QoS and Channel-Aware Distributed Link Scheduling for D2D Communication

Transcription

1 216 14th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networs (WiOpt) QoS and Channel-Aware Distributed Lin Scheduling for D2D Communication Hyun-Su Lee Dept. of Electrical and Electronic Eng., Yonsei University, Seoul, Korea Jang-Won Lee Dept. of Electrical and Electronic Eng., Yonsei University, Seoul, Korea Abstract In this paper, we study a distributed lin scheduling problem for device-to-device (D2D) communication with considering the quality-of-service (QoS) requirement and time-varying channel condition of each D2D lin. To this end, we first study an optimal centralized lin scheduling algorithm maximizing the total average sum-rate. We then abstract the important scheduling principles of the optimal algorithm in order to use them to develop a distributed lin scheduling algorithm. In our distributed lin scheduling algorithm, we develop a procedure with which D2D lins are able to share their degree of QoS satisfaction and channel condition with each other in a distributed manner. By utilizing those information for lin scheduling, our lin scheduling algorithm is able to satisfy the QoS requirement of each D2D lin while achieving throughput improvement by exploiting time-varying channel condition of each D2D lin in a distributed manner. 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 [1]. Hence, D2D communication is strongly expected to support many emerging services such as social networing, advertising, traffic safety, and emergency services. D2D communication can be classified into three categories in terms of control scenarios. The first one is networcontrolled D2D communication in which the networ fully coordinates D2D users. Thus, in networ-controlled D2D communication, the networ controls all operations for D2D communication such as synchronization, lin establishment, and resource allocation. The second one is networ-assisted D2D communication where D2D users coordinate their own lins and communication autonomously with a limited support from the networ such as synchronization and security. The last one is autonomous D2D communication where D2D users coordinate their communication in a fully distributed and autonomous manner without any support from the networ. For D2D communication, scheduling and resource management considering interference are one of the most important issues regardless of the categories. In [2], [3], [4], [5], [6], scheduling and resource allocation problems in networcontrolled D2D communication are studied, where a base This wor was supported in part by Mid-career Researcher Program through NRF grant funded by the MSIP, Korea (213R1A2A2A16953). station schedules D2D users and allocates radio resources in a centralized way in order to maximize the system throughput. Especially, in [4], [5], [6], the quality of service (QoS) requirements for D2D users 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 signalling overhead, and might be used only when the base station supports the D2D scheduling capability. Moreover, for networ-assisted D2D and autonomous D2D communication, it is necessary to have a distributed scheduling and resource allocation algorithm. Recently, Qualcomm has designed a D2D wireless PHY/MAC networ architecture called FlashLinQ [7], 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 GPS. With the global synchronization, FlashLinQ can perform device discovery and scheduling in a distributed way by using an analog energy-levelbased signalling procedure using OFDM single-tone channels. Especially, it provides a distributed scheduling algorithm in which D2D users are scheduled by the signal-to-interference ratio (SIR)-based yielding criterion with assigned scheduling priorities. By randomizing the scheduling priorities of D2D users over time, FlashLinQ can provide a fair opportunity to access the channel across D2D users. In addition, several distributed scheduling algorithms motivated by FlashLinQ are studied [8], [9], [1]. In [8], a distributed lin scheduling algorithm that mitigates the inefficiency in resource reuse of FlashLinQ is proposed. In this algorithm, D2D lins can be aware of whether other lins are scheduled or yielded by sharing the global interference conditions among them called an on-off interference map (I- Map). Thus, each D2D lin does not yield when its interfering lins are determined to yield, while unnecessary yielding could be happened in FlashLinQ due to the lac of the global information. However, the additional required signalling overhead to share and update the I-Map is quite large, and thus it updates the I-Map only once over multiple traffic slots. In [9], a distributed opportunistic scheduling algorithm under fairness constraints (DO-Fast) is proposed. In this algo /16/$ IEEE

2 TABLE I COMPARISON WITH RELATED WORKS QoS requirement Instantaneous channel-awareness Priority assignment Yielding criterion FlashLinQ [7], [8] Not considered Only for yielding criterion Random SIR threshold-based criterion [9] Not considered Only for yielding criterion Random with grouping SIR threshold-based criterion ITLinQ [1] Not considered Only for yielding criterion Random TIN-optimality inspired criterion Our wor Considered Priority & yielding criterion QoS and channel-aware SIR threshold-based criterion rithm, at the beginning of each frame which consists of multiple traffic slots, D2D lins broadcast and order their channel state indicators (CSI), e.g., signal-to-noise ratio (SNR). Then, D2D lins are divided into two groups with same number of lins according to their CSI order, i.e., high-csi-order and low-csi-order groups. In each traffic-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 adjust the chance to transmit for each group. The throughput performance is improved if the high-csi-order group obtains more chance to transmit than the low-csi-order group, and the delay performance is improved otherwise. In [1], an information-theoretic lin scheduling (ITLinQ) is developed by modifying the scheduling algorithm of Flash- LinQ. According to [11], treating interference as noise is information-theoretically optimal if the TIN-optimality condition is satisfied. Inspired by that condition, the authors in [1] develop a distributed lin scheduling algorithm which guarantees the condition with the same signalling overhead as that of FlashLinQ. Thus, ITLinQ achieves considerable throughput gain over FlashLinQ without any additional signalling overhead. In [8], [9], [1], the authors focused on the throughput improvement of FlashLinQ, 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 performance across D2D lins due to the different channel conditions of D2D lins. Thus, in order to resolve this issue, performance-wise fairness or QoS requirement, such as the minimum average data rate, should be considered in the distributed algorithm as in the centralized scheduling algorithms in [4], [5], [6]. In addition to considering the QoS requirement, it is also desirable to appropriately consider time-varying channel condition of each D2D lin, as in [6]. It is well nown that in wireless systems, a better channel condition provides a better throughput in general, and thus, throughput performance can be improved by exploiting the instantaneous channel conditions of D2D lins. In FlashLinQ, [8], [9], and [1], the time-varying channel conditions are implicitly considered by utilizing the instantaneous channel gain for their yielding criterions. In FlashLinQ, the SIR threshold-based yielding criterion is developed, and in [8] and [9], the same SIR thresholdbased yielding criterion is used. In [1], an yielding criterion inspired by the TIN-optimality condition is developed, and the considerable throughput gain over FlashLinQ is achieved with it. In this paper, we develop a distributed lin scheduling algorithm considering the QoS requirement, i.e., the minimum average data rate, of D2D lins, and the time-varying channel conditions of D2D lins to improve system performance. In order to develop the distributed algorithm, we first study an optimal centralized algorithm 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 algorithm and by using them we develop a heuristic and distributed lin scheduling algorithm. In order to apply the principles, we develop an analog-based signalling procedure for the lin scheduling algorithm. Through this signalling procedure, D2D lins are able to share information on their degree of QoS satisfaction and channel condition with each other in a distributed manner. In our distributed lin scheduling algorithm, the scheduling priorities are assigned to the D2D lins according to the shared information. By this, our distributed algorithm can satisfy the QoS requirement of each lin and achieve considerable throughput improvement compared to the other algorithms in which the time-varying channel condition is not considered on the scheduling priority assignment. We summarize the comparison of our distributed algorithm with the related wors in Table I. 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 algorithm and in Section IV, we develop a distributed lin scheduling algorithm based on the optimal algorithm. We provide numerical results in Section V and finally conclude in Section VI. II. SYSTEM MODEL We consider a synchronous OFDM time-slotted system consisting of multiple D2D lins, where each traffic slot is considered as a time-slot. 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, ur, 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 traffic 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 1 In the rest of this paper, we omit D2D from D2D lin, D2D TX, and D2D RX for the convenience.

3 as S = {1,2,...,S}. The system is in one of finite system states in each traffic slot and the probability that system is in system state s in a traffic slot is denoted as π s. At the beginning of each traffic slot, lin scheduling is conducted to decide lins which transmit data simultaneously in the traffic 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, and a scheduling indicator qz s {,1} where 1 represents that the lins in scheduling group z are scheduled in a traffic slot with system state s and represents otherwise. Then, the scheduling vector q s = [qz s] z Z indicates which lins are scheduled in a traffic slot with system state s, where Z is the power set of the set of lins, K. Naturally, at most one scheduling group can be scheduled in a traffic slot, i.e., the scheduling vector should be in the following constraint set: q s Q s = q z {,1}, z Z s qz s 1, s S. (1) z Z In each traffic 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 TX of lin as P. Then, from the Shannon capacity formula, the achievable instantaneous data rate 2 of lin in a traffic slot with system state s is obtained as r s ( q s) = ( ) qz s log h s 2 1+ P z Z z, hs P +N, (2) where Z is the set of scheduling groups in which lin is included,h s ij is the channel gain from the TX of lin i to the RX of lin j in a traffic slot with system state s, and N is noise power. Thus, the average data rate of lin can be calculated from (2) and the state probability π s as s S π sr s( q s) and the total average sum-rate of the system, which we want to maximize, is obtained as K s S π sr s( q s). In addition, each lin has a requirement for its minimum average rate, ξ, which is represented as s S π sr s( q s) ξ, K. III. CENTRALIZED OPTIMAL LINK SCHEDULING In this section, we formulate a lin scheduling 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 (P) maximize q π s r s ( q s) Ks S subject to s Sπ s r s ( q s ) ξ, K, q s Q s, s S, where q = [ q s ] s S. Problem (P) is a special case of the problem in [6]. Thus, we develop the centralized optimal lin scheduling algorithm for problem (P) by using a dual approach 2 In this paper, data rate implies data rate per unit bandwidth. and a stochastic subgradient method [12], [13] as in [6]. We refer readers to [6] for the details. We first define the dual problem from the relaxed problem of problem (P) where the constraint for the scheduling indicator in (1) is relaxed as continuous value. 3 In the optimal algorithm, in each time-slot t, the scheduling indicatorqz s(t) is determined by the central controller as q s(t) z ( λ (t) ) = {1, if z = argmax z Z ψ s(t) z ( λ (t) ), otherwise, z Z, where s (t) is the system state in time-slot t, λ(t) is a Lagrangian multiplier vector of dual problem in time-slot t, and ψz s ( λ) ) h (1+λ )log 2 (1+ s P z z, hs P +N (4). 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 (5) where α (t) is a step size at time-slot t and ν (t) is the corresponding stochastic subgradient of dual problem. The stochastic subgradient of dual problem is obtained by Dansin s Theorem [14] as (3) ν (t) = r s(t) ( λ (t) ) ξ, K, (6) 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 (5) converges to the optimal solution of dual problem, λ, with probability 1 as the time-slot t goes to infinity, if step size α (t) satisfies the following conditions [12]: α (t), t= α(t) =, and t=( ) α (t) 2 <. Then, the scheduling indicator q( λ ) is the optimal solution of problem (P), since the relaxed problem is convex programming and it satisfies the constraint (1) in the original problem (P). 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 large signalling overhead. In addition, the central controller finds the optimal lin scheduling by finding 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, where K is the number of lins, and thus the computational complexity of the optimal algorithm is quite high. Therefore, the optimal algorithm is hard to be implemented in practice due to its large signalling overhead and high computational complexity and we need to implement an algorithm with small signalling overhead and low computational complexity. In addition, for the case in 3 Note that the relaxed problem is convex programming which has zero duality gap.

4 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 next section, we will study a distributed lin scheduling algorithm that approximates the optimal algorithm while requiring small signalling overhead and having low computational complexity. IV. DISTRIBUTED LINK SCHEDULING In this section, we develop a distributed lin scheduling algorithm that approximates the optimal algorithm in the previous section with small signalling overhead and low computational complexity. To this end, we first abstract the fundamental principles of the optimal lin scheduling algorithm in previous section. We then develop a QoS and channelaware distributed lin scheduling algorithm by applying the fundamental principles. A. Fundamental Principles in the Optimal Algorithm In the optimal algorithm, lin scheduling is decided by the condition in (3) which finds the scheduling group z that has the maximum value of ψz s( λ) in (4). We call ψz s( λ) the sum of weighted achievable data rate of lins in scheduling group z in a traffic slot with system state s since 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. We now define the weight parameter of lin in traffic slot t as w (t) = 1+λ (t), (7) where λ (t) is the Lagrangian multiplier of lin in traffic slot t which is updated in each traffic slot as in (5) and (6). As we can see in (5) and (6), the weight parameter (i.e., the Lagrangian multiplier) of lin increases when its current achievable data rate is larger than its minimum average rate requirement and decreases otherwise. This implies that the weight parameter of each lin represents the degree of satisfaction of its minimum average rate requirement. We now abstract the scheduling principles of the optimal algorithm as follows: 1) Each lin updates its weighted parameter in each traffic slot as in (5) and (6). 2) The lins in the scheduling group which has the largest sum of weighted achievable data rate are scheduled as in (3) and (4). For each lin, its weight parameter represents its degree of satisfaction and its achievable data rate represents its channel condition. Thus, the scheduling principle implies that in each traffic slot, the lins which have lower degree of satisfaction for their QoS requirements and have higher achievable data rates should have higher scheduling priorities. B. Idea For Distributed Scheduling Algorithm Now, there arises a question that how to apply the scheduling principles in a distributed manner. At the end of each traffic slot, each lin can update its weighted parameter by using its transmission result in the traffic 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. To resolve this issue, we develop a signalling procedure inspired by FlashLinQ. In FlashLinQ, lin scheduling in each traffic slot is done based on priorities that are assigned to lins in that traffic slot and to guarantee fair access to channel among lins, in each traffic slot, priorities for lins are generated randomly. However, in our algorithm, to apply the second principle, in each traffic slot, we assign scheduling priorities to lins in a descending order of their weighted achievable data rates so that lins with higher weighted achievable data rates can have higher priorities to be scheduled in that traffic slot. Then, by conducting the lin scheduling algorithm with the assigned scheduling priorities in each traffic slot, the scheduled lins in the traffic slot are determined. Thus, in our algorithm, each lin should share its weighted achievable data rate with each other and we develop a signalling procedure to share the weighted achievable data rates among lins in a distributed way by using the analog energy-level-based signalling procedure. However, still we have one more difficulty to overcome. Since the achievable data rates for lins in (2) can be obtained only when 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, the sum of weighted achievable data rates of lins in scheduling group z in (4) can be rewritten as ψ s z = z w log 2 ( 1+ hs P I +N We call ψ z s the approximated sum of weighted achievable data rates of lins in scheduling group z with system state s and the assumption that the aggregate interference is I. From this, we now define the approximated weighted achievable data rate of lin in traffic slot t, ρ (t) as ) ρ (t) = w(t) log 2 (1+ hs(t) P, K. (8) I +N 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. Note that even with the assumption that all RXs receive the same and fixed aggregate interference, the degree of QoS satisfaction and the channel condition of lins are still considered in the approximated weighted achievable data rates, since the lins which have lower degree of QoS satisfaction and good channel condition have higher approximated weighted achievable data rates as in (8). Hence, as will be shown later, our distributed algorithm provides the ).

5 satisfaction of QoS requirement and sum-rate improvement even with this assumption. Thereafter, all lins share their approximated weighted achievable data rate with each other and 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. The detailed algorithm and signalling procedure for sharing the approximated weighted achievable data rates and determining the lin scheduling are described in the following subsection. C. Algorithm Description We now describe our distributed lin scheduling algorithm and signalling procedure in more detail. First of all, each lin should be able to share its approximated weighted achievable data rate with each other in order to generate the scheduling priorities. Thus, we propose the signalling procedure to share them in a distributed way while using a small amount of resource. The proposed procedure is based on a singletone OFDM signalling. The main idea here is to share the approximated weighted achievable data rates through analog signals. The structure of a traffic slot of our lin scheduling algorithm is presented in Fig. 1. As in this figure, a traffic slot in our algorithm is divided into seven sections, which consist of two pairs of TX-bloc and RX-bloc, rate scheduling, data segment, and Ac. Each bloc consists of 4 symbols and 28 frequency 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. 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, the lin scheduling is done through the two pairs of TX-bloc and RX-bloc. In rate scheduling, the scheduled lins estimate their SIR and choose code rate and modulation based on their estimated SIR. Then, the scheduled TXs transmit their data on the data segment, and the RXs received their data transmit the acnowledgement signal. At last, each RX updates its weight parameter by using its lin scheduling and transmission result. Note that in contrast to FlashLinQ in which there are one pair of TXbloc and RX-bloc, our algorithm needs two pairs of TXbloc and RX-bloc. Hence, the signalling overhead of our algorithm is larger than that of FlashLinQ. However, as we will show in numerical results, despite of this, our algorithm provides better performance since our algorithm exploits the time-varying channel condition of each lin. In addition, our algorithm can satisfy the QoS requirement of each lin, while FlashLinQ cannot. In order to simply present the algorithm, we consider a simple example which consists of lin 1 and lin 2, where T i and R i denote the TX and RX of lin i, respectively, as shown Frequency (28 tones) 1st TX bloc 1st RX bloc 2nd TX bloc 2nd RX bloc Rate Scheduling Data Segment 1st TX-bloc 1st RX-bloc 2nd TX-bloc 2nd RX-bloc 4 symbols 4 symbols 4 symbols 4 symbols Fig. 1. Structure of a traffic slot in the proposed lin scheduling algorithm. Direct power signal Direct power signal Fig. 2. Simple example with two D2D lins. Fig. 3. The first TX-bloc in simple example with two D2D lins. in Fig. 2. The algorithm which is represented by this simple example can be simply extended to the case with multiple lins. We assume that each lin and its reversed lin have a same channel gain, i.e., h TiR j = h RjT i. In addition, we assume that the transmission power of each TX is nown to its corresponding RX, e.g., R 1 nows P T1, where P T1 is the transmission power of T 1. We now describe the procedure in each section in a traffic slot. 1) First TX-bloc: As illustrated in Fig. 3, in the first TXbloc, T 1 transmits the analog-tone-signal using power P T1 and T 2 also transmits the analog-tone-signal using power P T2. We call these signals as the first direct power signals. Then,R 1 receives the signals from T 1 and T 2 with power of P T1 h T1R 1 and P T2 h T2R 1, respectively. Similarly, R 2 receives the signals from T 1 and T 2 with power of P T1 h T1R 2 and P T2 h T2R 2, respectively. Now, each RX can find out the channel gain of its own lin, i.e., h T1R 1 for R 1 and h T2R 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 4, i.e., ρ 1 for R 1 and ρ 2 for R 2, as in (8) 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. 4 In this section, we omit approximated from the approximated weighted achievable data rate for the convenience. Ac

6 Inverse power echo multiplied by Direct power signal multiplied by From Inverse power echo multiplied by Direct power signal multiplied by From Known from 1st Tx-bloc Fig. 4. The first RX-bloc in simple example with two D2D lins. Fig. 5. The second TX-bloc in simple example with two D2D lins. 2) First RX-bloc: In the first RX-bloc, each RX transmits the analog-tone-signal called as the first inverse power echo. K It is sent by RXs at power 1ρ 1 K P T1 h T1 for R R 1 and 1ρ 2 1 P T2 h T2 for R 2 R 2, where K 1 is the system constant which is assumed to be nown to all users in the system, as illustrated in Fig. 4. 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 from R 1 and R 2 at T 1 have power of and K 1 ρ 1 P T1 (9) K 1 h T1R 2 ρ 2 P T2 h T2R 2, (1) respectively. With the received signal from R 1, i.e., (9), 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 P T1 are nown. However, the weighted achievable data rate of lin 2, ρ 2, cannot be obtained from the received signal from R 2, i.e., (1), yet due to the lac of information. In order to obtain ρ 2 from the received signal at the first RXbloc, T 1 has to now the following value: K 1 h T1R 2 P T2 h T2R 2, (11) 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, e.g., T 1 stores (1) 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 the analog-tone-signal called as the second direct power signal. As illustrated in Fig. 5, 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 RXbloc. 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 signal with power of K 2 P T1 ρ 1 and T 2 transmits signal with power of K 2 P T2 ρ 2, where K 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 P T1 h T1R 1 ρ 1 and K 2 P T2 h T2R 1 ρ 2 from T 1 and T 2, respectively. From 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 P T2 h T2R 1 from the stored signal powers in the first TX-bloc and the system constant K 2. R 2 also can obtain the weighted achievable data rate of lin 1, ρ 1, in a similar way. 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 TXblocs. Then, with the generated scheduling priorities, they determine whether they will yield their transmission or not by checing a receive yielding criterion. If the criterion is violated for an RX, it yields its transmission, and this is called as RXyielding. Through RX-yielding, 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: P Ti h TiR i j L i P Tj h TjR 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. Note that P Tj h TjR i is the received power of the first direct power signal from T j 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 signal from other TXs, which is 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 as 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 K P T1 h T1 for R R 1 and 1 1 P T2 h T2 for R R 2. When only one RX 2 transmits the second inverse power echo due to RX-yielding, the corresponding TX is just scheduled. On the other hand, when both R 1 and R 2 transmit the second inverse power echo as illustrated in Fig. 6, T 1 receives the signal with power of K 1h T1 R 2 P T2 h T2 in (11) from R R 2. Hence, T 1 can obtain the weighted 2 achievable data rate of lin 2, ρ 2, from the stored signal power in (1) in the first RX-bloc by using the received signal from R 2, and 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

7 From Inverse power echo TABLE II SIMULATION PARAMETERS From Inverse power echo Fig. 6. The second RX-bloc in simple example with two D2D lins. generated scheduling priorities, they determine whether they will yield their transmission or not by checing a transmit yielding criterion. If the criterion is violated for a TX, it yields its transmission, and this is called as TX-yielding. Through TX-yielding, 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, the TX of lin i, T i, transmits only if the following condition is satisfied for all no-yielding RXs with higher priority than lin i: Bits/Sec/Hz Parameter Networ layout System bandwidth Carrier frequency Node antenna height TX power Noise spectral density Antenna gain Noise figure Pathloss model Shadowing Yielding threshold Value 5m 5m square 5 MHz 2.4 GHz 1.5 m 2 dbm -184 dbm/hz -2.5 db 7 db ITU-1411 LOS model Log-normal with standard deviation of 1 db γ = 9 db FlashLinQ ITLinQ Optimal algorithm Proposed algorithm QoS requirement P Tj h TjR j P Ti h TiR j > γ TX, j 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. Note that T i can obtain the estimated received SIR at R j due to the interference from itself, i.e., PT j ht j R j P Ti h Ti, by using its received power of the second R j inverse power echo from R j, which is r inv ji = K1hT i R j P Tj h Tj R j, as K 1 P Ti r inv ji = PT j ht j R j P Ti h Ti R j since T i nows K 1 and P Ti. 5) Rate Scheduling, Data Transmission, and Ac: From the TX- and RX-blocs, the scheduled lins of which both TX and RX did not yield are determined. In rate scheduling, they 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 segment, and the RXs received their data transmit the acnowledgement signal. After the transmission, each RX updates its weight parameter as in (5) and (7) using its transmission result. V. NUMERICAL RESULTS In this section, we provide simulation results to evaluate the performance of our distributed lin scheduling algorithm by comparing our algorithm to FlashLinQ and ITLinQ. In simulation results, the additional signalling overhead of our distributed algorithm compared to FlashLinQ and ITLinQ is fully accounted. In order to compare the performances of the optimal algorithm and our distributed algorithm, we assume that the signalling overhead of the optimal algorithm is same with that of our distributed algorithm. 5 For the optimal algorithm, only the results for 16 lins are provided due to its computational complexity. The implementation of ITLinQ follows the same steps as in [1] and the value of parameter η in ITLinQ is taen to be equal to.6 with which the highest sum-rate performance is achieved in our simulation settings. Simulation parameters are shown in Table II. 5 Note that this assumption is favorable to the optimal algorithm. Bits/Sec/Hz D2D lins (a) Data rate for 16 lins D2D lins (b) Data rate for 64 lins Fig. 7. Data rate with the QoS requirement. FlashLinQ ITLinQ Proposed algorithm QoS requirement We first show the satisfaction of the QoS requirement and the fairness of our distributed algorithm. We consider two topologies which consist of 16 lins and 64 lins, respectively. The QoS requirements for the topologies with 16 lins and 64 lins are chosen to be 1.2 bps/hz and.5 bps/hz, respectively. For each topology, lins are dropped randomly with a uniform distribution, and the length of each lin, which is the distance between its TX and RX, is randomly chosen between 25 m and 5 m with a uniform distribution. The value of parameter I in our distributed algorithm is taen to be equal to 1 dbm. The data rate of each lin with different scheduling algorithms are illustrated in Fig. 7. In this figure, lins are sorted in an ascending order of their lengths. In both Fig. 7a and Fig. 7b, the proposed algorithm well satisfies the QoS requirement for all lins, while FlashLinQ and ITLinQ do not satisfy it for some lins. Furthermore, in general, the data rate of a lin decreases as its length increases in both FlashLinQ and ITLinQ. 6 Note that FlashLinQ and ITLinQ try to provide fair opportunity to access the channel across D2D lins. However, since each D2D lin has a different channel condition that strongly depends on its length, even though D2D lins acquire the same opportunity to access the channel, they achieve different performances, as the figure shown. This result 6 Note that the data rate of a lin does not monotonically decrease as its length due to the different aggregate interference of each RX.

8 Average sum rate (Bits/Sec/Hz) FlashLinQ Distributed ITLinQ Proposed algorithm Number of D2D lins (a) Average sum-rate varying the number of D2D lins Probability FlashLinQ ITLinQ Proposed algorithm Sum rate (Bits/Sec/Hz) (b) The cumulative distribution function of the sum-rate for 124 lins Fig. 8. Comparison of the sum-rate performances of the proposed algorithm, ITLinQ and FlashLinQ. clearly shows that FlashLinQ and ITLinQ may fail to provide performance-wise fairness, which is more relevant to users, if D2D lins have different channel conditions to each other. On the other hand, in our distributed algorithm, the fairness among the lins in terms of the data rate is achieved through the satisfaction of the QoS requirement. We now show the effectiveness of channel-aware priority assignment of our distributed algorithm by comparing its throughput performance with that of FlashLinQ and ITLinQ. In this case, we do not consider the QoS requirement to achieve the maximum throughput of our distributed algorithm. This can be simply implemented by fixing the weight parameters of all lins in our distributed algorithm as a same and fixed value. Then, the lins which have a good channel condition are assigned to high scheduling priorities. We consider various simulation settings with varying the number of lins. For each setting, all lins are dropped randomly with a uniform distribution, and the length of each lin is randomly chosen between 25 m and 5 m with a uniform distribution. In Fig. 8, the comparison of the sum-rate performances of the proposed algorithm, FlashLinQ and ITLinQ are illustrated. The average sum-rate of each scheduling algorithm varying the number of lins is depicted in Fig. 8a. The proposed algorithm has a better sum-rate performance in every cases, and the performance differences from FlashLinQ and ITLinQ increase as the number of lins increases. This implies that utilizing the time-varying channel condition on the scheduling priorities is more effective to achieve the throughput gain than utilizing the time-varying channel condition on the yielding criterion as in FlashLinQ and ITLinQ. Especially, the proposed algorithm achieves 172% gain compared to FlashLinQ and 39% gain compared to ITLinQ for 124 lins in spite of its additional signalling overhead. In Fig. 8b, the cumulative distribution functions (CDFs) of the sum-rate are illustrated. The CDFs are obtained for the simulation setting which has 124 lins. The proposed algorithm achieves uniform gain compared to FlashLinQ and ITLinQ, i.e., the shape of the CDF of the proposed algorithm is similar to that of FlashLinQ and ITLinQ while the average sum-rate achieved by the proposed algorithm increases. Thus, the proposed algorithm achieves a higher sumrate than the FlashLinQ and ITLinQ with a high probability. VI. CONCLUSION AND FUTURE WORK In this paper, we developed a distributed lin scheduling algorithm for D2D communication considering the QoS requirement and time-varying channel condition of each D2D lin. In the proposed lin scheduling algorithm, in each traffic slot, the degree of QoS satisfaction 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. Through the simulation results, it is shown that the proposed lin scheduling algorithm provides not only the satisfaction of the QoS requirement of each D2D lin but also considerable throughput improvement over FlashLinQ and ITLinQ. This implies that utilizing the channel condition on the scheduling priorities is more effective to achieve the throughput gain than utilizing the channel condition only on the yielding criterion. 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