IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 12, DECEMBER

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1 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 12, DECEMBER QC 2 LinQ: QoS and Channel-Aware Distributed Lin Scheduler for D2D Communication Hyun-Su Lee and Jang-Won Lee, Senior Member, IEEE Abstract We study a distributed lin scheduling problem for device-to-device (D2D) communication considering the qualityof-service (QoS) requirements and time-varying channel conditions of D2D lins. To this end, we first study an optimal centralized lin scheduling problem maximizing the total average sum-rate while satisfying the QoS requirements of D2D lins. We then abstract the important scheduling principles of the optimal lin scheduling, i.e., giving more chance to be scheduled to the lins which have a good channel condition and do not satisfy the QoS requirement, in order to utilize them to develop distributed lin scheduling algorithms. With the scheduling principles, we develop a procedure with which D2D lins can share their degree of QoS unsatisfaction and channel condition with each other and generate their scheduling priorities according to the shared information in a distributed manner. We also develop a novel distributed lin scheduling criterion with which D2D lins determine their lin scheduling. By using them, we propose distributed lin scheduling algorithms, QCLinQ and QC 2 LinQ, which have significantly smaller signaling overhead and low computational complexity compared with the centralized optimal lin scheduling algorithm. Moreover, they closely meet the QoS requirements of D2D lins while achieving significant sum-rate improvement over conventional distributed algorithms. Index Terms D2D communication, distributed scheduling, QoS, time-varying channel. I. INTRODUCTION DEVICE-TO-DEVICE (D2D) communication is considered as a ey feature for the next-generation wireless networs. In D2D communication, D2D users in proximity exchange data with each other directly with several advantages such as higher throughput, lower energy consumption, lower delay, and data offloading [2]. Hence, D2D communication is strongly expected to support many emerging services such as Manuscript received April 1, 2016; revised August 1, 2016; accepted September 28, Date of publication October 11, 2016; date of current version December 8, This wor was supported in part by the Institute for Information and Communications Technology romotion Grant funded by the Korean Government (MSI) through the development on the core technologies of transmission, modulation and coding with low-power and low complexity for massive connectivity in the IoT environment under Grant B and in part by the Midcareer Researcher rogram through NRF Grant funded by MSI, Korea, under Grant 2013R1A2A2A The associate editor coordinating the review of this paper and approving it for publication was S. Muheree. This paper, in which only QCLinQ is studied, was presented at WiOpt 2016 [1]. The authors are with the Department of Electrical and Electronic Engineering, Yonsei University, Seoul 03722, South Korea ( angwon@yonsei.ac.r). Color versions of one or more of the figures in this paper are available online at Digital Obect Identifier /TWC public safety, social networing, advertising, gaming, streaming, traffic safety, emergency services, and so on. For D2D communication, scheduling and resource management considering interference are one of the most important issues. In [3] [7], scheduling and resource allocation problems in networ-controlled D2D communication are studied, where a base station schedules D2D lins and allocates radio resources in a centralized way in order to maximize the system throughput. Especially, in [5] [7], the quality of service (QoS) requirements for D2D lins are also considered. Generally, centralized scheduling algorithms provide higher spectrum utilization and easier way to guarantee QoS requirements than distributed scheduling algorithms. However, in general, centralized scheduling algorithms require high computational complexity and large signaling overhead, and might be used only when the base station supports the D2D scheduling capability. Hence, in practice, for networ-assisted D2D and autonomous D2D communication, it is necessary to have a distributed scheduling and resource allocation algorithm. Qualcomm has designed a D2D wireless HY/MAC networ architecture called FlashLinQ [8], which is the most representative networ-assisted D2D communication system. FlashLinQ is an OFDM-based synchronous system using a licensed spectrum, and all devices in the networ are globally synchronized by the aid of the infrastructure such as cellular networ and GS. With the global synchronization, FlashLinQ can perform device discovery and scheduling in a distributed way by using an analog-based signaling procedure with OFDM single-tone channels. In the analog-based signaling procedure, a signaling mechanism based on the energy-level on OFDM single-tone is used. Especially, it provides a distributed scheduling algorithm in which D2D lins are scheduled by the signal-to-interference ratio (SIR) threshold-based yielding criterion with assigned scheduling priorities. By randomizing the scheduling priorities of D2D lins over time, FlashLinQ can provide a fair opportunity to access the channel across D2D lins. Recently, several distributed scheduling algorithms improving FlashLinQ while using the random priority assignment and SIR threshold-based yielding criterion as in FlashLinQ are studied. In the previous algorithms, the sum-rate improvement of FlashLinQ is mainly focused, while maintaining the same fairness framewor provided by FlashLinQ, which gives the fair opportunity to access the channel across D2D lins. However, the access fairness may not guarantee fair IEEE. ersonal use is permitted, but republication/redistribution requires IEEE permission. See for more information.

2 8566 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 12, DECEMBER 2016 performance across D2D lins due to the different channel conditions and interference environments of D2D lins. Thus, in order to resolve this issue, performance-wise QoS requirement, such as the minimum average data rate, should be considered in the distributed algorithm as in the centralized scheduling algorithms in [5] [7]. In addition to considering the QoS requirement, it is also desirable to appropriately consider time-varying channel condition of each D2D lin, as in [7]. It is well nown that in wireless systems, a better channel condition provides a better throughput in general, and thus, the throughput performance can be improved by exploiting the instantaneous channel conditions of D2D lins. Hence, in order to achieve more performance improvement from utilizing the time-varying channel condition, we need explicit way to utilize it for lin scheduling. A. Related Wor 1) Introductory Surveys on D2D Communication: In [9] [12], comprehensive surveys of D2D communication in cellular networs are presented. Especially, in [12], a survey of in-band D2D communication, where D2D lins use the cellular spectrum, is provided. In [13], a survey of the interference management, which is one of the most critical issues on the D2D communication in cellular networs, is presented. In [14], a security architecture for D2D communication in cellular networs and possible security threats are investigated, and existing security solutions are surveyed. In [15], as the foundation for D2D communication system designs, the overview of the channel measurements and models for the D2D communication are provided. 2) Distributed Lin Scheduling Algorithms for D2D Communication: We now review some studies on the distributed lin scheduling for D2D communication. There are several distributed scheduling algorithms improving FlashLinQ while using the random priority assignment and SIR thresholdbased yielding criterion as in FlashLinQ are studied [16] [20]. In [16], a distributed interference channel resource allocation (DICRA) scheme is proposed. In this scheme, two neighboring D2D lins are grouped with a networ assistance and the groups are scheduled as in FlashLinQ. Then, the superposition coding scheme in [21], which is one of the interference handling schemes, is used for the D2D lin in the scheduled groups in order to overcome the intra group interference. Through the proposed scheme, the signaling overhead is reduced and the spectral efficiency is improved compared with FlashLinQ. In [17], a probabilistic medium access scheme for FlashLinQ is proposed to improve the sum-rate performance. In this scheme, as a D2D TX interferes with more number of D2D RXs of other D2D lins, it tries accessing to medium with a smaller probability. Through this, the sum-rate performance is improved compared with FlashLinQ. In [18], a distributed opportunistic scheduling algorithm under fairness constraints (DO-Fast) is proposed. In this algorithm, at the beginning of each frame which consists of multiple time-slots, D2D lins broadcast and order their priority scores which are calculated from their channel state indicators (CSI) and service types. Then, D2D lins are divided into two groups with the same number of lins according to their priority scores, i.e., high-score and lowscore groups. In each time-slot, the D2D lins in each group select their priorities randomly within their group. Then, the priority between the groups is assigned in order to adust the chance to transmit for each group. In this algorithm, the sum-rate performance is improved and the QoS differentiation according to the service type is provided as the high-score group obtains more chance to transmit than the low-score group. In FlashLinQ, the RX- and TX-yielding criterions are checed in the yielding procedure. Through it, a D2D lin yields its transmission when its RX receives too much interference from the higher priority lins or its TX strongly interferes to the higher priority lins. However, the RX of the D2D lin does not now that its higher priority interferers will be scheduled or not, and thus, it assumes that they are scheduled when determining its transmission yielding. Hence, in some cases where some higher priority interferers are not scheduled, lower priority D2D lins might unnecessarily yield their transmission, and this causes the inefficiency in resource reuse. We call this problem a cascade yielding problem, and in [19] and [20], the algorithms which mitigate this problem by using the additional signaling resources are proposed. In addition, distributed lin scheduling algorithms which use the different yielding criterion from that of FlashLinQ are studied [22] [25]. In [22], an information-theoretic lin scheduling (ITLinQ) is developed by modifying the scheduling algorithm of FlashLinQ. According to [26], treating interference as noise (TIN) is information-theoretically optimal if the TIN-optimality condition is satisfied. Inspired by this property, the authors in [22] develop a distributed lin scheduling algorithm which guarantees the TIN-optimality condition with the same signaling overhead as that of FlashLinQ. ITLinQ achieves a considerable sum-rate improvement over FlashLinQ without any additional signaling overhead. In [23], D2D lins chec the multiple thresholds for the receiver s yielding criterion and share the yielding results among them. Through this, D2D lins can estimate whether other lins are scheduled or yielded to mitigate the inefficiency due to the cascade yielding problem of FlashLinQ, as in [19] and [20]. In [24], an adaptive yielding mechanism is proposed to improve the spatial spectral efficiency. In this algorithm, if a high priority D2D lin has a relative small amount of buffered data to transmit compared to its achievable data rate, it accepts more interference from the lower priority D2D lins by preventing the lower priority D2D lins for yielding their transmission. To this end, the high priority D2D lin adusts its signal powers used for the yielding decision of the lower priority D2D lins. In [25], a scheduling algorithm using a pairwise SIR threshold-based yielding criterion is developed. Contrary to FlashLinQ, in this algorithm, the pairwise SIR is used for the RX-yielding criterion instead of the aggregated SIR. The authors model the scheduling algorithm as a random sequential adsorption (RSA) process in physics. Then, by using it, they

3 LEE AND LEE: QC 2 LinQ: QoS AND CHANNEL-AWARE DISTRIBUTED LINK SCHEDULER 8567 TABLE I COMARISON WITH RELATED WORKS obtain the optimal criterion threshold for maximizing the sumrate and the criterion threshold for guaranteeing the minimum SIR of scheduled D2D lins. In the previous wors, the authors mainly focused on the sum-rate improvement, however, in the following studies, the QoS is limitedly considered. In [18], only the QoS differentiation is provided for D2D lins according to their service types, and it is not considered whether the QoS requirement of each D2D lin is satisfied or not. In [25], the minimum SIR requirement is guaranteed only for the scheduled D2D lins. However, some D2D lins might be scheduled seldom due to its harsh interference environment, i.e., near interfering D2D lins, and the random priority assignment. Hence, they still may not guarantee fair performance across D2D lins. In addition to considering the QoS requirement, it is also desirable to appropriately consider time-varying channel condition of each D2D lin, as in [7]. In the previous wors including FlashLinQ [16] [20], the time-varying channel conditions are considered by utilizing the instantaneous channel gain in their yielding criterion indirectly, i.e., the SIR threshold-based yielding criterion. On the other hand, in [22] [25], various yielding criterions are used for lin scheduling. However, these yielding criterions have a limitation to utilize the time-varying channel condition since they only indirectly consider the time-varying channel condition. We summarize the comparison of our distributed algorithms with the related wors in Table I. 3) 3G Standardization Activities on D2D: In 3G, the standardization of D2D communication has been started since 2012, called roximity Services (rose) [27]. In rose, autonomous resource allocation mode (mode 2) is highly related with this paper. With the resource allocation mode 2, each transmitter selects radio resources for its transmission over the given resource pools according to time-frequency hopping patterns. By this basic lin scheduling mechanism, the interference due to resource collisions are consequently randomized/whitened. Thus, it is expected that this paper and the related wors in the previous subsection could be used to enhance it in the future. For more information on rose, we recommend referring to [28] which presents the comprehensive overview of D2D operations in 3G standards. B. Our Contributions In this paper, we develop two distributed lin scheduling algorithms considering the QoS requirement, i.e., the minimum average data rate, of D2D lins, and the timevarying channel conditions of D2D lins to improve system performance. In order to develop distributed algorithms, we first study an optimal centralized lin scheduling problem which maximizes the total average sum-rate while guaranteeing the minimum average data rate for each D2D lin. We then abstract the fundamental principles of the optimal lin scheduling, and by utilizing them, we develop distributed lin scheduling algorithms. In order to apply the principles, we first develop an energy-level-based signaling procedure for the lin scheduling algorithm, where OFDM single-tone channels are used as in FlashLinQ. Through this signaling procedure, D2D lins generate the scheduling priorities for all D2D lins according to the shared information in a distributed manner. We call this a QoS and channel-aware priority assignment, and by using it, we develop a distributed lin scheduling algorithm called QCLinQ. QCLinQ achieves a considerable sum-rate improvement compared to the other algorithms in which the time-varying channel condition is not considered on the scheduling priority assignment. We also develop a QoS and channel-aware yielding criterion inspired by the fundamental principles of the optimal algorithm. By applying it to QCLinQ, we develop another distributed lin scheduling algorithm called QC 2 LinQ which achieves better performance than QCLinQ. The main contributions of this paper are summarized as follows: We abstract the fundamental principles of the optimal lin scheduling considering the QoS requirement, i.e., giving more chance to be scheduled to the lins which have a good channel condition and do not satisfy the QoS requirement, that can be applied to develop distributed algorithms. In order to apply the fundamental principles, we develop an energy-level-based signaling procedure for the lin scheduling algorithm which allows D2D lins to share information with each other in a distributed manner. We then propose the QoS and channel-aware priority assignment and the QoS and channel-aware yielding

4 8568 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 12, DECEMBER 2016 criterion inspired by the fundamental principles of the optimal algorithm. We develop distributed lin scheduling algorithms, i.e., QCLinQ and QC 2 LinQ, which have significantly small signaling overhead and low computational complexity compared with the centralized optimal lin scheduling algorithm. Through the numerical results, it is shown that they achieve a considerable sum-rate improvement compared to the other algorithms. Moreover, they can closely meet the QoS requirement of each lin while the other algorithms cannot, and through this, the fairness among lins in terms of the satisfaction of their QoS requirement is achieved. C. aper Structure This paper is organized as follows. Section II provides the system model considered in this paper. In Section III, we study a centralized optimal lin scheduling problem and in Section IV, we describe the ideas for developing a distributed lin scheduling algorithm. In Section V, we develop distributed lin scheduling algorithms based on the optimal algorithm. We provide numerical results in Section VI and finally conclude in Section VII. II. SYSTEM MODEL We consider a synchronous time-slotted OFDM system consisting of multiple D2D lins. The set of lins is denoted as K = {1, 2,...,K } and each D2D lin consists of one D2D TX, u T, and one D2D RX, u R,pair. 1 The sets of TXs and RXs are denoted as U T = { u T, K } and U R = { u R, K }, respectively. For each lin, its TX, u T, has data to transmit to its RX, u R. We assume that the wireless channel is time-varying but unchanged during a time-slot and model the channel state of each lin on the wireless channel as a stationary stochastic process. The stochastic channel states of all lins in the system is represented as a system state defined as a combination of the current channel states. The set of system states is denoted as S = {1, 2,...,S}, i.e., the set of all possible channel states for all lins. The system is in one of finite system states in each time-slot and the probability that system is in system state s in a time-slot is denoted as π s. At the beginning of each time-slot, lin scheduling is conducted to decide lins which transmit data simultaneously in the time-slot, and those lins are called the scheduled lins. In order to represent lin scheduling, we define a scheduling group z which is the subset of the set of lins, K,anda scheduling indicator qz s as 1, if the lins in scheduling group z are scheduled qz s = in a time-slot with system state s 0, otherwise, s S, z Z, 1 In the rest of this paper, we omit D2D from D2D lin, D2D TX, and D2D RX for the convenience. where Z is the power set of the set of lins, K. Then, the scheduling vector q s = [ qz s ] indicates which lins z Z are scheduled in a time-slot with system state s. Naturally, at most one scheduling group can be scheduled in a timeslot, i.e., the scheduling vector should be in the following constraint set: q Q s = q z s {0, 1}, z Z s qz s 1, s S. (1) z Z In each time-slot, the TXs of the scheduled lins transmit their data using the entire wireless channel with their fixed transmission power. We denote the fixed transmission power of the TXs as. Then, from the Shannon capacity formula, the achievable instantaneous data rate 2 of lin in a time-slot with system state s is obtained as ( ) r s ( q s) = qz s z Z 1 + h s z, = hs + N 0, (2) where Z is the set of scheduling groups in which lin is included, h s i is the channel gain from the TX of lin i to the RX of lin in a time-slot with system state s, andn 0 is noise power. Thus, the average data rate of lin can be calculated from (2) and the state probability π s as π s r s ( q s), s S and the total average sum-rate of the system, which we want to maximize, is obtained as π s r s ( q s). (3) K s S In addition, each lin has a requirement for its minimum average rate, ξ, which is represented as π s r s ( q s) ξ, K. (4) s S III. CENTRALIZED OTIMAL LINK SCHEDULING In this section, we formulate a lin scheduling optimization problem and then develop a centralized optimal algorithm that solves the problem. From the system model in the previous section, the lin scheduling problem is formulated as 3 () maximize q π s r s ( q s) K s S subect to s S π s r s ( q s) ξ, K, q s Q s, s S, 2 In this paper, data rate implies data rate per unit bandwidth. 3 To generalize the problem in this paper, we can formulate the utilitymaximization problem whose obective is to maximize the sum of the utility functions of the rates, as shown in [29]. For simple presentation and due to the page limitation, we do not address it in detail. The utility-maximization problem can be solved by the same framewor which is introduced in this paper. The ideas to develop a distributed lin scheduling algorithm, which will be proposed in the following sections, can be also applied for it. By properly choosing the utility function, we can achieve the desired fairness criteria, e.g., by using the utility function proposed in [30], we can achieve ( p,α)-proportional fairness.

5 LEE AND LEE: QC 2 LinQ: QoS AND CHANNEL-AWARE DISTRIBUTED LINK SCHEDULER 8569 where q = [ q s ] s S. roblem () is a special case of the problem in [7]. Moreover, its complexity is greatly reduced compared with the problem in [7] since in roblem (), legacy cellular users and tow-hop transmission of lins through BS is ignored and only one subchannel exists. Hence, we can easily develop the centralized optimal lin scheduling algorithm for problem () by using a dual approach and a stochastic subgradient method as in [7]. Due to the page limitation, we briefly summarize the centralized optimal algorithm and we refer readers to [7] for the details of developing the optimal algorithm. In order to develop the optimal algorithm, we first define the dual problem from the relaxed problem of problem () where the constraint for the scheduling indicator in (1) is relaxed as continuous value. Note that the relaxed problem is convex programming which has zero duality gap. In the optimal algorithm, in each time-slot t, the scheduling indicator q s(t) z is determined by the central controller as {1, if z = argmax z Z ψs(t) z ( λ (t) ), z Z, 0, otherwise (5) q s(t) z ( λ (t) ) = where s (t) is the system state in time-slot t, λ (t) is a Lagrangian multiplier vector of the dual problem in time-slot t, and ψz s ( λ) h (1 + λ ) (1 s + ) z z, = hs + N. 0 (6) Note that ψz s can be calculated without π s. Then, after the transmission, the Lagrangian multiplier vector is updated as [ ] λ (t+1) = λ (t) α (t) ν (t) +, K, (7) where α (t) is a step size at time-slot t and ν (t) is the corresponding stochastic subgradient of the dual problem. The stochastic subgradient of dual problem is obtained by Dansin s Theorem [31] as ν (t) = r s(t) ( λ (t) ) ξ, K, (8) where r s(t) ( λ (t) ) is the achieved instantaneous data rate of lin for given s (t) and λ (t). The Lagrangian multiplier vector updated as (7) converges to the optimal solution of the dual problem, λ, with probability 1 as the time-slot t goes to infinity, if step size α (t) satisfies the following conditions [32]: ( α (t) 0, α (t) =, and α (t)) 2 <. t=0 Then, the scheduling indicator q( λ ) is the optimal solution of problem (), since the relaxed problem is convex programming and it satisfies the constraint (1) in the original problem (). However, to perform the optimal algorithm, the central controller needs the channel states of all lins, i.e., all channel gains between all TXs and all RXs. Thus, the lins have to report their channel states to the central controller, which needs a significant amount of signaling overhead. In addition, the central controller should find the optimal lin scheduling in (5) t=0 by searching the scheduling group z which has the largest ψz s exhaustively over all scheduling groups, i.e., Z. Note that the number of scheduling groups exponentially increases as the number of lins increases, i.e., Z =2 K,whereK is the number of lins, and thus the computational complexity of the optimal algorithm is quite high and increases exponentially with the number of lins. Therefore, the optimal algorithm is hard to be implemented in practice due to its large signaling overhead and high computational complexity and we need to implement an algorithm with small signaling overhead and low computational complexity. In addition, for the case in which we cannot resort to the central controller for scheduling as in networ assisted D2D communication and autonomous D2D communication, we need to have a distributed algorithm. Hence, in the following sections, we will study distributed lin scheduling algorithms that approximates the optimal algorithm while requiring small signaling overhead and having low computational complexity. IV. BACKGROUNDS FOR DEVELOING DISTRIBUTED LINK SCHEDULING In this section, we describe ideas for developing a distributed lin scheduling algorithm that approximates the optimal algorithm in the previous section with small signaling overhead and low computational complexity. We first abstract the fundamental principles of the optimal lin scheduling algorithm in the previous section. We then describe how to apply the fundamental principles in a distributed manner in order to develop a QoS and channel-aware distributed lin scheduling algorithm. A. Fundamental rinciples in the Optimal Algorithm In the optimal algorithm, lin scheduling is decided by the condition in (5) which finds the scheduling group z that has the maximum value of ψ s z ( λ) in (6). It is obtained by the sum of achievable data rates of lins in scheduling group z which are weighted by the coefficients, i.e., 1 + λ, z. Thus, we call ψ s z ( λ) the sum of weighted achievable data rate of lins in scheduling group z in a time-slot with system state s. We now define the weight parameter of lin in time-slot t as w (t) = 1 + λ (t), (9) where λ (t) is the Lagrangian multiplier of lin in time-slot t which is updated in each time-slot as in (7) and (8). As we can see in (7) and (8), the weight parameter (i.e., the Lagrangian multiplier) of lin decreases when its current achieved data rate is larger than its minimum average rate requirement and increases otherwise. This implies that the weight parameter of each lin represents the degree of unsatisfaction of its minimum average rate requirement. We now abstract the scheduling principles of the optimal algorithm as follows: (S1) Each lin updates its weighted parameter in each time-slot as in (7) and (8). (S2) The lins in the scheduling group which has the largest sum of weighted achievable data rates are scheduled as in (5) and (6).

6 8570 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 12, DECEMBER 2016 For each lin, its weight parameter represents its degree of unsatisfaction and its achievable data rate represents its channel condition. Thus, the scheduling principles imply that in each time-slot, the lins which have higher weight parameter and achievable data rates should be scheduled. B. Ideas for Distributed Scheduling Algorithm Now, there arises a question how to apply the scheduling principles in a distributed manner. At the end of each timeslot, each lin can update its weighted parameter by using its transmission result in the time-slot. Thus, naturally, the first principle can be implemented in a distributed manner. However, the second principle is hard to be applied in a distributed manner. In the distributed scheduling algorithms in the related wors, lin scheduling in each time-slot is done by checing yielding criterion based on scheduling priorities that are assigned to lins in that time-slot. 4 Thus, deciding which lins are scheduled depends on how scheduling priorities are assigned and which yielding criterion is used in the algorithm. Hence, to apply the second principle in a distributed manner, we develop a signaling procedure which allows us to utilize the second principle for both priority assignment and yielding criterion. In this subsection, we describe how the second principle can be utilized for priority assignment and yielding criterion. 1) QoS and Channel-Aware (QC) riority Assignment: We introduce the idea of a QoS and channel-aware (QC) priority assignment inspired by the second principle of the optimal algorithm. With this priority assignment method, in each timeslot, scheduling priorities are assigned to lins in a descending order of their weighted achievable data rates. Thus, lins with higher weighted achievable data rates can have higher priorities to be scheduled in that time-slot. To implement the QC priority assignment, each lin should share its weighted achievable data rate with each other. However, still we have one more difficulty to overcome. Since the achievable data rates for lins in (2) can be obtained only after the lin scheduling is determined, we cannot now them before lin scheduling is done. To resolve this issue, we will use the approximated weighted achievable data rates of lins to generate the scheduling priorities. First of all, to approximate the achievable data rate, we assume that all RXs receive the same and fixed aggregate interference I. With this assumption, we now define the approximated weighted achievable data rate of lin in time-slot t, ρ (t),as ρ (t) = w (t) (1 + hs(t) ), K. (10) I + N 0 We can easily see that the approximated weighted achievable data rate of each lin depends only on the channel gain between its own TX and RX. Hence, each lin can determine its approximated weighted achievable data rate using only its channel gain and weight parameter. Note that even with the assumption that all RXs receive the same and fixed aggregate 4 Note that through this yielding procedure, the hidden node problem is resolved as in FlashLinQ [8]. interference I, the weight parameter (i.e. the degree of QoS unsatisfaction) and the channel condition of lins are still considered in the approximated weighted achievable data rates, since the lins which higher weight parameter and better channel condition have higher approximated weighted achievable data rates as in (10). Hence, as will be shown later, our distributed algorithm considerably improves the degree of the satisfaction of QoS requirement and the sum-rate performance even with this assumption. Moreover, in (10), when I is large, the weight parameter affects more than the channel condition to decide the approximated weighted achievable data rate. Thus, in this case, the number of the lins which do not satisfy their QoS requirements decreases faster than the case in which I is small, while the average sum-rate is reduced. The effects of I to our distributed algorithm will be shown through the numerical results. Once all lins share their approximated weighted achievable data rate with each other, they generate scheduling priorities of all lins in a descending order of the approximated weighted achievable data rates. Finally, with the generated scheduling priorities, each lin performs the lin scheduling algorithm to determine its transmission attempt in a distributed way. To this end, by using the analog energy-level-based signaling procedure, we develop a signaling procedure to share the weighted achievable data rates among lins in a distributed way,whichisexplainedinsectionv. 2) QoS and Channel-Aware (QC) Yielding Criterion: We also develop a QoS and channel-aware (QC) yielding criterion for distributed lin scheduling inspired by the second principle of the optimal algorithm, i.e., scheduling the lins which maximize the sum of weighted achievable data rate. When a lin is scheduled, the weighted achievable data rates of the other lins with higher scheduling priorities decrease due to the interference from its TX. Thus, in order to exploit the second principle, each TX should determine its lin scheduling by comparing the following two values, i.e., (V1) and (V2), while each RX determines its lin scheduling not to receive too much interference from the higher priority lins for the reliable transmission of its lin. (V1) The decrement of the sum of the weighted achievable data rates of the higher priority lins due to its transmission. (V2) Its own weighted achievable data rate. When the value of (V1) is greater than that of (V2), the TX should yield its transmission since the sum of weighted achievable data rate decreases with its transmission. On the other hand, when the value of (V2) is greater than that of (V1), the TX should be scheduled to maximize the sum of weighted achievable data rates of the scheduled lins. In order to allow TXstobeabletodetermineitslin scheduling as described above, a novel TX-yielding criterion should be developed, while the SIR-based yielding criterion can be used for the RX-yielding criterion. Now, a question arises to develop such a yielding criterion: how does each lin obtain its weighted achievable data rate and the decrement of the sum of the weighted achievable data rates of the higher priority lins due to its interference? To answer to this question, we first use the approximated

7 LEE AND LEE: QC 2 LinQ: QoS AND CHANNEL-AWARE DISTRIBUTED LINK SCHEDULER 8571 weighted achievable data rate of lin in time-slot t in (10) as the expected weighted achievable data rate of lin in timeslot t. Then, the approximated weighted achievable data rate of lin in time-slot t with the additional interference from lin is calculated as 1 + w (t) h s(t) I + h s(t) + N 0. (11) The decrement of the weighted achievable data rate of lin in time-slot t due to the interference from lin can be calculated by subtracting (11) from (10), and we can approximate it with the high SINR assumption as hs(t) w (t) 1 +. (12) I + N 0 Fig. 1. Structure of a time-slot in QCLinQ. The derivation of (12) is provided in Appendix. Then, we develop a novel QC TX-yielding criterion for TX of lin in time-slot t as follows: w (t) (1 + hs(t) I + N 0 ) w (t) L hs(t) 1 +, I + N 0 (13) where L is the set of the lins which have higher priorities than lin. The right-hand-side and left-hand-side in (13) represent the values of (V1) and (V2), respectively. Thus, when the inequality in (13) is violated, TX of lin should yield its transmission. Note that I affects the QC yielding criterion similar to (10), and its effects will be shown through the numerical results. For the QC yielding criterion, each TX should share its weight parameters with each other and obtain its interference channel gains to the higher priority RXs, i.e., h in (13), to chec its QC yielding criterion in (13). The detailed algorithm and signaling procedure for sharing the weight parameters and obtaining the interference channel conditions in a distributed way are described in Section V. V. DISTRIBUTED LINK SCHEDULING In this section, we develop the QoS and channel-aware distributed lin scheduling algorithms, QCLinQ and QC 2 LinQ, by using the ideas in the previous section and also design their signaling procedures for sharing information among lins and obtaining the channel conditions used for lin scheduling in a distributed way. QCLinQ is a distributed lin scheduling algorithm with the QC priority assignment and the SIR threshold-based yielding criterion. QC 2 LinQ is a distributed lin scheduling algorithm with both QC priority assignment and QC yielding criterion. A. Description of QCLinQ We now describe QCLinQ and its signaling procedure in more detail. The structure of a time-slot of QCLinQ is presented in Fig. 1. As in this figure, a time-slot in QCLinQ is divided into seven blocs, which consist of two pairs of Fig. 2. Simple example with two lins. TX-bloc and RX-bloc, rate scheduling bloc, data segment bloc, and Ac bloc. Through two pairs of TX-bloc and RX-bloc, TXs and RXs share their approximated weighted achievable data rates to generate scheduling priorities and determine their scheduling based on those priorities. In other words, lin scheduling is done through the two pairs of TX- and RX-blocs. Note that in contrast to FlashLinQ in which there is one pair of TX- and RX-blocs, QCLinQ needs two pairs of them. Hence, the signaling overhead of QCLinQ is larger than that of FlashLinQ. However, as we will show in numerical results, despite of this, QCLinQ provides better performance than FlashLinQ since it exploits the timevarying channel condition of each lin. In addition, QCLinQ can closely meet the QoS requirement of each lin, while FlashLinQ cannot. We now describe the signaling procedure to share the information and determine the lin scheduling in a distributed way. The approximated weighted achievable data rates of lins have to be shared among the lins for the QC priority assignment. The main idea here is sharing the information and checing the yielding criterion through the analog signals which have different transmit powers. The structure of TX- and RX-blocs for QCLinQ is presented in Fig. 1. Each bloc consists of the same number of single tones, and the Lin ID (LID) of each lin is mapped to a single tone. Thus, the TX and RX of each lin can transmit the analog-tone-signals using their single-tones without the interference from other lins. In order to simply present the procedure, we consider a simple example which consists of two lins, lin 1 and lin 2, where T i and R i denote the TX and RX of lin i, respectively, as shown in Fig. 2. The procedure presented by this simple example can be simply extended to the general case with multiple lins. We assume that a lin and its reverse lin have the same channel gain, i.e., h Ti R = h R T i. We now describe the procedure in each bloc in a time-slot. 1) First TX-Bloc: As illustrated in Fig. 3a, in the first TX-bloc, T 1 and T 2 transmit analog-tone-signals using the

8 8572 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 12, DECEMBER 2016 Fig. 3. First TX-bloc and RX-bloc with two lins. Fig. 4. Second TX-bloc and RX-bloc with two lins. same power, where is the full power of TXs. We call these signals the first direct power signals. Then, R 1 receives the signals from T 1 and T 2 with power of h T1 R 1 and h T2 R 1, respectively. Similarly, R 2 receives the signals from T 1 and T 2 with power of h T1 R 2 and h T2 R 2, respectively. Now, each RX can find out the channel gain of its own lin, i.e., h T1 R 1 for R 1 and h T2 R 2 for R 2, since the transmitted power from its corresponding TX is nown to the RX. Hence, each RX can calculate its own weighted achievable data rate, 5 i.e., ρ 1 for R 1 and ρ 2 for R 2, as in (10) using its own weight parameter and channel gain. In addition, each RX stores the power of received signals from other TXs. The stored signal powers will be used to determine the lin scheduling and obtain the weighted achievable data rates of other lins in the second TX-bloc. 2) First RX-Bloc: In the first RX-bloc, each RX transmits an analog-tone-signal called the first inverse power echo. Itis sent by RXs at power K 1 ρ 1 h T1 R 1 for R 1 and K 1 ρ 2 h T2 R 2 for R 2,where K 1 is the system constant which is assumed to be nown to all lins in the system, as illustrated in Fig. 3b. In the first inverse power echo, the information of the weighted achievable data rate of each lin is included in order to let TXs now the weighted achievable data rate of each lin at the second RX-bloc. Then, the received signals at T 1 from R 1 and R 2 have power of K 1 ρ 1 (14) and K 1 h T1 R 2 ρ 2, (15) h T2 R 2 respectively. With the received signal from R 1, i.e., (14), T 1 can obtain its own weighted achievable data rate, ρ 1, since the system constant K 1 and the transmission power at the first TX-bloc are nown. However, the weighted achievable 5 In this section, we omit approximated from the approximated weighted achievable data rate for the convenience. data rate of lin 2, ρ 2, cannot be obtained from the received signal from R 2, i.e., (15), yet due to the lac of information. In order to obtain ρ 2 from the received signal at the first RX-bloc, T 1 has to now the following value: K 1 h T1 R 2, (16) h T2 R 2 which will be taen care of at the second RX-bloc later. Thus, each TX stores the power of received signals from other RXs to obtain weighted achievable data rates of other lins later, e.g., T 1 stores (15) to obtain the weighted achievable data rate of lin 2 later. In a similar way, T 2 can obtain its own weighted achievable data rate from the received signal from R 2 and stores the power of received signal from R 1 to obtain the weighted achievable data rate of lin 1 later. 3) Second TX-Bloc: In the second TX-bloc, each TX transmits an analog-tone-signal called the second direct power signal. As illustrated in Fig. 4a, it is sent at the power which is decided by multiplying the first direct power signal by the weighted achievable data rate obtained from the first RX-bloc. Thus, the information of the weighted achievable data rate of each lin is included to the second direct power signal in order to let RXs now the weighted achievable data rate of each lin. In the example, T 1 transmits a signal with power of K 2 ρ 1 and T 2 transmits a signal with power of K 2 ρ 2,whereK 2 is the system constant which is assumed to be nown to all users in the system. Then, R 1 receives the signals with power of K 2 h T1 R 1 ρ 1 and K 2 h T2 R 1 ρ 2 from T 1 and T 2, respectively. With the received signal from T 2, R 1 can obtain the weighted achievable data rate of lin 2, ρ 2,since R 1 nows the value of h T2 R 1 with the stored signal powers in the first TX-bloc and the system constant K 2. In a similar way, R 2 also can obtain the weighted achievable data rate of lin 1, ρ 1. Now, both R 1 and R 2 can generate the scheduling priorities of all lins, since they now the weighted achievable data rates of all lins from the first and second TX-blocs. Then, with the generated scheduling priorities, they determine whether they will yield their transmission or not by checing

9 LEE AND LEE: QC 2 LinQ: QoS AND CHANNEL-AWARE DISTRIBUTED LINK SCHEDULER 8573 a receive yielding criterion. Through the criterion, each RX does not allow the transmission of its corresponding TX if its received interference is not acceptable. In other words, the transmission of the TX of lin i, T i, is allowed only if the following condition is satisfied: Fig. 5. Structure of a time-slot in QC 2 LinQ. h Ti R i L i h T R i >γ RX, where L i is the set of the lins with higher priority than lin i and γ RX is the threshold for the receive yielding criterion. If the criterion is violated for an RX, it yields the transmission of its lin, and this is called as RX-yielding. Note that h T R i is the received power of the first direct power signal from T at R i. Thus, in order to obtain the received interference from the lins with higher priorities, each RX should now the received power of the first direct power signals from other TXs, which are stored in the first TX-bloc. Hence, each RX can determine its RX-yielding. 4) Second RX-Bloc: In the second RX-bloc, only RXs which did not yield in the second TX-bloc transmit the signal called the second inverse power echo, i.e., if only R 1 did not yield, then R 1 transmits its second inverse power echo and R 2 transmits nothing. The second inverse power echo is sent at the power which is decided by dividing the first inverse power echo by the weighted achievable data rate, i.e., K 1 h T1 R 1 for R 1 and K 1 h T2 R 2 for R 2. When only one RX transmits the second inverse power echo due to RX-yielding, the corresponding TX is ust scheduled. On the other hand, when both R 1 and R 2 transmit the second inverse power echo as illustrated in Fig. 4b, T 1 receives the signal with power of K 1 h T1 R 2 h T2 R 2 in (16) from R 2. Hence, T 1 can obtain the weighted achievable data rate of lin 2, ρ 2, from the stored signal power in (15) in the first RX-bloc by using the received signal from R 2. Similarly, T 2 can obtain ρ 1. Now, both T 1 and T 2 can generate the scheduling priorities of all lins from the weighted achievable data rates of all lins. Then, with the generated scheduling priorities, they determine whether they will yield their transmission or not by checing a transmit yielding criterion. Through the criterion, each TX decides not to transmit if it causes too much interference to the RXs with higher priorities that decided not to do RX-yielding. In other words, T i, transmits only if the following condition is satisfied for all no-yielding RXs with higher priority than lin i: h T R h Ti R >γ TX, L i, where L i is the set of the lins with higher priority than lin i that decided not to do RX-yielding and γ TX is the threshold for the transmit yielding criterion. If the criterion is violated for a TX, it yields its transmission, and this is called TX-yielding. Note that T i can obtain the estimated received SIR at R due to the interference from itself, i.e., h T R h Ti, from R its received power of the second inverse power echo from R, i.e., K 1 h Ti R h T R. 5) Rate Scheduling, Data Transmission, and Ac: Through the TX- and RX-blocs, the scheduled lins both of whose TX and RX did not yield are determined. In the rate scheduling bloc, the scheduled lins estimate their SIR by using a wideband pilot signal and choose code rate and modulation based on their estimated SIRs. Then, the scheduled TXs transmit their data on the data transmission bloc, and the RXs received their data transmit their acnowledgement signal on the Ac bloc. After the transmission, each RX updates its weight parameter as in (7) and (9) using the transmission result of its lin. B. Description of QC 2 LinQ We now describe QC 2 LinQ and its signaling procedure in more detail. Basically, QC 2 LinQ has a similar signaling procedure to that of QCLinQ, and thus, we describe only the additional and different parts from QCLinQ with the simple example in Fig. 2. QC 2 LinQ is a distributed algorithm with both QC priority assignment and QC yielding criterion. Thus, as in QCLinQ, the approximated weighted achievable data rates should be shared among the lins for the QC priority assignment. In addition, in QC 2 LinQ, the weight parameters of lins should be shared among the lins in order to apply the QC yielding criterion. Thus, for QC 2 LinQ, we develop the signaling procedure to share the approximated weighted achievable data rates and the weight parameters, and determine the lin scheduling in a distributed way. In the signaling procedure for QC 2 LinQ, the third RX-bloc is added after two pairs of TX-bloc and RX-bloc as in Fig. 5, and the additional RX-bloc is utilized to share the weight parameters. In the first and second TX-blocs, rate scheduling bloc, data transmission bloc, and Ac bloc, the signals are same as those of QCLinQ. Thus, we describe only the signals in the RX-blocs. We summarize the comparison of the signaling procedures in QCLinQ and QC 2 LinQ in Table II. In the first RX-bloc, each RX transmits the direct power signal multiplied by its weight parameter, while the inverse power echo multiplied by its weighted achievable data rate is transmitted in QCLinQ. It is sent by RXs at power K 2 w 1 for R 1 and K 2 w 2 for R 2. Then, the received signals at T 1 from R 1 and R 2 have power of K 2 w 1 h T1 R 1 and K 2 w 2 h T1 R 2, respectively. With the received signals, T 1 can obtain the channel gain of its own lin from the received power, i.e., h T1 R 1 since it nows the system constant, K 2, the transmission power,, and its weight parameter, w 1. Thus, it can calculate its own weighted achievable data rate, ρ 1, as in (10) using its own weight parameter and channel gain. However, the weight parameter of lin 2, w 2, cannot be obtained from the received signal from R 2 yet due to the lac of information. Thus, each TX stores the power of received signals from other RXs to obtain the weight parameters of other lins later.

10 8574 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 12, DECEMBER 2016 TABLE II COMARISON OF SIGNALING IN ROOSED ALGORITHMS In a similar way, T 2 can obtain h T2 R 2 and calculate ρ 2.Italso stores the power of received signal from R 1. In the second and third RX-blocs, only RXs which did not yield in the second TX-bloc transmit the signals. In the second RX-bloc, RXs transmit the direct power signal, while the inverse power echo is transmitted in QCLinQ. It is sent by RXs at power for both R 1 and R 2. As in QCLinQ, if only one RX did not yield, the corresponding TX is ust scheduled. On the other hand, when both R 1 and R 2 did not yield, T 1 receives the signal with power of h T1 R 2 from R 2. Hence, T 1 can obtain the weight parameter of lin 2, w 2, with the stored signal power in the first RX-bloc, K 2 h T1 R 2 w 2. Similarly, T 2 can obtain w 1. In the third RX-bloc, RXs transmit the direct power signal multiplied by the weighted achievable data rate. It is sent by RXs at power K 2 ρ 1 for R 1 and K 2 ρ 2 for R 2. Then, similar to the signals in the first RX-bloc, each TX i can obtain the weighted achievable data rates of each lin with the stored signal power in the second RX-bloc, h Ti R. Now, both T 1 and T 2 can generate the scheduling priorities of all lins from the weighted achievable data rates of all lins. Then, with the generated scheduling priorities, they determine their transmission by checing the QC TX-yielding criterion as in (13). Note that each T can obtain the channel gains from itself to the RXs of other lins which are needed in (13), i.e., h, from the direct power signal in the second RX-bloc. QC 2 LinQ has an additional signaling overhead compared to that of QCLinQ due to the third RX-bloc. Thus, we also propose a signaling method reducing the signaling overhead. In the signaling method, the third RX-bloc is transmitted in every T sp time-slots, and in the first RX-bloc of the timeslots where the third RX-bloc is not transmitted, the signal with the weighted achievable data rate is transmitted instead of the signal with the weight parameter. Thus, each TX can update the weight parameters of other lins in every T sp timeslots where the third RX-bloc is transmitted. Then, for the QC TX-yielding criterion, it uses the same weight parameters until the next update. We call T sp as the weight parameter sharing period length. Hence, the additional signaling overhead is reduced as 1/T sp while the weight parameters of lins are shared in every T sp time-slots. Nevertheless, in the numerical results, it is shown that the QoS requirements of the lins are closely satisfied even the weight parameters are not shared in every time-slot. Moreover, the effects of T sp on the performance of QC 2 LinQ such as the average sum-rate and the number of the lins which do not satisfy their QoS requirements are also shown in the numerical results. C. Overhead Comparisons With Centralized Lin Scheduling We now analyze and compare the signaling overhead and computational complexity of centralized optimal lin scheduling algorithm and our distributed lin scheduling algorithms, i.e., QCLinQ and QC 2 LinQ. In the centralized algorithm, all RXs should report their channel gains from all TXs. Thus, its signaling overhead is given by O(K 2 ),wherek is the number of lins. On the other hand, in QCLinQ, the signaling overhead due to the single-tones used in the signaling procedure, i.e., the number of necessary single-tones, is given by 4K,and similarly, that in QC 2 LinQ is given by 5K. Thus, the signaling overheads of QCLinQ and QC 2 LinQ are O(K ). In the centralized algorithm, lin scheduling is determined by finding the optimal lin scheduling among the possible 2 K lin schedules in an exhaustive manner. Thus, its computational complexity on the centralized scheduler is given by O(2 K ). On the other hand, in QCLinQ and QC 2 LinQ, each lin schedules its own transmission by checing the yielding criterion. Thus, the computational complexities of them on each lin is given by O(K ). From those analyses, we can see that QCLinQ and QC 2 LinQ have much smaller signaling overhead and lower computational complexity than the centralized algorithm. In the centralized algorithm, lins should report their channel gains but they do not have to determine their scheduling. Thus, when using our distributed algorithm instead of the centralized algorithm, the energy consumption on each lin due to the computation for lin scheduling becomes smaller, while that due to the uplin transmission for reporting channel gains becomes larger. However, in cellular networs, uplin transmission is one of the most maor power consuming procedure on mobile device [33], and note that the computation on QCLinQ and QC 2 LinQ is quite simple. Thus, we can infer that the energy consumption on each lin of QCLinQ and QC 2 LinQ is lower than that of the centralized algorithm. VI. NUMERICAL RESULTS In this section, we provide simulation results to evaluate the performances of our distributed lin scheduling algorithms, QCLinQ and QC 2 LinQ, by comparing them with those of FlashLinQ and ITLinQ. To this end, we develop a dedicated C++-based simulator on which the following D2D system

11 LEE AND LEE: QC 2 LinQ: QoS AND CHANNEL-AWARE DISTRIBUTED LINK SCHEDULER 8575 TABLE III SIMULATION ARAMETERS can run. In simulation results, we use the Shannon capacity formula as in (2), 6 and the additional signaling overheads of our algorithms compared with those of FlashLinQ and ITLinQ are fully accounted. The following simulation parameters are used unless mentioned explicitly. The implementation of ITLinQ follows the same steps as in [22] and the value of parameter η in ITLinQ is set to be 0.6 with which the highest sum-rate performance is achieved for ITLinQ in our simulation settings. Here, we assume that each lin can be aware of the active higher priority lins as in [22] for FlashLinQ, ITLinQ, and our algorithms. As described in [22], it is available through multiple iterations of the yielding mechanism. We do not consider the signaling overhead for those multiple iterations since it needs for all algorithms. The values for parameters I and T sp in our algorithms are set to be 10 dbm and 10 time-slots, respectively. 7 Note that in the implementation of our algorithms, the parameters such as I and T sp can be agreed by lins through the initial access procedure. For each topology, lins are randomly dropped in a 500m 500m square region, and the length of each lin, i.e., the distance between its TX and RX, is randomly chosen between 25 m and 50 m with a uniform distribution. Simulation parameters are summarized in Table III. Note that the fixed aggregated interference and the high SINR assumptions in QCLinQ and QC 2 LinQ are not used in simulation, i.e., the real interference power is used to obtain the achieved data rates in the simulation. Thus, the following results validate that QCLinQ and QC 2 LinQ perform well in practice even they designed with the fixed aggregated interference and the high SINR assumptions. 6 We may apply the CQI-MCS matching in LTE, i.e., SINR-to-data rate mapping, to the simulation. Then, due to the quantized data rates, the sumrate performances might be degraded. However, since this degradation also occurs in FlashLinQ and ITLinQ, it does not affect the relative performance of our algorithms to FlashLinQ and ITLinQ. 7 The values of I and T sp are reasonably selected from the simulation results varying them, which will be shown later. Fig. 6. Comparison of the average sum-rate. We first show the effectiveness of channel-awareness of the QC priority assignment and QC yielding criterion of our algorithms by comparing their average sum-rates with those of FlashLinQ and ITLinQ. To this end, the average sum-rates of our algorithms are achieved without considering the QoS requirement. This can be simply implemented by fixing the weight parameters of all lins in our algorithms to be a same andfixedvalue,e.g.,w = 1, K. Thus, both QCLinQ and QC 2 LinQ have the same signaling overhead since the weight parameters do not have to be shared in QC 2 LinQ. In Fig. 6, the average sum-rates of the optimal centralized algorithm, QCLinQ, QC 2 LinQ, FlashLinQ, and ITLinQ are compared varying the number of lins. From Fig. 6a, we see that both QCLinQ and QC 2 LinQ provide higher average sum-rates than FlashLinQ and ITLinQ in all the cases, and the performance differences increase as the number of lins increases. This implies that our algorithms can achieve the sum-rate gain over FlashLinQ and ITLinQ by utilizing the time-varying channel more effectively. Moreover, QC 2 LinQ provides a higher performance than QCLinQ. This implies that the QC yielding criterion in QC 2 LinQ is more effective to achieve the sum-rate gain than the SIR threshold-based yielding criterion in other algorithms in spite of its additional

12 8576 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 12, DECEMBER 2016 TABLE IV QOSOUTAGE (%) AND AVERAGE SUM-RATES WITH QoS REQUIREMENT (Bits/Sec/Hz) signaling overhead. From the result with 16 lins, we can see that QCLinQ and QC 2 LinQ achieve the average sumrate, (26.04 and bps/hz, respectively) over 80% of that (31.46 bps/hz) of the optimal algorithm. Note that the average sum-rate of the optimal algorithm is provided only for 16 lins due to its high computational complexity. In Fig. 6b, the cumulative distribution functions (CDFs) of the average sum-rates are provided. The CDFs are obtained for the simulation setting with 1024 lins. The shapes of the CDFs of our algorithms are similar to those of FlashLinQ and ITLinQ while providing higher average sum-rates than FlashLinQ and ITLinQ. This implies that both QCLinQ and QC 2 LinQ achieve uniform gain compared with FlashLinQ and ITLinQ, and the formers achieve higher sum-rates than the latters with a high probability. We now compare the QoS outages and the average sumrates of the lin scheduling algorithms varying the number of lins. The QoS requirements for the settings with 128, 256, 512, and 1024 lins are chosen to be 0.25, 0.15, 0.085, and 0.05 bps/hz, respectively. The QoS outage is defined by N out /N tot,wheren out is the number of the lins which do not achieve the QoS requirement and N tot is the total number of the lins. The QoS outages and the average sumrates of algorithms are provided in Table IV. In all settings, FlashLinQ fails to satisfy the QoS requirement of more than 50% of lins, and ITLinQ fails to satisfy the QoS requirement of more than 30% of lins. Note that both FlashLinQ and ITLinQ try to provide fair opportunity to access the channel across lins. However, since each lin has a different channel condition that depends on its length and neighbor interfering lins, even though lins can acquire the same opportunity to access the channel, they achieve different performances. Thus, as shown in the table, FlashLinQ and ITLinQ may fail to provide performance-wise QoS, which is more relevant to users. On the other hand, our algorithms fails to satisfy the QoS requirement of only around 1% of lins, 8 i.e., the fairness among lins in terms of the satisfaction of their QoS requirement is achieved. To satisfy the QoS requirement, in our algorithms, when the degree of QoS unsatisfaction of a lin gets high, i.e., the weight parameter of the lin gets large, the scheduling priority of the lin becomes higher by the QC priority assignment. Moreover, in QC 2 LinQ, the QC yielding criterion gets weaened as shown in (13). 8 Note that some lins may not be able to satisfy the QoS requirement due to their lin quality or the topology, since each topology for the simulation setting is generated in a random way. Fig. 7. CDF of the average interschduling delay for 1024 lins. In all settings, the average sum-rates of our algorithms are higher than those of FlashLinQ and ITLinQ. Moreover, QC 2 LinQ provides better sum-rate performances than QCLinQ, while both provide similar degrees of QoS satisfaction. This result clearly shows that our algorithms (especially QC 2 LinQ) provide not only the higher average sum-rates for the system but also the higher degrees of QoS satisfaction for individual lins by explicitly considering timevarying channel condition and QoS requirement of each lin through QC priority assignment and QC yielding criterion. We compare the average scheduling delay of the lin scheduling algorithms in Fig. 7, where the scheduling delay is defined as the interschedule delay. We see that the average scheduling delays of QCLinQ and QC 2 LinQ are shorter than those of FlashLinQ and ITLinQ with a high probability. Note that this implies that in QCLinQ and QC 2 LinQ, lins are scheduled more frequently than in other algorithms. By the QC priority assignment and QC yielding criterion, QCLinQ and QC 2 LinQ try to mae a lin not miss its favorable condition to be scheduled, i.e., good channel condition. Thus, in QCLinQ and QC 2 LinQ, lins are more frequently scheduled than in other algorithms. We also see that the effect of considering the QoS requirement to the average scheduling delay in QCLinQ and QC 2 LinQ. When considering the QoS requirement, the lins which have bad average channel conditions are frequently scheduled in order to satisfy the QoS requirement. Thus, the average scheduling delay of such lins (high delay region) decreases compared with that in the case without considering the QoS requirement. On the other hand, for the lins which have good average channel conditions, more yielding occurs since they can satisfy the QoS requirement with small number of transmissions. Thus, the average scheduling delay of such lins (low delay region) increases.

13 LEE AND LEE: QC 2 LinQ: QoS AND CHANNEL-AWARE DISTRIBUTED LINK SCHEDULER 8577 Fig. 8. Comparison of the performances of QC X LinQ varying the fixed aggregate interference I. Fig. 9. Comparison of the performances with varying its weight parameter sharingperiodlengthinqc 2 LinQ. In Fig. 8, we show that the effects of the fixed aggregate interference approximation, I, in (10) in our algorithms. We consider the simulation setting with 128 lins varying I as 35, 1, 10 and 100 dbm, where -35 dbm represents the actual aggregate interference value which is typically produced between about -33 and -37 dbm in the simulation. The QoS requirement is chosen to be the same as the previous one, i.e., 0.25 bps/hz. In Fig. 8a, the QoS outages of our algorithms varying I are provided. Note that our algorithms have a transient behavior at the beginning as shown in the figure since they are iterative algorithms. Then, as iteration goes on, even though it is not shown in the figure, the QoS outages eventually converge (decrease) to the value around 1% in all cases as shown in Table IV. In the case with the large value of I, i.e., I = 100 dbm, the QoS outages of both QCLinQ and QC 2 LinQ converge (decrease) faster than those in the cases with the lower values of I, i.e., I = 35, I = 1 and 10 dbm, which implies that a large value of I helps the QoS requirement of each lin to be satisfied within a shorter time period. However, on the other hand, as shown in Fig. 8b, a larger value of I results in a lower average sumrate in general. As the value of I becomes larger, the weight parameter becomes more critical than the channel condition in deciding the QC priority assignment as in (10) and in checing the QC yielding criterion as in (13). Thus, in this case, the QoS outages of our algorithms converge faster while the average sum-rates of our algorithms decrease. It is worth noting that with the large value of I, QC 2 LinQ provides significantly much higher improvement of the convergence speed of QoS outage than QCLinQ while providing much less decrement of the average sum-rate. From the results, we can see that our algorithms are not sensitive to I when the value of I is low, and the fixed aggregate interference I can be used to address the trade-off between convergence speed of QoS outage and average sum-rate. We now show the effect of the weight parameter sharing period length, T sp,inqc 2 LinQ by comparing its performance with those of FlashLinQ, ITLinQ, and QCLinQ varying its value in Fig. 9. We consider the simulation setting with 128 lins, and only the value of T sp in QC 2 LinQ varies from 1 time-slot to 10 time-slots. The QoS requirement is chosen to be the same as the previous one. When the value of T sp is small, the QoS outage of QC 2 LinQ is degraded compared with that of QCLinQ due to its large additional signaling overhead for sharing the weight parameters as in Fig. 9a. However, as Fig. 10. Convergence of the average data rate of a lin in QC 2 LinQ varying its weight parameter sharing period length. its value increases, the QoS outage of QC 2 LinQ decreases, and eventually, it reaches that of QCLinQ. From Fig. 9b, we see that with increasing the value of T sp,qc 2 LinQ achieves a better sum-rate performance than QCLinQ since the former can effectively utilizes its QC yielding criterion with smaller additional signaling overhead. In addition to the average sum-rate and QoS satisfaction of QC 2 LinQ, the value of T sp also affects its convergence property. In Fig. 10, the average data rates of a lin with QC 2 LinQ varying the value of T sp as 1, 10, and 1000 time-slots for the cases with 128 lins and 16 lins are shown. From Fig. 10a and Fig. 10b, we see that when the value of T sp is 1000 time-slots, the average data rate of a lin converges much slower than when its value is 1 or 10 time-slots in both cases with 128 lins and 16 lins. Especially, in the case with 16 lins, the average data rate of a lin is severely fluctuating when the value of T sp is 1000 time-slots. When the number of lins is small and the value of T sp is too large, TXs chec the TX-yielding criterion with the outdated weight parameters many times. Hence, in this case, the average data rate of a lin is severely fluctuating since the outdated favorable or unfavorable condition for the TX-yielding criterion last longer until the next update of the weight parameters. VII. CONCLUSION In this paper, we developed distributed lin scheduling algorithms, QCLinQ and QC 2 LinQ, for D2D communication considering the QoS requirement and time-varying channel condition of each D2D lin. In QCLinQ, in each timeslot, the degree of QoS unsatisfaction and channel condition of each D2D lin are shared among D2D lins in a distributed way, and the scheduling priorities are assigned based on them. Then, with the assigned scheduling priorities, each D2D lin determines its lin scheduling by checing a SIR-based threshold criterion. In QC 2 LinQ, in addition that

14 8578 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 12, DECEMBER 2016 the scheduling priorities are assigned as in QCLinQ, a QoS and channel-aware yielding criterion is used to determine lin scheduling instead of the SIR-based threshold criterion. Through the simulation results, it is shown that both QCLinQ and QC 2 LinQ provide better performance than FlashLinQ and ITLinQ in terms of both the sum-rate performance for the system and the QoS satisfaction for each individual D2D lin. In addition, the simulation results also show that QC 2 LinQ provides better properties than QCLinQ in several aspects. This implies that utilizing the degree of QoS unsatisfaction and channel condition on scheduling priorities and yielding criterion is effective to improve the sum-rate performance and the degree of the satisfaction for the QoS requirement. AENDIX DERIVATION OF (12) The decrement of the weighted achievable data rate of lin in time-slot t due to the interference from lin can be calculated as w (t) (i) w (t) hs(t) 1+ I + N 0 = w (t) = w (t) w (t) h s(t) 1+ I + h s(t) + N 0 h s(t) h s(t) log I + N 2 0 I + h s(t) + N 0 I + N 0 + h s(t) I + N 0 hs(t) 1 +. I + N 0 The approximation in (i) follows from the high SINR assumption. REFERENCES [1] H.-S. Lee and J.-W. Lee, QoS and channel-aware distributed lin scheduling for D2D communication, in roc. 14th Int. Symp. Modeling Optim. Mobile, Ad Hoc, Wireless Netw. (WiOpt), May 2016, pp [2] K. Doppler, M. Rinne, C. Witing, C. B. Ribeiro, and K. Hugl, Deviceto-device communication as an underlay to LTE-advanced networs, IEEE Commun. Mag., vol. 47, no. 12, pp , Dec [3] M. Zulhasnine, C. Huang, and A. Srinivasan, Efficient resource allocation for device-to-device communication underlaying LTE networ, in roc. IEEE 6th Int. Conf. Wireless Mobile Comput., Netw. Commun. 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15 LEE AND LEE: QC 2 LinQ: QoS AND CHANNEL-AWARE DISTRIBUTED LINK SCHEDULER 8579 Hyun-Su Lee received the B.S. degree in electrical and electronic engineering from Yonsei University, Seoul, South Korea, in 2012, where he is currently pursuing the h.d. degree. His research interests include communication networs, mobile cloud computing, and smart grid. Jang-Won Lee (M 04 SM 12) received the B.S. degree in electronic engineering from Yonsei University, Seoul, South Korea, in 1994, the M.S. degree in electrical engineering from the Korea Advanced Institute of Science and Technology, Daeeon, South Korea, in 1996, and the h.d. degree in electrical and computer engineering from urdue University, West Lafayette, IN, USA, in From 1997 to 1998, he was with Dacom Research and Development Center, Daeeon, South Korea. From 2004 to 2005, he was a ost-doctoral Research Associate with the Department of Electrical Engineering, rinceton University, rinceton, NJ, USA. Since 2005, he has been with the School of Electrical and Electronic Engineering, Yonsei University, where he is currently a rofessor. His research interests include resource allocation, QoS and pricing issues, optimization, and performance analysis in communication networs, and smart grid.