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Overlapping coalition formation games based interference coordination for D2D underlaying LTE-A networks
Int. J. Electron. Commun. (AEÜ) 70 (2016) 204–209
Contents lists available at ScienceDirect
International Journal of Electronics and Communications (AEÜ) journal homepage: www.elsevier.com/locate/aeue
SHORT COMMUNICATION
Overlapping coalition formation games based interference coordination for D2D underlaying LTE-A networks Shaoyi Xu a,∗ , Chunmei Xia a , Kyung Sup Kwak b a b
School of Electronics and Information Engineering, Beijing Jiaotong University, Beijing 100044, China UWB-ITRC, Inha University, Republic of Korea
a r t i c l e
i n f o
Article history: Received 29 April 2015 Accepted 19 October 2015 Keywords: Device-to-device (D2D) LTE-Advanced (LTE-A) Overlapping coalition formation game (OCFG) Interference coordination Resource sharing
a b s t r a c t In the device-to-device (D2D) underlaying LTE-Advanced (LTE-A) systems, unlike the existing works which formulate the resources sharing problem as a disjoint coalition formation game, in this letter we propose a novel overlapping coalition formation game (OCFG) based scheme to coordinate the interference between these two subsystems. By sharing uplink spectrums, in this game each D2D pair is allowed to join multiple coalitions simultaneously to improve the spectral efficiency and maximize the system utility. The merge-and-split rule is designed to adapt to the dynamic environment and a discrete-time Markov chain based analysis is utilized to present the stability. Compared with traditional methods, simulations demonstrate the significant performance enhancement of the proposed algorithm in terms of the complexity and D2D system sum throughput. © 2015 Elsevier GmbH. All rights reserved.
1. Introduction To adapt to the explosive upsurge of mobile services and user demands, 3GPP provided some technologies to improve the spectral efficiency and increase system capacity for coming LTEAdvanced (LTE-A) systems. Among them, device-to-device (D2D) which utilizes physical proximity to enable high date rates, low power consumption and delay is one of the key components and receives much attention recently. However, sharing uplink (UL) or downlink resources with cellular networks, D2D users impose interference to the cellular devices and suffer interference from them as well. Most existing work focused on the scenarios of a single D2D pair sharing spectrums with only one cellular user equipment (CUE) and proposed centralized methods by allowing the evolved NodeB (eNB) to coordinate such interference such as power control [1], spectrums allocation [2], transmission modes selection [3], spatial multiplexing [4] or interference alignment [5]. Although distributed methods are investigated in [3,6,7], the interference problem is formulated as a noncooperative game in [7] by considering co-channel interference between a CUE and a D2D pair. In [3,6], resources are assigned by using a cooperative coalition formation game, however, authors assume that the finally formatted coalitions are disjoint which means that one D2D pair only participates in one coalition at most.
From the practical perspective, it is a more general scenario to consider multiple D2D pairs and CUEs by allowing D2D pairs to autonomously decide which coalitions they can join in order to maximize the system utility. As a result, the final coalitions are not disjoint and a D2D pair may belong to several coalitions simultaneously to further improve the spectral efficiency and enable higher flexibility by cooperation. Fig. 1 illustrates the basic concept of overlapping and non-overlapping coalitions. In this context, different from prior works, we address the interference coordination by introducing a cooperative overlapping coalition formation game (OCFG) when UL spectrums are reused. In this game, a single D2D pair is allowed to join multiple coalitions and to cooperate with other D2D user equipments (DUEs) within the same coalition to maximize the system utilities in terms of the D2D system sum throughput meantime guaranteeing cellular users’ quality of service (QoS). The proposed distributed OCFG makes the eNB’s involvement unnecessary and it has lower computation complexity compared with the exhaustive search method. Specifically, the proposed scheme only requires partial channel state information (CSI) which further decreases the system realization complexity. We analyze the properties of the developed algorithm and show the stability of the finally formatted overlapping coalition structure. Simulations demonstrate the effectiveness of our proposed scheme compared with the existing methods. 2. System model and problem formulation
∗ Corresponding author. Tel.: +86 10 51684628. E-mail address: [email protected] (S. Xu). http://dx.doi.org/10.1016/j.aeue.2015.10.007 1434-8411/© 2015 Elsevier GmbH. All rights reserved.
Consider a single-cell scenario where there exist M CUEs and N D2D pairs to reuse L UL subchannels with L ≥ M. The sets of
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205
Fig. 1. An illustrative example of overlapping and non-overlapping coalitions in a D2D underlying LTE-A network.
the CUEs, DUEs and subchannels are M = {C1 , C2 , . . ., CM }, N = {D1 , D2 , . . ., DN } and L = {B1 , B2 , . . ., BL } respectively. We assume that frequencies are allocated orthogonally among these M CUEs by the eNB according to existing methods and each CUE uses one subchannel whose bandwidth is B. In this paper, the nth D2D pair (Dn ) may reuse the spectrums with multiple CUEs and D2D pairs and its received signal to interference and noise ratio (SINR) on the lth subchannel (Bl ) can be represented as D n,l =
xn,l Pn,l hn,l Pm,l hm,n,l +
=
M
C log2 (1 + m,l ) and
m=1
RD =
L
RlD = B
l=1
L N
n=1
l=1
D log2 (1 + n,l )
(3)
In this letter, we aim to maximize the system utility in terms of D2D system sum throughput taking into account the QoS of DUEs and CUEs by developing a distributed OCFG. Consequently, we can formulate the frequency resource optimization problem as
(2)
max RD
Similarly, for a CUE m (Cm ) ∈ M, its SINR can be given as Pm,l hm,l
RC = B
(1)
xi,l Pi,l hi,n,l + n2
i ∈ N,i = / n
C m,l
D2D system sum throughput can be obtained respectively as
xi,l Pi,l hi,m,l + n2
i∈N
Here, Pn,l and Pm,l are respectively the transmission power of Dn and Cm on Bl . hn,l , hm,l and hm,n,l mean the channel gains of Dn , that from Cm to the eNB and from Cm to Dn on Bl . hi,n,l and hi,m,l represent the channel gains from Di to Dn , and that from Di to Cm on Bl . xn,l is the subchannel selection indicator, if the lth subchannel is used by Dn then xn,l = 1, otherwise xn,l = 0. We should note that there maybe exist the case that a subchannel is uniquely utilized by a D2D pair when it can not join any existing coalitions and resources are abundant. In this case, the SINR for Dn is obtained as D = (x P h )/ 2 . n,l n,l n,l n,l n For such a hybrid system, when UL spectrums are reused, the interference from the D2D pair to the eNB, from a CUE to the adjacent DUE and among different D2D pairs is needed to consider. We assume that Pm,l is decided by the eNB according to the existing power allocation methods in a LTE-A network and Pn,l is assigned by Pn,l = Proom /Nl where Proom means the left power room after allocated to a CUE on Bl , Nl is the estimated number of D2D pairs that Bl may accommodate. To coordinate such interference by cooperation among UEs, it is feasible to design a coalition game in which UEs sharing spectrums are grouped into one coalition and different coalitions use different frequency resources. Based on the fact that resources are all allocated orthogonally among CUEs, there exist at least M coalitions. Without loss of generality, we assume that each coalition contains only one subchannel and totally L coalitions are formatted at last with L ≥ M, consequently, the cellular system and
=
L l=1
RlD
=B
N L l=1
D log2 (1 + n,l )
n=1
(4)
C , C2 : RD ≥ RD , C3 : P ≤ P D , C4 : P ≤ P C . s.t. C1 : RC ≥ Rth n m max max th
To guarantee the QoS of the system, we have four constraints, where C1 and C2 assure that the rates of each CUE and DUE exceed the required threshold. C3 and C4 force the maximum transmission power of each user to be below the predefined limit. The above problem is obviously a nonlinear 0–1 programming problem and it is NP-hard. In the following, we introduce the overlapping coalition formation gaming to solve this optimization problem from the view point of game theory. 3. Interference coordination as an OCFG As illustrated in Fig. 1, in a classical coalition formation game in [3,6], each D2D pair is limited into one coalition which includes at most one CUE and different coalitions are allocated different resources. To further improve spectral efficiency and enhance system flexibility, an OCFG is proposed in which a D2D pair is allowed to participate in multiple coalitions simultaneously. To better explain our scheme, several definitions are stated as follows. Definition 1. An OCFG G = (N, v, S) with a transferable utility (TU) is defined by a set of players N, a characteristic function v that assigns a real value to each coalition and a coalition structure (CS) S which is defined as a set of coalitions, namely, S = (S1 , S2 , . . ., Sl , . . ., SL ), where Sl is the lth coalition and each coalition consists of one subchannel.
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Here, the TU property implies that the total utility can be divided in any manner among the coalition members. In our model, a DUE’s payoff is the sum throughput among F coalitions it participates in F D , the current S, that is to say v(Dn ) = v(Dnl ) and v(Dnl ) = Rn,l l,S ⊂S l
D is defined as where Rn,l
D Rn,l
=
0,
D and RD = min RD , i = 1, 2, . . ., N RnD < Rth s n,l i,l
D ), Blog2 (1 + rn,l
otherwise
where Ns is the D2D pair number in Sl . Eq. (5) implies that if the sum rate of Dn is under the threshold and its throughput is also the minimum in Sl , then its payoff in Sl is 0. From (5) we can conclude that this utility is a TU since the rate of a DUE in Sl can be apportioned among D2D users by using feasible modulation and coding strategies or setting up different transmission power. Furthermore, the utility of a coalition Sl is defined as the sum Ns payoff of all DUEs in Sl as v(Sl ) = v(Dnl ). Consequently, the utility n of a CS is expressed as v(S) =
L l
v(Sl ).
Definition 2. An overlapping coalition structure is defined as / j to make Si ∩Sj = / ∅. Compared S = {S1 , S2 , . . ., Sl , . . ., SL } where ∃i = with a traditional non-overlapping coalition formation game with / j, it is expected that the proposed OCFG can obtain Si ∩Sj = ∅ for ∀ i = better performance.
Definition 3. Given two CSs S and S , Dn switches from S to S through the transfer rule, we say that S prefers to S which is denoted by S S. And the transfer rule is defined as
⎧ D v n (S ) > vDn (S) ⎪ ⎪ ⎪ ⎪ ⎨ v(Sl∗ ⊂ S |Dn ∈ Sl∗ ) > v(Sl ⊂ S|Dn ∈ Sl ) . S⇔ ⎪ v(S ) ≥ v(S) ⎪ ⎪ ⎪ ⎩
S
increased, (ii) the individual utility of the newly formatted coalition Sl* is increased, (iii) the total utility of the new CS S is not reduced after Dn ’s joining, (iv) four constraints aforementioned in (4) are satisfied. Based on the above definitions, the OCFG is proposed which adopts the merge-and-split rule as the transfer rule and allows
(6)
C1∼C4 are satisfied
The transfer rule implies that four conditions need to be satisfied to perform the switching operation: (i) the individual utility of Dn is
,
(5)
a D2D pair to participate in multiple coalitions dynamically by joining or quitting from coalitions. The initialization procedures are divided into three steps. (1) Environment sensing. This step avoids Dn being interfered from the neighboring CUE. In this step, Dn obtains a sequence with a descending rank according to the sensing result about which CUEs it can reuse resources with according to [8]. For example, if the sequence is (CUE1 , CUE2 , . . ., CUEM ), it means that CUE1 imposes the least interference to Dn and CUEM will incur the most serious interference to Dn . Thus, Dn should select CUE1 to share resources to form a coalition rather than CUEM . (2) Initial overlapping coalitions. Dn joins F best coalitions to enable the initial overlapping coalitions. In this step, multiple D2D pairs are members of one coalition and one D2D pair may participate in sevF D . (3) Avoid the eral coalitions simultaneously to ensure l=1 RlD ≥ Rth interference to the eNB. If the eNB finds that Dn ’s joining decreases the mth CUE’s rate to be under a predefined threshold, the eNB will refuse Dn to be a member of this coalition. For the proposed mergeand-split rule, the key point for a DUE to leave a coalition is to find that its current rate is under the predefined threshold and its rate is minimum in this coalition. Similarly, to ensure the utility of a coalition not to be reduced after Dn ’s participating, the rate between Dn and the sum of all reduced rate will be compared. Only when the former is larger than the latter, Dn is allowed to participate in this coalition. An interesting result is that only one DUE shares resources with a CUE or one coalition consists of one DUE. Our overlapping coalition formation game is summarized in Algorithm 1. Algorithm 1.
OCFG for UL spectrums sharing
Initialization: The network consists of sets of DUEs N, CUEs M and subchannels L, and the initial formatted overlapping coalition structure S according to the above three initialization procedures. Merge-and-split: 1) Players split the current coalition: Dn calculates the sum rates in all F coalitions as RDn =
F
RDn . l=1 l
D If RDn ≥ Rth and no any broadcasted information is received, OCFG ends.
S. Xu et al. / Int. J. Electron. Commun. (AEÜ) 70 (2016) 204–209
207
Algorithm 1. (Continued ) 2) Players merge into another existing coalition:
From Algorithm 1 we see that the eNB is not involved into the OCFG except for the CUE’s rate being under the predefined threshold. And all operations are performed among D2D pairs so that the global CSI is not required to exchange between the eNB and UEs. Next we will investigate the properties of the proposed OCFG in terms of the convergence, stability and complexity. Convergence: Starting from any initial network coalitional structure, the proposed distributed algorithm will always converge to an overlapping coalition formation. Proof: Given the numbers of the D2D pairs and subchannels, the total number of possible overlapping coalitional structures is finite. Furthermore, each switch operation of a D2D user leads to a higher payoff and the history information is used to avoid the repeating choices. Consequently, each reallocation of DUEs’ subchannels will yield a new coalitional structure and given the finite number of these structures, our proposed algorithm is guaranteed to reach a final coalitional structure with overlapping coalitions. Stability: An outcome (N, v, S) is stable if no any player in N has a profitable deviation from it. We say that the proposed OCFG will always converge to the stable network coalition partition. Proof: The analysis of the discrete-time Markov chain demonstrates the stability [9]. We give the transfer probability Sl∗ →Sl from a coalition Sl* to Sl as follows
Sl∗ →Sl =
1,
v(Sl∗ ) ≥ v(Sl )
0,
Otherwise
4. Simulation results and analysis We consider a cell with a radius of 500 m and cellular users are dropped uniformly whereas D2D pairs are distributed in a randomly placed cluster with a radius of 20 m. The used system bandwidth is 1.44 MHz, i.e., 6 subchannels altogether and the path loss (PL) for these two systems are respectively PLLTE = 15.3 + 37.6log10(r) and PLD2D = 14.2 + 30log10(r) where r is the transmitter–receiver separation in meters. The maximal power constraint for the CUE is 23 dBm with respect to that of a DUE is 13 dBm to favor the short distance between one D2D pair. The small-scale fading is modeled by the multipath Rayleigh fading process. We fix the cellular users and D2D users are 4 separately in Figs. 2 and 3 to investigate the D2D system sum throughput by comparing our algorithm (‘Proposed Algorithm’) with other four methods. ‘Traditional Algorithm’ means the traditional nonoverlapping CFG in [2]. ‘Random Algorithm’ is to select the coalition
(7)
Given the transition matrix P whose elements are Sl∗ →Sl , the stationary probability vector can be obtained by solving the following equation: T P = T , where T = [S1 , S2 , . . ., Sl , . . ., SL ] and Sl is the probability that Sl will be formed. Therefore, we can acquire the stationary distribution of the Markov chain as Sl = , proving that the coalition state is ∗ l = / l Sl∗ Sl∗ →Sl stable. Complexity: In general, the complexity is closely related to the number of merge-and-split operations. Compared with the exhaustive optimal algorithm whose complexity is O(LN ), our proposed algorithm has the complexity of O(LN) in the worst case.
Fig. 2. D2D system sum throughput with different CUE numbers for different schemes.
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S. Xu et al. / Int. J. Electron. Commun. (AEÜ) 70 (2016) 204–209 50 Our Algorithm: 5 coalitions Our Algorithm: 8 coalitions Our Algorithm: Worst Case
Average numbers of switching operations
45 40 35 30 25 20 15 10 5 0 1
2
3
4
5
6
7
8
Number of D2D pairs Fig. 3. D2D system sum throughput with different DUE numbers for different schemes.
coalitions are 5 and 8 respectively and this result is presented in Fig. 5. The result shows that the switching numbers is usually lower than 20 and this convergence rate is acceptable.
7
3.5
x 10
3
D2D system sum throught (bps)
Fig. 5. Average numbers of switching operations with different DUE numbers.
DUE=8
5. Conclusions
DUE=6 DUE=4
2.5
In this letter, a novel distributed OCFG based resources allocation scheme is proposed for the D2D underlaying LTE-A network when UL spectrums are shared. By cooperation among multiple D2D users, overlapping coalitions are formed to coordinate the interference and improve the D2D system sum throughput. Simulations prove that the proposed OCFG based scheme outperforms the traditional methods and yields a similar result to the optimal approach but with lower computational and realization complexity.
DUE=2
2
1.5
1
Acknowledgements 0.5 13
14
15
16
17
18
19
20
21
22
23
DUE Transmiss ion Power (dBm) Fig. 4. D2D system sum throughput with different DUE transmission power.
randomly from the coalitions where the distance between the DUE and the CUE is beyond 200 m. ‘Chen Algorithm’ is based on the ‘Traditional Algorithm’ but allows the DUE to switch to the traditional cellular mode when it cannot find an appropriate coalition to join [3]. The benchmark (‘Optimal Algorithm’) is the optimal exhaustive search. Figs. 2 and 3 show that our OCFG based algorithm has significant performance improvement compared with the ‘Traditional Algorithm’, ‘Random Algorithm’ and ‘Chen Algorithm’, it can obtain performance nearly same to the optimal exhaustive search but with lower computational complexity. To investigate the impact of the transmission power on the system performance, we set up different maximal transmission power for DUEs from 13 dBm to 23 dBm and show the results in Fig. 4. From Fig. 4 we may conclude that increasing transmission power will not motivate significant gain in terms of D2D system sum throughput since the interference between D2D pairs is also increased and thus impairs the system performance. We also simulate the coalition switching numbers when the formed
This work was supported by China NSFC Project 61571038, the Important National Science & Technology Specific Projects of China with Grant 2016ZX03001011-004, Beijing Natural Science Foundation (4132041), and the open research fund of National Mobile Communications Research Laboratory and MSIP, Korea, under the ITRC support program (NIPA-2014-H0301-14-1042) supervised by the NIPA. References [1] Wang JH, Zhu D, Zhao C, Li JCF, Lei M. Resource sharing of underlaying device-to-device and uplink cellular communications. IEEE Commun Lett 2013;17(6):1148–51, http://dx.doi.org/10.1109/LCOMM.2013.042313.130239. [2] Zhu D, Wang J, Swindlehurst AL, Zhao C. Downlink resource reuse for device-todevice communications underlaying cellular networks. IEEE Signal Process Lett 2014;21(5):531–4, http://dx.doi.org/10.1109/LSP.2014.2309143. [3] Chen HL, Wu D, Cai YM. Coalition formation game for green resource management in D2D communications. IEEE Commun Lett 2014;18(8):1395–8, http://dx.doi.org/10.1109/LCOMM.2014.2326852. [4] Tang H, Zhu C, Ding Z. Cooperative MIMO precoding for D2D underlay in cellular networks. In: IEEE ICC. June 2013. p. 5517–21, http://dx.doi.org/10.1109/ICC.2013.6655469. [5] Zhao N, Yu FR, Leung VCM. Opportunistic communications in interference alignment networks with wireless power transfer. IEEE Wireless Commun 2015;22(1):88–95. [6] Li Y, Jin DP, Yuan J, Han Z. Coalitional games for resource allocation in the deviceto-device uplink underlaying cellular networks. IEEE Trans Wireless Commun 2014;13(7):3965–77, http://dx.doi.org/10.1109/TWC.2014.2325552.
S. Xu et al. / Int. J. Electron. Commun. (AEÜ) 70 (2016) 204–209 [7] Xu C, Song LY, Han Z, Zhao Q, Wang XL, Cheng X, et al. Efficiency resource allocation for device-to-device underlay communication systems: a reverse iterative combinatorial auction based approach. IEEE J Sel Areas Commun/Suppl 2013;31(9):348–58, http://dx.doi.org/10.1109/JSAC.2013.SUP.0513031. [8] Xu S, Wang HM, Chen T, Peng T, Kwak KS. Device-to-device communication underlaying cellular networks: connection establishment and interference
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avoidance. KSII Trans Internet Information Syst 2012;6(January (1)): 203–28. [9] Zhao Y, Li Y, Cao Y, Jiang T, Ge N. Social-aware resource allocation for device-to-device communications underlaying cellular networks. IEEE Trans Wireless Commun 2015;14(12):6621–34, http://dx.doi.org/10.1109/ TWC.2015.245742714.
Contents lists available at ScienceDirect
International Journal of Electronics and Communications (AEÜ) journal homepage: www.elsevier.com/locate/aeue
SHORT COMMUNICATION
Overlapping coalition formation games based interference coordination for D2D underlaying LTE-A networks Shaoyi Xu a,∗ , Chunmei Xia a , Kyung Sup Kwak b a b
School of Electronics and Information Engineering, Beijing Jiaotong University, Beijing 100044, China UWB-ITRC, Inha University, Republic of Korea
a r t i c l e
i n f o
Article history: Received 29 April 2015 Accepted 19 October 2015 Keywords: Device-to-device (D2D) LTE-Advanced (LTE-A) Overlapping coalition formation game (OCFG) Interference coordination Resource sharing
a b s t r a c t In the device-to-device (D2D) underlaying LTE-Advanced (LTE-A) systems, unlike the existing works which formulate the resources sharing problem as a disjoint coalition formation game, in this letter we propose a novel overlapping coalition formation game (OCFG) based scheme to coordinate the interference between these two subsystems. By sharing uplink spectrums, in this game each D2D pair is allowed to join multiple coalitions simultaneously to improve the spectral efficiency and maximize the system utility. The merge-and-split rule is designed to adapt to the dynamic environment and a discrete-time Markov chain based analysis is utilized to present the stability. Compared with traditional methods, simulations demonstrate the significant performance enhancement of the proposed algorithm in terms of the complexity and D2D system sum throughput. © 2015 Elsevier GmbH. All rights reserved.
1. Introduction To adapt to the explosive upsurge of mobile services and user demands, 3GPP provided some technologies to improve the spectral efficiency and increase system capacity for coming LTEAdvanced (LTE-A) systems. Among them, device-to-device (D2D) which utilizes physical proximity to enable high date rates, low power consumption and delay is one of the key components and receives much attention recently. However, sharing uplink (UL) or downlink resources with cellular networks, D2D users impose interference to the cellular devices and suffer interference from them as well. Most existing work focused on the scenarios of a single D2D pair sharing spectrums with only one cellular user equipment (CUE) and proposed centralized methods by allowing the evolved NodeB (eNB) to coordinate such interference such as power control [1], spectrums allocation [2], transmission modes selection [3], spatial multiplexing [4] or interference alignment [5]. Although distributed methods are investigated in [3,6,7], the interference problem is formulated as a noncooperative game in [7] by considering co-channel interference between a CUE and a D2D pair. In [3,6], resources are assigned by using a cooperative coalition formation game, however, authors assume that the finally formatted coalitions are disjoint which means that one D2D pair only participates in one coalition at most.
From the practical perspective, it is a more general scenario to consider multiple D2D pairs and CUEs by allowing D2D pairs to autonomously decide which coalitions they can join in order to maximize the system utility. As a result, the final coalitions are not disjoint and a D2D pair may belong to several coalitions simultaneously to further improve the spectral efficiency and enable higher flexibility by cooperation. Fig. 1 illustrates the basic concept of overlapping and non-overlapping coalitions. In this context, different from prior works, we address the interference coordination by introducing a cooperative overlapping coalition formation game (OCFG) when UL spectrums are reused. In this game, a single D2D pair is allowed to join multiple coalitions and to cooperate with other D2D user equipments (DUEs) within the same coalition to maximize the system utilities in terms of the D2D system sum throughput meantime guaranteeing cellular users’ quality of service (QoS). The proposed distributed OCFG makes the eNB’s involvement unnecessary and it has lower computation complexity compared with the exhaustive search method. Specifically, the proposed scheme only requires partial channel state information (CSI) which further decreases the system realization complexity. We analyze the properties of the developed algorithm and show the stability of the finally formatted overlapping coalition structure. Simulations demonstrate the effectiveness of our proposed scheme compared with the existing methods. 2. System model and problem formulation
∗ Corresponding author. Tel.: +86 10 51684628. E-mail address: [email protected] (S. Xu). http://dx.doi.org/10.1016/j.aeue.2015.10.007 1434-8411/© 2015 Elsevier GmbH. All rights reserved.
Consider a single-cell scenario where there exist M CUEs and N D2D pairs to reuse L UL subchannels with L ≥ M. The sets of
S. Xu et al. / Int. J. Electron. Commun. (AEÜ) 70 (2016) 204–209
205
Fig. 1. An illustrative example of overlapping and non-overlapping coalitions in a D2D underlying LTE-A network.
the CUEs, DUEs and subchannels are M = {C1 , C2 , . . ., CM }, N = {D1 , D2 , . . ., DN } and L = {B1 , B2 , . . ., BL } respectively. We assume that frequencies are allocated orthogonally among these M CUEs by the eNB according to existing methods and each CUE uses one subchannel whose bandwidth is B. In this paper, the nth D2D pair (Dn ) may reuse the spectrums with multiple CUEs and D2D pairs and its received signal to interference and noise ratio (SINR) on the lth subchannel (Bl ) can be represented as D n,l =
xn,l Pn,l hn,l Pm,l hm,n,l +
=
M
C log2 (1 + m,l ) and
m=1
RD =
L
RlD = B
l=1
L N
n=1
l=1
D log2 (1 + n,l )
(3)
In this letter, we aim to maximize the system utility in terms of D2D system sum throughput taking into account the QoS of DUEs and CUEs by developing a distributed OCFG. Consequently, we can formulate the frequency resource optimization problem as
(2)
max RD
Similarly, for a CUE m (Cm ) ∈ M, its SINR can be given as Pm,l hm,l
RC = B
(1)
xi,l Pi,l hi,n,l + n2
i ∈ N,i = / n
C m,l
D2D system sum throughput can be obtained respectively as
xi,l Pi,l hi,m,l + n2
i∈N
Here, Pn,l and Pm,l are respectively the transmission power of Dn and Cm on Bl . hn,l , hm,l and hm,n,l mean the channel gains of Dn , that from Cm to the eNB and from Cm to Dn on Bl . hi,n,l and hi,m,l represent the channel gains from Di to Dn , and that from Di to Cm on Bl . xn,l is the subchannel selection indicator, if the lth subchannel is used by Dn then xn,l = 1, otherwise xn,l = 0. We should note that there maybe exist the case that a subchannel is uniquely utilized by a D2D pair when it can not join any existing coalitions and resources are abundant. In this case, the SINR for Dn is obtained as D = (x P h )/ 2 . n,l n,l n,l n,l n For such a hybrid system, when UL spectrums are reused, the interference from the D2D pair to the eNB, from a CUE to the adjacent DUE and among different D2D pairs is needed to consider. We assume that Pm,l is decided by the eNB according to the existing power allocation methods in a LTE-A network and Pn,l is assigned by Pn,l = Proom /Nl where Proom means the left power room after allocated to a CUE on Bl , Nl is the estimated number of D2D pairs that Bl may accommodate. To coordinate such interference by cooperation among UEs, it is feasible to design a coalition game in which UEs sharing spectrums are grouped into one coalition and different coalitions use different frequency resources. Based on the fact that resources are all allocated orthogonally among CUEs, there exist at least M coalitions. Without loss of generality, we assume that each coalition contains only one subchannel and totally L coalitions are formatted at last with L ≥ M, consequently, the cellular system and
=
L l=1
RlD
=B
N L l=1
D log2 (1 + n,l )
n=1
(4)
C , C2 : RD ≥ RD , C3 : P ≤ P D , C4 : P ≤ P C . s.t. C1 : RC ≥ Rth n m max max th
To guarantee the QoS of the system, we have four constraints, where C1 and C2 assure that the rates of each CUE and DUE exceed the required threshold. C3 and C4 force the maximum transmission power of each user to be below the predefined limit. The above problem is obviously a nonlinear 0–1 programming problem and it is NP-hard. In the following, we introduce the overlapping coalition formation gaming to solve this optimization problem from the view point of game theory. 3. Interference coordination as an OCFG As illustrated in Fig. 1, in a classical coalition formation game in [3,6], each D2D pair is limited into one coalition which includes at most one CUE and different coalitions are allocated different resources. To further improve spectral efficiency and enhance system flexibility, an OCFG is proposed in which a D2D pair is allowed to participate in multiple coalitions simultaneously. To better explain our scheme, several definitions are stated as follows. Definition 1. An OCFG G = (N, v, S) with a transferable utility (TU) is defined by a set of players N, a characteristic function v that assigns a real value to each coalition and a coalition structure (CS) S which is defined as a set of coalitions, namely, S = (S1 , S2 , . . ., Sl , . . ., SL ), where Sl is the lth coalition and each coalition consists of one subchannel.
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Here, the TU property implies that the total utility can be divided in any manner among the coalition members. In our model, a DUE’s payoff is the sum throughput among F coalitions it participates in F D , the current S, that is to say v(Dn ) = v(Dnl ) and v(Dnl ) = Rn,l l,S ⊂S l
D is defined as where Rn,l
D Rn,l
=
0,
D and RD = min RD , i = 1, 2, . . ., N RnD < Rth s n,l i,l
D ), Blog2 (1 + rn,l
otherwise
where Ns is the D2D pair number in Sl . Eq. (5) implies that if the sum rate of Dn is under the threshold and its throughput is also the minimum in Sl , then its payoff in Sl is 0. From (5) we can conclude that this utility is a TU since the rate of a DUE in Sl can be apportioned among D2D users by using feasible modulation and coding strategies or setting up different transmission power. Furthermore, the utility of a coalition Sl is defined as the sum Ns payoff of all DUEs in Sl as v(Sl ) = v(Dnl ). Consequently, the utility n of a CS is expressed as v(S) =
L l
v(Sl ).
Definition 2. An overlapping coalition structure is defined as / j to make Si ∩Sj = / ∅. Compared S = {S1 , S2 , . . ., Sl , . . ., SL } where ∃i = with a traditional non-overlapping coalition formation game with / j, it is expected that the proposed OCFG can obtain Si ∩Sj = ∅ for ∀ i = better performance.
Definition 3. Given two CSs S and S , Dn switches from S to S through the transfer rule, we say that S prefers to S which is denoted by S S. And the transfer rule is defined as
⎧ D v n (S ) > vDn (S) ⎪ ⎪ ⎪ ⎪ ⎨ v(Sl∗ ⊂ S |Dn ∈ Sl∗ ) > v(Sl ⊂ S|Dn ∈ Sl ) . S⇔ ⎪ v(S ) ≥ v(S) ⎪ ⎪ ⎪ ⎩
S
increased, (ii) the individual utility of the newly formatted coalition Sl* is increased, (iii) the total utility of the new CS S is not reduced after Dn ’s joining, (iv) four constraints aforementioned in (4) are satisfied. Based on the above definitions, the OCFG is proposed which adopts the merge-and-split rule as the transfer rule and allows
(6)
C1∼C4 are satisfied
The transfer rule implies that four conditions need to be satisfied to perform the switching operation: (i) the individual utility of Dn is
,
(5)
a D2D pair to participate in multiple coalitions dynamically by joining or quitting from coalitions. The initialization procedures are divided into three steps. (1) Environment sensing. This step avoids Dn being interfered from the neighboring CUE. In this step, Dn obtains a sequence with a descending rank according to the sensing result about which CUEs it can reuse resources with according to [8]. For example, if the sequence is (CUE1 , CUE2 , . . ., CUEM ), it means that CUE1 imposes the least interference to Dn and CUEM will incur the most serious interference to Dn . Thus, Dn should select CUE1 to share resources to form a coalition rather than CUEM . (2) Initial overlapping coalitions. Dn joins F best coalitions to enable the initial overlapping coalitions. In this step, multiple D2D pairs are members of one coalition and one D2D pair may participate in sevF D . (3) Avoid the eral coalitions simultaneously to ensure l=1 RlD ≥ Rth interference to the eNB. If the eNB finds that Dn ’s joining decreases the mth CUE’s rate to be under a predefined threshold, the eNB will refuse Dn to be a member of this coalition. For the proposed mergeand-split rule, the key point for a DUE to leave a coalition is to find that its current rate is under the predefined threshold and its rate is minimum in this coalition. Similarly, to ensure the utility of a coalition not to be reduced after Dn ’s participating, the rate between Dn and the sum of all reduced rate will be compared. Only when the former is larger than the latter, Dn is allowed to participate in this coalition. An interesting result is that only one DUE shares resources with a CUE or one coalition consists of one DUE. Our overlapping coalition formation game is summarized in Algorithm 1. Algorithm 1.
OCFG for UL spectrums sharing
Initialization: The network consists of sets of DUEs N, CUEs M and subchannels L, and the initial formatted overlapping coalition structure S according to the above three initialization procedures. Merge-and-split: 1) Players split the current coalition: Dn calculates the sum rates in all F coalitions as RDn =
F
RDn . l=1 l
D If RDn ≥ Rth and no any broadcasted information is received, OCFG ends.
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Algorithm 1. (Continued ) 2) Players merge into another existing coalition:
From Algorithm 1 we see that the eNB is not involved into the OCFG except for the CUE’s rate being under the predefined threshold. And all operations are performed among D2D pairs so that the global CSI is not required to exchange between the eNB and UEs. Next we will investigate the properties of the proposed OCFG in terms of the convergence, stability and complexity. Convergence: Starting from any initial network coalitional structure, the proposed distributed algorithm will always converge to an overlapping coalition formation. Proof: Given the numbers of the D2D pairs and subchannels, the total number of possible overlapping coalitional structures is finite. Furthermore, each switch operation of a D2D user leads to a higher payoff and the history information is used to avoid the repeating choices. Consequently, each reallocation of DUEs’ subchannels will yield a new coalitional structure and given the finite number of these structures, our proposed algorithm is guaranteed to reach a final coalitional structure with overlapping coalitions. Stability: An outcome (N, v, S) is stable if no any player in N has a profitable deviation from it. We say that the proposed OCFG will always converge to the stable network coalition partition. Proof: The analysis of the discrete-time Markov chain demonstrates the stability [9]. We give the transfer probability Sl∗ →Sl from a coalition Sl* to Sl as follows
Sl∗ →Sl =
1,
v(Sl∗ ) ≥ v(Sl )
0,
Otherwise
4. Simulation results and analysis We consider a cell with a radius of 500 m and cellular users are dropped uniformly whereas D2D pairs are distributed in a randomly placed cluster with a radius of 20 m. The used system bandwidth is 1.44 MHz, i.e., 6 subchannels altogether and the path loss (PL) for these two systems are respectively PLLTE = 15.3 + 37.6log10(r) and PLD2D = 14.2 + 30log10(r) where r is the transmitter–receiver separation in meters. The maximal power constraint for the CUE is 23 dBm with respect to that of a DUE is 13 dBm to favor the short distance between one D2D pair. The small-scale fading is modeled by the multipath Rayleigh fading process. We fix the cellular users and D2D users are 4 separately in Figs. 2 and 3 to investigate the D2D system sum throughput by comparing our algorithm (‘Proposed Algorithm’) with other four methods. ‘Traditional Algorithm’ means the traditional nonoverlapping CFG in [2]. ‘Random Algorithm’ is to select the coalition
(7)
Given the transition matrix P whose elements are Sl∗ →Sl , the stationary probability vector can be obtained by solving the following equation: T P = T , where T = [S1 , S2 , . . ., Sl , . . ., SL ] and Sl is the probability that Sl will be formed. Therefore, we can acquire the stationary distribution of the Markov chain as Sl = , proving that the coalition state is ∗ l = / l Sl∗ Sl∗ →Sl stable. Complexity: In general, the complexity is closely related to the number of merge-and-split operations. Compared with the exhaustive optimal algorithm whose complexity is O(LN ), our proposed algorithm has the complexity of O(LN) in the worst case.
Fig. 2. D2D system sum throughput with different CUE numbers for different schemes.
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S. Xu et al. / Int. J. Electron. Commun. (AEÜ) 70 (2016) 204–209 50 Our Algorithm: 5 coalitions Our Algorithm: 8 coalitions Our Algorithm: Worst Case
Average numbers of switching operations
45 40 35 30 25 20 15 10 5 0 1
2
3
4
5
6
7
8
Number of D2D pairs Fig. 3. D2D system sum throughput with different DUE numbers for different schemes.
coalitions are 5 and 8 respectively and this result is presented in Fig. 5. The result shows that the switching numbers is usually lower than 20 and this convergence rate is acceptable.
7
3.5
x 10
3
D2D system sum throught (bps)
Fig. 5. Average numbers of switching operations with different DUE numbers.
DUE=8
5. Conclusions
DUE=6 DUE=4
2.5
In this letter, a novel distributed OCFG based resources allocation scheme is proposed for the D2D underlaying LTE-A network when UL spectrums are shared. By cooperation among multiple D2D users, overlapping coalitions are formed to coordinate the interference and improve the D2D system sum throughput. Simulations prove that the proposed OCFG based scheme outperforms the traditional methods and yields a similar result to the optimal approach but with lower computational and realization complexity.
DUE=2
2
1.5
1
Acknowledgements 0.5 13
14
15
16
17
18
19
20
21
22
23
DUE Transmiss ion Power (dBm) Fig. 4. D2D system sum throughput with different DUE transmission power.
randomly from the coalitions where the distance between the DUE and the CUE is beyond 200 m. ‘Chen Algorithm’ is based on the ‘Traditional Algorithm’ but allows the DUE to switch to the traditional cellular mode when it cannot find an appropriate coalition to join [3]. The benchmark (‘Optimal Algorithm’) is the optimal exhaustive search. Figs. 2 and 3 show that our OCFG based algorithm has significant performance improvement compared with the ‘Traditional Algorithm’, ‘Random Algorithm’ and ‘Chen Algorithm’, it can obtain performance nearly same to the optimal exhaustive search but with lower computational complexity. To investigate the impact of the transmission power on the system performance, we set up different maximal transmission power for DUEs from 13 dBm to 23 dBm and show the results in Fig. 4. From Fig. 4 we may conclude that increasing transmission power will not motivate significant gain in terms of D2D system sum throughput since the interference between D2D pairs is also increased and thus impairs the system performance. We also simulate the coalition switching numbers when the formed
This work was supported by China NSFC Project 61571038, the Important National Science & Technology Specific Projects of China with Grant 2016ZX03001011-004, Beijing Natural Science Foundation (4132041), and the open research fund of National Mobile Communications Research Laboratory and MSIP, Korea, under the ITRC support program (NIPA-2014-H0301-14-1042) supervised by the NIPA. References [1] Wang JH, Zhu D, Zhao C, Li JCF, Lei M. Resource sharing of underlaying device-to-device and uplink cellular communications. IEEE Commun Lett 2013;17(6):1148–51, http://dx.doi.org/10.1109/LCOMM.2013.042313.130239. [2] Zhu D, Wang J, Swindlehurst AL, Zhao C. Downlink resource reuse for device-todevice communications underlaying cellular networks. IEEE Signal Process Lett 2014;21(5):531–4, http://dx.doi.org/10.1109/LSP.2014.2309143. [3] Chen HL, Wu D, Cai YM. Coalition formation game for green resource management in D2D communications. IEEE Commun Lett 2014;18(8):1395–8, http://dx.doi.org/10.1109/LCOMM.2014.2326852. [4] Tang H, Zhu C, Ding Z. Cooperative MIMO precoding for D2D underlay in cellular networks. In: IEEE ICC. June 2013. p. 5517–21, http://dx.doi.org/10.1109/ICC.2013.6655469. [5] Zhao N, Yu FR, Leung VCM. Opportunistic communications in interference alignment networks with wireless power transfer. IEEE Wireless Commun 2015;22(1):88–95. [6] Li Y, Jin DP, Yuan J, Han Z. Coalitional games for resource allocation in the deviceto-device uplink underlaying cellular networks. IEEE Trans Wireless Commun 2014;13(7):3965–77, http://dx.doi.org/10.1109/TWC.2014.2325552.
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