communications in Chapter Motivation and Background The performance of modern and future cellular networks (i.e., LTE [2] and LTE- Advanced [52]) is significantly limited by inter-cell interference (ICI). Inter-cell interference is originated from the transmissions in nearby cells if the same radio resources are re-used without appropriate interference management. In this regard, coordinated beamforming is as a promising approach to enhance the performance of cellular networks since it controls the generated inter-cell interference [53]. The main idea behind the coordinated beamforming is that each data stream is transmitted from a single BS while the transmissions over multiple BSs are coordinated in order to manage the caused interference. Along with network MIMO [53], coordinated beamforming belongs to a specific interference management approach called coordinated multipoint transmission [53]. In general, coordinated beamforming is a less complex approach than network MIMO since carrier phase synchronization is not needed and the amount of signaling is reduced. Coordinated beamforming can be operated in centralized or decentralized manners. In a centralized case, a central controlling unit is responsible for interference coordination requiring global CSI of all active links. In a decentralized case, coordination is performed between BSs via information exchange using backhaul links and/or over-the-air signaling while only local CSI is needed per BS. In a practical point of view, decentralized approaches are more appealing than centralized ones since the potentially reduced signaling load, lower computational requirements per decision making unit and less complex network structure [54]. Coordinated beamforming approaches with a wide variety of optimization targets have been studied intensively in the literature, for instance, weighted sum rate (WSR) maximization [55, 56], maximization of the minimum SINR\rate [57] and sum power minimization [54, 58]. In general, the first two approaches do not guarantee the target QoS of users, while the third approach aim to provide a predefined QoS per each user. Moreover, in the power minimization approach, the overall interference in the whole network is mitigated since the target is to minimize the sum power. In the rest of this chapter, the particular interest is in the sum power minimization with per user SINR constraints.

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16 Joint Transmit Power Control and Receive Beamforming The problem (3) can be optimally solved using the iterative algorithms proposed in [59 61]. These algorithms are inherently amenable to decentralized implementations. The main idea is to optimize the transmit powers of the users via fixed-point iterations, and then, use the linear MMSE receivers at the BSs for optimal reception. The iterative approach is summarized in Algorithm 1. Algorithm 1 Joint uplink power control and receive beamforming 1: Set t = 0. Initialize {p j } j U. 2: Repeat 3: Calculate the optimal transmit powers for each user using fixed-point iterations: p j [t + 1] = γ j 1 ( 1 + γ j h bj,j N 0 I + 1, j U. p n [t]h H b j,n h b j,n) h H b j,j n U (4) 4: Set t = t + 1 5: Until stopping criterion is satisfied. 6: Calculate the receive beamformers using the linear MMSE receiver: w j = ŵj ŵ j 2, ŵ j = ( N 0 I + n U p n h H b j,nh bj,n) 1 h bj,j, j U. (5) Algorithm 1 can be solved in centralized and decentralized manners. Centralized approach operates as follows. All the BSs transmit their local CSIs to a central controlling unit, which then has global CSI. Central unit iteratively computes the optimal user specific transmit powers using (4) and signals them back to the BSs, which signal them to the corresponding users. Then, all the users transmit using the optimal powers and the BSs employ the MMSE receivers. In the decentralized approach, each BS is responsible for the power update process of its own users. This is possible since it is assumed that each BS can estimate its received signal covariance matrix. Thus, each BS updates its own users powers using (4) and signals them to the corresponding users, which then transmit with the updated powers. At the receiver side, each BS employs MMSE receiver for reception. This procedure is repeated until convergence Multi-cell Multi-user MISO Downlink This section provides an overview on the main coordinated beamforming approaches for the sum power minimization in multi-cell multi-user MISO downlink systems. The system set up considered herein for the downlink is similar as in the previous section for the uplink, and it is illustrated in Figure 4.

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18 18 problem can be solved easier than solving the downlink problem itself. Hence, the uplink-downlink duality was introduced as a practical approach to solve the downlink beamforming problem in [63]. By reversing the input and output of the the downlink channel the dual uplink can be achieved [63]. The dual uplink problem of the primal downlink problem (7) can be written as min. λ j N 0 s. t. j U n U\{j} N 0 λ j w H j h H b j,j 2 N 0 λ n w H j hh b n,j 2 + N 0 w j 2 2 γ j, j U where {w j } j U and {λ j } j U are the optimization variables. In (8), {w j } j U and {λ j } j U can be interpreted as the uplink receive beamformers and the transmit powers, respectively. The problem (7) can be optimally solved via the following three steps: (i) computation of uplink transmit powers {λ j } j U, (ii) computation of uplink receive beamformers {w j } j U and (iii) computation of downlink transmit beamformers {m j } j U. The uplink-downlink duality-based beamforming design approach is summarized in Algorithm 2 [63]. Algorithm 2 Coordinated downlink beamforming via uplink-downlink duality 1: Set t = 0. Initialize {λ j } j U. 2: Repeat 3: Calculate the optimal uplink transmit powers {λ j } j U using fixed-point iterations: (8) λ j [t + 1] = γ j 1 ( 1 + γ j h bj,j N 0 I + 1, j U λ n [t]h H b j,n h b j,n) h H b j,j n U (9) 4: Set t = t : Until stopping criterion is satisfied. 6: Compute the uplink receive beamformers {w j } j U using the linear MMSE receiver: ( w j = ŵj, ŵ j = N 0 I + 1 N 0 λ n h H b ŵ j j,nh bj,n) h bj,j, j U (10) 2 n U 7: Calculate the optimal downlink transmit beamformers {m j } j U by scaling the optimal uplink receive beamformers {w j } j U : m j = σ j w j, j U (11) where {σ j } j U are the scaling factors, which are defined in [66]. Algorithm 2 can be solved in a centralized or decentralized manner. In the centralized processing case, each BS measures its local channels and signals them to the

19 19 central controlling unit. This is a valid assumption in TDD mode where the downlink channels can be measured from the uplink due to the channel reciprocity. Central unit computes the optimal beamformers using the steps in Algorithm 2, and signal them to the corresponding BSs. Then, each BS employs the optimal beamformers for the data transmissions. In the decentralized processing case, the first implementation steps, i.e., computing the uplink powers and receive beamformers, are similar to that in Algorithm 1. On the top of that, Algorithm 2 employs a scaling process in order to adjust the results of the dual-uplink problem for the downlink beamforming problem. This can be performed also in a decentralized way through downlink per-user power update as explained in [63] Coordinated Beamforming via Dual Decomposition This section describes a dual decomposition-based decentralized beamforming design [54], which relies on local CSI and limited information exchange between BSs. Dual decomposition method can be applied for optimization problems which have coupling constraints such that the problem decouples into multiple subproblems when the coupling constraints are relaxed. Hence, the original one-level optimization problem is turned into two levels of optimizations. In particular, lower-level subproblems (one for each BS) with fixed dual variables are controlled by a master problem which is responsible of updating the dual variables. This problem structure can be solved via decentralized processing. The problem (7) can be equivalently reformulated in a form to which dual decomposition is applicable. In this respect, the first step is to equivalently rewrite the SINR formulation as follows: This is expressed as n U bj \{j} h bj,jm j 2 h bj,jm n 2 + b B\{b} ψ 2 b,j + N 0 where the set B is defined as B = {1,..., B} and ψ 2 b,j = γ j, b B, j U b (12) n U b h b,jm n 2 is the intercell interference from the BS b to the user j. Now (7) can be equivalently reformulated as min. m j 2 2 s. t. j U n U bj \{j} h bj,jm j 2 h bj,jm n 2 + n U b h b,j m n 2 ψ 2 b,j b B\{b} ψ 2 b,j + N 0, b B, j U b γ j, b B, j U b where the optimization variables are {m j } j U and {ψ b,j } b B, j Ub. In (13), the second set of constraints, i.e., the inter-cell interference constraints, are relaxed by inequality since they hold with equality at the optimal solution. Next step is to introduce (13)

20 20 ψ (b)2 b,j as a local copy of the inter-cell interference term ψ2 b,j. By enforcing the two local copies to be equal, i.e., ψ (b)2 b,j = ψ (b j) 2 b,j, (13) can be equivalently reformulated as min. m j 2 2 s. t. j U n U bj \{j} h bj,jm j 2 h bj,jm n 2 + b B\{b} n U b h b,j m n 2 ψ (b) b,j 2, b B, j Ub ψ b,j (b) = ψ b,j (b j ), j, b B \ {b j } ψ (b) 2 γ j, b B, j U b b,j + N0 where the optimization variables are {m j } j U and ψ. All the local ICI terms are stacked into the vector ψ. In order to decouple (14) between BSs, the consistency constraints can be relaxed by utilizing the partial Lagrangian. The resulting relaxed problem can be divided into two levels, which are introduced next. The lower level subproblem for the BS b is written as min. m j µ T b ψ (b) j U b s. t. n U bj \{j} h bj,jm j 2 h bj,jm n 2 + b B\{b j } n U b h b,j m n 2 ψ (b) b,j 2, j Ub ψ (b) 2 γ j, j U b b,j + N0 where the optimization variables are {m j } j Ub and ψ (b). The vector ψ (b) consists of the local ICI terms that are related to the BS b. The vector µ b consists of the dual variables associated with ψ (b). The problem (15) can be equivalently reformulated as an SOCP, and thus, solved optimally. With the knowledge of local CSI, subproblem b can be solved independently at the BS b, for all b in parallel. The higher level master problem is given by (14) (15) maximize f(µ 1,..., µ B ) = b B f b (µ b ) (16) where f b (µ b ) is the optimal value obtained from solving (15) for a given µ b. The master problem (16) can be solved (in a component wise) using the following subgradient method: µ b,j (t + 1) = µ b,j (t) + ω(ψ b,j (b) (t) ψ b,j (b j ) (t)), b B, j U b (17) where ω and t are indicating the step-size and the index of iteration, respectively. The term ψ b,j (b) (t) ψ b,j (b j ) (t) is the subgradient of f at a point µ b,k. The subgradient step (17) requires that the local ICI terms are exchanged between the coupled BSs. This can be performed via backhaul signaling. Decentralized downlink coordinated beamforming approach [54] is summarized in Algorithm 3.

21 Algorithm 3 Coordinated downlink beamforming via dual decomposition 1: Set t=0. Initialize µ b (0). 2: Repeat 3: Solve the subproblem (15), and signal the resulting ICI terms ψ (b) to the coupled BSs via backhaul links. 4: Update the dual variables µ b using the subgradient method (17). 5: Set t = t + 1 6: Until stopping criterion is satisfied 21

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24 24 be equal for uplink and downlink phases for both cellular and D2D communications. Thus, the overall problem can be separated between uplink and downlink. The resulting uplink problem can be written as min. p cu + p dtx ) p cu w s. t. log 2 (1 H + cuh H cu 2 R p dtx wcuh H H cu dtx 2 + N 0 ( log p ) dtx g dtx,drx 2 R p cu g cu,drx 2 drx + N 0 (23) where the optimization variables are p cu, p dtx and w cu. Note that the receive beamforming vector is normalized, i.e., w cu 2 = 1.. The fixed values R cu and R drx are the minimum rate targets for the cellular user and D2D pair, respectively. Note that the rate constraints in (23) can be equivalently mapped into the SINR constraints. The resulting equivalent uplink optimization problem is given by min. s. t. p cu + p dtx p cu wcuh H H cu 2 γ p dtx wcuh H H cu dtx 2 + N 0 p 2 g dtx,drx 2 γ p cu g cu,drx 2 drx + N 0 (24) where the optimization variables are the same as in (23), and γ cu = 2 Rcu 1 and γ drx = 2 R drx 1 are the fixed SINR targets. Similarly, the downlink sum power minimization problem is expressed as min. s. t. m cu p dtx h cu m cu 2 γ p dtx g dtx,cu 2 cu + N 0 p dtx g dtx,drx 2 γ h drx m cu 2 drx + N 0 (25) where the optimization variables are p dtx and m cu Solution for Uplink Communications In this section, joint power control and receive beamforming algorithm is proposed to optimally solve the uplink power minimization problem (24). The proposed algorithm extends the ideas from the conventional cellular communications described in section 3.2 to the underlaying D2D communication system. After setting the Lagrangian of (24) to zero (w.r.t. w cu ) and some rearranging, similar to that in [63], the optimal powers of the cellular user and D2D transmitter can be iteratively calculated via the following fixed-point iterations p cu [t + 1] = γ cu h cu (N 0 I + p dtx [t]h H dtx h dtx) 1 h H cu (26)

25 25 p dtx [t + 1] = γ drx ( g dtx,drx N0 + p cu [t]gcu,drx H g ) 1. cu,drx g H (27) dtx,drx The optimal receive beamformer at the BS can be calculated by using the (scaled) linear MMSE receiver: w cu = ŵcu ŵ cu 2, ŵ cu = ( N 0 I + p dtx h H dtxh dtx ) 1 hcu. (28) The proposed uplink power control and receive beamforming approach is summarized in Algorithm 4. The implementation requirements of Algorithm 4 are discussed in section 4.4. Algorithm 4 Joint uplink power control and receive beamforming 1: Set t = 0. Initialize p cu (0) and p dtx (0) 2: Repeat 3: Calculate the transmit powers p cu (t + 1) and p dtx (t + 1) using (26) and (27), respectively. 4: Set t = t + 1 5: Until stopping criterion is satisfied. 6: Calculated the receive beamformer w cu using (28) Solutions for Downlink Communications Centralized SOCP-based Algorithm In this section, an optimal centralized approach is proposed to solve the downlink sum power minimization problem (25). By denoting ˆp dtx = p dtx, and following the similar procedure as in [64], (25) can be equivalently reformulated as the following convex SOCP: min. q 1 s. t. h cu m cu ˆp dtxg 2 N0 dtx,cu γ cu 1 ˆp dtx g dtx,drx γ dtx h dtxm 2 N0 cu (29) m cu q 2 ˆp dtx where the optimization variables are q, ˆp dtx, and m cu. The problem (29) can be solved via centralized processing if global CSI is available at the BS. In other words, the BS needs to know all the channels depicted in Figure 6. Assuming TDD mode, the BS can acquire its own local channels from the uplink phase. However, the channels from the D2D transmitter to the D2D receiver and to the cellular user need to be delivered to the BS via over-the-air signaling.

26 Decentralized Dual Decomposition-based Algorithm In this section, a decentralized solution is presented for the sum power minimization problem (25). The proposed approach extends the coordinated beamforming approach from cellular networks, as described in section and in [54], to the underlaying D2D communication system. The idea is to use dual decomposition to turn the original one-level optimization problem (25) into two levels of optimizations, i.e., a master problem and several subproblems with fixed dual variables. In particular, the master problem is responsible for updating the dual variables and each dual variable dependent subproblem is to be solved accordingly. This two-level optimization can be solved at the BS via decentralized processing with the aid of limited over-the-air signaling between the transmitters (i.e., the BS and D2D transmitter). In order to apply dual decomposition method, (25) needs to be reformulated. The first step is to equivalently rewrite the SINR constraints as h cu m cu 2 ψ 2 dtx,cu + N 0 γ cu (30) p dtx g dtx,drx 2 ψ 2 bs,drx + N 0 γ drx (31) where ψdtx,cu 2 = p dtx g dtx,cu 2 denotes the interference from the D2D transmitter to the cellular user and ψbs,drx 2 = h drxm cu 2 denotes the interference from the BS to the D2D receiver. Now, the original downlink optimization problem (25) can be equivalently rewritten as min. m cu p dtx s. t. h cu m cu 2 ψ 2 dtx,cu + N 0 p dtx g dtx,drx 2 ψ 2 bs,drx + N 0 γ cu γ drx p dtx g dtx,cu 2 ψ 2 dtx,cu h drx m cu 2 ψ 2 bs,drx where the optimization variables are m cu, p dtx, ψ dtx,cu and ψ bs,drx. The problem (32) is equivalent to (25) since the third and fourth constraints hold with equality at the optimal solution. Now (32) is coupled between the transmitters by the interference terms ψ dtx,cu and ψ bs,drx. By fixing the interference terms, (32) would decouple, and thus, each transmitter (i.e., the BS and D2D transmitter) could minimize its transmit power separately. Next step is to introduce transmitter specific (i.e., local) auxiliary variables and additional equality constraints such that the coupling in the SINR constraints is transferred to the added equality constraints. After this reformulation, equality constraints can be decoupled via standard dual decomposition method. The aforementioned auxiliary variables are the transmitter specific copies of ψ dtx,cu and ψ bs,drx, and they are denoted by ψ bs dtx,cu, ψdtx dtx,cu and ψbs bs,drx, ψdtx bs,drx (32). The additional equality con-

27 27 straints enforce the two transmitter specific copies to be equal, i.e., ψdtx,cu bs = ψdtx dtx,cu and ψbs,drx = ψdtx bs,drx. Now (32) can be equivalently reformulated as min. s. t. m cu p dtx h cu m cu 2 ψ bs dtx,cu 2 + N 0 γ cu p dtx g dtx,drx 2 ψ dtx bs,drx 2 + N 0 γ drx 2 dtx,cu 2 p dtx g dtx,cu 2 ψ dtx h drx m cu 2 ψ bs bs,drx ψdtx,cu = ψdtx,cu bs ψbs,drx = ψbs,drx dtx where the optimization variables are p dtx, m cu, ψ dtx dtx,cu, ψbs dtx,cu, ψbs bs,drx (33) and ψdtx bs,drx. In (33), the coupling is only involved in the equality constraints since the objective and inequality constraints can be separated between the transmitters. To achieve a distributed algorithm, a standard dual decomposition method is applied next. First, we take the partial Lagrangian by relaxing the consistency constraints as follows: L(m cu, p dtx, ψbs,drx, ψbs,drx, dtx ψdtx,cu, ψdtx,cu, bs µ bs,drx, µ dtx,cu ) = m cu p dtx + µ bs,drx (ψbs,drx bs ψbs,drx) dtx + µ dtx,cu (ψdtx,cu dtx ψdtx,cu) bs where µ bs,drx and µ dtx,cu are the dual variables associated with the equality constraints. The dual function is formulated as where g cu (µ b ) and g dtx (µ dtx ) are defined as (34) g(µ bs, µ dtx ) = g cu (µ bs ) + g dtx (µ dtx ) (35) g cu (µ bs ) = g dtx (µ dtx ) = inf m cu,ψ bs m cu µ bs T ψ bs (36) inf p dtx,ψ dtx p dtx + µ dtx T ψ dtx. (37) The vectors are defined as µ b = [µ bs,drx, µ dtx,cu ] T, µ dtx = [ µ bs,drx, µ dtx,cu ] T, ψ bs = [ψbs,drx, ψbs dtx,cu ]T and ψ dtx = [ψbs,drx dtx, ψdtx dtx,cu ]T. Finally, the lower level subproblems for the BS and D2D transmitter can be formulated as min. m cu µ T bs ψ bs and s. t. min. s. t. h cu m cu 2 + N 0 γ cu ψ bs2 dtx,cu h bs,drx m cu 2 ψbs,drx 2 p dtx + µ dtx T ψ dtx p dtx g dtx,drx 2 ψ dtx bs,drx 2 + N 0 γ drx p dtx g dtx,cu 2 ψ dtx dtx,cu 2 (38) (39)

28 28 where m cu, ψ bs are the optimization variables in (38) and p dtx and ψ dtx are the optimization variables in (39). The subproblems (38) and (39) can be written in epigraph forms as follows: min. z bs and s. t. m cu µ bs T ψ bs z bs min. h cu m cu 2 ψ bs dtx,cu 2 + N 0 γ cu h drx m cu 2 ψ bs bs,drx z dtx 2 (40) s. t. p dtx + µ dtx T ψ dtx z dtx p dtx g dtx,drx 2 ψ dtx bs,drx 2 + N 0 γ drx p dtx g dtx,cu 2 ψ dtx dtx,cu where the optimization variables for (40) are m cu, ψ bs, and z bs. In (41), the optimization variables are p dtx, ψ dtx, and z dtx. By denoting ˆp dtx = p dtx and following the similar procedure as in [54], the optimization problems (40) and (41) can be casted as the following SOCPs: 2 (41) min. s. t. z bs (1 µ T bs ψ bs + z bs )/2 (1 + µ T bs ψ bs z bs )/2 SOC 0 m cu γ cu h cu m cu ψdtx,cu bs SOC 0 N0 [ ] ψ bs bs,drx m H H SOC 0 cu h drx (42) and min. s. t. z dtx (1 µ T dtx ψ dtx + z dtx )/2 (1 + µ T dtx ψ dtx z dtx )/2 SOC 0 ˆp dtx γ dtx ˆp dtx g dtx,drx ψbs,drx dtx SOC 0 N0 [ ] ψ dtx dtx,cu SOC 0 ˆp dtx g dtx,cu (43)

29 29 where the optimization variables are m cu, ψ bs, and z bs for (42), and p dtx, ψ dtx, and z dtx for (43). The master problem for the dual decomposition is expressed as maximize µ bs,µ dtx g(µ bs, µ dtx ). (44) The sub-gradient method can be used to solve the master problem. Thus, (44) can be solved iteratively by using the following sub-gradient updates: µ bs,drx (t + 1) = µ bs,drx (t) + ω(ψdtx,cu dtx ψdtx,cu) bs µ dtx,cu (t + 1) = µ dtx,cu (t) + ω(ψbs,drx bs ψbs,drx) dtx (45) where t is the iteration index and ω is a positive step-size. To find a feasible transmission solution at any iteration, (43) and (42) can be solved with the following fixed average values of interference terms ψ dtx,cu (t) ψ bs,drx (t) = 1 2 (ψbs dtx,cu(t) + ψdtx,cu(t)) = 1 2 (ψdtx bs,drx(t) + ψ bs bs,drx(t)). (46) The proposed decentralized transmission strategy is illustrated in Figure 7., and it is summarized in Algorithm 5. The implementation challenges of Algorithm 5 are considered in section 4.4. Figure 7. Decentralized power control and beamforming approach.

30 30 Algorithm 5 Decentralized coordinated beamforming and power control via dual decomposition 1: Set t = 0. Initialize µ bs (0) = 0 and µ dtx (0) = 0 2: Repeat 3: Solve the independent subproblems (42) and (43) at the corresponding transmitters. Exchange the resulting interference terms between the transmitters using over-the-air signaling. 4: Update the dual variables using (45). 5: Set t = t + 1 6: Until stopping criterion is satisfied Practical Considerations This section discusses how the proposed algorithms operate, and what are the possible implementation requirements and challenges. Prior works in [41], [17] and [23] studied the implementation challenges of outband D2D communications in cellular networks. In fact, the authors of [23] showed that the real world implementation of outband D2D communication, which is believed to be even more complex than inband, can be achieved in LTE-A systems. Since operations such as session establishment, connection management and security are relatively similar in outband and inband D2D, this section only addresses the main (physical layer) aspects of the proposed algorithms, such as availability of global/local CSI and limited over-the-air signaling for power control or other information exchange purposes. In the uplink phase, the proposed joint power control and receive beamforming approach (i.e., Algorithm 4) operates as follows. First, it is required that global CSI, i.e., all the channels in the system, is available at the BS. It is assumed that the BS can measure its local uplink channels, i.e., the channels from the cellular user and the D2D transmitter. In addition, the D2D receiver can also estimate its local channels, i.e., the channels from the D2D transmitter and the cellular user. These channels should be then send to the BS via over-the-air signaling. Having the global CSI, the BS can perform the iterative power control step from Algorithm 4. The resulting optimal uplink powers need to be signaled to the cellular user and D2D transmitter over-the-air. After this, the cellular user and D2D transmitter can use the optimal powers for the physical uplink transmissions. At the BS, the linear MMSE receiver is used for the optimal reception. In order the obtain the optimal solution and satisfy the rate targets, the global CSI needs to be perfect and all the channels have to be static for the whole process. This power control and beamforming design can be seen as a centralized processing case since the BS is responsible for the power computations relying on the global CSI. In the downlink phase, the power minimization problem can be solved both in centralized and decentralized manners. In the first approach, the original problem is reformulated as a convex problem, which can be solved via centralized processing if global CSI is available at the BS. Assuming TDD mode, the BS can acquire its own local downlink channels from the uplink phase due to the channel reciprocity. In addition, the channels from the D2D transmitter to the D2D receiver and to the cellular user need to be delivered to the BS via over-the-air signaling. After this phase, the

31 BS can compute the optimal transmit beamformer for the cellular user and the optimal power for the D2D transmitter. Over-the-air signaling is again used to deliver the power information to the D2D transmitter. Finally, the BS and the D2D transmitter can physically transmit with optimal parameters. Similarly as in the uplink case, the global CSI needs to be perfect and all the channels have to be static in order to achieve optimal performance with rate targets satisfied. In the second approach, the dual decomposition is first used to reformulate the original problem in a form where a decentralized implementation is possible. In this case, the BS and D2D transmitter can be seen as separate entities, both of which are responsible of serving their own users independently. Thus, both the BS and D2D transmitter rely only on the local CSI and limited information exchange between them via overthe-air signaling. Local CSI can be acquired from the uplink measurements (assuming that also D2D receiver is sometimes in transmitting mode). At each iteration of the Algorithm 5, limited amount of information, i.e., the coupled ICI terms, is exchanged between the BS and D2D transmitter. If the local CSI is perfect and all the channels remain static, Algorithm 5 will converge to the optimal solution. Note that feasible iterates, where the rate targets are satisfied, can also be achieved during the convergence process. Hence, to avoid long delays and to reduce signaling/computational load, Algorithm 5 can be stopped at intermediate iterations. This comes at the cost of (somewhat) sub-optimal performance. It is worth noting that in this simple system model case, where there are only few single antenna users, centralized processing may be a better choice. However, for the larger multi-cell multiuser systems, decentralized implementation might be beneficial by potentially reducing the amount of the exchanged control information between the BS and D2D transmitter as compared with the centralized case. Furthermore, the proposed decentralized approach can operate even if the exchanged information between the transmitters is outdated. 31

32 32 5. NUMERICAL EVALUATION In this chapter, the performance of the algorithms proposed in the previous chapter are numerically evaluated. The chapter is arranged such that, first, the simulation model and parameters are introduced. Then, the performance of the D2D communication approach is numerically compared with the pure cellular case Simulation Model and Parameters The simulation model consists of a single cell with a BS serving a single cellular user and an underlaying D2D user pair. The BS is equipped with T = 4 antennas, whereas each user has a single antenna. In all simulation scenarios, the D2D pair and the cellular user have fixed distances from the BS, i.e., the users are located on the cell-edge, whereas the channels between the BS and users are simulated by applying a simple distance dependent pathloss model. The channel between the BS and the cellular user is expressed as ( ) R h cu = α hcu (47) where R is the cell radius, α is the pathloss exponent and r 0 is the far field reference distance. In the simulations, macro and small cells are modeled by setting the cell radius R to 400 m and 50 m, respectively. Furthermore, the channel vector h cu consists of i.i.d. complex random elements that are generated from Gaussian distribution, each with zero mean and unit variance. The same model is used to generate the channels from the BS to the D2D transmitter and receiver, i.e., h dtx and h drtx, respectively. Moreover, the similar pathloss model as in (47) is also considered for the channels between the cellular and D2D users. Precisely, the channel from the D2D transmitter to the D2D receiver is given by r 0 g dtx,drx = (Ldtx,drx l 0 ) α ḡ dtx,drx (48) where L dtx,drx is the distance between the D2D transmitter and receiver, l 0 is the far field reference distance and ḡ dtx,drx is the i.i.d. complex scalar channel generated from Gaussian distribution with zero mean and unit variance. The channels g dtx,cu and g cu,drx are also generated using the pathloss model in (48). The simulation model is depicted in Figure 8.

33

34

35 35 90 D2D downlink D2D uplink Cellular uplink Cellular downlink g = 0dB, R = 50m, L cu,drx = 27m D2D downlink D2D uplink Cellular uplink Cellular downlink g = 0dB, R = 400m, L cu,drx = 27m Sum Power [dbm] Sum Power [dbm] D2D Distance, L [m] dtx,drx (a) D2D Distance, L dtx,drx [m] (b) 80 D2D downlink D2D uplink Cellular uplink Cellular downlink g = 10dB, R = 50m, L cu,drx = 27m D2D downlink D2D uplink Cellular uplink Cellular downlink g = 10dB, R = 400m, L cu,drx = 27m Sum Power [dbm] Sum Power [dbm] D2D Distance, L dtx,drx [m] (c) D2D Distance, L dtx,drx [m] (d) D2D downlink D2D uplink Cellular uplink Cellular downlink g = 20dB, R = 50m, L cu,drx = 27m D2D downlink D2D uplink Cellular uplink Cellular downlink g = 20dB, R = 400m, L cu,drx = 27m Sum Power [dbm] Sum Power [dbm] D2D Distance, L dtx,drx [m] D2D Distance, L dtx,drx [m] (e) (f) Figure 10. Sum power versus D2D distance for uplink and downlink communications.

36 γ= 0dB, R = 50m, L cu,drx = 27m p dtx, D2D uplink p cu, D2D uplink p, D2D downlink dtx p, D2D downlink cu γ = 0dB, R = 400m, L cu,drx = 27m p dtx, D2D uplink p cu, D2D uplink p, D2D downlink dtx p, D2D downlink cu Power [dbm] 120 Power [dbm] D2D Distance, L [m] dtx,drx (a) D2D Distance, L dtx,drx [m] (b) γ = 10dB, R = 50m, L = 27m cu,drx p, D2D uplink dtx p, D2D uplink cu p, D2D downlink dtx p, D2D downlink cu γ = 10dB, R = 400m, L cu,drx = 27m p dtx, D2D uplink p cu, D2D uplink p, D2D downlink dtx p, D2D downlink cu Power [dbm] 100 Power [dbm] D2D Distance, L dtx,drx [m] (c) D2D Distance, L dtx,drx [m] (d) γ = 20dB, R = 50m, L cu,drx = 27m p dtx, D2D uplink p cu, D2D uplink p, D2D downlink dtx p, D2D downlink cu γ = 20dB, R = 400m, L cu,drx = 27m p dtx, D2D uplink p cu, D2D uplink p, D2D downlink dtx p, D2D downlink cu Power [dbm] Power [dbm] D2D Distance, L dtx,drx [m] D2D Distance, L dtx,drx [m] (e) (f) Figure 11. Individual transmitter powers versus D2D distance for uplink and downlink communications. Figure 11 illustrates the individual per-transmitter powers versus the D2D distance. The simulation set-ups are the same as in Figure 10, except only the D2D communication scenario is considered. Note that in the Figures the transmission power of the cellular user is denoted by p cu = m cu 2 2. The results in the small cell scenarios (i.e.,

37

38 g = 0dB, R = 50m, L dtx,drx = 10m D2D downlink D2D uplink Cellular uplink Cellular downlink D2D downlink D2D uplink Cellular uplink Cellular downlink g = 0dB, R = 400m, L dtx,drx = 10m Sum Power [dbm] Sum Power [dbm] cu drx Distance, L cu,drx [m] cu drx Distance, L cu,drx [m] (a) (b) D2D downlink D2D uplink Cellular uplink Cellular downlink g = 10dB, R = 50m, L dtx,drx = 10m D2D downlink D2D uplink Cellular uplink Cellular downlink g = 10dB, R = 400m, L dtx,drx = 10m Sum Power [dbm] Sum Power [dbm] cu drx Distance, L cu,drx [m] cu drx Distance, L cu,drx [m] (c) (d) Figure 13. Sum power versus distance between cellular user and D2D receiver for uplink and downlink communications. Figures 13(a) and 13(c) present the sum transmission power versus the distance between the cellular user and D2D receiver in small cell scenario for 0dB and 10dB SINR targets, respectively. The performance of the D2D communication scenario is compared with the pure cellular system both in uplink and downlink phases. The sum power performance is similarly demonstrated in macro cell scenario in Figures 13(b) and 13(d). The simulation results show that the locations of the cellular user and D2D pair play important roles for the resource sharing between them. As can be seen from the results, there are four different areas in the Figure 13. In the first area, the cellular user is far enough from the D2D pair. Therefore, the generated interference between the D2D pair and the cellular user is negligible. Since both uplink and downlink resource sharing are beneficial in this area, it is referred to as open-sharing-area (OSA). In the second area, the cellular user is close to the D2D receiver. Therefore, the D2D receiver experiences high level of interference, making it a disadvantageous scenario for the uplink resource sharing. Hence, only the downlink resource sharing adds sum power gain to the system. This area is referred to as uplink-exclusive-area (UL-EA). In the third area, the cellular user is located between the D2D pair. Neither the uplink nor the downlink resource sharing is possible in this area. This area is referred

39 39 to as D2D-exclusive-area (DEA). In the fourth area, the cellular user is moving away from the D2D transmitter. In this area, the uplink resource sharing adds sum power gain to the system. Nevertheless, the downlink resource sharing is not advantageous because the source of interference for the cellular user (i.e., the D2D transmitter) is close, making it a worst case scenario for the downlink resource sharing. The aforementioned area is defined as downlink-exclusive-area (DL-EA). Table 2 summarizes the characteristics of four D2D resource sharing areas. Table 2. Characteristics of four D2D resource sharing areas. Region D2D Feasibility Uplink Underlay Downlink Underlay D2D-exclusive-area x x x Uplink-exclusive-area x Downlink-exclusive-area x Open-sharing-area It can be observed that the level of the SINR targets has an impact on the sizes of the four defined areas. The higher the targets, the smaller the areas where the D2D communication is beneficial. Moreover, the results also imply that the larger cell size increases the sum power levels, but does not have much of an effect to the sizes of the defined areas. Figure 14 illustrates the individual transmit powers of the cellular user and the D2D transmitter versus the distance between the cellular user and the D2D receiver for uplink and downlink communications. The simulation set-up is the same as used for Figure 13, but only the D2D communication scenario is considered herein. In the uplink case, the transmission power of the cellular user slightly increases when the cellular user is in DEA, and for the rest of locations it remains approximately fixed. On the contrary, the transmission power of the D2D transmitter is varying significantly while the distance between the cellular user and the D2D receiver is changing. When this distance is short, the source of the interference for the D2D receiver is closer than the desired transmitter. Therefore, the D2D transmitter needs to transmit with higher power level to satisfy the SINR target. This behavior is emphasized in the higher SINR target case. In the downlink communication, the interference towards the D2D receiver is from the BS. Since the BS is in charge of designing the transmission parameters, this interference can be coordinated due to the transmit beamforming capabilities of the BS. Hence, the transmission power of the D2D transmitter does not vary significantly in UL-EA, DL-EA and OSA, but when the cellular user is located in the DEA, the transmission power of D2D transmitted slightly decreases. It is due to the fact that the transmit beamforming of the BS is close to the zero-forcing (ZF) beamforming. The BS apply ZF to have null towards the D2D pair which decrease the generated interference from BS to D2D pair. Hence, the D2D transmitter transmit with lower power. This effect is more obvious in Figures 14(c) and 14(d), because for the high SINR targets, ZF beamforming behavior is emphasized. However, the interference experienced by the cellular user is increasing when the cellular user moves towards the D2D transmitter. Thus, the BS needs to use significantly higher transmission power in order to meet the SINR target of the cellular user. As expected, the power increase is emphasized when the SINR targets are higher. Moreover, it can be seen that in the macro cell case all the other power levels are significantly higher than in the small cell case,

40 40 except the power of the D2D transmitter. This can be explained by the interference coordination performed by the BS via transmit beamforming. Moreover, the pathloss between the interfering BS and the D2D receiver is also increased with the larger cell size. 60 γ = 0dB, R = 50m, L dtx,drx = 10m p dtx, D2D uplink 30 γ = 0dB, R = 400m, L dtx,drx = 10m p dtx, D2D uplink 70 p cu, D2D uplink p, D2D downlink dtx p, D2D downlink cu p cu, D2D uplink p, D2D downlink dtx p, D2D downlink cu Sum Power [dbm] Sum Power [dbm] cu drx Distance, L cu,drx [m] cu drx Distance, L cu,drx [m] (a) (b) 40 γ = 10dB, R = 400m, L dtx,drx = 10m p dtx, D2D uplink 0 γ = 10dB, R = 400m, L dtx,drx = 10m p dtx, D2D uplink p cu, D2D uplink p, D2D downlink dtx p, D2D downlink cu 20 p cu, D2D uplink p, D2D downlink dtx p, D2D downlink cu Sum Power [dbm] Sum Power [dbm] cu drx Distance, L cu,drx [m] cu drx Distance, L cu,drx [m] (c) (d) Figure 14. Individual transmitter powers versus distance between cellular user and D2D receiver for uplink and downlink communications Impact of SINR Targets This section provides a study on the effect of the different target SINRs on the achievable power gain. In this simulation scenario, the D2D distance is fixed to 10m and the

41 41 distance between the cellular user and D2D receiver is fixed to 27m for both cases of small and macro cells D2D downlink D2D uplink Cellular uplink Cellular downlink R = 50m, L cu,drx = 27m, L dtx,drx = 10m D2D downlink D2D uplink Cellular uplink Cellular downlink R = 400m, L cu,drx = 27m, L dtx,drx = 10m Sum Power [dbm] Sum Power [dbm] SINR target, g [db] SINR target, g [db] (a) (b) Figure 15. Sum power versus SINR target for uplink and downlink communications. 80 R = 50m, L cu,drx = 27m, L dtx,drx = 10m p dtx, D2D uplink 40 R = 400m, L cu,drx = 27m, L dtx,drx = 10m p dtx, D2D uplink p cu, D2D uplink p, D2D downlink dtx p, D2D downlink cu p cu, D2D uplink p, D2D downlink dtx p, D2D downlink cu Sum Power [dbm] Sum Power [dbm] SINR target, γ [db] SINR target, γ [db] (a) (b) Figure 16. Individual transmitter powers versus SINR target for uplink and downlink communications. Figures 15(a) and 15(b) show the sum power versus the SINR target for the small and macro cell cases, respectively. The sum power performance of the underlay D2D and pure cellular systems are compared in uplink and downlink phases. The results demonstrate that the power gain from the D2D communication decreases when the SINR target increases. Furthermore, for this specific simulation setup, the performance of the D2D communication using the uplink resources is better than in the downlink

42 case. It can be seen that when the SINR targets increase, the sum power gain decreases for both downlink and uplink, but the degradation of the downlink power gain is faster than the uplink power gain. Hence, for the SINR targets higher than 10dB the D2D downlink degrade the performance of cellular network. In Figures 16(a) and 16(b), the individual per-transmitter powers are plotted against the SINR target for the same small and macro cell scenarios as previously. In these Figures, only the underlaying D2D communication scenario is considered. It can be seen that the transmit powers of the D2D communication are much lower in comparison to the powers in the cellular communication. Furthermore, the used power of the D2D transmitter is significantly lower in the downlink than in the uplink phase. This is again due to the transmit beamforming performed at the BS. This performance behavior is further emphasized when the cell size grows. Consequently, in the macro cell case, all the other power levels are significantly increased, except the D2D transmit power in the downlink phase. 42

43 43 6. DISCUSSION The goal of this thesis is to study network assisted D2D communications underlaying cellular networks while proposing the algorithms to underlay uplink and downlink resources. To achieve this purpose, coordinated beamforming approaches in cellular networks are studied. Both centralized and decentralized approaches of coordinated beamforming in cellular networks has been considered. It leads to facilitating D2D communication underlaying cellular networks to increase the energy efficiency of the cellular networks. Based on the algorithms studied in Chapter 3, novel algorithms are proposed to enhance energy efficiency of D2D communications underlaying cellular networks. The algorithms minimize the total transmission power while guaranteeing the user specific rate constraints. The algorithm proposed for D2D communications underlaying uplink is based on the joint power control and receive beamforming algorithm using similar ideas as presented in [59 61]. For D2D communications underlaying downlink, the proposed algorithm is based on the SOCP. The performance of the algorithms are benchmarked with conventional cellular networks. The results show that algorithms add significant power gain to the cellular networks. This gain is achieved because the proposed algorithms manage to successfully reduce the interference using power control and beamforming techniques. In particular, the proposed algorithms harness the interference caused by D2D communications so that successful cellular communications is guaranteed. Additionally, a decentralized approach is designed based on the principles introduced in [54]. This algorithm uses standard dual decomposition approach to solve the optimization problem individually at each transmitter. Therefore, the original optimization problem can be solved at each BS using local CSI. The decentralized algorithm aims to reduce the amount of control information exchange in comparison with the centralized approach. Majority of prior works on power allocation for D2D communications underlaying cellular networks did not consider the implementation requirements and challenges of their proposed algorithms. However, Chapter 4 discussed the implementation challenges of the proposed centralized and decentralized algorithms. The main challenges for implementing the proposed sum power minimization algorithms are channel measurements, CSI feedback, and power updates via over-the-air signaling. Although the proposed centralized algorithms require global CSI knowledge at the BS side, sending the channel states of the users in scalar forms greatly reduces the bandwidth consumed for feedback reporting. Moreover, the decentralized algorithm allows the BS to perform beamforming with limited information exchange among interfering transmitter. It is worth mentioning that in the considered simple system model, the use of the centralized approach might be a better choice since only the scalar channels need to be signaled to the BS by the users via over-the-air signaling. However, the role of the decentralized approach is emphasized for larger multi-cell systems with multiantenna users. The numerical analysis of the algorithm is provided in Chapter 5. There are three parameters which play the main role in the considered simulation scenarios, i.e., the distance between users, the SINR targets, and the cell size. The numerical simulations showed that: (i) increasing the distance between the D2D pairs reduce the system performance. This happens because the D2D transmission power is higher for larger

44 distances which in turn results in higher interference; (ii) larger distance between the D2D pair and cellular user leads to better system performance because the interference between the D2D and cellular transmission is inversely proportional with distance; (iii) for the higher SINR targets, the D2D performance gain decreases more rapidly as compared with the lower SINR targets. This is due to the increased interference since the transmission powers need to be higher; (iv) the total sum power increases with cell size due to the pathloss effect. Considering the importance of these parameters on the system performance, it is crucial to take them into account in the design of D2D systems. Interestingly, studying the impact of these parameters on the system performance showed that the cell area can be divided into four different areas. Each area has certain characteristics in terms of the feasibility of D2D communication and the type of resources used for D2D communication. The characteristic of these areas are shown in Table 2. It should be noted that the aforementioned parameters (e.g., user distance, target SINR, etc.) affect the coverage of these areas. One of the main outcome of the numerical analysis is that implementation of smart mode selection can increase the performance of algorithm. According to the position of the cellular user, the algorithm should decide about the optimal transmitter and the best resource to be shared. Therefore, the algorithm combines the second and third areas. Thus, adding smart mode selection to the current algorithms is an interesting future research direction. The aforementioned results are obtained from a simple scenario consisting of a BS, a cellular user, and a D2D pair. However, the results can be better justified in a more realistic multi-cell scenario with higher number of D2D and cellular users, and more sophisticated channel model. Nevertheless, these additions make the sum power minimization problem more complicated. Another potential future direction is to investigate the behavior of the system when the users are not only located on the edge. Investigating the performance of the proposed decentralized algorithm in a multi-cell scenario is also an interesting future research direction. For the sake of tractability, the sum power minimization design was considered so that a clear understanding of pros and cons of the D2D underlaying cellular network can be provided. Furthermore, considering other optimization criteria such as spectral efficiency or WSR maximizations are good candidates for further research. These new optimization criteria are more interesting from the practical point of view. Channel estimation and CSI availability at the BS (especially from D2D transmitter) is also an important issue. For instance, the BS may not be able to sense the pilot signals from D2D transmitters due to their low transmission power. A potential solution could be defining D2D specific signaling in which the transmitter sends pilot signals with higher power. Thus, design of D2D specific signaling can be another line for future research. 44

45 45 7. SUMMARY The aim of this thesis was to study the energy efficiency of D2D communications underlaying cellular networks. In particular, algorithms for sum power minimization for both uplink and downlink resource sharing between D2D pair and cellular user are proposed. Moreover, the proposed algorithms are benchmarked against conventional cellular systems. In Chapter 2, D2D communications in cellular networks is introduced and the related literature on the topic is reviewed. Chapter 3 reviews network-coordinated beamforming techniques in cellular networks. In Chapter 4, the problem of the interference management in underlay D2D scenarios is elaborated. In particular, the sum power optimization problems for the downlink and uplink resource sharing are formulated. The objective of the optimization problems is to minimize the sum power consumption of the network constrained with per user rate target. In order to solve the optimization problems, novel algorithms are proposed which minimize the sum power consumption of the network in both uplink and downlink directions. The proposed algorithm for solving the optimization problem in uplink is based on joint uplink power control and receive beamforming algorithm. In the downlink, the power minimization problem is casted as an SOCP, which can be then solved optimally via centralized processing. In addition to the centralized solution, a decentralized dual decomposition-based algorithm is proposed for the downlink case. The implementation challenges of the proposed power control and beamforming algorithms for the D2D communications are also discussed. The proposed algorithms are benchmarked against the conventional cellular network via Matlab-based simulations. The single-cell simulation model consists of a cellular user and a single D2D pair, which share the same cellular spectrum. The simulation results showed that the locations of the cellular user and D2D pair play important roles for the resource sharing between them. Based on these results, four different resource sharing areas, namely, D2D-exclusive-area, uplink-exclusive-area, downlinkexclusive-area, and open-sharing-area, for D2D communication are defined. The results showed that the proposed algorithms can reduce the sum power consumption of the network by 5dB at best.

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