QUALITY OF SERVICE (QoS) is driving research and

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1 482 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 33, NO. 3, MARCH 2015 Joint Allocation of Resource Blocks, Power, and Energy-Harvesting Relays in Cellular Networks Sobia Jangsher, Student Member, IEEE, Haojie Zhou, Student Member, IEEE, Victor O. K. Li, Fellow, IEEE, and Ka-Cheong Leung, Member, IEEE Abstract Relaying is a promising technique in cellular networks for improving system capacity and coverage. To facilitate the deployment of relays in remote areas without ready access to the electrical grid, energy-harvesting relays may be deployed. Energy-harvesting has been studied extensively for sensor networks, but it is still an open problem for cellular networks. In this paper, we study the problem of the joint allocation of orthogonal frequency division multiplexing access resource blocks and transmission power to users in a cellular network with energyharvesting relays. The energy-harvesting process is stochastically described by a time-varying Poisson process. We propose a new metric called survival probability as the selection criteria for an energy-harvesting relay to support data transmissions. We propose a survival probability-based resource allocation SPRA algorithm. The algorithm solves the joint problem of resource block allocation, power control, and associating relays to users in a cellular network. We show the achievable data rates of SPRA for different energy harvesting rates. Index Terms Cellular network, energy-harvesting, OFDMA, power control, relaying, resource allocation, survival probability. I. INTRODUCTION QUALITY OF SERVICE QoS is driving research and development in cellular networks. Providing high level of QoS to the users at the edges of a macrocell is very challenging. One method that has gained popularity in overcoming this challenge is relaying. Relaying increases coverage and QoS by dividing a long transmission hop from a user to a base station BS into two shorter user-to-relay and relay-to-bs transmission hops. There are mainly two types of relays, namely, fixed relays and mobile relays. Fixed relays are deployed at fixed locations. Mobile relays may be further divided into two types, with cellular users acting as relays, or relays deployed on vehicles. In this paper, we consider fixed relays only. These relays are deployed by cellular operators, and the predetermined number of the relays to be deployed in a cell depends on the size and density of users in the cell. To facilitate the deployment of relays in remote areas without ready access to the electrical grid, fixed relays with energy-harvesting capability may be deployed. Manuscript received April 1, 2014; revised September 15, 2014; accepted December 16, Date of publication January 13, 2015; date of current version March 19, This research is supported in part by the University of Hong Kong Strategic Research Theme on Computation and Information. The authors are with the Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong sobiaj@eee.hku.hk; hjzhou@eee.hku.hk; vli@eee.hku.hk; kcleung@ieee.org. Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /JSAC Energy-harvesting, a promising technique for green communications [19], allows the relays to generate energy from the environment. The harvested energy can be solar energy, wind energy, radio frequency RF energy, and so on. The harvested energy is random in nature. In other words, the exact time and the amount of energy harvested by a relay are not known in advance. This stochastic nature of harvested energy of a relay makes the resource allocation in cellular networks with relays a challenging problem. In sensor networks, deployment and energy management policies of energy-harvesting sensors have been studied [13], [22]. Power allocation in an energy-harvesting relay system is studied in [1], [2], [8], [15], [16]. In [16], authors have studied the performance benefits of using energy-harvesting relays and how they differ from the conventional cooperative relays. They have a system with multiple relays and the relays volunteer to relay if and only if they have enough energy to transmit data. In [8], a two-hop network has been considered, where source and relay both have the energy-harvesting capability. An optimal offline scheme for allocating transmission power in full duplex and half duplex relay is studied. The objective is to maximize the total transmitted number of data bits in a time interval. The scheduling and power allocation of a communication system with an energy-harvesting source and a nonenergyharvesting relay was studied in [15], in which a modification of a directional water-filling algorithm was proposed to solve the allocation problem. In [8], [15], the amount of energy harvested and the time at which the energy will arrive have been assumed to be known ahead of time. In [1], an online algorithm was developed considering a random energy-harvesting process to maximize the average throughput over time. Joint relay selection with power allocation has been studied in [2]. Both [1] and [2] considers energy-harvesting source and relay. However, none of these papers discusses the allocation of orthogonal frequency division multiple access OFDMA resource blocks RBs with power allocation. An RB is defined as the smallest time-frequency unit in an OFDMA system. A user must be allocated RBs before transmission. Relaying will inherently use more RBs, as an additional RB needs to be provided to the relay a user gets associated with, for each RB allocated to the user. The associations among users and relays RBs require the problem to be solved jointly. Some recent work on transmission policies for energyharvesting can be found in [17], [27]. Research in wireless communication with energy-harvesting constraints is discussed in [10], [11]. In cellular networks, BSs having energy-harvesting capability are discussed in [5], [28], but no relays are IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See for more information.

2 JANGSHER et al.: RESOURCE BLOCKS, POWER, AND ENERGY-HARVESTING RELAYS IN CELLULAR NETWORKS 483 considered. Although studies have discussed energy-harvesting relays, research in energy-harvesting relays is still in its initial phase. We believe that the deployment of energy-harvesting relays in a cellular network is important, as they can be employed in remote areas where there is no access to the power grid. To the best of our knowledge, studies have not yet discussed resource allocation with energy-harvesting relays in a cellular network. A. Our Contributions In this paper, the problem investigated is: How do we allocate resources RBs and transmission power to users and associate users to energy-harvesting relays with random energyharvesting profile in a macrocell such that the achievable data rates of the users are maximized? We consider energyharvesting as a stochastic process and introduce a probability called survival probability SP as the selection criteria for a relay to support data transmissions. SP measures the probability of an energy-harvesting relay to have energy. The main contributions of this paper are as follows: We formulate a problem to jointly optimize RB, transmission power, and user-to-relay association in a cellular network with energy-harvesting relays; We define and study SP of a relay analytically in a frame in the cellular network; We develop an SPRA algorithm, survival probabilitybased-resource allocation SPRA algorithm to jointly allocate RB, power, and user-to-relay association; and We study the performance of SPRA and compare it with a Naive Resource Allocation NRA algorithm to observe the improvement that SPRA offers, and b Charged- SPRA, an SPRA under the assumption of fully charged relay batteries. Our results show that there is a percentage difference of 11.5% in simulated and analytical achievable data rates averaged over different mean energy harvesting rates. An increase of 20.2% in the achievable data rate is observed with SPRA by setting the threshold g to be 0.9 as compared to NRA, averaged over different risk factors. Similarly, a decrease of 29.2% is observed in SPRA g = 0.9 as compared to Charged-SPRA. B. Organization of the Paper The rest of the paper is organized as follows. Section II discusses the system model. Section III studies the problem formulation for resource allocation. Section IV analyzes the survival probability. In Section V, SPRA is proposed. The performance evaluation of SPRA is shown in Section VI. Section VII concludes the paper. II. SYSTEM MODEL In this section, we discuss the system model. We consider an uplink cellular network with a BS in a macrocell, with M relays and N users. The macrocell is of radius L. We denote the BS, relay set, and user set as n 0, K, and J, respectively, where K = {1,2,...,M} and J = {1,2,...,N}. The relays are stationary and have energy-harvesting capabilities. The smallest unit in an Fig. 1. Time slot and frame structure. TABLE I MODEL PARAMETERS OFDMA system is called an RB. The RB set is denoted as B, where B = {1,2,...,Q}. The problem of resource allocation is considered in a scenario with equal-sized time frames. Each frame is further divided into T time slots with a duration of δ units each. Thus, the duration of a frame is δt units. Fig. 1 shows the structure of the time frames in an interval. We assume a block fading Raleigh channel, where the channel gain h is invariant over each frame. Table I summarizes the notations used in this paper. The users can be classified into two categories: a a cooperative communication CC user and b a non-cooperative communication NCC user. A user-to-relay association needs to be done for CC users. RBs are assigned to all users and the relays that are associated to CC users. If RB b is assigned to User j, User j will transmit its data on RB b with the power of P b j. Furthermore, if User j is a CC user, an additional RB b is assigned to Relay k associated to User j. We call this assignment of RB to a relay for transmission of a particular user data as coupling, and the assigned RB is called the coupled RB. Relay k transmits its data with power P b.bothpb j

3 484 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 33, NO. 3, MARCH 2015 is the coupling variable which indicates whether Relay k uses RB b to forward the data from RB b. It is defined as follows: β b,b β b,b = { 1 ifrb b assigned to Relay k and coupled with RB b 0 otherwise, 2 Fig. 2. Uplink cooperative communication with energy-harvesting relay. and P b need to be controlled to minimize conflicts or interferences between users. RBs, power levels, and user-to-relay associations are performed at the beginning of each frame, and will remain unchanged during the frame. Next, we discuss in detail the transmission and interference models, and the energyharvesting model. A. Transmission Model An uplink cooperative cellular communication system is considered in this paper. The downlink scenario can be solved in a similar way. User j can communicate to the BS directly in one hop or in two hops via an energy-harvesting relay k. Fig.2 shows a cooperative communication scenario with OFDMA RBs. RB b is used for direct transmission, and RB b and b are used for transmission through a relay. BS receives both the signals through the direct link as well as the signal via the relay, and combines them with reference to the Signal-to-Interference Noise Ratio SINR. Maximal Ratio Combining MRC is used at the BS. The relaying protocol used at the relay is a decodeand-forward DF protocol [26]. The Interference Range Model [18] is considered. In this model, two users operating on the same RB are said to interfere or have a conflict, if one is present in the interference range of the other. To avoid interference, any two conflicting users must be assigned different RBs. Once an RB is allocated to a user in a cell, it is assigned with the allocated power to transmit from the user to either BS or a relay k. The allocated power is a variable and depends on whether the user uses one-hop transmission to the BS or two-hop transmission to the BS via a relay. The allocated power determines the transmission and the interference range of a user or a relay. We now introduce the decision variables α b, γ b j, βb,b P b j, and Pb to indicate the assignment of an RB to a user, a coupled RB to a relay, cooperative communication to a user, power for a user on an RB, and power for a relay on the coupled RB, respectively. P b j and P b are continuous variables varying from 0 to P max. Here, P max represents the maximum power budget of a user or a relay. α b, and γ b j j, βb,b are binary variables. αb j, which indicates whether RB b is assigned to User j or Relay j, is defined as follows: { 1 ifrb b is assigned to User j α b j = or Relay j 1 0 otherwise, j, and γ b j specifies whether User j uses CC or not. It is defined as follows: γ b j = { 1 User j usingcconrbb 0 otherwise. The signal strength of User j to BS on RB b is h j,n0 P b j,n 0 αb j, where h j,n 0 is the channel gain between User j and BS, P b j,n0 is the emission power, and αb j is the decision variable defined in 1. Interference from all users and relays present in the macrocell using the same RB b will effect the quality of User j s signal. The cumulative interference from all the users is α b m Pb m,n m J 0 h m,n 0, where α b m is the decision variable given in 1, P b m,n 0 is the emission power, and h m,n 0 is the channel gain between User m and BS. Furthermore, the cumulative interference from all the relays is α b Pb k,n k K 0 h k,n 0, where α b is the decision variable given in 1, Pb is the k,n 0 emission power, and h k,n0 is the channel gain between Relay k and BS. With Gaussian noise N 0,SINRσ b j,n 0, from User j to BS on RB b is defined as: σ b j,n 0 αb j j,n 0 = h j,n0 P b N 0 + α b m Pb m,n m J 0 h m,n 0 + α b Pb k,n k K 0 h k,n For a CC user j, data is transmitted on RB b to Relay k and Relay k then further transmits the data on RB b to BS. RB b is the coupled RB of RB b. The signal strength from Relay k to BS is given as h k,n0 P b b k,n 0 αb βb,b. Here, the summation is B done to account for the coupled RB for RB b, h k,n0 represents the channel gain from Relay k to BS, Pk,n b 0 is the emission power, α b is given in 1, and βb,b is given in 2. Similarly, interference from users and relays will affect the signal quality of data sent by Relay k. Thus, with Gaussian noise N 0,SINR σ b k,n 0, from Relay k to BS n 0 for data from RB b is defined as: σ b k,n 0 = h k,n0 P b b k,n 0 αb βb,b B N 0 + α b j Pb j,n j J 0 h j,n 0 + α b q Pb q,n q K 0 h k,n 0. 5 The achievable data rate of an NCC user is a function of the SINR from the user to the BS σ j,n0, and is defined as: R b,ncc j = log 1 + σ b j,n 0. 6

4 JANGSHER et al.: RESOURCE BLOCKS, POWER, AND ENERGY-HARVESTING RELAYS IN CELLULAR NETWORKS 485 Similarly, the achievable rate of User j on RB b of a CC user depends on the SINR from the user to the BS, σ b j,n 0, and the last hop SINR from the relay to the BS, σ b k,n 0, and is defined as: R b,cc j = log 1 + σ b j,n 0 + σb k,n 0. 7 Furthermore, the achievable rate of any user j on RB b depends on its decision to use cooperative communication or not. It is defined as: R b j =γb j Rb,CC j + =γ b j log + 1 γ b j 1 + σ b log 1 γ b j R b,ncc j j,n 0 + σb k,n σ b j,n 0, 8 where γ b j is a binary variable defined in 3. A two-hop communication improves the performance of users near the cell edge as compared to a single hop communication. The performance of the user is measured by QoS defined as follows: Definition II.1 QoS: We define the QoS of a user as the achievable data rate for the user. We denote the total achievable data rate of User j as R j, which is the sum of the data rates on all RBs assigned to it as: R j = R b j. 9 b B Here, R b j is the achievable data rate of User j on RB b. The achievable data rate of a network is the sum of the data rates of all its users given by: R n0 = N j=1 R j. 10 B. Energy-Harvesting Model We have stationary relays present in our cooperative communication network with energy-harvesting capabilities. For harvesting energy, we assume that each relay in the network has a solar panel attached to it. Furthermore, each relay is equipped with a battery to store the energy harvested. In this section, we will define the energy-harvesting model. Some studies have considered the energy-harvesting process as deterministic [8], [15], whereas others have considered it as a stochastic process [1], [2], [16], [17], [27]. When considering energy-harvesting as a stochastic process, mainly, the incoming energy process is considered as a Poisson process. In [1] and [2], energy-harvesting is considered as a first-order stationary Markov process, whereas, in [17] and [27], a compound Poisson process has been considered. The Poisson process model is validated in [20] for different energy harvestors. We consider a solar panel as our energy harvestor. A solar panel consists of a number of subpanels. Energy is harvested by all the subpanels and accumulated from the subpanels to the battery attached to it. Assume that energy is accumulated from the subpanels of a solar panel in the form of energy packets, each of which contains ω J of energy. We count the number of energy packet arrivals in a frame. When the number of subpanels is large, the distribution of the number of energy packets harvested and stored in the battery during a frame approaches a Poisson process with a mean µ [9]. Furthermore, the number of energy packets harvested depends upon the radiance of the sun, which varies from time to time. Therefore, our energy-harvesting model on the number of energy packets harvested in a time frame is a time-varying Poisson process with mean µ i, where i is the frame number and k is the relay number. Each relay with its solar panel is placed at a different position in a cell and the mean of energy packets harvested is different for each relay. The probability that z i packets of energy are harvested with mean µ i by Relay k in Frame i is given by a Poisson distribution as follows: p z i ;µi i = eµ i µ iz z i!. 11 The initial amount of energy of Relay k for a Frame i is represented as E i 1. It varies for different relays as the amount of energy consumed and harvested in Frame i 1wouldbe different for different relays. As z i packets of size ω Jare harvested during a frame of length δt, the energy that the solar panel will be harvesting on Relay k in Frame i is given as z i ωt δ and represented by φi. The maximum charging rate of the battery is denoted as e max c. If a battery is being charged with rate e max c, then the maximum energy that can be charged is e max c δt and represented as φ max. The maximum amount of energy that a relay can charge if the incoming energy is coming with maximum charging rate, e max,isφ max = e max δt.the maximum amount of energy Relay k can store in the battery is E max J. A relay battery has a certain amount of energy at the start of the frame and a certain amount of energy will be harvested during the frame. Resource allocation is done at the start of the frame and we are not aware of the amount of energy that will be harvested during the frame. If we can estimate the amount of energy harvested during the frame, it is then possible to utilize it for transmission of data during that frame. To this end, we introduce a new metric, called survival probability SP defined as follows: Definition II.2 Survival Probability: Survival Probability is defined as the probability that the remaining energy in a relay throughout the frame is greater than zero. The survival probability of Relay k for Frame i is denoted as p i. Mathematically, it can be expressed as: c p i = Pr E i t > 0, 0 t δt. 12 Here, t is any time instant in a frame of length δt. A high SP means that the chance of the energy state of a relay being greater than zero is high. The number of transmissions a relay can support depends upon the energy state of the relay. We c

5 486 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 33, NO. 3, MARCH 2015 have defined SP as a selection criteria for a relay to support data transmissions. Generally, a relay with a high SP is likely to support more packet transmissions in a time frame as compared to a lower-sp relay. III. PROBLEM FORMULATION In this section, we will formulate the problem of resource allocation in a cooperative cellular network defined in Section II. As mentioned, two types of users are present in the system. The first type of users use cooperative communication, whereas the second type of users do not. Therefore, the users in the first type need to be associated to relays. In this paper, we allocate RBs and transmission powers to users and relays, and associate relays to users as well. The problem can be formulated as a power minimization problem or a utility maximization problem. We choose to use the latter approach for our problem formulation, since this gives more flexibility to determine the transmission power range of users and relays. The achievable data rate of the network is selected as the objective to be maximized in this work. We have formulated the problem in a particular frame. BS aims to assign available resources for Frame i such that the achievable data rate, R n0, of the network is maximized in that frame and the constraints of the relay survivability, relay battery, OFDMA RBs, and power are not violated. The problem formulated for a particular Frame i is shown in 13 22, shown at the bottom of the page. The objective function is formed by substituting 8 and 9 in 10. Constraint 14 dictates that RB b assigned to Relay k to forward the data transmitted on RB b from User j. In other words, each RB allocated to a relay needs to be coupled with another RB of a user to complete the CC transmission. Constraints 15 and 16 ensure that the RBs assigned to relays and users cannot exceed the available RBs. Constraints 17 and 18 ensure that the power allocated to all RBs for a user and a relay, respectively, should be less than the maximum power available. Constraint 19 says that the SP of a relay k in the network should be greater than a threshold g. This threshold is defined to ensure that relays can have energy with a reasonably high probability. Constraint 20 is the battery capacity constraint. It says that the energy in the frame cannot exceed the maximum amount of energy stored in the battery. The spent energy, ΔE i 1, is defined as b B the two sets of the variables {α b P b δt. The relationship between j,βb,b,γ b j,pb j,pb } and {σ b j,n 0,σb k,n 0 } is given in Constraints 21 and 22. The problem is a mixed integer non-linear optimization problem. The constraints are non-linear and the objective function is a weighted average of a sum-rate utility problem [14]. When the cooperative communication decision variable γ b for all the users is either zero or one, the function is reduced to a sum-rate utility function. Moreover, the sum-rate utility problem can be transformed from an equipartition problem that can be solved j maximize α b j,βb,b,γ b j,pb j,pb subject to N Q j=1 b=1 γ b j log 1 + σ b j,n 0 + σb k,n γ b j log 1 + σ b j,n 0, 13 β b,b = 1, b B j b B and b b, 14 0 b B, b B, 15 0 b B, b B, 16 P b j Pmax, j J and b B, 17 P b P max, k K and b B, 18 p i > g, k K, 19 e max δt + E i 1 where ΔE i 1 σ b ΔE i 1 E max, = P b δt, k K, 20 b B j,n 0 = h j,n0 P b N 0 + m J σ b k,n 0 = j,n 0 αb j α b m Pb m,n 0 h m,n 0 + α b Pb k,n k K 0 h k,n 0 h k,n0 P b b k,n 0 αb βb,b B N 0 + α b j Pb j,n j J 0 h j,n 0 + α b q Pb q,n q K 0 h k,n 0,

6 JANGSHER et al.: RESOURCE BLOCKS, POWER, AND ENERGY-HARVESTING RELAYS IN CELLULAR NETWORKS 487 IV. ANALYSIS OF RELAY SURVIVAL PROBABILITY In this section, we will discuss the survival probability of an energy-harvesting relay. The number of data transmissions supported by an energy-harvesting relay in Frame i depends on the energy stored in the battery of the relay at the end of Frame i 1 and the energy the relay will harvest during Frame i. A frame is divided into T equal sized time slots. Fig. 1 shows the division of time frame into time slots. Bursts of energy will be arriving at random time instants over the whole frame. It is difficult to obtain the exact value of SP, and hence we need to estimate SP instead. We represent an approximate SP ASP of Relay k for a frame i as p i. A relay is said to have approximately survived in the network over a time frame if the relay has some energy at the end of the frame. Due to practical considerations, we consider the end state of energy in a frame and cumulative energy coming in that frame instead of dealing with energy coming at all time instants in the frame given by: p i = Pr E i > 0, 23 where E i is the energy of Relay k at the end of Frame i. The value of ASP is estimated at the start of the frame before the allocation takes place. The remaining amount of energy of Relay k at the end of the frame depends upon the amount of energy at the start of the frame, the energy harvested during the frame, and the consumed energy in supporting the transmissions in the frame. The amount of energy at the end of the frame can be expressed as: E i min = min φ i,φi,max + E i 1,E max ΔE i Here, E i 1 is the energy that Relay k has at the beginning of Frame i, ΔE i 1 is the amount of energy spent by Relay k in Fig. 3. An example to illustrate the effect of risk factor. a Energy in a relay without considering the risk factor. b Energy in a relay considering the risk factor. in polynomial time. Consider that the equipartition problem Frame i. Thetermmin φ i,φi,max specifies the incoming is NP-complete, the sum-rate utility maximization problem is energy for Relay k in Frame i. For the incoming energy, a bottleneck of energy is created by the maximum amount of energy therefore NP-complete [6] as proved in [14]. Therefore, we can conclude that our problem is NP-complete. Hence, we are going that can be charged by Relay k in Frame i, φ i,max. Moreover, to devise a heuristic algorithm that can be solved in polynomial time. the term min min φ i,φi,max + E i 1,E max will ensure that the amount of energy harvested and the amount of energy present at the start of the frame is not more than the maximum amount of energy stored in the relay battery. Then, 23 becomes: min = Pr min p i E max φ i,φi,max ΔE i 1 > 0 + E i 1,. 25 In practice, the energy expenditure of a relay in a frame will not be uniform over all time slots. There would be cases when transmissions are scheduled at the beginning of the time slots whereas the harvested energy will arrive in the later time slots. The transmission of data by the relay may fail as the relay will be out of energy in the starting time slots. To avoid this case when energy is used up in the starting of the frame, an extra amount of energy ξ is reserved to take this risk into consideration. We call this extra energy as the risk factor ξ and define it as the extra amount of energy which is present in the buffer as the safety margin. We would like to illustrate the significance of ξ in the following example. Consider that a time frame with the amount of energy a relay has at the beginning of the time frame is 1 J and an energy packet of size 1 J will be harvested in the frame at t 2. We assume that the energy is harvested at a rate less than the maximum charging rate of the relay battery and the maximum amount of energy that can be stored in the battery is 5 J. Each transmission takes 0.75 J. In this scenario a relay should be able to serve two transmissions as > 0. Suppose the transmission is scheduled at t 1, where t 1 < t 2, as shown in Fig. 3. The relay will not have enough energy to serve a transmission at t 1, the energy level will go to zero and the transmission will fail. In the figure, we are showing the amount of energy as negative indicating how much more energy is required to serve the transmission. On the other hand, if we change the condition of the amount of energy of a relay in a frame, E i k > 0toEi k > ξ, this ξ will be an extra amount of energy that the relay can have so as to avoid transmission failure. If we consider ξ = 1.5J,the

7 488 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 33, NO. 3, MARCH 2015 relay can only serve one transmission and > 1.5. If an amount of energy is left as a safety margin, the relay does not run out of energy during the transmission allocated to it as shown in Fig. 3b. Then, ASP will become: min = Pr min p i E max ΔE i 1 φ i,φi,max > ξ + E i 1,, 26 where φ i is a random variable, Ei 1 and ΔE i 1 are deterministic, and ξ is a system parameter and can be specified by the designer. When ξ = 0, p i. Separating the condition, min = Pr min p i E max =Pr min ΔE i 1 I =Pr min E i 1 I =Pr min I E max = p i φ i,φi,max > ξ + ΔE i 1 φ i,φi,max E max φ i,φi,max E max φ i,φi,max > ξ + ΔE i 1, + E i 1 + E i 1 > ξ+ > ξ + ΔE i 1, > ξ + ΔE i 1 > ξ + ΔE i 1 > ρ i,,, 27 where I is an indicator function. It takes the value of one if E max > ξ + ΔE i 1 ; otherwise, I =0. This condition ensures that the battery capacity should be more than the sum of the energy that will be spent and the risk factor. If this is not true, ASP becomes zero. We substitute ξ+δe i 1 E i 1 by ρ i and name it as excessive energy. Again, separating the second condition from 27: p i = Pr φ i > ρi,φi,max I = Pr I E max > ξ + ΔE i 1 φ i > ρi E max I φ i,max > ξ + ΔE i 1 > ρ i > ρ i. 28 I takes a value of one if φ i,max > ρ i ; otherwise, I =0. Intuitively, this condition means that if the maximum amount of charging energy on a relay is not greater than ρ i,therelayis unable to transmit in Frame i and ASP is zero. If both conditions are true, then the survival probability depends on the number of energy packets harvested. The maximum charging energy depends on the maximum charging rate of the battery and is defined as φ i,max = e max c T δ, where e max c is the maximum charging rate of the battery. As we have already discussed in the energy-harvesting model, energy is harvested in packets each of size ω J. According to our energy-harvesting model, the harvested energy φ i = zi ωt δ, where z i is the number of energy packets harvested. Taking φ i = zi ωt δ, p i = Pr ρ i < zi I E max I ωt δ > ξ + ΔE i 1 = Pr ρi < z i ωt δ I I E max φ i,max φ i,max > ρ i > ρ i > ξ + ΔE i 1, 29 where z i follows Poisson distribution with mean of µi and may be determined from 11. Then, the ASP of Relay k is: p i =P ρi < z i ωt δ I φ i,max > ρ i = I E max z i = ρi ωt δ I E max > ξ + ΔE i 1 e µi µ zi z i! I φ i,max > ρ i > ξ + ΔE i The conditions in the indicator function should be true to keep ASP greater than zero. Since SP cannot be computed easily, we use 30 to approximate the value of SP of a relay for the rest of the paper. V. S URVIVAL PROBABILITY-BASED-RESOURCE ALLOCATION SPRA ALGORITHM In this section, we propose an SPRA algorithm to solve the joint RB allocation, power allocation, and user-to-relay association problem. There are three problems coupled in above optimization problem including RB allocation, power control, and user-to-relay association. In RB allocation, RBs are allocated to users and relays so that data from users can be relayed towards to BS. When an RB is allocated to a user and the user is using cooperative communication, then another RB needs to be coupled with the RB allocated to the user. The coupled RB is provided to the relay that the user is associated with. In power control, relays and users determine their power levels. Since RBs will be reused by different users, power level needs to be controlled so that users will transmit on the same RBs without any interference. In user-to-relay association, we determine the relay to be used by a user. These three problems are jointly solved to maximize the data rate of the network. Once a user is associated to a relay, the data are needed to be

8 JANGSHER et al.: RESOURCE BLOCKS, POWER, AND ENERGY-HARVESTING RELAYS IN CELLULAR NETWORKS 489 transmitted on an RB arriving at a relay first, and then the relay needs another RB to forward the data. Moreover, the energyharvesting capability of relays further complicates the problem as the energy-harvesting process is random. SPRA is a centralized algorithm, where BS acts as the central node, allocates RBs to users, assigns power to the RBs, and associates users to relays. BS is responsible for running the algorithm and all the required data can be collected via the request messages sent by users of the cellular network. 1 We assume a block-fading Raleigh channel. The problem is solved on a frame by frame basis. SPRA runs at the beginning of each time frame to provide a solution for RB allocation, power control, and user-to-relay association for that frame. The key idea behind SPRA is to maximally reuse RBs and utilize the energy of relays to increase the data transmission rate of the network. Basically, there are three steps, i.e., the association between users and relays, the RB allocation according to the association results, and finally the power control. The survivability of relay in the network is observed using the SP value given in 30. The amount of energy used guarantees that the SP of each relay should be greater than a threshold g. Once the value of SP goes below the threshold, the relay is likely to run out of energy in the upcoming frame. Therefore, SP provides a measure of the likelihood that the relay is part of the network and is the key parameter in solving this problem. Power levels of RBs are determined with the allocation of RBs till SPs of all relays are equal to the threshold g and all RBs are allocated B = 0. SPRA allocates RBs, determines the power level for the RBs, and assigns relays to users in a stepwise fashion. In each step, certain amount of energy is consumed leading to decrease in value of SPs of relays. Once the SP of a relay is equal to the threshold g, the power of the relay cannot be used anymore. In other words, users cannot be associated with this relay and RBs are no longer assigned to this relay. To evaluate the interferences among different users on the same RBs, conflict graph is introduced. In each step of RB allocation, the same RBs are allocated to the nodes without interfering with each other. In each step, since some relays can no longer be used, the conflict graph needs to be updated at each iteration by excluding those relays that cannot be used. A conflict graph is formed for each iteration after checking the survivability of relays. Based on the conflict graph, RBs can be allocated to the users and relays. After the RB allocation, the power levels of RBs are determined. The power levels are increased from the previous power levels. Moreover within each iteration, the assignments of transmissions to a relay will decrease the survivability of the relay. As the number of iterations increases, the SP of a relay in the network will decrease. Once the survivability condition as given in Constraint 19 is violated, the relay will not be used in the following transmissions. Meanwhile, the relay will be removed from the conflict graph 1 In cellular network, when a user requests service, a request will be sent to BS [3]. In our work, position information is additionally required to be sent with the request. If the additional information is represented by U bytes. In each frame with duration T δ, N users will generate additional N U 8 bits. As a result, the bandwidth overhead to realize this algorithm is N U 8 T δ bps. and the graph will be updated accordingly. According to the conflict graph, certain RBs will be allocated to the users and relays. Those nodes that will not interfere with each other will be assigned the same RB to improve the reuse of RBs which further improves the data rate of the system. Algorithm 1 shows the pseudo code of SPRA. In each iteration, the algorithm contains three basic functions. These are a user classification and initialization Lines 4 16, b RB

9 490 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 33, NO. 3, MARCH 2015 allocation Lines 18 21, and c power control Lines Next, we will discuss these functions of the algorithm in detail. A. User Classification and Initialization This function of the algorithm classifies the users into CC and NCC users, and determines an initial power for all users. For each frame, SPRA classifies the users first Lines 4 9 of Algorithm 1. Users are classified into two categories, namely, a R c, the set of users which require a relay to communicate to the BS, i.e., the CC users, and b users which directly communicate to the BS, i.e., NCC users. These users are classified based on their distances from the BS. We deployed relays at a distance of 2 3 of the macrocell radius L from the BS as assumed in [21], [24], [25]. The condition is shown in Line 5, which means that, if the distance of the user from the BS is greater than 2L 3, it will use cooperative communication. Intuitively, it can be explained by the fact that the channel quality of users close to the BS is better as compared to the channel quality of users far from the BS. Therefore, the users close to the BS does not require the assistance of the relay and users far from the BS do require the assistance of the relay. If Line 5 holds true for User j, Line 6 puts j in the cooperative communication user set R c. All users are classified accordingly. Line 9 initializes the power for all users. We start by assigning the minimum power to all users. B. RB Allocation As analyzed above, this function contains two parts. The first part is updating the conflict graph and the second part is the assignment of the RBs based on the updated conflict graph. We use the graph colouring algorithm to determine which network nodes can transmit simultaneously without creating interference. Those nodes are given the same colour. Then, the node with the same colour are assigned the same RBs. The nodes with different colors will be assigned different RBs so that the interferences can be avoided. We represent the cellular network as a conflict graph GV, E. Here, V is the set of vertices and E is the set of edges. Each vertex represents a user or an available relay, whereas an edge connecting any two vertices represents interference between them. There are three types of vertices, namely, a a user who uses cooperative communication, b a user who does not use cooperative communication, and c relays available in the frame. In Line 18, a conflict graph is formed without relays as the user-to-relay association has not been determined yet. This graph will represent the interference relationship among users only. A user who has to use cooperative communication needs to be associated to a relay. Line 19 calls a function to associate users to relays. Algorithm 2 shows the pseudo code of the userto-relay association algorithm, which works as follows. Let r k be the radius of a relay k s coverage area. A user j will get associated to a relay k, if it is in its coverage area. In case a user is in the coverage areas of multiple relays, it will get associated to the closest one. For example, let d j,k and d j,k be the distances from User j to Relays k and k, respectively. User j is associated to Relay k,ifd j,k < d j,k ; otherwise, Relay k is selected. 2 R c is computed with relay numbers corresponding to R c, the set of users who require cooperative communication and the user-to-relay associations are further added to the conflict graph in Line 20. A conflict graph is formed with all the user and relay information. Next, RBs are assigned to the conflict graph formed using the graph colouring algorithm in Line 21. Any existing graph colouring algorithm can be used. We use a greedy graph coloring algorithm [7] to assign the RBs to the conflict graph. Algorithm 3 shows the pseudo code of the greedy graph colouring algorithm. This greedy algorithm arranges the vertices in descending order of degree and assigns the first available RB colour to the vertex. The process is repeated until all vertices are assigned without any two neighbouring vertices having the same RB. Each user, irrespective of whether it is using cooperative communication or not, will be assigned an RB. For a user who uses cooperative communication, a corresponding coupled RB is allocated to the associated relay. The number of RBs allocated to a relay is equal to the number of users associated with it. The graph colouring algorithm outputs the RB allocation. In particular, Lines 7 11 in Algorithm 3 assigns one available RB to the nodes which can be coloured the same. It checks 2 The distance is computed by measuring the signal strength of control sequences of Request To Send RTS and Clear To Send CTS [12].

10 JANGSHER et al.: RESOURCE BLOCKS, POWER, AND ENERGY-HARVESTING RELAYS IN CELLULAR NETWORKS 491 the interferences node by node until all possible nodes are examined. Then, the process will be repeated until all nodes are coloured Lines The exact number of RBs assigned to a relay depends on the number of users associated to it. C. Power Control This is the core part of SPRA. Its basic function is to determine the power level of each RB so that SPs of relays are guaranteed to be greater than a threshold. We start with the minimum power assigned to users and relays and increase it stepwise in each iteration. Lines show the corresponding pseudo code. The power levels for users will be determined first. The transmission powers for users increase as shown in Lines Line 23 shows an increase of Δ j for each user if it can support transmission; otherwise, the transmission power remains the same. After power control of users, the power levels of relays will be determined. As mentioned above, after the use of energy in relays, some relays will be out of energy. These relays will be excluded in the next iteration. The alive relay set R a needs to be updated by checking SP after the power determination. In Line 28, the transmission power levels of the relays are determined. Line 29 computes the SP and updates the alive relay set R a. If a relay is out of energy, it is removed from the set R a in Line 31. RB allocation and power control will be executed alternatively until all RBs are allocated. Note that, in each iteration, the relay-to-user association may change, since the power level of each user may change. E i rises when SP drops with each iteration. The details of the changes between successive iterations, from n 1 th to n th, in the values of energy spent ΔE i 1,Δ n+1, the excess energy ρ i 1,Δ n+1, and the minimum number of energy packets that can be harvested z i 1,n+1 min are discussed in the Appendix. The decrease in the SP value with each iteration depends on the change in the minimum number of energy packets harvested z i 1,n+1 min. Since SPRA only guarantees the SPs of relays to be greater than a certain threshold, there is still a chance that the relay may run out of energy in a frame. The unfinished data will be re-scheduled in the next frame. In SPRA, there are O B steps in the while-loop. Each while loop contains Algorithm 2, Algorithm 3, and two for-loops. The computational complexity of Algorithm 2 is O J K while the complexity of Algorithm 3 is O J + K 2.The computational complexities of the two for-loops inside the main while loop are O J and O K, respectively. As a result, the computational complexity of SPRA is O B J + K 2. VI. PERFORMANCE EVALUATION In this section, we show our simulation results to demonstrate the performance of SPRA. We compare the achievable rate of the network using SPRA with the following: Naive Resource Allocation NRA: The RBs and power levels are allocated according to SPRA but energy harvested during the frame is not taken into consideration. It only considers the battery power at the start of the frame, say, Frame i, to perform allocation and the energy harvested during Frame i is stored in the battery and taken into consideration during the allocation in Frame i + 1. SPRA with a fully charged battery Charged-SPRA: The RBs and power levels are allocated according to SPRA but the battery attached to each relay in the network is assumed to be fully charged. Therefore, if any energy is harvested, the battery is not storing any further energy. For Charged-SPRA, another factor which needs to be discussed is the maximum amount of energy stored in the battery, that plays a critical role in the resource allocation process. The physical characteristics of the solar panel can be used to compute the maximum excess charge and the minimum excess charge a battery is left. Using these excess charges of the battery, the minimum and maximum sizes of the battery can be defined. The minimum excess charge of the battery at a relay k is E a,min ρ max = e max δt and the maximum excess charge is E a,max = e max δt ρ min. We compare SPRA with these two SPRA variations because no state-of-the-art algorithm deals with the resource allocation while accounting for the three dimensions of RB, power, and relay association, with energy-harvesting relays in a cellular network. Following the example of [1], we decide to compare our results with NRA, as it will provide insights on improvements due to utilizing the energy harvested during the frame with the stored energy, instead of just using the stored energy of the battery. We also compare SPRA with Charged-SPRA as the latter approximates the ideal situation of fully charged batteries. We evaluate the resource allocation algorithm in MATLAB. We consider a macrocell with a radius L of 1 km. A total of 500 users are spreaded randomly in the macrocell. Nine fixed relays are placed, equally spaced, on the circumference of a circle with radius of 2L 3 from the BS. Fig. 4 shows the scenario of the simulation. The users within 2L 3 of the BS will transmit directly to the BS, while the users more than 2L 3 from the BS will communicate via relays. A total of 20,000 RBs are available. SPRA is run at the start of a frame. The duration of a frame is 300 seconds. The frame is divided into 10 4 slots, each of duration 3 milliseconds. The slot is of the same size as that of a Long Term Evolution LTE RB. For the simulation, we consider that all relays have the same energy-harvesting characteristics. We also assume that each user battery is enough to support all transmissions at all power levels it is assigned to do. In the first set of simulation results in Fig. 5, we show the effect of different parameters of the SPRA on the achievable rate of the network. Fig. 5a shows the relationship between risk factor and survival probability. We can see that as the risk factor increases, SP decreases. More risk factor means that we keep more energy in reserve and hence means less energy of the relay can be utilized for transmissions, and the relay will have less survivability in the network. In addition, we can also see that for a certain risk factor, SP at low transmission power

11 492 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 33, NO. 3, MARCH 2015 Fig. 4. A macrocell with energy-harvesting relays deployed at 2L 3 BS and users randomly spreaded in the cell. from the is high as compared to high transmission power. This can be explained by the fact that more transmission power means more energy spent and less probability of survivability of relay in the network. Fig. 5b shows the relationship of risk factor with achievable data rate and compares the performance of SPRA with its variations, i.e., NRA and charged-spra. For NRA, as we do not take into consideration the energy harvested during the frame, SP is not computed and thus achievable data rate is constant with increase in risk factor. For Charged-SPRA, in which the battery is full, survival probability is one. A decrease in the achievable data rate can be observed for charged-spra with increase in risk factor. For SPRA, the threshold g plays an important role. We plotted SPRA for different values of g, namely, 0.8, 0.9, and More risk factor means less SP, which means less energy can be used for transmission. Moreover, less energy transforms into a lower data rate. However, there exists a tradeoff between the success of transmission and survival probability. For any energy harvesting rate, the optimal risk factor and threshold need to be found. For a certain threshold g = 0.9, we can observe that as risk factor increases from 100 J to 200 J, the data rate increases, while from 200 J onwards the data rate decreases. Intuitively, we can explain the increase in data rate by the fact that at lower risk factor, the chance of over estimating the survivability of relay is high and so is the chance of unsuccessful transmission. This unsuccessful transmission leads to a lower data rate at a low risk factor. With the increase in risk factor, we are moving from over estimating the survivability of relay to underestimating the survivability of relay. An increase of 20.2% in the achievable data rate is observed within SPRA g = 0.9 as compared to NRA. That means that using the energy harvested during the frame on average increases the data rate by 20.2%. Similarly, an increase of 29.2% is observed in SPRA g = 0.9 as compared to Charged-SPRA. For an energy harvesting rate of Fig. 5. Relationship between different parameters of SPRA. a Effect of risk factor on survival probability of a relay for different minimum power values. b Effect of risk factor on the achievable data rate. Fig. 6. Comparison of simulated and analytical achievable data rate for different energy harvesting rates. 10 packets/frame, the best risk factor is 200 with a threshold of 0.9. In the simulation results shown in Fig. 6, we show the effect of the approximation that we made in the calculation of survival

12 JANGSHER et al.: RESOURCE BLOCKS, POWER, AND ENERGY-HARVESTING RELAYS IN CELLULAR NETWORKS 493 resource allocation heuristics in terms of achievable data rate is better than that of IPOPT. This can be explained by the fact that IPOPT can only find local solutions, and the survivability constraint is tightened as compared to the original problem. Due to the tightened constraint less energy of the relay can be utilized for transmission of data. Thus, from our results we can conclude that the energy harvested during a frame can increase the achievable data rate of the network and should be taken into consideration while allocating the resources. Fig. 7. Comparison of OPTI solver and analytical achievable data rate for different energy harvesting rates. probability on the achievable data rate of the network. For the analytical achievable data rate we use the survival probability defined in 30, whereas for the simulated achievable data rate we use the definition in 12. In 12, we use a Poisson arrival rate and the inter-arrival distribution is exponential. An average percentage difference of 11.5% is observed between the two achievable data rates. An increase in data rate is observed with increase in the energy harvesting rate of the relay in the network. From this, we can conclude that the effect of the approximation in survival probabilities on the objective of the problem, i.e., the achievable data rate, is small. The computational complexity of the existing optimization solvers for an NP hard problem is very high. Therefore, we compare the performance of the algorithm with an existing optimization solver for a small problem. We chose to use OPTI solver [4], which is a MATLAB toolbox for constructing optimization problems. A list of solvers are associated with OPTI, and we use an Interior Point OPTimizer IPOPT [23] solver to solve our problem owing to the non linearity of the problem. IPOPT can only find local solutions. Constraint 19 contains a summation up to infinity and a factorial containing the variable of the formulated problem. This makes the implementation of this constraint computationally very expensive. We have tightened this constraint to make it computationally less complex. Using the tail bound on Poisson distribution [9], Constraint 19 becomes: e z i µi µi z i z i I φ i,max I E max > ρ i > ξ + ΔE i 1 < g. 31 Using this tightened constraint, we solved a small problem of 20 users and 50 RBs. We randomly defined an interference relationship between the users. For IPOPT, the relay-to-user association is already defined if a user is using cooperative communication. Fig. 7 shows the comparison between our algorithm and the a global optimization scheme for different harvesting rates. We can observe that the performance of our VII. CONCLUSION In this paper, we discuss the joint allocation of resource blocks and powers for a cellular network with energyharvesting relays. Energy-harvesting relays will improve the performance of the cellular network in remote areas where the power grid is unavailable. We propose a novel metric SP for each relay. SP quantifies the availability of a relay in the network and plays a vital role in the resource allocation of an energy-harvesting network. We formulate an optimization problem for resource allocation. We then propose an algorithm to solve this problem and name it SPRA, which is an iterative algorithm that allocates RBs, powers and relays to users in each time frame. Our results show that an improvement in the achievable data rate can be realized by taking into consideration the harvested energy during the frame instead of just relying on the energy stored in the battery. We have not taken into account the mobility of the users. We plan to study the effect of mobility on resource allocation and energy-harvesting. Furthermore, the power decrement with each iteration is equal in SPRA, it will be interesting to adapt the power in SPRA according to the channel conditions of each user. APPENDIX As already discussed, RB allocation, power allocation, and user-to-relay association are coupled with each other. Here, we discuss how they affect each other in SPRA. SPRA allocates RBs and powers iteratively. The user-to-relay association changes in each iteration, as the energy of the relay is committed to be used in each iteration. If s u represents the number of users allocated to a relay k in the u th iteration, the amount of energy spent by a relay k after the n th iteration in Frame i is given by: ΔE i 1,n =ΔE i 1,1 + δ P min + Δ s 2 + s s n, 32 where ΔE i 1,1 is the amount of energy spent by a relay k after the first iteration. Then, ρ i 1,n+1 after the n th iteration is given by: ρ i 1,n+1 = E i 1 + ΔE i 1,1 + δ P min + Δ s 2 + s s n + ξ. 33

13 494 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 33, NO. 3, MARCH 2015 Furthermore, z i 1,n+1 min after the n th iteration is: z i 1,n+1 min = ρi 1,n ωt δ The increase in the amount of energy spent from the n 1 th to the n th iteration in Frame i is given by: Thus, ρ i 1,Δ n+1 ΔE i 1,Δ n = δ P min + Δ s n. 35 between successive iterations is given by: ρ i 1,Δ n+1 = ΔE i 1,Δ n = δ P min + Δ s n. 36 The change of z i 1,Δ n+1 min z i 1,Δ n+1 min = is given by: δ Pmin + Δ s n. 37 ωt δ Thus, ρ i decreases corresponding to the above value of z min when n increases. It can be clearly seen that more users being associated to a relay and increase in transmission power will both affect ρ i in each iteration. The number of RBs allocated to a relay is equal to the number of users associated to the relay. REFERENCES [1] I. Ahmed, A. Ikhlef, R. Schober, and R. Mallik, Power allocation in energy harvesting relay systems, in Proc. IEEE VTC,May 2012,pp.1 5. [2] I. Ahmed, A. Ikhlef, R. 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Her research mainly focuses on resource allocation in future wireless Haojie Zhou S 13 received the bachelor s and Chu Kochen Honors degree in 2009 from Zhejiang University. From 2009 to 2010, he worked with Prof. A. Huang and Dr. C. Hua on the network planning of scrambling codes in TD-SCDMA for China Mobile Inc. He attained the doctoral degree in 2014 at the University of Hong Kong under the supervision of Prof. Victor O.K. Li and Dr. Ka-Cheong Leung. His Ph.D. thesis discusses the privacy in selfish communication networks and adopts auction theory to allocate resources. He is currently an Analyst at Alibaba Inc., where he is in charge of data analysis to support business decision in e-commerce.

14 JANGSHER et al.: RESOURCE BLOCKS, POWER, AND ENERGY-HARVESTING RELAYS IN CELLULAR NETWORKS 495 Victor O. K. Li S 80 M 81 F 92 received the S.B., S.M., E.E. and Sc.D. degrees in electrical engineering and computer science from MIT in 1977, 1979, 1980, and 1981, respectively. He is Chair Professor of Information Engineering and Head of the Department of Electrical and Electronic Engineering at the University of Hong Kong HKU. He has also served as Associate Dean of Engineering and Managing Director of Versitech Ltd., the technology transfer and commercial arm of HKU. He served on the board of China.com Ltd., and now serves on the board of Sunevision Holdings Ltd. and Anxin-China Holdings Ltd., listed on the Hong Kong Stock Exchange. Previously, he was Professor of Electrical Engineering at the University of Southern California USC, Los Angeles, CA, USA, and Director of the USC Communication Sciences Institute. His research interests are in information technology and its applications, including smart grid, social networks, cloud computing, and big data analytics. Sought by government, industry, and academic organizations, he has lectured and consulted extensively around the world. He has received numerous awards, including the PRC Ministry of Education Changjiang Chair Professorship at Tsinghua University, the UK Royal Academy of Engineering Senior Visiting Fellowship in Communications, the Croucher Foundation Senior Research Fellowship, and the Order of the Bronze Bauhinia Star, Government of the Hong Kong Special Administrative Region, China. He is a Registered Professional Engineer and a Fellow of the Hong Kong Academy of Engineering Sciences, the Hong Kong Institution of Engineers, and the Institute for the Advancement of Engineering. Ka-Cheong Leung S 95 M 01 received the B.Eng. degree in computer science from the Hong Kong University of Science and Technology, Hong Kong, in 1994, the M.Sc. degree in electrical engineering computer networks and the Ph.D. degree in computer engineering from the University of Southern California, Los Angeles, CA, USA, in 1997 and 2000, respectively. He worked as Senior Research Engineer at Nokia Research Center, Nokia Inc., Irving, TX, USA from 2001 to He was Assistant Professor at the Department of Computer Science at Texas Tech University, Lubbock, TX, USA, between 2002 and Since June 2005, he has been with the University of Hong Kong, Hong Kong, where he is currently Assistant Professor at the Department of Electrical and Electronic Engineering. His research interests include transport layer protocol design, wireless packet scheduling, congestion control, routing, and vehicle-togrid V2G.