Resource allocation for maximizing the device-to-device ...

The First IEEE ICCC International Workshop on Interference Management of Wireless Networks (IMWN 2013)

Resource Allocation for Maximizing the Device-to-Device Communications Underlaying LTE-Advanced Networks Hongguang Sun, Min Sheng, Member, IEEE, Xijun Wang, Member, IEEE, Yan Zhang, Member, IEEE, Junyu Liu, and Kan Wang State Key Laboratory of Integrated Service Networks Institute of Information Science, Xidian University, Xi’an, Shaanxi, 710071, China Email: {hgsun, xijunwang, yanzhang}@xidian.edu.cn, [email protected], {jyliu, wangkan}@stu.xidian.edu.cn

Abstract—Device-to-device (D2D) communications as an underlaying LTE-Advanced network has proven to be efficient in improving the network performance and releasing the traffic load of eNodeB. By sharing radio resource with cellular user equipments (CUEs), D2D communications can significantly enhance the overall spectral efficiency. However, the resulting mutual interference may cancel or even outweigh the gain brought by D2D communications. In this paper, we avoid the interference through a well designed resource allocation scheme. We formulate the uplink resource allocation problem where more than one D2D pair can share the same resource with one CUE under the constraint that the SINR requirements of CUEs and admitted D2D pairs are satisfied. The optimization resource allocation is shown to be NP-hard, and an interference degree based Greedy heuristic Resource Allocation algorithm (GRA) is explored to maximize the number of admitted D2D pairs by properly selecting a group of D2D pairs for each CUE. Simulation results show the efficacy of the proposed algorithm.

mutual interference may occur between DUEs and cellular entities, e.g., eNodeB and CUEs. To manage the interference incurred by the resource reusing, several schemes were investigated in the prior work, including power control [1], [3], receive mode selection [4], rate splitting [5] and resource allocation [6], [7], [8]. Doppler [1] proposed a power control mechanism, in which the base station (BS) restricts the maximum transmit power of DUE, so that the quality of service (QoS) of CUE can be guaranteed. Employing the retransmission by BS, Min et al. [4] proposed an interference cancellation scheme to improve the reliability of D2D communication in the middle interference regime. Similarly, the interference of DUE to BS is managed by controlling the transmit power of DUE. However, the method of limiting the transmit power of D2D to mitigate the interference to BS may lead to degradation on D2D performance. An interferenceaware resource allocation scheme was proposed in [6], where BS allocates DUEs resources that preassigned to CUEs least interfering with the DUEs. Though throughput of DUEs is improved, the performance of CUEs are not concerned. Taking the QoS of both CUEs and DUEs into account, Zulhasnine et al. [7] designed a greedy heuristic resource allocation algorithm, where interference can be avoided or diminished with the intelligent coordination from the eNodeB. Based on the proportionally-fair (PF) scheduling algorithm, Lee et al. [8] proposed a resource allocation scheme which can improve the throughput fairness among user equipments while maintaining the system capacity. However, all the aforementioned works assume that at most one D2D pair can share the same RB resources with one CUE. While it is reasonable in the scenario where more D2D pairs coexist with less CUEs with limited RBs being used. In fact, from the viewpoint of spatial reuse, allowing more D2D pairs to share the same RB resource with one CUE is beneficial to the overall system performance as well as the number of concurrent D2D transmissions. In this paper, we investigate the resource allocation problem where more than one D2D pair can share the same RB resource with one CUE and prove its NP-hardness. We give priority to

I. I NTRODUCTION Device-to-device (D2D) communications as an underlay to cellular networks have been introduced as a promising component to LTE-Advanced [1]. Supported by the evolved NodeBs (eNodeBs), D2D communication holds three potential types of gains [2]. First, the reuse gain can be achieved if the spectrum resources can be simultaneously used by cellular user equipments (CUEs) as well as D2D user equipments (DUEs). Second, the proximity allows DUEs to obtain high bit rates with low transmit power level. Third, the hop gain refers to using a direct link in the D2D mode rather than communicating via the eNodeB, which helps to release the congestion at the eNodeB. DUEs can share the same LTE resource blocks (RBs) with CUEs in the uplink (UL) phase or downlink (DL) phase. And resources of UL are preferred being reused due to the heavier download traffic, which is a characteristic of Internet data. Therefore, by efficiently utilizing UL resources, the overall system capacity can be greatly improved. However, This paper is supported by National Natural Science Foundation of China (61231008, 61172079, and 61201141), 973 Program (2009CB320404), 111 Project (B08038), National S&T Major Project (2012ZX03002009-003, 2012ZX03004002-003), Shaanxi Province Science and Technology Research and Development Program (2011KJXX-40).

978-1-4799-1403-6/13/$31.00 ©2013 IEEE

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CUEs and consider the QoS of both CUEs and DUEs. The mutual interferences among different D2D pairs as well as that between DUE and CUE sharing the same RB resource are considered. The resource allocation problem is formulated to maximize the number of admitted D2D pairs by enabling more D2D pairs to reuse the same RB resource subject to the constraint of the maximum tolerable interference level at each RB. Due to the NP-hardness of the problem, we alternatively propose a greedy resource allocation algorithm GRA based on the smallest degree interference criterion from the graph theory. Simulation results prove the efficacy of the proposed algorithm over the existing schemes. To the best of our knowledge, we are the first to explore the resource allocation for D2D communications where more than one D2D pair can share the same RB resource with one CUE in the LTE-Advanced networks. The rest of this paper is organized as follows. Section II describes the system model of D2D communication underlaying LTE-Advanced networks. In Section III, we first study and formulate the resource allocation problem. And then, we give the greedy heuristic resource allocation algorithm GRA. Later, in Section IV, we verify the validity of the proposed GRA algorithm by extensive simulations. Finally, in Section V, we conclude the main results in this paper.

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Figure 1. System model of D2D communications reusing the UL resources of CUEs in LTE-Advanced Networks

be attained to meet the QoS requirement of each CUE and D2D pair. The thermal noise power σ 2 is assumed to be the same for eNodeB and all the D2D receivers. We give priority to CUEs and take them as the primary users. A D2D pair can not share the same RB resource with a CUE unless the imposed interference to the RB by the D2D transmitter not affect the QoS requirement of the corresponding CUE. Particularly, the received SINR of uplink transmission of CU Em should meet the following requirement pm gm,BS c ≥ γm , m ∈ {1, 2, ..., M }, (1) σ 2 + Im,max

II. S YSTEM M ODEL We consider that D2D communications reuse the UL period of LTE-Advanced networks. As shown in Fig. 1, there exists two types of user equipments: CUE and DUE. CUEs communicate through the eNodeB, and the DUEs directly communicate with each other. In Fig. 1, CU E1 transmits uplink date to eNodeB, while the other two D2D pairs, D2D1 and D2D2 may reuse the same RB preassigned to CU E1 to complete their transmissions. Note that two types of interference exist in this scenario: interference between CUE pair and D2D pair, and interference among D2D pairs. Assume M CUEs and N D2D pairs coexist in the same single cell, where N > M . We set the group of CUEs as M={CU Em | m = 1, 2, ..., M }, and the group of D2D pairs as N = {D2Dn |n = 1, 2, ..., N }, respectively. The corresponding transmitter and receiver in D2Dn are denoted by DnT and DnR . In LTE-Advanced, bandwidth is divided into equal size RBs. In this model, we assume the total number of RBs in the UL period is equal to the number of CUEs, i.e., M . To prioritize the cellular communications, we assume that all the RBs have been preassigned to the M CUEs by the eNodeB, i.e., each CUE occupies one separate RB in the UL period and no interference exists among CUEs. To be explicit, the index of the RB occupied by CU Em is denote by m. The transmit power of CUEs, denoted by PC = {pm | m = 1, 2, ..., M }, are predetermined and sufficient to meet the QoS of their own. All the D2D pairs are assumed to have the same transmit power p0 . In the resource allocation process, we assume all the transmit powers are constant and power control is not considered. We c | m = 1, 2, ..., M } and ΓD = {γnd | n = define ΓC = {γm 1, 2, ..., N } as the corresponding SINR thresholds that must

where gm,BS represents the channel gain from CU Em to the eNodeB and Im,max is the maximum tolerable interference that the eNodeB can bear at the m-th RB. III. R ESOURCE A LLOCATION In this section, we first formulate the problem of assigning D2D pairs to share the appropriate RBs with the corresponding CUEs as an optimization problem that maximize the number of admitted D2D pairs. Then we give analysis about the problem, and show that the problem is NP-hard, which motivates us to propose a heuristic algorithm to solve the problem based on graph theory. A. Problem formulation Our purpose is to allow as many as D2D pairs to reuse RBs that have been preassigned to CUEs under the constraint that the QoS of CUEs can be guaranteed. Since DUEs are actually cellular equipments that communicate in D2D mode, the QoS requirement of DUEs should also be satisfied. Without considering power control, we need to utilize some form of admission control. In order to satisfy the SINR requirement of CU Em as shown in (1), the maximum tolerable interference from D2D pairs to m-th RB can be

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Im,max =

pm gm,BS − σ 2 , m ∈ {1, 2, ..., M }. c γm

thus, it can implement GRA centrally. First, we utilize the widely used Conflict Graph (CG) model [9] to model network interference and then give the procedure of GRA algorithm.

(2)

Let D denote the set of D2D pairs that can be admitted in the hybrid system, and Dm represent the set of D2D pairs that can share the m-th RB with CU Em . For simplicity, in the following formulation, we use subscripts, e.g., m or n, to represent the corresponding user equipments, e.g., CU Em or D2Dn , when needed. Mathematically, the problem can be formulated as follows: D = arg maxDm ⊆N |

s.t.

M

Dm |

B. Network Interference Model In conflict graph model, each link is taken as a vertex, and two vertices are connected with an edge if the corresponding links cannot transmit simultaneously. In the wireless network, CG can be constructed among links sharing the same resources, e.g., RBs in the LTE-A. The pairwise interference is represented by an edge to indicate the conflict of the two relevant links. Those links that are not conflicted with each other constitute an Independent Set, and can be scheduled by the network at one time. The Interference degree (ID) of link, say L, is used to estimate the number of links that interfere and are interfered by L. In CG, ID is the number of edges that are associated with the vertex representing link L. However, CG can only describe the pairwise interference among links, ignoring the accumulated interference of a subset of links to any other link. Thus, the links in an independent set, may not be scheduled at the same time if the accumulated interference is considered. To be explicit, we denote the maximum independent set with and without considering accumulated interference as Final Independent Set (FIS) and Candidate Independent Set (CIS), respectively. Obviously, FIS is a subset of the relevant CIS. Definition 1. The CG of D2D pairs coexisting with CU Em is denoted by Gm = (Vm , Em ), m ∈ {1, 2, ..., M }, where Vm represents the set of D2D pairs that each of them has no conflict with CU Em , and Em represents the pairwise interference among links inVm , e.g., el,n ∈ Em , l, n ∈ Vm , indicates that D2Dl and D2Dn interfere with each other. The ID of D2Dn , n ∈ Vm is denoted by IDnm , which indicates the interference relationship between D2Dn and other D2D pairs that belong to the same CG. Definition 2. The CISs of D2D pairs coexisting with CU Em are denoted by CISM = {CISm,1 , CISm,2 , ..., CISm,K }, K > 1, ∀CISm,i , CISm,j ∈CISM , CISm,i CISm,j . Definition 3. The FISs of D2D pairs coexisting with CU Em are denoted by FISM = {F ISm,1 , F ISm,2 , ..., F ISm,K }, K > 1, F ISm,i ⊆ CISm,i ,i ∈ {1, 2, ..., K}. Definition 4. Based on the conflict graph model, the objective in (3) is equivalent to choosing a FIS from each FISM , such that the union of these chosen FISs are maximized i.e.,

(3)

m=1

p0 gn,BS ≤ Im,max , ∀m ∈ {1, 2, ..., M }

(4)

n∈Dm

Dm

p0 gn,n ≥ γnd , 2 p g + p g + σ 0 l,n m m,n l∈Dm ,l=n

∀m ∈ {1, 2, ..., M }, ∀n ∈ Dm Dk = ∅, m = k, ∀m, k ∈ {1, 2, ..., M }.

(5) (6)

Here, our objective (3) is to maximize the number of reliable D2D pairs that can be admitted in the system. | · | and ∪ denote the cardinality of the corresponding set and union operation, respectively. Constraints in (4) guarantees that the total interference imposed by the admitted D2D pairs included in Dm should satisfy the interference constraint on m-th RB. Constraints in (5) ensure that the SINR requirement of each admitted D2D pair be satisfied, and the term pm gm,n in the denominator accounts for the interference caused by CU Em to D2Dn . Since we assume that more D2D pairs can reuse the same RB, the interference among D2D pairs should also be considered, see the first term in the denominator of (5). And constraints in (6) ensure that each D2D pair can at most reuse one CUE’s RB resource. Theorem 1. The D2D pair selection problem in (3)-(6) is NP-hard. Proof: Consider the special case of (3)-(6) in the following, where we let M = 1, i.e., only one RB resource can be reused. With knowledge from graph theory, we will show that the problem above includes the maximum independent set problem, which is known to be NP-hard. Let G = (V, E) be a conflict graph, where V denotes the set of vertices, representing the D2D pairs that have no conflict with the corresponding CUE occupying the RB resource and and E denotes the set of edges, representing the pairwise interference among different D2D pairs. Edge el,n ∈ E indicates that D2Dl and D2Dn can not coexist with each other. Actually, the D2D pairs selected from V is a special case of the above D2D pair selection problem, i.e., when there is no accumulated interference. Since the problem is NP-hard, we propose an alternative Greedy heuristic Resource Allocation algorithm (GRA). We assume that the eNodeB can get all the related channel gain,

∗ ∈F IS | D = arg maxF ISm M

M

∗ F ISm |,

(7)

m=1 ∗ where F ISm represents the chosen FIS from FISM , m ∈ {1, 2, ..., M }.

C. Greedy heuristic Resource Allocation Algorithm In this section, we give the procedure of GRA algorithm to find a suboptimal solution to problem (7). Let Gm = (Vm , Em ) denote the conflict graph of D2D pairs with CU Em , and the total admitted D2D pairs will be placed in set D. The

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Table I SIMULATION PARAMETERS AND ASSUMPTIONS

performance of the greedy algorithm is determined by the way ∗ is generated. Since our how the final independent set F ISm objective is to maximize the total admitted D2D pairs in the system, we consider the Smallest Degree First (SDF) scheme [10], which favors the D2D pairs with smaller interference degree.

Parameters Carrier frequency System Bandwidth CUE TX power D2D TX power Radius of eNodeB coverage Path loss model for Cellular link Path loss model for D2D pair Antenna gain Shadow fading standard deviation

Algorithm 1 GRA-Smallest Degree First based Allocation Data: Conflict Graph Gm = (Vm , Em ), m ∈ {1, 2, ..., M } Result: A feasible set of admitted D2D pairs D 1 for m =1 to M do 2 Update CG Gm ; 3 Choose a D2D pair D2Dn ∈ Vm that has the minimum interference degree IDnm in Gm , and move it from Vm to set D; 4 Update the maximum tolerable interference Im,max ; 5 Remove all the D2D pairs that have conflict with D2Dn 6 while Im,max > 0 do 7 Choose another D2D pair D2Dl ∈ Vm that has the minimum interference degree IDlm in Gm , and for each D2Dn ∈ D ∪ {D2Dl }, compute the current SINR and compare with their own SINR requirement; 8 If all the SINR requirements are satisfied, then 9 add D2Dl to set D and update Im,max , remove all the D2D pairs that have conflict with D2Dl ; 10 else 11 remove D2Dl from Vm ; 12 end 13 end 14 end 15 return the set of admitted D2D pairs D;

small-scale fading Noise spectral density SINR requirement for D2D pair Number of CUEs

has the minimum interference degree. Compute the SINR of each D2D pair that belongs to D ∪ {D2Dl }. If all the SINR requirements are met, place D2Dl in set D and remove all the D2D pairs that have conflict with D2Dl . Update the maximum tolerable interference of RB Im,max by subtracting the interference imposed by D2Dn . Otherwise, remove D2Dl from Vm . The total ∗ . admitted D2D pairs in the current RB constitute F ISm The two procedures are sequentially implemented in each RB, until all the M RBs have been checked. Then we get all the D2D pairs that can be admitted in the system. IV. S IMULATION R ESULTS In this section, we present simulation results on the performance of the proposed resource allocation algorithm. We compare the performance of the greedy resource allocation algorithm (GRA), the random resource allocation algorithm (RRA) and the optimal solution of scheme where one CUE can be reused by at most one D2D pair. RRA has the similar procedures with GRA, except for the selection criterion of D2D pair in the formation of final independent set. Rather than choose D2D pair based on the smallest degree first (SDF) rule, RRA selects each D2D pair randomly without considering the interference degree (ID) of the pair. In the scheme where one CUE can be reused by at most one D2D pair [6], [7], [8], the resource allocation problem is equivalent to finding the maximum matching between CUEs and D2D pairs. The optimal solution can be found by using the Hungarian Algorithm, a classical algorithm to resolve the maximum matching problem [10] in a bipartite graph. For simplicity, we denote the Optimal solution to Maximum Matching by OMM. In our simulation, we assume that all the CUEs have the same SINR requirements and transmit at the same maximum power pmax = 23dBm. All the CUEs and the D2D transmitters are randomly distributed in the same single cell with an eNodeB at the center. Each D2D transmitter is assumed to have an assigned receiver at a fixed distance Rd away. The simulation parameters are given in Table I. Along with the number of admitted D2D pairs, we also give the normalized

We consider a sequential resource allocation mode, where the eNodeB determines the admitted D2D pairs according to the index of RB. That means the set of D2D pairs that can reuse the 1-th RB, i.e., F IS1∗ is first determined. If a D2D pair has been admitted in the previous FIS, then it will be removed from the remaining conflict graphs containing it, and CG is updating based on the admitted D2D pairs in the current CG. It is worth noting that the update of CG is very helpful to increase the number of admitted D2D pairs. It gives more chance to other unadmitted links. The process of GRA is summarized in Algorithm 1. There are two major procedures: •

•

Values/assumptions 2 GHz 2 MHz (10 RBs per frame) 23 dBm 20 dBm 500 m 37.6log10(d[km])+128.1 40log10(d[km])+148 14dBi for eNodeB and 0dBi for user 10dB for Cellular link and 12dB for D2D pair i.i.d. complex Gaussian with zero mean and unit variance -174 dBm/Hz 10dB 10 (each CUE occupies one RB)

Update the CG in the current RB, say, m-th RB, according to the previous scheduling results. Choose the first D2D pair D2Dn ∈ Vm that has the minimum interference degree. Place D2Dn in set D and remove all the D2D pairs D2Dl ∈ Vm that have conflict with D2Dn . Update the maximum tolerable interference of RB Im,max by subtracting the interference imposed by D2Dn . While Im,max is larger than zero, do the following: choose another unadmitted D2D pair D2Dl ∈ Vm that

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55 System Throughput(Bits/Sec/Hz)

Mean number of admitted D2D pairs


30

25

20 GRA RRA OMM

15

10

50 45 40 35 GRA RRA OMM

30 25

5 20

40

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80 100 120 140 Total Number of D2D pairs

160

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20 20

Figure 2. Mean number of admitted D2D pairs vs. Total number of D2D pairs with length of D2D pair Rd = 20m, and SINR requirement of CU Em c = 10dB, for m ∈ {1, 2, ..., M }. γm

40

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80 100 120 140 Total Number of D2D pairs

160

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Figure 3. System throughput vs. Total Number of D2D pairs with length of c = 10dB, for D2D pair Rd = 20m, and SINR requirement of CU Em γm m ∈ {1, 2, ..., M }.

system throughput in the corresponding case, which is simply derived by Shannon theorem under the condition that the SINR requirement of the corresponding user equipment is satisfied. In the following, each figure reports simulation results averaged over 1000 scenarios to reflect the average system performance. Fig. 2 and Fig. 3 give the mean number of admitted D2D pairs and system throughput versus the total number of D2D pairs, respectively. From the curve, we can see that the number of admitted D2D pairs and system throughput achieved by OMM saturate much earlier and at a much lower value as compared to the proposed greedy algorithms GRA and RRA, and that the achieved throughput gain is as much as 245% and 190%, respectively. This is because in OMM the RB resource of each CUE can be reused by at most one D2D pair, while GRA and RRA can significantly improve the system performance by squeezing as many as D2D pairs to each RB resource, thus making full use of the cellular resources and tightening the reuse factor. Obviously, the number of admitted D2D pairs is bounded by the number of CUEs. Given the number of CUEs Nc = 10 in our simulation, the upper bound of admitted D2D pairs achieved by OMM is 10. Due to the use of smallest degree first (SDF) criterion, GRA can get better performance than RRA, in which D2D links are chosen randomly without considering their interference degree on other links.

its interference degree. Compared with the schemes where at most one D2D pair can reuse one CUE, the proposed algorithm can significantly increasing the number of admitted D2D pairs while guarantying the QoS of CUE and the admitted D2D pairs. The simulation results suggest that the proposed GRA algorithm is very promising in improving the number of admitted D2D pairs and the overall spectrum efficiency. R EFERENCES [1] K. Doppler, M. Rinne, C. Wijting, C. Ribeiro, and K. Hugl, “Device-todevice communication as an underlay to lte-advanced networks,” IEEE Commun. Mag., vol. 47, no. 12, pp. 42–49, Dec. 2009. [2] G. Fodor and N. Reider, “A distributed power control scheme for cellular network assisted d2d communications,” in Proc. IEEE GLOBECOM, Houston, USA, Dec. 5-9, 2011, pp. 1–6. [3] C.-H. Yu, O. Tirkkonen, K. Doppler, and C. Ribeiro, “Power optimization of device-to-device communication underlaying cellular communication,” in Proc. IEEE, ICC, Dresden, Germany, June 14-18, 2009, pp. 1–5. [4] H. Min, W. Seo, J. Lee, S. Park, and D. Hong, “Reliability improvement using receive mode selection in the device-to-device uplink period underlaying cellular networks,” IEEE Trans. Wireless Commun.,, vol. 10, no. 2, pp. 413–418, 2011. [5] C.-H. Yu and O. Tirkkonen, “Device-to-device underlay cellular network based on rate splitting,” in Proc. IEEE WCNC, Paris, France, Apr. 1-4, 2012, pp. 262–266. [6] P. Janis, V. Koivunen, C. Ribeiro, J. Korhonen, K. Doppler, and K. Hugl, “Interference-aware resource allocation for device-to-device radio underlaying cellular networks,” in Proc. IEEE VTC Spring, Barcelona, Spain, Apr. 26-29, 2009, pp. 1–5. [7] M. Zulhasnine, C. Huang, and A. Srinivasan, “Efficient resource allocation for device-to-device communication underlaying lte network,” in Proc. IEEE WiMob, Niagara Falls, Canada, Oct. 11-13, 2010, pp. 368– 375. [8] J. Lee, J. Gu, S. J. Bae, and M. Y. Chung, “A resource allocation scheme for improving user fairness in device-to-device communication based on cellular networks,” in Proc. ACM ICUIMC, New York, USA, Jan. 17-19, 2013, pp. 1–6. [9] K. Jain, J. Padhye, V. N. Padmanabhan, and L. Qiu, “Impact of interference on multi-hop wireless network performance,” in Proc. ACM MobiCom, New York, USA, Sept. 14-19, 2003, pp. 66–80. [10] A. Gibbons., Algorithm Graph Theory. Cambridge University Press, 1985.

V. C ONCLUSIONS In this paper, we investigate resource allocation in the D2D communications underlaying LTE-Advanced networks, under the constraint that the SINR requirement of the reused CUE is satisfied. In order to maximize the number of admitted D2D pairs, we consider the resource sharing where more than one D2D pair can share the same resource with one CUE. The mutual interference between CUE and D2D pair, and among D2D pairs that reusing the same resource is considered. We formulated the problem first and proved its NP-hardness. Then, we gave the proposed greedy heuristic algorithm GRA, where the D2D pairs are chosen to reuse a certain CUE based on

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