WIRELESS energy transfer (WET), where receivers harvest

Transcription

1 6898 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 10, OCTOBER 2016 User-Centric Energy Efficiency Maximization for Wireless Powered Communications Qingqing Wu, Student Member, IEEE, Wen Chen, Senior Member, IEEE, Derric Wing Kwan Ng, Member, IEEE, JunLi,Member, IEEE, and Robert Schober, Fellow, IEEE Abstract In this aer, we consider wireless owered communication networs WPCNs where multile users harvest energy from a dedicated ower station and then communicate with an information receiving station in a time-division manner. Thereby, our goal is to maximize the weighted sum of the user energy efficiencies WSUEEs. In contrast to the existing system-centric aroaches, the choice of the weights rovides flexibility for balancing the individual user EEs via joint time allocation and ower control. We first investigate the WSUEE maximization roblem without the quality of service constraints. Closed-form exressions for the WSUEE as well as the otimal time allocation and ower control are derived. Based on this result, we characterize the EE tradeoff between the users in the WPCN. Subsequently, we study the WSUEE maximization roblem in a generalized WPCN where each user is equied with an initial amount of energy and also has a minimum throughut requirement. By exloiting the sum-of-ratios structure of the objective function, we transform the resulting nonconvex otimization roblem into a two-layer subtractive-form otimization roblem, which leads to an efficient aroach for obtaining the otimal solution. The simulation results verify our theoretical findings and demonstrate the effectiveness of the roosed aroach. Manuscrit received Aril 12, 2016; acceted July 3, Date of ublication July 19, 2016; date of current version October 7, The wor of W. Chen was suorted by the National 973 Project under Grant 2012CB316106, in art by the National 863 Project under Grant 2015AA01A710, and STCSM Project under Grant 16JC The wor of D. W. Kwan Ng was suorted by the Australian Research Council Linage Project LP under Grant The wor of J. Li was suorted in art by the National Natural Science Foundation of China under Grant , in art by the Jiangsu Provincial Science Foundation under Project BK , in art by the Secially Aointed Professor Program in Jiangsu Province, 2015, and in art by the Fundamental Research Funds for the Central Universities under Grant The wor of R. Schober was suorted by the Alexander von Humboldt Professorshi Program. The associate editor coordinating the review of this aer and aroving it for ublication was E. Uysal Biyioglu. Q. Wu and W. Chen are with the Shanghai Key Laboratory of Navigation and Position Based Services, Shanghai Jiao Tong University, Shanghai , China, and also with the School of Electronic Engineering and Automation, Guilin University of Electronic Technology, Guilin , China wu.qq@sjtu.edu.cn; wenchen@sjtu.edu.cn. D. W. Kwan Ng is with the School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, NSW 2052, Australia wingn@ece.ubc.ca. J. Li is with the School of Electronic and Otical Engineering, Nanjing University of Science and Technology, Nanjing , China jun.li@njust.edu.cn. R. Schober is with the Institute for Digital Communications, Friedrich- Alexander-University Erlangen-Nurnberg, Erlangen 91054, Germany frschoberg@ece.ubc.ca. Color versions of one or more of the figures in this aer are available online at htt://ieeexlore.ieee.org. Digital Object Identifier /TWC Index Terms User energy efficiency, wireless owered communication networs, resource allocation. I. INTRODUCTION WIRELESS energy transfer WET, where receivers harvest energy from radio frequency RF signals, is considered to be a romising solution for rolonging the lifetime of wireless devices. Combined with wireless information transmission WIT, WET introduces a aradigm shift for the design of wireless communication systems and has been studied for various system architectures [1] [14]. In [11], the authors established a harvest-then-transmit rotocol for wireless owered communication networs WPCNs, where the time allocated to the base station for downlin DL WET and the time allocated to the users for ulin UL WIT were jointly otimized for maximization of the system throughut. Similar roblems were studied in the contexts of WPCNs with relays [12] and massive multile-inut multile-outut MIMO [13]. These wors either focused on the sectral efficiency SE or the outage robability of WPCNs while the energy consumtion of both energy transfer and information transmission was not considered, desite its imortance for the design of future wireless communication systems. The exlosive growth of high-data-rate alications and services has triggered a dramatic increase in the energy consumtion of wireless communications. Due to the raidly rising energy costs and tremendous carbon footrints of communication systems [15], energy efficiency EE, measured in bits-er-joule, has attracted considerable attention as a new erformance metric in both academia and industry [16] [20]. In fact, EE is articularly imortant in WPCNs since the harvested RF energy is attenuated by signal roagation. Resource allocation for system-centric EE maximization was studied in [8] for simultaneous wireless information and ower transfer SWIPT systems. Secifically, the subcarrier assignment, ower allocation, and ower slitting ratio were jointly otimized for maximization of the system EE, while guaranteeing both a minimum amount of harvested energy and also a minimum user data rate. Chen et al. [21] investigated energyefficient ower allocation for large-scale MIMO systems for a single-user setu. However, emloying large numbers of antennas may not be energy efficient if the energy consumtion of the antennas is taen into account IEEE. Personal use is ermitted, but reublication/redistribution requires IEEE ermission. See htt:// for more information.

2 WU et al.: USER-CENTRIC EE MAXIMIZATION FOR WIRELESS POWERED COMMUNICATIONS 6899 In our revious wor [2], we studied system-centric EE maximization via joint time allocation and ower control. We showed that from the system s ersective, only users who have a better energy utilization efficiency than the system itself should be scheduled while the rest of the users should remain silent during UL WIT. However, such a resource allocation algorithm design may lead to starvation of some users and thus their quality of service QoS cannot be guaranteed in ractice. In fact, most existing wors focus on otimizing the systemcentric EE from the system s ersective [7], [16] [19], [22], and little effort has been made to investigate the user-centric EE from the terminals ersective. Since the caacities of batteries are limited but the demand for heterogeneous user exerience increases, the EEs of individual users become increasingly critical for the oeration of ractical wireless communication systems [23]. However, a resource allocation aiming at otimizing the system-centric EE, which is defined as the ratio of the system throughut to the system energy consumtion, is in general subotimal as far as the EE of the individual users is concerned [1], [19], [24]. In contrast, in WPCNs, where users harvest energy and transmit information signals indeendently, the user-centric EE focuses on the EE of each user and is thus more relevant for ractical user-centric alications than the system-centric EE [1]. In addition, user-centric EE otimization rovides insights into the EE tradeoff between different users. For conventional SE otimization, the tradeoff between users is quite obvious and simle: the throughut of one user cannot be imroved without decreasing the throughut of the other users. This is because utilizing more resources, such as transmit ower and transmission time, is always beneficial for increasing the data rate of a user. However, this simle relationshi may not hold for EE otimization. It is well nown that exceedingly large transmit ower will lead to a lower individual user EE [25], which suggests that users may not always comete for resources with each other. In other words, it may be ossible to maximize the EEs of all users simultaneously. Furthermore, if the users have high minimum throughut requirements, users that are allocated short transmission times have to transmit with larger owers in order to meet the throughut requirements which may result in lower user EEs. In contrast, users that are allocated longer transmission times have higher flexibility in adjusting their transmit owers which facilitates higher user EEs. In this case, the EEs of the users may not be maximized simultaneously. Therefore, it is interesting to study the EE tradeoff between different users in WPCNs and it is exected that the adoted resource allocation olicy lays an imortant role in balancing the individual EEs [1]. In this aer, we consider a WPCN where multile users first harvest energy from a ower station and then use the harvested energy to transmit data to an information receiving station. As mentioned before, our revious wor [2] focused on evaluating the system EE, which is beneficial for striing a balance between the system throughout and the system energy consumtion. In contrast, in this wor, we aim to unveil the user EE tradeoff in WPCNs and design a comutationally efficient resource allocation algorithm to balance the individual EEs of the users. Furthermore, the resource allocation algorithm roosed in [7] is based on the Dinelbach method which is only alicable for otimization roblems with a single-ratio objective function. Hence, this technique cannot be alied to the roblem studied in this wor where the system design objective function has a sum-of-ratios structure. The main contributions of this aer are summarized as follows: Different from most existing wors [2], [5], [7], [8], [21], we study the energy-efficient resource allocation in WPCNs from a user-centric ersective. Time allocation and ower control are jointly otimized to maximize the weighted sum of the user energy efficiencies WSUEE. Thereby, our roblem formulation taes also into account the circuit ower consumtion for WIT and WET. We first investigate the WSUEE maximization roblem without minimum user throughut constraints, which rovides useful insights into the EE tradeoff between the users of WPCNs. Subsequently, we extend the WSUEE maximization roblem to a generalized WPCN where each user has a certain amount of initial energy and also a minimum throughut requirement. This generalization rovides more flexibility for users to imrove their EEs while guaranteeing QoS. For WPCNs without QoS requirements, we reveal that it is otimal to let the ower station transmit with the maximum allowed ower while letting each user exhaust its own harvested energy using a fixed transmit ower. Based on this insight, we derive closed-form exressions for the maximum WSUEE as well as the otimal time allocation and ower control, which facilitates the characterization of the EE tradeoff between users in WPCNs. It is found that within a throughut region, all users can achieve their individual maximum EEs simultaneously while only beyond that region, there exists non-trivial tradeoff among user EEs. This is unlie the conventional user SE tradeoff in [11] where users are always cometing for resources and a non-trivial user SE tradeoff always exists. For generalized WPCNs, the WSUEE maximization roblem is more difficult to solve since in contrast to the case without QoS requirements, some users may not exhaust all of their available energies in order to save transmission time for users with high throughut requirements. Exloiting the sum-of-ratios structure of the objective function, we transform the original non-convex otimization roblem into an equivalent arameterized otimization roblem which can be solved iteratively via solving a two-layer otimization roblem. For the inner-layer, we show that the joint time allocation and ower control otimization roblem in subtractive form is a standard convex otimization roblem and can be efficiently solved using Lagrangian dual decomosition. For the outer-layer, the arameters for the equivalent arametric otimization roblem are udated with the damed Newton method having a suerlinear convergence seed. The roosed two-layer algorithm is guaranteed to converge to the otimal solution. The remainder of this aer is organized as follows. Section II introduces the WPCN system model. In Section III, we study energy-efficient transmission in WPCNs without

3 6900 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 10, OCTOBER 2016 both much smaller than the transmit ower of the ower station in ractice [11], [26]. Thus, the amount of energy harvested at user can be modeled as E H = η τ 0 P 0 h, 1 Fig. 1. The system model of a wireless owered communication networ WPCN. QoS requirements. In Section IV, we consider the WSUEE maximization for generalized WPCNs. Section V rovides simulation results for verification of our theoretical findings and the effectiveness of the roosed algorithm. Finally, Section VI concludes the aer. II. SYSTEM MODEL In this section, we first introduce the WPCN system model. Then, the WPCN ower consumtion model for the wireless terminals is rovided. Finally, we define the objective function, i.e., the WSUEE. A. Signal and Energy Harvesting Models We consider a WPCN which consists of a ower station, K wireless-owered users, and an information receiving station, as deicted in Fig. 1. The harvest-then-transmit rotocol is emloyed [11], i.e., all users first harvest energy from the RF signal broadcasted by the ower station in the DL, and then transmit information signals individually to the information receiving station in the UL. For the ease of imlementation, the ower station and all users are equied with a single antenna and use time division dulex to transmit in the same frequency band [8], [11]. Both the DL and the UL channels are modeled as quasi-static bloc fading channels, where the channel coefficients are assumed to be constant during each transmission time bloc corresonding to e.g. one data acet, but vary indeendently from one bloc to the next [8], [11], [12]. The DL channel gain between the ower station and user terminal and the UL channel gain between user terminal and the information receiving station are denoted as h and g, resectively. We also assume that the channel state information CSI is erfectly nown at the ower station since our goal is to obtain an EE uer bound for ractical WPCNs [11]. Once calculated, the resource allocation olicy is conveyed to the users to erform energyefficient transmission. Thereby, we assume that the energy consumed for estimating and exchanging CSI can be drawn from a dedicated battery which does not rely on the harvested RF energy [5]. In the DL WET stage, the ower station broadcasts an energy signal with transmission ower P 0 during transmission time τ 0. The energy harvested from the noise and the UL WIT signals received from other users is assumed to be negligible, since the thermal noise ower and the user transmit owers are where η 0, 1] is the energy conversion efficiency [11]. In the UL WIT stage, user transmits an indeendent information signal x to the information receiving station with transmission ower during transmission time τ. Then, the achievable throughut of user, denoted as B, is given by 1 B = τ W log γ, 2 where γ = g denotes the channel-to-noise-ower ratio for σ 2 UL WIT. Constants W and σ 2 are the bandwidth of the considered system and the variance of the additive white Gaussian noise, resectively. B. Power Consumtion Model for Wireless Terminals Since we focus on user-centric EE maximization, it is imortant to roerly model the energy consumtion of the user terminals in WPCNs. Here, we adot the ower consumtion model from [23] and [27], which taes into account the transmit ower, transmit circuit ower, and receive circuit ower of the user terminals for system design. In WPCNs, the overall energy consumtion of each wireless owered terminal consists of two arts: the energies consumed during DL WET and UL WIT, resectively. In the DL WET stage, as the terminal is in recetion mode, only a constant circuit ower is consumed for receive signal rocessing, i.e., r,. Thus, the energy consumtion in this stage is r, τ 0. Note that E H r, τ 0 = η P 0 h r, τ 0 > 0 should always hold. If E H r, τ 0 0, it means that user cannot store any energy during energy harvesting. This can be caused by a low energy conversion efficiency η,asmall transmit ower of the ower station P 0, a degraded DL channel gain h, or a large receive circuit ower consumtion r,. In this case, user should be shut down and not be considered for resource allocation. Hence, in the following, we only consider those users which satisfy E H r, τ 0 0. In the UL WIT stage, the wireless terminal is in the transmission mode, and the ower consumtion includes not only the overthe-air information transmit ower, denoted as,butalso the circuit ower consumed for transmit signal rocessing, denoted as c,. Therefore, the overall energy consumtion of user can be exressed as E = τ 0 r, + τ + τ c,, 3 where 0, 1] is a constant which accounts for the ower amlifier PA efficiency of user terminal. 1 Here, the achievable throughut of user, B,, corresonds to the total number of bits transmitted by user in the duration of a transmission time bloc, T max.

4 WU et al.: USER-CENTRIC EE MAXIMIZATION FOR WIRELESS POWERED COMMUNICATIONS 6901 C. Objective Function: User-Centric EE The EE of each user in WPCNs is defined as the ratio of its achievable throughut during UL WIT and its overall energy consumtion during both DL WET and UL WIT, i.e., EE = B = τ W log γ E τ 0 r, + τ. 4 + τ c, In this aer, we aim at balancing the EEs of the users in WPCNs. To achieve this goal, we adot WSUEE as the objective function, which is in fact a scalarization of the EEs of multile users. This metholodolgy is commonly used for the investigation of ossibly conflictling design objectives [19], [28]. The WSUEE of WPCNs can be exressed as EE sum = ω EE, 5 where the constant weight factors ω 0,, arerovided by uer layers and reflect the riorities of the different users. These redefined weights introduce a flexibility for customizing the erformance of different users. For examle, the system designer can assign higher weights to users with less energy storage but higher throughut requirements to mae them more energy efficient. III. WSUEE MAXIMIZATION XWITHOUT USER QOS REQUIREMENTS In this section, we investigate the WSUEE maximization roblem when QoS constraints are not imosed, which rovides useful design insights for energy-efficient transmission and characterization of the user EE tradeoff in WPCNs. Our goal is to jointly otimize time allocation and ower control for both DL WET and UL WIT for maximization of the WSUEE, i.e., EE sum = K ω EE.TheWSUEE maximization roblem can be formulated as τ W log max ω EE = ω γ τ 0,{τ }, τ P 0,{ } 0 r, + τ + τ c, s.t. C1: P 0 P max, C2: τ 0 r, + τ + τ c, η P 0 τ 0 h,, C3: τ 0 + τ T max, C4: τ 0 0, τ 0,, C5: P 0 0, 0,. 6 In roblem 6, C1 constrains the maximum DL transmit ower of the ower station to P max. C2 guarantees that the total energy consumed by user fordlwetandulwit does not exceed the available harvested energy η P 0 τ 0 h. In C3, T max is the total available transmission time. C4 and C5 are non-negativity constraints on the time allocation and ower control variables, resectively. Note that roblem 6 is neither convex nor quasi-convex due to the sumof-ratios objective function and the roducts of otimization variables in C2 and C3. In general, there is no standard method for solving non-convex otimization roblems efficiently. Nevertheless, in the following, we first investigate the roerties of energy-efficient transmission in WPCNs, and then we derive a closed-form exression for the maximum WSUEE based on these roerties. A. Otimal Solution We first study the transmit ower of the ower station in energy-efficient WPCNs. Proosition 1: For WSUEE maximization, the ower station of the WPCN always transmits with the maximum allowed ower during DL WET, i.e., P 0 = P max. Proof: Please refer to Aendix A. The intuition behind Proosition 1 is that letting the ower station transmit with the maximum allowed ower reduces the recetion time needed for DL WET, and thereby reduces the receive energy consumtion of the wireless terminals. In addition, this transmission strategy also rovides users with more transmission time, and thereby increases their throughuts for UL WIT, which imroves the user EEs. Next, we investigate how the wireless owered users utilize their harvested energy for energy-efficient transmission. Proosition 2: For WSUEE maximization, each user in the WPCN uses u all of its harvested energy, i.e., τ 0 r, +τ + τ c, = η P 0 τ 0 h,. Proof: Please refer to Aendix B. Proosition 2 reveals that the otimal strategy for energy utilization by the users of energy-efficient WPCNs is to fully utilize the harvested energy. Since DL WET incurs receive circuit energy consumtion for users, if they do not fully utilize the harvested energy during UL WIT, the user EE can always be imroved by decreasing the time for DL WET. The following roosition characterizes the time utilization in energy-efficient WPCNs. Proosition 3: For WSUEE maximization, the maximum value of the WSUEE can always be achieved by using u all the available transmission time T max. Proof: Please refer to Aendix C. In fact, if τ 0 + K τ < T max holds, we can always increase τ 0 and τ by the same factor such that constraint C3 in 6 is satisfied with strict equality, i.e., τ 0 + K τ = T max. Then, it is easy to chec that the scaled τ 0 and τ also always satisfy constraint C2 and achieve the same WSUEE. However, it is worth noting that the achieved user throughut increases linearly with τ and will be scaled accordingly when we scale τ 0 and τ. This has an interesting interretation: the throughut can be imroved without decreasing the EE but at the cost of increasing the transmission time. In Proositions 1-3, we have revealed some useful roerties of WSUEE maximization in WPCNs.Based on these roerties, we derive in the following the otimal transmission times and transmit owers and exress them in terms of the so-called transmit EEs of the users. Theorem 4: In WPCNs, the maximum WSUEE, EEsum,is given by EE sum = K 1 r, η P max h ω ee, 7

5 6902 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 10, OCTOBER 2016 where ee max can be interreted as the ε + c, transmit EE of user for UL WIT. Corresondingly, the otimal ower control and time allocation are given by [ = Wε ee ln 2 1 ] +,, 8 γ τ = η P max h r, ee W log 2 W ε τ 0,, 9 γ ee ln 2 τ 0 W log 2 1+ g 0, T max 1 + K η P max h r, ee W log 2 W γ ee ln Proof: Please refer to Aendix D. Theorem 4 rovides an exression for the maximum WSUEE by using the WPCN system arameters and the defined transmit EE. Since η P max h τ 0 is the total energy harvested at user and r, τ 0 is the circuit energy consumed during DL WET, then the actual energy stored in the battery is given by η P max h r, τ 0. Therefore, if a user has r, τ 0 r, η P max h alower η P max h τ 0 = in 7, it indicates that this user has more energy available for storage in its battery. η Then, P max h r, τ 0 η P max h τ 0 = η P max h r, η P max h = 1 r, η P max h can be interreted as the receive efficiency which indicates the caability of user to store energy during DL WET. Hence, the EE of user, EE, can be exressed as the roduct of the receive efficiency for DL WET, the transmit EE for UL WIT, and the corresonding weight, i.e., 1 r, η P max h ω ee. Moreover, in 8, we also observe that the otimal transmit ower of each user,, is solely determined by its own local arameters, i.e., c,, g,and. This imlies that the maximum WSUEE can always be achieved by allowing each user to maximize its own EE. This can be exlained as follows. In the absence of minimum user throughut requirements, the otimal strategy is to let each user use u all of its harvested energy, which results in a linear relationshi between τ 0 and τ as shown in 9. In addition, scaling τ 0 and τ with the same factor does not affect the user EE in 4. Thus, the system can always find a sufficiently small τ 0 and τ,, to satisfy time constraint C3 in 6 for a given T max,such that the EEs of the different users do not conflict with each other. Note that the user transmit EE, ee,, is a quasiconcave function with resect to,. Hence, the maximum value, ee, can be readily calculated by the simle bisection method [27], [29]. Then, we can obtain the maximum WSUEE as well as the otimal transmission times and transmit owers from Remar 5: It is worth noting that achieving the maximum user EE simultaneously for all users may not always be ossible in WPCNs if minimum user throughut constraints have to be fulfilled, see Section IV for details. This is because if user throughut requirements are considered, users may comete for the time resource in order to meet their required throughuts, and thus a non-trivial tradeoff for the time allocation to the users may exist. For instance, if a user is allocated a small τ, the only way for it to meet its minimum throughut requirement is to increase its transmit ower, which may lead to a lower user EE. In contrast, if a user is allocated a larger τ, it has more flexibility in adjusting which hels in achieving a higher user EE as well as in meeting the secified throughut requirement. Therefore, it is of interest to investigate the user EE tradeoff in WPCNs which is considered in the next subsection. B. User EE Tradeoff The following corollary characterizes the EE tradeoff between the users of a WPCN. Corollary 6: The achievable user throughut region, C, in which all users can achieve the maximum user EEs simultaneously, is given by { C = B 1,...,B,...,B K B R max...,b K R max K B 1 R1 max,..., }, 11 where R max = τ W log 2 1+ γ and τ0 + K τ = T max. B is the throughut of user during UL WIT which has been defined in 2., τ,andτ 0 are given in 8, 9, and 10, resectively. If the minimum throughut requirement of any user exceeds R max, then at least one user s EE has to be strictly decreased. Proof: Please refer to Aendix E. Corollary 6 indicates that if the users throughut requirements are inside region C, each user can achieve its own maximum EE without decreasing the EE of other users. In contrast, outside region C, there exists a non-trivial EE tradeoff between the users. It is worth noting that the user EE tradeoff between the users is unlie the conventional user throughut tradeoff for SE maximization [11] where users are always cometing for resources, such as ower and time, in order to maximize their own throughuts and thus a strict user SE tradeoff always exists. However, for the EE otimization considered in this wor, an exceedingly large transmit ower may not be beneficial. Thus, the EEs of the users can ossibly be maximized simultaneously within a certain user-throughut region of C in 11. In contrast, in a user-throughut region with non-trivial user EE tradeoff, the EEs of the users can be balanced by assigning different riorities to different users, which results in different time allocation and ower control strategies. For ractical WPCNs, where users may demand heterogeneous services, it is desirable to investigate the WSUEE maximization roblem with QoS constraints for WPCNs. This roblem will be addressed in the next section. Remar 7: It is exected that comared to system-centric EE maximization, maximizing the WSUEE will lead to a lower system EE. For examle, for system-centric EE maximization, it was found that the otimal strategy is to schedule only those users whose user EEs are higher than the system EE [2]. This imlies that to maintain high system EE, users with low user EEs have to remain silent for UL WIT. In contrast, for WSUEE maximization, we have shown that each user will be assigned a non-zero time interval for UL WIT, c.f. Proosition 3.2. This generally leads to a lower system EE. However, this loss in system EE is unavoidable if fairness among users is desired.

6 WU et al.: USER-CENTRIC EE MAXIMIZATION FOR WIRELESS POWERED COMMUNICATIONS 6903 Furthermore, the total system throughut is also degraded due to the similar reason. IV. WSUEE MAXIMIZATION WITH USER QOS REQUIREMENTS In this section, we study energy-efficient resource allocation for a general WPCN where each user is equied with a certain amount of initial energy and has a minimum throughut requirement. In this case, the WSUEE maximization roblem is formulated as max τ 0,{τ }, P 0,{ } ω EE s.t. C1, C4, C5, C2: τ 0 r, + τ + τ c, η P 0 τ 0 h + Q,, C3: τ 0 + τ T max, C6: τ W log γ Rmin,, 12 where Q in C2 and Rmin > 0 in C6 denote the amount of initial energy and the minimum required throughut of user, resectively. All other variables, constants, and constraints are identical to those in roblem 6. Remar 8: Note that in order to meet the throughut requirements of some users in C6, other users may not have sufficient time to fully use u their harvested energies in the current transmission bloc, i.e., τ 0 r, + τ + τ c, η P 0 τ 0 h may hold with strict inequality for some. In other words, at the end of some transmission blocs, some users may have energy left. To achieve a high user EE, it is referable to use the energy left from revious transmission blocs in the current transmission bloc. Therefore, in C2, we assume that each user terminal has a certain amount of initial energy Q available. Moreover, Q could also be the energy harvested from others sources such as solar and wind. Hence, the roosed otimization can account for the effects of various energy harvesting techniques when combined with WET. This setu rovides users with a higher flexibility in utilizing the available energy and in imroving their individual EEs, and is thereby more general than the setus considered in revious wors [5], [11]. Furthermore, if each user has sufficient initial energy Q, the otimal value of τ 0 can even be zero which suggests that WET is not needed. Thus, in this case, roblem 12 can be simlified to WSUEE maximization in conventional time division multile access TDMA systems without WET. In addition, under energy causality constraint C2 in 12, DL WET leads to receive ower consumtion which reduces user EE, while UL WIT imroves user EE. This motivates the system to decrease the time for DL WET and to increase the time for UL WIT. Therefore, for the generalized roblem where each user may have some initial energy in the battery, the deendence of UL WIT on DL WET is reduced. However, if the amount of initial energy is not sufficient to meet the minimum required throughut, then there exists a strict tradeoff between DL WET and UL WIT. Thus, the time allocation between DL WET and UL WIT is more comlicated than in the case without initial energy and minimum required throughut. In Section III, we have shown that roblem 6 can be solved by exloiting the roerties of the roblem itself, desite its non-convexity. However, comared to roblem 6, roblem 12 is more general and hence more interesting. However, roblem 12 is also much more challenging to solve for designing a comutationally efficient resource allocation algorithm. For examle, for given Q and Rmin,someusers may not use u all of their available energies, which is unlie the conclusion in Proosition 2. The reasons for this are twofold. First, if some user has large amounts of initial energy, e.g. Q +, it is intuitive that user cannot use u all of its available energy given the maximum available transmission time T max, otherwise, it has to transmit with an exceedingly large transmit ower which results in a low user EE. Second, if some user has a stringent throughut requirement Rmax, then a large amount of transmission time will be allocated to this user for UL WIT and the other users may not have sufficient time to use u all of their available energies. Nevertheless, in the following, we show that the considered roblem can be efficiently solved by exloiting the sum-of-ratios structure of the objective function in 12. The following roosition characterizes the transmit ower of the ower station. Proosition 9: For roblem 12, the maximum WSUEE can always be achieved for P0 = P max. Proof: Please refer to Aendix F. Alying Proosition 9 in roblem 12, we only have to otimize τ 0, { },and{τ },. The commonly used method for solving EE maximization roblems is the Dinelbach method [8], [21], [30]. However, the Dinelbach method can only solve fractional otimization roblems with a single-ratio objective function, and thus is not alicable to roblem 12 which has a sum-of-ratios objective function. In the next section, we exloit the sum-of-ratios structure of the WSUEE to transform the original roblem into a more tractable roblem, which facilitates the develoment of a comutationally efficient resource allocation algorithm. A. Problem Transformation The following theorem states the equivalence of a sum-ofratios otimization roblem and a arameterized subtractiveform roblem. Theorem 10: If τ 0, { }, {τ } is the otimal solution to roblem 12, then there exist α = α 1,,α K and β = β 1,,β K such that τ 0, { }, {τ } is the otimal solution to the following roblem with α = α and β = β : max {τ 0,{ },{τ }} F α ω B β E, 13 where F is the feasible set of roblem 12. Furthermore, τ 0, { }, {τ } have to satisfy the following system of

7 6904 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 10, OCTOBER 2016 equations for α = α and β = β : α E 1 = 0, {1,, K }, 14 β E ω B = 0, {1,, K }. 15 Proof: We refer the interested reader to [31] for a detailed roof of Theorem 10. Theorem 10 suggests that for the sum-of-ratios maximization roblem 12, there exists an equivalent arameterized maximization roblem with an objective function in subtractive form, i.e., roblem 13, with some additional given arameters. In fact, the arameterized objective function of roblem 13 has an interesting interretation from the economics ersective: β reresents the rice for the cost of each item in an investment ortfolio, e.g. the ower consumtion in the system, while α coordinates all items to see the maximum rofit. By alying Theorem 10 to roblem 12, we can obtain the otimal solution to roblem 12 by solving roblem 13 for α = α and β = β. Therefore, in the sequel, we first solve roblem 13 for given α, β and then develo an efficient aroach to udate α, β until 14 and 15 are both satisfied. Based on Theorem 10, roblem 12 is transformed into the following otimization roblem for given α, β max τ 0,{τ }, { } α ω τ W log γ β τ 0 r, + τ + τ c, s.t. C2, C3, C4, C5, C6. 16 Although roblem 16 is more tractable than the original roblem 12, it is still non-convex due to the roducts of otimization variables in the objective function, C2, and C6, resectively. Hence, we further introduce a set of auxiliary variables, i.e., Ẽ = τ,for, which can be interreted as the actual energy consumed for information transmission by user. Relacing with Ẽ τ, roblem 16 can be written as max τ 0,{τ }, Ẽ α ω τ W log Ẽ γ τ β τ 0 r, + Ẽ + τ c, s.t. C3, C4, C5: Ẽ 0,, C2: τ 0 r, + Ẽ + c, τ η P max τ 0 h + Q,, ε C6: τ W log Ẽ γ Rmin,. 17 τ After this substitution, it can be easily verified that roblem 17 is a standard convex otimization roblem. Hence, in the following, we analyze the Karush-Kuhn-Tucer KKT conditions of roblem 17 which leads to an otimal and comutationally efficient algorithm. B. Joint Time Allocation and Power Control The artial Lagrangian function for roblem 17 can be written as Lτ 0, Ẽ,τ, λ, μ,δ = α ω τ W log Ẽ γ τ β τ 0 r, + Ẽ + τ c, + λ η P max τ 0 h + Q τ 0 r, Ẽ c, τ + μ τ W log Ẽ γ Rmin τ + δ T max τ 0 τ, 18 where λ = λ 1,,λ K 0 and μ = μ 1,,μ K 0 are Lagrange multilier vectors associated with the energy causality constraint C2 and the minimum user throughut constraint C6, resectively. δ is the non-negative Lagrange multilier corresonding to the total time constraint C3. Note that the non-negativity constraints of the otimization variables, i.e., C4 and C5, will be absorbed into the otimal solution in the following. Accordingly, the associated dual function of roblem 17 is given by Gλ, μ,δ = max τ 0,{ },{τ } D Lτ 0, Ẽ,τ, λ, μ,δ,whered is the feasible set secified by C4 and C5. The dual roblem of 17 is thus given by min λ 0,μ 0,δ 0 max Lτ 0, Ẽ,τ, λ, μ,δ. 19 τ 0,{Ẽ },{τ } D Since the original roblem 17 is a standard convex otimization roblem which also satisfies Slater⣠s constraint qualification, the duality ga between roblem 17 and its dual roblem 19 is zero [32]. This means that the otimal solution of roblem 17 can be obtained by solving two otimization roblems iteratively: the rimal variable otimization which maximizes Lτ 0, Ẽ,τ, λ, μ,δ over τ 0, Ẽ,τ for given λ, μ, δ, and the dual variable otimization that minimizes Gλ, μ,δ over λ, μ,δ for given τ 0, Ẽ,τ.Inthe following, we discuss the solution methodology in detail. 1 Primal Variable Otimization: Since the maximization of Lτ 0, Ẽ,τ, λ, μ,δ over τ 0, Ẽ,τ for given λ, μ,δ is a standard concave otimization roblem, the otimal solution can be obtained from the KKT conditions. Taing the artial derivative of L with resect to τ 0, Ẽ,andτ, resectively, yields L = λ η P max h r, τ 0 L = Wα ω + μ τ γ Ẽ τ + Ẽ γ ln 2 L τ = α ω + μ W log 2 Wα ω + μ Ẽ γ τ + Ẽ γ ln 2 α β r, δ, 20 α β + λ, 21 ε 1 + Ẽ γ τ α β + λ c, δ. 22

8 WU et al.: USER-CENTRIC EE MAXIMIZATION FOR WIRELESS POWERED COMMUNICATIONS 6905 Setting L = 0, the relationshi between Ẽ Ẽ and τ is obtained as [ = Ẽ Wα ω + μ = τ α β + λ ln 2 1 ] +,, 23 γ where [x] + max{x, 0}. From 23, we can see that increases with both the PA efficiency and the UL channel gain γ. This suggests that in order to maximize the WSUEE, a user with the higher PA efficiency and a higher UL channel gain should transmit with higher ower as this user is more efficient in utilizing energy. Substituting 23 into 22 and after some maniulations, L τ can be exressed as L Wα ω + μ = α ω + μ W log τ 2 α β + λ ln 2 γ δ Wα ω + μ α β + λ α β + λ ln c,. γ 24 From 20 and 24, we observe that the Lagrangian function L is a linear function of both τ 0 and τ. This means that the otimal values of τ 0 and τ can always be found at the vertices of the feasible region [32]. Therefore, in order to obtain τ 0 and τ, we substitute 23 into 17, which yields the following otimization roblem max τ 0,{τ } τ 0 τ α ω W log 2 1+ γ α β + c, K α β r, s.t. C3, C4, C2: τ + c, τ 0 η P max h r, + Q,, C6: τ W log γ R min,. 25 We observe that roblem 25 is a linear rogramming roblem with resect to τ 0 and τ. Therefore, standard linear otimization tools, such as the simlex method [32], can be emloyed to obtain the otimal solution efficiently. Substituting τ bac into 23, Ẽ is obtained immediately. 2 Dual Variable Otimization: After comuting the rimal variables τ 0, Ẽ, τ, we now roceed to solve dual roblem 19, i.e., min Gλ, μ,δ. Since a dual function is λ 0,μ 0,δ 0 always convex by definition, we adot the gradient method for udating λ, μ,δ. The Lagrange multilier udate equations are given by [ λ n + 1 = λ n ɛ 1 η P max τ 0 h + Q ] + τ 0 r, Ẽ c, τ,, 26 ε [ μ n + 1 = μ n ɛ 2 τ W log Ẽ γ τ R min] +,, 27 [ ] + δn + 1 = δn ɛ 3 T max τ 0 τ, 28 where index n 0 is the iteration index and ɛ i, i {1, 2, 3}, are ositive ste sizes. A discussion regarding the choice of the ste size for gradient methods is rovided in [32] and is thus omitted here for brevity. The udated Lagrange multiliers in can be used for udating the time allocation and ower control variables in the rimary variable otimization. Due to the concavity of rimary roblem 17, the iterative otimization of τ 0, Ẽ,τ in 1 and λ, μ,δ in 2 is guaranteed to converge to the otimal solution of 17. C. Udating α, β Having obtained τ 0, Ẽ,τ in Section IV-B, we are now ready to develo an algorithm for udating α, β. Let ψ α = α E 1 and ψ +K β = β E ω B, = 1,, K. It is shown in [31] that the unique otimal solution of α, β is obtained if and only if ψα, β = [ψ 1,ψ 2,,ψ 2K ]=0 is satisfied, i.e., 14 and 15 hold. Thus, the well-nown damed Newton method [19], [31], defined by 29-31, can be emloyed to udate α, β as follows α n+1 = α n + ζ n q n, 29 β n+1 = β n + ζ n q n, 30 q n =[ψ α, β] 1 ψα, β, 31 where ψ α, β is the Jacobian matrix of ψα, β, n is the iteration index, and ζ n is the greatest ξ satisfying ψα n + ξ q n, β n + ξ q n 1 ςξ ψα n, β n, 32 where ξ 0, 1, ς 0, 1, and denotes the standard Euclidean norm. Secifically, for the roblem at hand, the ointwise udate equations for α and β can be exressed as α n+1 β n+1 = 1 ζ n α n + ζ n 1 E n, 33 = 1 ζ n β n + ζ n ω B n E n. 34 The details of obtaining the otimal solution to roblem 12 are summarized in Algorithm 1. A flow chart for Algorithm 1 is resented in Figure 2. The comlexity of Algorithm 1 can be evaluated as follows. First, the comlexity for obtaining τ 0,,andτ,, linearly increases with the number of users, K. Second, since there are 2K + 1 dual variables, the comlexity of the subgradient method is OK 2 [32] where Ox means that there is an uer bound for the comlexity which grows with order x. Finally, the comlexity for udating α and β is indeendent of K [31]. Therefore, the total comlexity of the roosed algorithm is OK 3. V. NUMERICAL RESULTS In this section, we resent simulation results to validate our theoretical findings and to demonstrate the user EE. Four users are randomly and uniformly distributed on the right hand side of the ower station with a reference distance of 2 meters and a maximum service distance of 10 meters. The information receiving station is located 100 meters away from the ower

9 6906 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 10, OCTOBER 2016 Algorithm 1 Energy-Efficient Resource Allocation Algorithm for WPCNs 1: Initialize the algorithm accuracy indicator t; 2: Initialize α and β, andsetn = 0; 3: reeat 4: Initialize λ, μ, andδ; 5: reeat 6: Obtain the time allocation variables τ 0 and τ by solving roblem 25; 7: Obtain the ower control variables from 23; 8: Udate the dual variables λ, μ, andδ in 26, 27, and 28, resectively; 9: until λ, μ, andδ converge; 10: Comute B and E from 2 and 3; 11: Comute q n from 31; 12: Comute the largest ξ satisfying 24; 13: Udate α and β in 33 and 34; 14: n = n + 1; 15: until ψα, β t. Fig. 3. station. WSUEE versus the maximum allowed transmit ower of the ower Fig. 4. The imact of the PA efficiency on WSUEE. Fig. 2. Flow chart of the roosed Algorithm 1. station. The system bandwidth is set to 20 Hz and the time duration is set as 1 s [11]. The ath loss exonent is 2.4 and the thermal noise ower is -110 dbm. The small scale fading for WET and WIT is Rician fading with Rician factor 7 db and Rayleigh fading, resectively. For the urose of comarison, the maximum transmit owers of the ower stations are set as 30 dbm and 46 dbm in Figure 4-5 and Figure 6-9 [11]. Unless secified otherwise, we assume that all users have the same receive and transmit circuit ower consumtion as well as the same weight, the same energy conversion efficiency, and the same PA efficiency. The corresonding values are set to r, = r = 30 mw, ω = ω = 1, c, = c = 50 mw, η = η = 0.9, and = ε = 0.9,, resectively [8]. A. WSUEE Versus Maximum Transmit Power In Figure 3, we comare the erformance of the following schemes: 1 WSUEE otimal: roosed aroach; 2 System EE otimal: maximization of the system EE which is defined Fig. 5. Average system EE erformance of the system EE otimal scheme and the WSUEE otimal scheme. as a ratio of the system throughut and the system energy consumtion [2]; 3 Throughut otimal: conventional throughut maximization [11]; 4 Partial utilization: each user consumes only art of its harvested energy, i.e., τ + τ c, = ρ η P max h r, τ 0, where ρ 0 < ρ < 1 can be adjusted to strie a balance between the energy consumed in

10 WU et al.: USER-CENTRIC EE MAXIMIZATION FOR WIRELESS POWERED COMMUNICATIONS 6907 Fig. 7. User EE versus the minimum throughut requirement for different weights when Rmin 1 = R2 min = R min. Fig. 6. User EE versus the minimum throughut requirement for different weights, ω =[ω 1 ω 2 ]. the current transmission bloc and the energy stored for the next transmission bloc. From Figure 3, we observe that the WSUEE of the roosed aroach first increases quicly with the transmit ower of the ower station and then exeriences marginal increases in the high transmit ower region. This is because when P max is low, to transfer a certain amount of energy, a small increase of P max can significantly reduce the time needed for DL WET and thus reduce the receive circuit energy consumtion. Therefore, the user EE imroves quicly. On the other hand, in the high P max region, the time needed for DL WET is already so short that the receive circuit energy consumtion does no longer have a large imact on the total user energy consumtion, and thus, further increasing the transmit ower leads only to a marginal increase in the WSUEE. We also observe from Figure 3 that the roosed aroach outerforms all other considered schemes which can be exlained as follows. First, the artial utilization scheme is based on the assumtion that each user has harvested more energy during DL WET than it utilizes during UL WIT. Since the DL transmit ower of the ower station is fixed to P max, it imlies that users consume more time during DL WET and hence consume more receive circuit energy than the otimal amount, which thereby leads to low user EEs. Therefore, not fully utilizing the harvested energy is subotimal. However, as P max increases, the receive circuit energy consumed for RF energy harvesting decreases due to the short energy harvesting time. Thus, the artial utilization scheme gradually converges to the otimal scheme. Second, as mentioned in [11], although the throughut otimal scheme also lets each user utilize all of its harvested energy, the time allocation between the DL ower station and the UL users is not EE oriented which thus leads to a strictly subotimal erformance in terms of user-centric EE. Finally, the systemcentric EE sees to imrove the system EE by exloiting multiuser diversity [2]. This ind of otimization leads to starvation of some users which may not be scheduled at all. This leads to an unsatisfactory WSUEE. B. WSUEE Versus User PA Efficiency Figure 4 illustrates the imact of the user PA efficiency on the WSUEE of the considered schemes. As can be observed, the erformance of all schemes increases with the PA efficiency, as exected from the analytical exression for the WSUEE in 7. In addition, the erformance gains of the roosed aroach comared to the other schemes are also enhanced as the PA efficiency increases. This can be attributed to the fact that a higher PA efficiency allows a user to have more energy for information transmission, which rovides the roosed otimization aroach with more degrees of freedom for imroving the user-centric EE. C. System EE Versus Maximum Transmit Power In Figure 5, we illustrate the achieved system EE of the roosed WSUEE otimal resource allocation, which is generated by taing the result of the WSUEE otimal aroach into the system EE exression. As can be seen, WSUEE maximization incurs a erformance loss in terms of system EE comared to system-centric EE maximization and the erformance loss increases with increasing maximum transmit ower. This is due to the following two reasons. First, WSUEE maximization does not tae into account the energy loss caused by signal

11 6908 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 10, OCTOBER 2016 Fig. 9. WSUEE versus the minimum user throughut requirement. Fig. 8. Illustration of EE tradeoff between four users. attenuation during DL WET and thus, the obtained time allocation between DL WET and UL WIT is not otimal in terms of the system EE. Second, as revealed in Proosition 3.2, for WUSEE maximization, each user is assigned a non-zero time interval for UL WIT, which is not beneficial for the overall system throughut and limits the system s ability to exloit multi-user diversity. In contrast, system-centric EE maximization selectively schedules only those users whose user EEs are higher than the system EE while forcing the rest of the users to be silent. Therefore, the system EE gain of the system-centric EE maximization aroach over the WSUEE maximization aroach is at the exense of sacrificing user fairness, which is not desirable from the ersective of the end users. D. User EE Tradeoff Region In Figure 6, we illustrate the findings of Corollary 6. A WPCN with two users is considered. Secifically, we set h [h 1, h 2 ]=[0.1, 0.1] and γ [γ 1,γ 2 ]=[1000, 500]. We lot the achieved user EE versus the user throughut requirements for different weights. In Figure 6b, we switch the weights of the two users in 12 comared to Figure 6a, and then evaluate the individual user EEs resectively to illustrate the effect of the weights on the user EEs. Comaring Figure 6a and Figure 6b, we can see that when the required throughuts of the two users are small, both of their EEs are constant with resect to the required throughuts, which suggests that changing the weights has no imact on the EE of either user. This is because both users achieve their own maximum EE simultaneously. However, when the throughut requirements become stringent, the user EEs of the two users can be adjusted by selecting different weights for different users. Particularly, in Figure 6b, by assigning a larger weight to user 2 which has the worse UL WIT channel, we can imrove its user EE significantly comared to Figure 6a. To mae this oint clearer, in Figure 7, we show the nontradeoff and tradeoff regions in terms of the user throughut when R min = Rmin, = 1, 2. Secifically, for ω = [5 1], we observe that the EE of user 1 decreases slowly while the EE of user 2 decreases sharly as R min increases. In contrast, for ω = [1 5], the EEs of user 1 and user 2 show the oosite behaviours. In articular, for R min = bits, user 1 and user 2 achieve almost identical EEs. This suggests that in the user EE tradeoff region, assigning different weights to different users can indeed enforce a certain notion of fairness among users and hel imrove the individual EEs of users having degraded channels. E. Illustration of EE Tradeoff Between Users Figure 8 illustrates the tradeoff between four users where users 1, 2, 3, and 4 are located at distances of 80 m, 70 m, 90 m, and 95 m from the ower station, resectively. Without loss of generality, we assume that all users have the same minimum throughut requirement, i.e., Rmin = R min = bits,. We assign the same weights to users 2, 3, and 4, i.e., ω 2 = ω 3 = ω 4 = 1, and vary the weight of user 1, ω 1, between 1 and 15. As can be seen from Figure 8a, as ω 1 increases, the EE of user 1 increases while the EEs of users 2, 3, and 4, decrease, which further demonstrates that assigning higher weights to some users indeed hels imrove their EEs. In addition, it is worth noting that as ω 1 increases, the EE of user 1 first gradually increases and finally aroaches a constant value, which is the maximum EE that user 1 can

12 WU et al.: USER-CENTRIC EE MAXIMIZATION FOR WIRELESS POWERED COMMUNICATIONS 6909 achieve. The user EE tradeoff is further studied in Figure 8b, where the EEs of users 2, 3, and 4 versus the EE of user 1 are deicted. As the EE of user 1 increases, the EE of the other users strictly decreases, which illustrates the non-trivial tradeoff between the EEs of individual users. F. WSUEE Versus Minimum User Throughut Requirement In Figure 9, we consider a symmetric networ where all users have the same minimum throughut requirement, i.e., R min = Rmin,, and show the WSUEE versus R min. We observe that for all considered numbers of users, the WSUEE first remains constant and then decreases as R min increases, which further illustrates the fundamental tradeoff between EE and SE. In addition, as R min increases, the WSUEE for a larger number of users decreases more raidly than that for a small number of users. This is because for a smaller number of users, a longer UL WIT transmission time is available for each user, and thus the achieved throughut of each user is also larger. However, for a larger number of users, the available UL WIT transmission time allocated for each user is shorter, and the achieved throughut of each user is thus smaller. Therefore, as R min increases, the WSUEE of a larger number of users decreases faster than that of a smaller number of users. Besides, when R min is relatively high, users have to comete for time resources more fiercely and thus have to transmit with larger owers during UL WIT in order to meet their throughut requirements, which thus leads to a faster decay in the user EE and thereby the WSUEE. VI. CONCLUSIONS In this aer, we investigated the energy-efficient resource allocation in WPCNs from a user-centric ersective. The time allocation and ower control of DL WET and UL WIT were jointly otimized to maximize the WSUEE. For the WUSEE maximization roblem without minimum user throughut requirements, we derived a closed-form exression for the WSUEE by carefully studying the roerties of energyefficient transmission. For the WUSEE maximization roblem with minimum user throughut requirements, we roosed a comutationally efficient resource allocation algorithm to obtain the otimal solution by exloiting the sum-of-ratios structure of the objective function. Simulation results demonstrated the gains in EE achieved by the roosed joint otimization aroach and also unveiled the tradeoff between the EEs of different users in WPCNs. In articular, 1 for low user throughut requirements, all users can achieve their individual maximum EEs simultaneously; 2 for high user throughut requirements, the individual user EEs can be balanced by assigning different weights to different users; 3 neither the system-centric EE scheme nor the throughut otimal scheme are user-centric EE otimal and the erformance loss caused by adoting traditional schemes for user-centric EE systems is higher for larger ower station transmit owers and for smaller user receive circuit owers. APPENDIX A PROOF OF PROPOSITION 1 We rove Proosition 1 by contradiction. Suose that {P0, { },τ 0, {τ }} achieves the maximum WSUEE of roblem 6 satisfying P0 < P max. The corresonding EE of user is denoted as EE. Then, we construct another solution { P 0, { }, τ 0, { τ }} satisfying P 0 = P max, τ 0 = P 0 τ 0, = P, 0 and τ = τ, resectively. The corresonding EE of user is denoted as ÊE. It is easy to chec that { P 0, { }, τ 0, { τ }} does not violate any of the constraints and is thus a feasible solution. Furthermore, since P 0 = P max > P0, it follows that τ 0 <τ0. Then, the energy consumtion of user satisfies τ 0 r, + τ + τ c, <τ 0 r, + τ + τ c,. 35 Thus, from 35 and 4, it follows that EE < ÊE,. Therefore, we have K ω EE < K ω ÊE. Hence, {P0, { },τ 0, {τ }} cannot be the otimal solution. APPENDIX B PROOF OF PROPOSITION 2 We rove Proosition 2 by contradiction. Suose that {P max, { },τ 0, {τ }} achieves the maximum WSUEE of roblem 6 while there exists a user m who does not use u all of its harvested energy, i.e., τ 0 r,m + τ m εm + τ m c,m < η m P max τ 0 h m and τ 0 r, + τ + τ c, = η P max τ 0 h for = m. The corresonding EE of user, denoted as EE, is given by 1 + γ EE = τ W log 2 τ0 r, + τ + τ c,,. 36 Then, we construct another solution {P max, { }, τ 0, { τ }} satisfying =,, τ 0 = βτ0, τ m = ατm,and τ = βτ for = m, resectively, where 0 < β < 1andα > 1. Note that for β 0, it follows that η m P max τ 0 h m τ 0 r,m = βτ0 η m P max h m r,m 0; while as α increases, τ m m εm + τ m c,m = ατm m εm + c,m increases. Thus, there always exist α and β such that both ατm m εm + c,m = βτ0 η m P max h m r,m and τ 0 + K τ = β τ0 + K =m τ + ατm T max are satisfied. It is also easy to verify that τ 0 r, + τ + τ c, = η P max τ 0 h still holds. Thus, the corresonding user EEs, ÊE m and ÊE for = m, can be exressed as ÊE m = τ m W log m γ m τ 0 r,m + τ m m εm + τ m c,m ατm = W log m γ m, 37 βτ0 r,m τ + α m m ε m + τm c,m ÊE = τ W log γ τ 0 r, + τ + τ c, βτ = W log γ, = m. 38 βτ0 r, τ + β + τ c,

13 6910 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 10, OCTOBER 2016 Comaring 36 with 37 and 38, we observe that ÊE m > EE m and ÊE = EE for = m, asα > 1 and 0 < β < 1. Therefore, we have K ω ÊE > K ω EE, which contradicts that user m does not use u all of its harvested energy. This comletes the roof. APPENDIX C PROOF OF PROPOSITION 3 Suose that {P max, { },τ 0, {τ }} achieves the maximum WSUEE, EEsum, and satisfies 0 τ 0 + K τ < T max. Then, we can construct another solution { P 0, { }, τ 0, { τ }} with P 0 = P max, =, τ 0 = ατ0, τ = ατ, resectively, T where α = max τ0 + K > 1 such that τ τ 0 + K τ = T max. The corresonding WSUEE is denoted as ÊE sum. First, it is easy to verify that { P 0, { }, τ 0, { τ }} still satisfies constraints C1-C3. Then, substituting { P 0, { }, τ 0, { τ }} into roblem 6 yields ÊE sum = EEsum, which means that the maximum WSUEE can always be achieved by using u all the available time, i.e., T max. APPENDIX D PROOF OF THEOREM 4 From Proosition 2, we obtain τ = η P max h r, τ c, Substituting 39 into the objective function of roblem 6 yields EE sum = ω η P max h r τ 0 W log ε γ c, + c, r τ 0 + η P max h r τ 0 + c, r W log2 1 + γ = ω 1 η P max h c, From 40, we observe that ω 1 r η P max h is a constant for each user. Letee W log 2 1+ γ, which can be interreted ε + c, as the transmit EE of user. Thus, to maximize EE sum, we only have to maximize ee. It is easy to rove that ee is a strictly quasiconcave function of and its unique stationary oint is also the maximum oint. Thus, by setting the derivative of ee with resect to to zero, we obtain the following relationshi between ee and [ = Wε ee ln 2 1 ] +, 41 γ where ee is the maximum transmit EE of user. The numerical values for ee and can be easily obtained by the bisection method [32]. APPENDIX E PROOF OF COROLLARY 6 From 7 in Theorem 4, we now that the maximum value of WSUEE does not deend on the value of τ 0 in the feasible region while the achieved throughut R increases linearly with the transmit time τ as is given by 8. Therefore, τ 0 and τ,, reach their maximum feasible values if and only if K τ0 + τ = T max. 42 Thus, the maximum achieved throughut at the maximum WSUEE, denoted as R max,isgivenby R max = τ W log γ = η P max h r τ0 W log γ + c, = η P max h r τ 0 ee. 43 Thus, if the minimum throughut requirement of any user exceeds R max, we can see from 43 that the only way to meet the requirement is to increase the DL WET time τ0 as ee already assumes its maximum value ee. Then, from 42, it follows that K τ has to be decreased which suggests that at least one user s τ has to be decreased. As EE increases with τ and decreases with τ 0, we conclude that at least one user s EE has to be decreased. APPENDIX F PROOF OF PROPOSITION 9 As the ower transfer may not always be activated due to the initial energy of the users, we discuss the following two cases. First, if the ower transfer is activated for the otimal solution, i.e., τ0 > 0, then we can show P 0 = P max following a similar roof as for Proosition 1. Second, if τ0 = 0 holds true, then the value of the ower station s transmit ower P0 does not affect the maximum value of WSUEE, and thus P 0 = P max is also an otimal solution. REFERENCES [1] Q. Wu and W. Chen, User-centric energy-efficient resource allocation for wireless owered communications, in Proc. IEEE WCSP, Oct. 2015, [2] Q. Wu, M. Tao, D. W. K. Ng, W. Chen, and R. Schober, Energy-efficient transmission for wireless owered multiuser communication networs, in Proc. IEEE ICC, Jun. 2015, [3] Z. Ding, I. Kriidis, B. Sharif, and H. V. Poor, Wireless information and ower transfer in cooerative networs with satially random relays, IEEE Trans. Wireless Commun., vol. 13, no. 8, , Aug [4] X. Chen, C. Yuen, and Z. Zhang, Wireless energy and information transfer tradeoff for limited-feedbac multiantenna systems with energy beamforming, IEEE Trans. Veh. Technol., vol. 63, no. 1, , Jan [5] C. Zhong, H. A. Suraweera, G. Zheng, I. Kriidis, and Z. Zhang, Wireless information and ower transfer with full dulex relaying, IEEE Trans. Commun., vol. 62, no. 10, , Oct [6] C. Zhong, G. Zheng, Z. Zhang, and G. K. Karagiannidis, Otimum wirelessly owered relaying, IEEE Signal Process. Lett., vol. 2, no. 10, , Oct [7] Q. Wu, M. Tao, D. W. K. Ng, W. Chen, and R. Schober, Energyefficient resource allocation for wireless owered communication networs, IEEE Trans. Wireless Commun., vol. 15, no. 3, , Mar [8] D. W. K. Ng, E. S. Lo, and R. Schober, Wireless information and ower transfer: Energy efficiency otimization in OFDMA systems, IEEE Trans. Wireless Commun., vol. 12, no. 12, , Dec

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Xu, Energy- and sectral-efficiency tradeoff in downlin OFDMA networs, IEEE Trans. Wireless Commun., vol. 10, no. 11, , Nov [26] Q. Shi, L. Liu, W. Xu, and R. Zhang, Joint transmit beamforming and receive ower slitting for MISO SWIPT systems, IEEE Trans. Wireless Commun., vol. 13, no. 6, , Jun [27] Q. Wu, M. Tao, and W. Chen, Joint Tx/Rx energy-efficient scheduling in multi-radio wireless networs: A divide-and-conquer aroach, IEEE Trans. Wireless Commun., vol. 15, no. 4, , Ar [28] E. Björnson and E. Jorswiec Otimal Resource Allocation in Coordinated Multi-Cell Systems. [Online]. Available: htt:// com/sites/default/files/ublications/387/ bjornson-vol9-cit -069.df [29] G. Miao, N. Himayat, and G. Y. Li, Energy-efficient lin adatation in frequency-selective channels, IEEE Trans. Commun., vol. 58, no. 2, , Feb [30] W. Dinelbach, On nonlinear fractional rogramming, Manage. Sci., vol. 13, no. 7, , Mar [31] Y.-C. Jong An Efficient Global Otimization Algorithm for Nonlinear Sum-of-Ratios Problem. [Online]. Available: htt://www. otimization-online.org/db_html/2012/08/3586.html [32] S. Boyd and L. Vandenberghe, Convex Otimization. Cambridge, U.K.: Cambridge Univ. Press, Qingqing Wu S 13 received the B.S. degree in electronics engineering from the South China University of Technology, Guangzhou, China, in He is currently ursuing the Ph.D. degree with the Networ Coding and Transmission Laboratory, Shanghai Jiao Tong University. Since 2015, he has been a Visiting Scholar with the School of Electrical and Comuter Engineering, Georgia Institute of Technology, Atlanta, GA, USA. His current research interests include energy-efficient otimization and wireless information and ower transfer. He serves as a TPC member of Chinacom 2015, the IEEE ICCC 2016, the IEEE Globecom 2016, and the IEEE VTC He was a reciient of the International Conference on Wireless Communications and Signal Processing Best Paer Award in Wen Chen M 03 SM 11 received the B.S. and M.S. degrees from Wuhan University, Wuhan, China, in 1990 and 1993, resectively, and the Ph.D. degree from The University of Electro- Communications, Toyo, Jaan, in From 1999 to 2001, he was a Researcher with the Jaan Society for the Promotion of Sciences. In 2001, he joined the University of Alberta, Edmonton, AB, Canada, starting as a Post-Doctoral Fellow with the Information Research Laboratory and continuing as a Research Associate with the Deartment of Electrical and Comuter Engineering. Since 2006, he has been a Full Professor with the Deartment of Electronic Engineering, Shanghai Jiao Tong University SJTU, Shanghai, China, where he is also the Director of the Institute for Signal Processing and Systems. From 2014 to 2015, he was the Dean of the School of Electronic Engineering and Automation with the Guilin University of Electronic Technology, China. Since 2016, he has been the Chairman of SJTU Intelligent Proerty Management Cororation. He is the author of 74 aers in the IEEE journals and transactions and more than 110 aers in IEEE conference ublications. His research interests include networ coding, cooerative communications, multile access technique, and multile-inut multile-outut orthogonal-frequency-division multilexing systems. Derric Wing Kwan Ng S 06 M 12 received the bachelor s degree Hons. and the M.Phil. degree in electronics engineering from the Hong Kong University of Science and Technology in 2006 and 2008, resectively, and the Ph.D. degree from the University of British Columbia UBC in In the summer of 2011 and sring of 2012, he was a Visiting Scholar with the Centre Tecnològic de Telecomunicacions de Catalunya Hong Kong. He was a Senior Post-Doctoral Fellow with the Institute for Digital Communications, Friedrich-Alexander- University Erlangen-Nürnberg, Germany. He is a Lecturer with the University of New South Wales, Sydney, Australia. His research interests include convex and non-convex otimization, hysical layer security, wireless information and ower transfer, and green energy-efficient wireless communications. Dr. Ng has served as an Editorial Assistant to the Editor-in-Chief of the IEEE TRANSACTIONS ON COMMUNICATIONS since He is currently aneditoroftheieeecommunications LETTERS. HewasaCo-Chair for the Wireless Access Trac of the 2014 IEEE 80th Vehicular Technology Conference. He has been a TPC member of various conferences, including the Globecom, WCNC, ICC, VTC, and PIMRC. He was honored as an Exemlary Reviewer of the IEEE TRANSACTIONS ON COMMUNICATIONS in 2015, the To Reviewer of the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY in 2014, and an Exemlary Reviewer of the IEEE WIRELESS COMMUNICATIONS LETTERS in 2012, 2014, and He received best aer awards at the IEEE International Conference on Comuting, Networing and Communications 2016, the IEEE Wireless Communications and Networing Conference WCNC 2012, the IEEE Global Telecommunication Conference Globecom 2011, and the IEEE Third International Conference on Communications and Networing in China He also received IEEE student travel grants to attend the IEEE WCNC 2010, the IEEE International Conference on Communications ICC 2011, and the IEEE Globecom He was a reciient of the 2009 Four Year Doctoral Fellowshi from the UBC, the Sumida & Ichiro Yawata Foundation Scholarshi in 2008, and the R&D Excellence Scholarshi from the Center for Wireless Information Technology at HKUST in 2006.

15 6912 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 10, OCTOBER 2016 Jun Li M 09 received the Ph.D. degree in electronics engineering from Shanghai Jiao Tong University, Shanghai, China, in In 2009, he was with the Deartment of Research and Innovation, Alcatel Lucent Shanghai Bell, as a Research Scientist. From 2009 to 2012, he was a Post-Doctoral Fellow with the School of Electrical Engineering and Telecommunications, University of New South Wales, Australia. From 2012 to 2015, he was a Research Fellow with the School of Electrical Engineering, University of Sydney, Australia. Since 2015, he has been a Professor with the School of Electronic and Otical Engineering, Nanjing University of Science and Technology, Nanjing, China. His research interests include networ information theory, channel coding theory, wireless networ coding, and cooerative communications. Robert Schober S 98 M 01 SM 08 F 10 was born in Neuendettelsau, Germany, in He received the Diloma Univ. and Ph.D. degrees in electrical engineering from the University of Erlangen Nuermberg in 1997 and 2000, resectively. From 2001 to 2002, he was a Post-Doctoral Fellow with the University of Toronto, Canada, sonsored by the German Academic Exchange Service DAAD. Since 2002, he has been with the University of British Columbia UBC, Vancouver, Canada, where he is a Full Professor. Since 2012, he has been an Alexander von Humboldt Professor and the Chair of Digital Communication with the Friedrich Alexander University, Erlangen, Germany. His research interests fall into the broad areas of communication theory, wireless communications, and statistical signal rocessing. Dr. Schober is a fellow of the Canadian Academy of Engineering and the Engineering Institute of Canada. From 2012 to 2015, he served as the Editorin-Chief of the IEEE TRANSACTIONS ON COMMUNICATIONS. Since 2014, he has been the Chair of the Steering Committee of the IEEE TRANSACTIONS ON MOLECULAR, BIOLOGICAL AND MULTISCALE COMMUNICATION. Furthermore, he is a Member-at-Large of the Board of Governors of the IEEE Communications Society. He received several awards for his wor, including the 2002 Heinz MaierLeibnitz Award of the German Science Foundation DFG, the 2004 Innovations Award of the Vodafone Foundation for Research in Mobile Communications, the 2006 UBC Killam Research Prize, the 2007 Wilhelm Friedrich Bessel Research Award of the Alexander von Humboldt Foundation, the 2008 Charles McDowell Award for Excellence in Research from UBC, a 2011 Alexander von Humboldt Professorshi, and a 2012 NSERC E.W.R. Steacie Fellowshi. In addition, he has received several best aer awards for his research.