Device-to-Device Communications Underlaying Cellular Networks

IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 61, NO. 8, AUGUST 2013

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Device-to-Device Communications Underlaying Cellular Networks Daquan Feng, Lu Lu, Yi Yuan-Wu, Geoffrey Ye Li, Gang Feng, and Shaoqian Li

Abstract—In cellular networks, proximity users may communicate directly without going through the base station, which is called Device-to-device (D2D) communications and it can improve spectral efficiency. However, D2D communications may generate interference to the existing cellular networks if not designed properly. In this paper, we study a resource allocation problem to maximize the overall network throughput while guaranteeing the quality-of-service (QoS) requirements for both D2D users and regular cellular users (CUs). A three-step scheme is proposed. It first performs admission control and then allocates powers for each admissible D2D pair and its potential CU partners. Next, a maximum weight bipartite matching based scheme is developed to select a suitable CU partner for each admissible D2D pair to maximize the overall network throughput. Numerical results show that the proposed scheme can significantly improve the performance of the hybrid system in terms of D2D access rate and the overall network throughput. The performance of D2D communications depends on D2D user locations, cell radius, the numbers of active CUs and D2D pairs, and the maximum power constraint for the D2D pairs. Index Terms—Device-to-device communications, spectrum sharing, maximum weighted bipartite matching.

I. I NTRODUCTION

T

O satisfy the increasing demand for local traffic load and provide better user experience, device-to-device (D2D) communications have been proposed for LTE-Advanced [1]– [3]. With D2D communications, proximity users in a cellular network can communicate directly with each other without going through the base station (BS). It increases the overall network spectral efficiency and thus allows the network to admit more users. However, D2D communications may generate interference into the existing cellular network if not designed properly [4]. Thus, interference management is one of the most critical issues for D2D underlaying cellular networks where D2D and cellular communications coexist in the network. To limit

Manuscript received October 17, 2012; revised February 25 and June 6, 2013. The editor coordinating the review of this paper and approving it for publication was P. Popovski. D. Feng, G. Feng, and S. Li are with the National Key Lab on Communications, UESTC, Chengdu, China. D. Feng is the corresponding author (e-mail: [email protected]). Y. Yuan-Wu is with Orange Lab Network, Department of Wireless Technology Evolution, Paris, France. L. Lu and G. Y. Li are with the School of ECE, Georgia Institute of Technology, Atlanta, GA, USA. This work was supported in part by the National Science Foundation (NSF) under Grant No.1247545, the European Sharing project, the National Basic Research Program of China (973 Program) under Grant No.2012CB316003, the National High-tech R&D Program of China under Grant No.2012AA011402, the NSFC under Grant No.61071098, the Doctor Foundation of Ministry of Education under Grant No.20110185130003, and China Scholarship Council (CSC). Digital Object Identifier 10.1109/TCOMM.2013.071013.120787

interference to the existing cellular users (CUs), restricting the transmit power of D2D links and the distance between the users of a D2D pair has been suggested in [1]. Furthermore, a fixed booster factor and a backoff factor have been proposed in [2] to dynamically control D2D power levels and limit D2D interference. Based on a predefined interference-to-signal ratio (ISR), an interference limited area (ILA) has been suggested in [5], where the D2D users are allowed to share resources with a CU outside the ILA. The aforementioned works have either aimed at increasing the network throughput [1], [2] or guaranteeing the reliability of D2D communications [3]–[5]. The works in [6]–[9] consider both of the metrics simultaneously. In [6], throughput has been maximized for a network with a single D2D pair and a single CU while the QoS of the CU is considered. For scenarios with multiple D2D users and CUs, the QoS requirements for both CUs and D2D users have been investigated in [7]–[9]. Particularly, in [8] and [7], a fixed power margin scheme has been suggested to coordinate interference between D2D users and regular CUs1 while a heuristic algorithm has been proposed in [9] to solve the formulated mixedinteger-nonlinear-programming (MINLP) resource allocation problem. These algorithms are not necessarily optimal since they miss some feasible regions. For the algorithms in [8] and [7], a suitable power margin is not trivial to find. Fewer CUs will allow D2D access with a higher margin while a lower margin will decrease the probability that the QoS requirements of D2D users can be satisfied. For the heuristic algorithm in [9], the cooperation between the CUs and D2D pairs has not been considered. Moreover, only the interference channel gain has been utilized to pair regular CUs and D2D pairs, which is sometimes far away from the optimal. Inspired by the works in [6]–[9], we present a framework of resource allocation for D2D communications underlaying cellular networks to maximize the overall network throughput of existing CUs and admissible D2D pairs while guaranteeing the QoS requirements for both CUs and D2D pairs. The framework includes three parts. First, a minimum distance metric is proposed for the BS to decide whether a D2D pair can be accessed or not under QoS requirements for both CUs and D2D pairs. Then, an optimal power control scheme is investigated for each D2D pair and its possible CU partners to maximize the overall throughput. At last, a maximum weight bipartite matching based scheme is developed to determine a specific CU partner for each admissible D2D pair. Based on 1 Throughout the context, interference between D2D users and regular CUs means the D2D interference to the regular CUs at BS and the CU interference to D2D pairs at the receiver side of the D2D pairs.

c 2013 IEEE 0090-6778/13$31.00

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Pair 1 D_Tx1

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Fig. 1: System model of D2D communications sharing UL resources of cellular systems.

the proposed scheme, significant improvement of the system performance can be obtained in terms of D2D access rate and the overall network throughput. Our work is also related to resource allocation with QoS requirements in cognitive radio (CR) networks [10]–[13], especially for the underlying scenarios [14]. A linear programming deflation algorithm has been introduced to maximize the number of admitted secondary users with QoS requirements in [10] while gradual removal schemes have been proposed to maximize the transmission rate of the secondary link with the max-min criterion in [11]. In [12], both maximizing the number of admitted secondary users and maximizing the secondary throughput have been investigated through centralized geometric programming algorithm and distributed game theory algorithm. Later, geometric programming algorithm has also been proposed to maximize the overall network throughput when guaranteeing a minimum SINR requirements for the primary users in [13]. The work on CR mainly focuses on the performance of the secondary network while our study considers the performance of the whole system, including both D2D users and the CUs. Moreover, the cooperation between primary users and secondary users, in general, are not allowed in CR while the cellular BS in our framework can coordinate the whole procedure to get optimal performance. Even though the cooperation between primary users and secondary users has been considered in [13], the QoS requirement of the secondary users has not been considered. The rest of the paper is organized as follows. In Section II, we describe the system model and formulate the optimization problem. Then, in Section III, the optimal resource allocation algorithm is investigated. Numerical results are presented in Section IV to demonstrate the performance of the proposed schemes. Finally, conclusions are given in Section V. II. S YSTEM M ODEL AND P ROBLEM F ORMULATION In this section, we first introduce system model and then formulate the resource allocation problem of D2D communications.

A. System Model We will investigate spectrum sharing for D2D communications underlaying cellular networks as in Fig. 1, where M D2D pairs coexist with N CUs. In particular, uplink (UL) resource sharing is considered since UL spectrum is underutilized comparing to that of downlink (DL) in the frequency division duplexing (FDD) based cellular systems [9], [15]. Furthermore, UL resource sharing in D2D communications only affects the BS and incurred interference can be mitigated by BS coordination. We also assume a fully loaded cellular network scenario similar to [7], [8]. That is, N active CUs occupy the N orthogonal channels in the cell and there is no spare spectrum. In the following, we use C = {1, ..., N } and D = {1, ..., M } to denote the index sets of active CUs and D2D pairs, respectively. In addition, we assume both CUs and D2D pairs have their minimum QoS requirements in terms of SINR, and the BS has the perfect CSI information of all the links. Besides the distanced based pathloss model used in [6], [7], we consider both the fast fading due to multi-path propagation and slow fading due to shadowing. Thus, the channel gain between CU i and the BS can be expressed as gi,B = Kβi,B ζi,B ·L−α i,B ,

(1)

where K is a constant determined by system parameters, βi,B is fast fading gain with exponential distribution, ζi,B is the slow fading gain with log-normal distribution, α is the pathloss exponent, and Li,B is the distance between CU i and the BS. Similarly, we can express the channel gain of D2D pair j, gj , and the channel gains of the interference links, from the transmitter of D2D pair j to the BS, hj,B , and that from CU i to the receiver of D2D pair j, hi,j . The power of additive 2 . white Gaussian noise on each channel is assumed to be σN B. Problem Formulation D2D communications can be used to improve the performance of fully loaded cellular networks. A D2D pair is set up only when the minimum SINR requirement can be guaranteed and incurred interference to the CUs is below a threshold. In this case, we call it an admissible pair and the CU to be shared resource as reuse partner. Let Pic and Pjd denote the transmit power of CU i and that of D2D pair j, respectively, and ξic and ξjd denote the SINR of CU i and that of D2D pair j, respectively. The overall throughput optimization problem can be formulated as follows ⎧ ⎫ ⎨ ⎬ log(1 + ξic ) + ρi,j log(1 + ξjd ) , max ⎭ ρi,j ,Pic ,Pjd ⎩ i∈C j∈S

(2) c g P i,B c i ≥ ξi,min , ∀i ∈ C, (2a) subject to ξic = 2 σN + ρi,j Pjd hj,B Pjd gj d ≥ ξj,min , ∀j ∈ S, (2b) ξjd = 2 σN + ρi,j Pic hi,j ρi,j ≤ 1, ρi,j ∈ {0, 1}, ∀i ∈ C, (2c) j

i

ρi,j ≤ 1, ρi,j ∈ {0, 1}, ∀j ∈ S,

(2d)

FENG et al.: DEVICE-TO-DEVICE COMMUNICATIONS UNDERLAYING CELLULAR NETWORKS

c Pic ≤ Pmax , ∀i ∈ C,

(2e)

d , ∀j ∈ S, Pjd ≤ Pmax

(2f)

where S (S ⊆ D) denotes the set of admissible D2D pairs, ρi,j is the resource reuse indicator for CU i and D2D pair j, ρi,j = 1 when D2D pair j reuses the resource of cellular user c d and ξj,min denote the minimum i; otherwise, ρi,j = 0. ξi,min SINR requirements of CU i and D2D pair j, respectively, and c d Pmax and Pmax denotes the maximum transit power of CU or D2D pair, respectively. Constraints (2a) and (2b) represent the QoS requirements of CUs and D2D pairs, respectively. Constraint (2c) ensures that the resource of an existing CU can be shared at most by one D2D pair. While constraint (2d) indicates that a D2D pair shares at most one existing CU’s resource. Both constraints are used for reducing the complicated interference environment brought by the D2D communications. Constraints (2e) and (2f) guarantee that the transmit powers of cellular users and D2D pairs are within the maximum limit. It can be easily seen that the throughput optimization problem in (2) is a nonlinear constraint optimization problem. It is difficult to obtain the solution directly. In the following section, we will divide the problem into three subproblems and solve them one by one.

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III. O PTIMAL R ESOURCE A LLOCATION In this section, we will solve the overall throughput optimization problem by dividing the original one into three subproblems. The first one is QoS-aware admission control for D2D pairs, where we determine whether a D2D pair with a targeted SINR can be admissible or not. The second one is the power control for a single D2D pair and its reuse partner, where we allocate transmit power to maximize the overall throughput for the D2D pair and its reuse partner. The third one is the resource allocation for multiple D2D pairs, where we find the optimal reuse partner for each D2D pair.

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Fig. 2: Admissible area of D2D communication. A. QoS-Aware Admission Control of D2D Users To solve the optimization problem in (2), we first determine whether a D2D pair can be admitted or not. Furthermore, if it can, we need to decide which CUs’ spectrum it can use. In this subsection, we will focus on these issues. If D2D pair j can share the spectrum with CU i, those constraints in (2a), (2b), (2e), and (2f) must be satisfied, that is, ⎧ P c gi,B ⎪ c ⎪ ξic = 2 i d ≥ ξi,min , (3a) ⎪ ⎪ ⎪ σN + Pj hj,B ⎪ ⎨ Pjd gj d d ⎪ = ≥ ξj,min , ξ (3b) ⎪ 2 + P ch ⎪ j σ i,j ⎪ i N ⎪ ⎪ ⎩ Pc ≤ Pc , Pd ≤ Pd . (3c) i max j max It means that a D2D pair can share resource with an existing user only when both their SINR requirements are satisfied. Let Rj denote the set of reuse candidates for D2D pair j. D2D pair j is admittable (j ∈ S) if and only if Rj = Ø. In the following, we will demonstrate how to find the reuse candidates.

Without D2D user sharing resource with CU i (Pjd = 0), the SINR of CU i can be guaranteed by transmitting a signal at the power, c ξi,min σN 2 c Pi,min = . (4) gi,B Similarly, without CU i, the minimum SINR of D2D user j can be reached by transmitting a signal at the power, d Pj,min =

d ξj,min σN 2 . gj

(5)

The admission constraints in (3) can be shown as in Fig. 2, where lines lc and ld represent constraints (3a) and (3b) with equality, respectively. The area on the right of line ld is where the minimum SINR for D2D pair j is satisfied. The area above line lc is where the minimum SINR of CU i is satisfied. The square area denotes the maximum power constraints in (3c) for CU i and D2D pair j. Denote point A to be the intersection of lc and ld . To ensure

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lc and ld to have an intersection point in the first quarter so that all constraints in (3) are statisfied, the slope of ld must be larger than that of lc , that is c ξi,min hj,B

gi,B

ξi,min , d hj,B max

g

j where β = hj,B represents the D2D channel gain advantage over traditional user-BS link.

Accordingly, BS can easily find suitable CU candidates for a D2D pair based on the distances between the CUs and the D2D receiver. It can be also seen that a D2D pair with a d , and bigger D2D channel smaller SINR requirement, ξj,min gain, gj , will be easier to find a reuse candidate. Similarly, a CU with a better channel gain, gi,B , and a lower SINR c , is more likely to be a reuse candidate. requirement, ξi,min

Pjd

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Let Li,jRx denote the distance between CU i and the reviver of D2D pair j. We have the following proposition to select reuse candidates for D2D pair j. Its proof is given in Appendix A.

N

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which are the minimum transmission powers for CU i and D2D pair j to satisfy the minimum SNIR requirements if the maximum transmission power constraints are not considered. If point A is within the square area as in Fig. 2a, then it is possible to find transmit powers for CU i and D2D pair j to satisfy all constraints in (3). In that case, any point in the shaded area will satisfy (3). If point A is beyond the square area as in Fig. 2b, D2D pair j is not admissible to share the spectrum with CU i due to the maximum power limit. In summary, the admissible conditions will be ⎧ c c d 2 ξj,min )σN c ⎨0 < (gj ξi,min +hc j,B ξi,min ≤ Pmax , d gj gi,B −ξi,min ξj,min hi,j hj,B (9) c d d 2 (h ξ ξ +g ξ )σ i,j i,B i,min j,min j,min N d ⎩0 < ≤ P . c d max g g −ξ ξ h h i,min j,min

c Pmax

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c c d 2 (gj ξi,min +hj,B ξi,min ξj,min )σN , c d gj gi,B −ξi,min ξj,min hi,j hj,B c d d 2 (hi,j ξi,min ξj,min +gi,B ξj,min )σN c d gj gi,B −ξi,min ξj,min hi,j hj,B

j i,B

lc

ld

(6)

which is the condition for CU i and D2D pair j to be possible to share resource without transmission power constraints in d c , Pi,A ), can be found by (3c). The coordinates of A, (Pj,A ⎧ P c gi,B c ⎨ 2 i,Ad = ξi,min , σN +Pj,A hj,B (7) d d ⎩ 2 Pj,Ac gj = ξj,min . σ +P hi,j N

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Fig. 3: Optimal power allocation for cellular user D2D user.


B. Optimal Power Control for a Single D2D Pair

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D2D pair

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In the previous subsection, we have addressed admission control for a D2D pair. Here, we investigate how to allocate T T T T T power for the D2D transmitter and the corresponding reuse . . . 1 2 3 Reuse candidate K-2 K-1 K partner to maximize the overall throughput. Mathematically, the problem can be expressed as,

Fig. 4: Bipartite graph for D2D pairs and the reuse candidates ∗ (Pic ∗ , Pjd ) = arg max log2 (1 + ξic ) + log2 (1 + ξjd ) , matching problem. c d G 1, 2

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(11) P c gi,B c ≥ ξi,min , subject to. ξic = 2 i d σN + Pj hi,B Pjd gj d ≥ ξj,min , 2 + P ch σN i,j i c d Pic ≤ Pmax , Pjd ≤ Pmax . ξjd =

(11a) (11b) (11c)

In the previous section, we have addressed admission control for CU i and D2D pair j, from the discussion there, three possible shapes of the admissible area are shown as in Fig. 3. Note that all power pairs within the admissible area satisfy constraints (11a)-(11c). Therefore, the optimization problem in (11) is to find the power pair in the admissible area. From Appendix B, we can find the solution, which can be expressed in the following proposition. Proposition 2. Denoting f (Pic , Pjd ) log2 (1 + ξic ) + ∗ log2 (1 + ξjd ), the optimal power vector, (Pic ∗ , Pjd ), in (11) can be expressed as follows, ⎧ f (Pic , Pjd ) ⎪ ⎪arg (P cmax d ⎪ i ,Pj )∈P1 ⎪ ⎪ c ⎪ Pmax gi,B c ⎪ if σ2 +P ≤ ξi,min , ⎪ d ⎪ max hj,B N ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ arg max f (Pic , Pjd ) ⎪ c ,P d )∈P ⎪ (P 2 ⎪ i j ⎪ c ⎪ Pmax gi,B ⎨if c > ξi,min and ∗ 2 d σN +Pmax hj,B (Pic ∗ , Pjd ) = (12) c Pmax gj ⎪ d ⎪ < ξj,min , 2 +P d ⎪ σ h i,j ⎪ max N ⎪ ⎪ ⎪ ⎪arg max ⎪ f (Pic , Pjd ) ⎪ ⎪ ⎪ (Pic ,Pjd )∈P3 ⎪ ⎪ c ⎪ ⎪if 2 Pmaxdgi,B > ξ c ⎪ i,min and ⎪ σ +P max hj,B N ⎪ ⎪ c ⎩ Pmax gj d ≥ ξj,min , σ2 +P d hi,j N

max

where c c P1 = {(Pmax , P1 ), (Pmax , P2 )}, d d P2 = {(P3 , Pmax ), (P4 , Pmax )}, c c d d P3 = {(Pmax , P1 ), (Pmax , Pmax ), (P4 , Pmax )}, c 2 d (Pmax hi,j + σN )ξj,min , gj c c 2 Pmax gi,B − ξi,min σN , P2 = c ξi,min hj,B

P1 =

P3 = P4 =

d d 2 Pmax gj − ξj,min σN d ξj,min hi,j

,

d 2 c (Pmax hj,B + σN )ξi,min . gi,B

From the above proposition, the optimal power pair for CU i and D2D pair j resides on one of the corner points of the

admissible area as points C, D, O, E, and F in Fig. 3. Besides, at least one user is transmitting at the peak power to maximize the overall throughput. C. Resource Allocation for Multiple D2D Pairs In the above, we have discussed how to find reuse candidates for a D2D pair with a targeted QoS requirement and the optimal power allocation schemes for it and the reuse partners. Now, we can find the optimal reuse partner for a D2D pair when more than one partner users are available. For CU i (i ∈ Rj ), when there is no D2D, the maximum throughput on the used spectrum is Ti,max = log2 (1 +

c gi,B Pmax ). 2 σN

(13)

When it shares resource with D2D pair j, the maximum sum , can be expressed as achievable sum throughput, Ti,j ∗

Pjd gj P c ∗ gi,B = log2 (1 + d ∗ i )+ log (1 + 2 ∗ c 2 ), 2 Pi hi,j + σN Pj hj,B + σN (14) ∗ where (Pic ∗ , Pjd ) is given by Proposition 2. Thus, the D2D throughput gain can be expressed as sum Ti,j

G sum = Ti,j − Ti,max . Ti,j

(15)

Hence, we can find the optimal reuse partner of D2D pair j, G i∗ = arg max Ti,j . i∈Rj

(16)

By now, we can get the optimal solutions of (2) for a single D2D scenario. However, if there are multiple D2D pairs, the problem becomes much more complicated since different D2D pairs may have the same optimal reuse partner. In [8], [9], they both use an intuition based methods to match the D2D pairs and their user partners. The methods are simple but not necessary optimal. If there are multiple D2D pairs in the system, the optimal resource allocation problem turns to be a maximum weight bipartite matching problem. It can be formulated as G ρi,j Ti,j , (17) max i∈C ,j∈S

s.t.

ρi,j ≤ 1, ρi,j ∈ {0, 1}, ∀i ∈ C ,

(17a)

ρi,j ≤ 1, ρi,j ∈ {0, 1}, ∀j ∈ S,

(17b)

j

i

where C is the union of all the reuse candidate sets of D2D pairs. Fig. 4 explains the maximum weight bipartite matching

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TABLE I: Optimal Resource Allocation Algorithm Algorithm Optimal Resource Allocation Algorithm 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20:

C : The set of existing cellular users D : The set of D2D pairs Rj : The set of reuse candidates of D2D pair j Step 1 for all j ∈ D and i ∈ C do calculate Lmin ←Proposition 1 i,jRx if Li,jRx ≥ Lmin then i,jRx i ∈ Rj (Find reuse candidates) end if end for if Rj = ∅ then D =D−j (Delete not accessible D2D) end if Step 2 for all j ∈ D and i ∈ Rj do ∗ calculate (Pic ∗ , Pjd ) ←Proposition 2 end for Step 3 if |D|=1 then G i∗ = arg maxTi,j (For only one D2D pair) i∈Rj

else get i∗ from (17) 23: end if 21: 22:

TABLE II: Simulation Parameters Parameter Cell radius (R) Uplink bandwidth 2 Noise power (σN ) Pathloss exponent (α) Pathloss constant (K) Maximum CU Tx power c (Pmax ) Maximum D2D Tx power d (Pmax ) Fixed power margin (κ) Cellular user SINR c ) (ξi,min d D2D user SINR (ξj,min )

D2D cluster radius (r) D2D cluster location (Lr) Number of active CUs (N ) Number of D2D pairs (M ) Multiple-path fading

(Kuhn-Munkres algorithm)

problem in (17), where the set of D2D pairs and the union of all the reuse candidate of D2D pairs are assumed as the two groups of vertices in the bipartite graph. Vertex i is joined with vertex j by an edge ij, when the user i is a reuse candidate G is considered as the of D2D pair j. D2D throughput gain Ti,j weight of edge ij. We can use the classic Kuhn-Munkres algorithm [16] to solve (17). Specifically, to reduce the computational complexity, the connectivity of the graph is checked first. If the graph is connected, the Kuhn-Munkres algorithm is applied for the whole graph; otherwise, the algorithm is applied for each connected component2 of the graph separately. Thus, the solution of the optimal resource allocation problem for multiple D2D pairs with targeted QoS requirements can be derived and illustrated by the algorithm in Table I. IV. N UMERICAL R ESULTS We consider a single cell network, where conventional CUs are uniformly distributed in the cell. Since the D2D users are usually within short distances, we adopt the clustered distribution model as in [7], where D2D users are uniformly distributed in a randomly located cluster with radius r. In our simulation, we assume different D2D pairs are within different clusters, and also suppose that all the CUs share the total bandwidth equally. Our simulation parameters are summarized in Table II. 2 Connected components of a graph G are the set of largest subgraphs of G in which any two two vertices are connected and there is no connections with the vertices outside the subgraph.

Shadowing

Value 0.5, 1 km 5 MHz -114 dBm 4 10−2 24 dBm 21, 24 dBm 10 dB Uniform distributed in [0, 25] dB Uniform distributed in [0, 25] dB 20, 30, 40, ..., 100 (m) Uniform distributed in [0, R] 20, 40, 80 10%, 20%, ..., 100% of active CUs Exponential distribution with unit mean Log-normal distribution with standard deviation of 8dB

Two metrics are used to evaluate the performance: D2D access rate defined as the ratio of the number of accessed D2D pairs and the total D2D pairs; and D2D throughput gain defined as the maximum increased throughput brought by the accessed D2D pairs. Moreover, we compare our scheme with the fixed margin scheme in [7], [8] and heuristic scheme in [9]. For the fixed margin scheme in [7], [8], it is assumed that there exists a power margin in the SINR of CUs to compensate for the interference from D2D pairs at CUs’ side and D2D pairs, with the knowledge of the power margin, can adjust their transmit power to satisfy the QoS requirements. In this way, all the D2D reuse candidates can be found and suitable powers for D2D pairs and the reuse partner CUs can be allocated. Similar to our algorithm, the Kuhn-Munkres algorithm is then used to find the optimal D2D pair and CU matching. For the heuristic scheme [9], the BS prioritily selects the CU with highest channel power gain of the CUBS link to share resource with the D2D pair with the lowest interference channel power gain of the CU-D2D receiver link. The uplink resource allocation algorithm in [9] is executed with the maximum power constraints for the partner CU and the D2D pair. Fig. 5 compares the performance of the three algorithms for different D2D cluster radii with and without fading. From the figure, both access rate and throughput gain decrease with the increase of the radius of the D2D cluster. Since the channel gain of D2D link declines when the cluster radius increases, more transmit power is required for D2D pair to guarantee its QoS requirement and causes more interference to the reuse partner. It is also seen that the performance with


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40

Proposed Heuristic Fixed margin 50

60 r (m)

Fig. 5: D2D access rate and throughput gain for different D2D cluster radii with and without fading, where R = 0.5km, α = c d = Pmax = 24dBm, and r = 60m. 4, N = 20, M = 2, Pmax

Fig. 6: D2D access rate and throughput gain for different maximum transmit powers of D2D pairs, where R = 0.5km, c = 24dBm, and r = 60m. α = 4 , N = 20, M = 2, Pmax

fading is better than that of without fading, especially when the D2D cluster radius become large. That is because, fading can bring more diversities in the wireless channel and increase the chance of running into a good channel. Thus, additional access opportunities are harvested. These results are also consistent with the latest research in [17], where it has shown that QoS in interference limited wireless networks sometimes will increase with the fading. Note that the proposed algorithm always provides the best performance among the three approaches for two reasons. First, the proposed algorithm searches all the reuse candidates for each D2D pair while some feasible reuse candidates are missing in the other two schemes. Second, the proposed algorithm always allocates the optimal powers for each D2D pair and its reuse partner. In Fig. 6, the effect of different maximum transmit power is illustrated. It is seen that the performance of the proposed and fixed margin algorithms declines with the decrease of the maximum transmit power of D2D pairs, and the degradation becomes fast when the D2D cluster radius is large. That can be easily understood from the D2D admissible area in Fig.2 since a lower maximum transmit power of D2D pairs will reduce the probability of access. However, it is also shown that the performance of heuristic algorithm increases with the reduced

maximum transmit power of D2D pairs when the D2D cluster radius is relatively small. It is somewhat surprising, but makes sense. When the D2D cluster radius is small, the channel gain of D2D link is high and SINR requirement of D2D pair can be easily satisfied. Therefore, the main obstacle for D2D access is to satisfy the minimum SINR of the regular CU. As we have mentioned in the introduction part, the heuristic algorithm have not considered the cooperation between the CUs and D2D pairs and always transmits at the maximum power. Hence, reducing the maximum transmit power of D2D pairs will reduce the interference to the CUs and thus help to satisfy the QoS requirement. Fig. 7 demonstrates the effect of different cellular cell radii. To have a fair comparison environment, we keep the same user density and the same ration between the number of D2D pairs and active CUs in the cell for both R = 0.5 km and R = 1 km. Since the CUs are uniformly distributed in the cell, we have choose N = 20, M = 2 and N = 80, M = 8 for R = 0.5 km and R = 1 km respectively. From the figure, the performance of the proposed and heuristic algorithms improves with the increase of cell radius. That is because increasing the cell radius will increase the distance between the CUs and D2D pairs and also the distance to the BS. Hence, the interference

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(a)

(a) 100%

100%

90%

90%

80% Access rate

Access rate

80%

70%

60%

50%

40% 20

R=0.5km, Proposed R=0.5km, Heuristic R=0.5km, Fixed margin R=1km, Proposed R=1km, Heuristic R=1km, Fixed margin 30

40

50

70% 60% N=20, Proposed N=20, Heuristic N=20, Fixed margin N=40, Proposed N=40, Heuristic N=40, Fixed margin

50% 40%

60 r (m) (b)

70

80

90

100

30% 0.1

0.2

0.3

0.4

0.5

0.6

0.7

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1

M/N (b)

14

50 45

12 Throughput gain (Mbps)


40 10 8 6 4 2 0 20

R=0.5km, Proposed R=0.5km, Heuristic R=0.5km, Fixed margin R=1km, Proposed R=1km, Heuristic R=1km, Fixed margin 30

40

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35 30 25 20

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15 10 5

60 r (m)

70

80

90

100

0 0.1

0.2

0.3

0.4

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Fig. 7: D2D access rate and throughput gain for different number of active cellular user and D2D pairs, where α = 4, c d = Pmax = 24dBm, and r = 60m. M/N = 0.1, Pmax

Fig. 8: D2D access rate and throughput gain for different number of active cellular user and D2D pairs, where R = 0.5km, c d = Pmax = 24dBm, and r = 60m. α = 4, Pmax

from CUs to the D2D receivers and the interference from D2D pairs to CUs at the BS will be decreased. Note that like the heuristic algorithm is sensitive to the change of the maximum transmit power of D2D pairs, the fixed margin algorithm has shown a similar sensitivity to the cell radius in this figure. That is because the fixed margin algorithm keeps a fixed power margin at the CUs without considering the channel condition and the QoS requirement. Thus, when the cell radius increases, the channel power gain of the CUs to BS will decline. As a result, the number of CU who can provide such a margin will be fewer and thus access rate decreases. Fig. 8 illustrates the effect of the number of active CUs and D2D pairs on the performance. From the figure, there exists a crossover in the proportion of D2D pairs, about 60%, 50%, and 40% for the proposed, the heuristic and the fixed margin algorithm, respectively. Below the crossover point, the average throughput gain of D2D communications increases linearly with the proportion of D2D pairs; above it, the average throughput gain increases slightly. It means that for a fixed number of active CUs, N , when the number of D2D pairs, M , increases to a certain amount, the network will be saturated, no more D2D pairs can be accessed and the multi-D2D pair diversity can only provide some secondary increase on the

throughput gain. This is also demonstrated at Fig. 8a. In addition, for any proportion of D2D pairs, the performance slightly increases with the number of the active CUs due to the increase of the potential multiuser diversity gain. V. C ONCLUSION AND F UTURE W ORK In this paper, we have investigated resource allocation for D2D communications sharing uplink resource in a fully loaded cellular network. To maximize the overall throughput while guaranteeing the QoS requirements of both CUs and DUs, we formulate the optimization problem and then find the solution through three steps: QoS-aware admission control for D2D pairs; optimal power control for the D2D pair and its reuse partner; maximum weighted matching to find the optimal reuse partner for each admissible D2D pair. Simulation results show that our scheme always performs best in terms of D2D access rate and D2D throughput gain compared with other well-known schemes. In future research, we will consider the optimal resource allocation with imperfect CSI at the BS and multiple-input multiple-output (MIMO) techniques. Meanwhile, the scenarios when multiple D2D pairs reuse the same source and a D2D pair share the resource with multiple regular CUs should be also addressed.

1


A PPENDIX A P ROOF OF P ROPOSITION 1

can be expressed as ∗

(Pic ∗ , Pjd ) = arg

Proof: If D2D pair j is admissible to sharing resource with CU i, the constraint (9) must be satisfied. Simplifying the two inequalities in (9), we can get ⎧ P c g g −σ2 (ξc g −ξc ξd h ) ⎨ max i,B j c N di,min jc i,min j,min j,B hci,j , ξi,min ξj,min Pmax hj,B hi,j ≤ d d 2 Pmax gi,B gj −ξj,min gi,B σN d ⎩ c d 2 ) hi,j . d ξi,min ξj,min (Pmax hj,B +σN (A.1) Thus, (A.2) hi,j ≤ min{hci,j , hdi,j } By comparing hci,j and hdi,j , we get ⎧ c c ⎨hci,j if 2 Pmaxdgi,B ≤ ξi,min , σN +Pmax hj,B hi,j ≤ c P g i,B d c max ⎩hi,j if 2 > ξi,min . σ +P d hj,B

where P2 = {(

log2 (1 +

log2 (1 +

c 2 d (Pmax hi,j +σN )ξj,min c ), (Pmax , gj

Pc

Pc

g

g

max

(Pic ,Pjd )∈P2

d d 2 Pmax gj −ξj,min σN d ξj,min hi,j

f (Pic , Pjd ),

d , Pmax ), (

(B.4)

d 2 c (Pmax hj,B +σN )ξi,min , gi,B

d Pmax )}. c c Pmax gi,B Pmax gj c For scenario (iii) σ2 +P > ξi,min and σ2 +P ≥ d d h j,B max max hi,j N N d ξj,min , the admissible area is shown in Fig. 3c. According to (B.1), the optimal power pair will reside on line CO or OF. When the optimal power resides on line CO, similar to (i), the optimal power pair will be at point C or O; when the optimal power resides on line OF, similar to (ii), the optimal power pair will be at point O or F. Hence, the optimal power allocation for this scenario can be expressed as ∗


(

max

(Pic ,Pjd )∈P3

f (Pic , Pjd ),

(B.5)

c 2 d (Pmax hi,j +σN )ξj,min c d ), (Pmax , Pmax ), gj

d 2 c (Pmax hj,B +σN )ξi,min d , Pmax )}. gi,B

Thus, Proposition 2 is proved.

f (λPic , λPjd ) > f (Pic , Pjd ),

(B.3)

}.

c , where P3 = {(Pmax

Proof: In [18], it has proved that for any given power pair (Pic , Pjd ) in the interior of the admissible area, there always exists another power pair (λPic , λPjd ) (λ > 1) in the admissible area such that

Pjd gj ). 2 +P c h σN i i,j

f (Pic , Pjd ),

c max i,B max j > ξi,min and σ2 +P < For scenario (ii) σ2 +P d d max hj,B max hi,j N N d ξj,min , the admissible area is shown in Fig. 3b. According to (B.1), the optimal power pair will reside on line EF. On the d d and at the same time f (Pic , Pmax ) is a line EF, Pjd = Pmax c convex function on Pi , thus the optimal power pair can be found at the corner point E or F. That means

(A.3)

A PPENDIX B P ROOF OF P ROPOSITION 2

f (Pic , Pjd )

c c 2 Pmax gi,B −ξi,min σN c ξi,min hj,B

max

(Pic ,Pjd )∈P1

∗

By substituting into the channel model as in (1), we can have, ⎧ 1 c d c α Kβi,j ζi,j ξi,min ξj,min Pmax ⎪ ⎪ ⎪[ (P c gi,B −ξc σ2 )β−ξc ξd σ2 ] ⎪ max ⎪ i,min N i,min j,min N ⎪ c ⎪ Pmax gi,B c ⎪ if σ2 +P ≤ ξi,min , ⎨ d max hj,B N Li,jRx ≥ 1 ⎪ c d 2 d ⎪ Kβi,j ζi,j ξi,min ξj,min (σN +Pmax hj,B ) α ⎪ ⎪ [ ] d 2 d ⎪ gi,B (Pmax gj −ξj,min σN ) ⎪ ⎪ c ⎪ Pmax gi,B c ⎩ if σ2 +P > ξi,min , d max hj,B N (A.4) Thus, Proposition 1 is obtained.

where

c where P1 = {(Pmax ,


max

N

3549

(B.1) Pic gi,B 2 +P d h σN j j,B

)

+

This implies at least one power ∗

in the optimal power pair (Pic ∗ , Pjd ) will be bound by the peak power constraint. c Pmax gi,B c ≤ ξi,min , the admissible area For scenario (i) σ2 +P d max hj,B N is shown in Fig. 3a. According to the above conclusion, the optimal power pair will reside on line CD as shown in Fig. 3a. That means, in this case, the optimal power for CU i, Pic ∗ , is c , and the optimal power for D2D pair j satisfies always Pmax c 2 d c c 2 Pmax (Pmax hi,j + σN )ξj,min gi,B − ξi,min σN ≤ Pjd ≤ . c gj ξi,min hj,B (B.2) Furthermore, in [18], it also proves that f (Pic , Pjd ) is a convex function on one variable Pic or Pjd when the other variable Pjd or Pic is fixed at its maximal power. That implies the optimal power pair on line CD will be either located at the end point C or D. Thus, the optimal power allocation for scenario (i)

R EFERENCES [1] K. Doppler, M. Rinne, C. Wijting, C. Ribeiro, and K. Hugl, “Deviceto-device communication as an underlay to LTE-Advanced networks,” IEEE Commun. Mag., vol. 47, no. 12, pp. 42–49, 2009. [2] P. J¨anis, C. Yu, K. Doppler, C. Ribeiro, C. Wijting, K. Hugl, O. Tirkkonen, and V. Koivunen, “Device-to-device communication underlaying cellular communications systems,” Int’l J. of Commun., Network and Syst. Sci., vol. 2, no. 3, pp. 169–178, 2009. [3] G. Fodor, E. Dahlman, G. Mildh, S. Parkvall, N. Reider, et al., “Design aspects of network assisted device-to-device communications,” IEEE Commun. Mag., vol. 50, no. 3, pp. 170–177, 2012. [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] H. Min, J. Lee, S. Park, and D. Hong, “Capacity enhancement using an interference limited area for device-to-device uplink underlaying cellular networks,” IEEE Trans. Wireless Commun., vol. 10, no. 12, pp. 3995– 4000, 2011. [6] C. Yu, K. Doppler, C. Ribeiro, and O. Tirkkonen, “Resource sharing optimization for device-to-device communication underlaying cellular networks,” IEEE Trans. Wireless Commun., vol. 10, no. 8, pp. 2752– 2763, 2011. [7] B. Kaufman and B. Aazhang, “Cellular networks with an overlaid device to device network,” in Proc. 2008 IEEE Asilomar Conf. on Signals, Syst. and Comput., pp. 1537–1541. [8] P. J¨anis, 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. 2009 IEEE Veh. Technology Conf. – Spring, pp. 1–5.

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[9] M. Zulhasnine, C. Huang, and A. Srinivasan, “Efficient resource allocation for device-to-device communication underlaying LTE network,” in Proc. 2010 IEEE Int. Conf. on Wireless and Mobile Computing, Networking and Commun., pp. 368–375. [10] I. Mitliagkas, N. Sidiropoulos, and A. Swami, “Convex approximationbased joint power and admission control for cognitive underlay networks,” in Proc. 2008 IEEE Int. Wireless Commun. and Mobile Computing Conf., pp. 28–32. [11] L. B. Le and E. Hossain, “Resource allocation for spectrum underlay in cognitive radio networks,” IEEE Trans. Wireless Commun., vol. 7, no. 12, pp. 5306–5315, Dec. 2008. [12] Y. Xing, C. N. Mathur, M. Haleem, R. Chandramouli, and K. Subbalakshmi, “Dynamic spectrum access with QoS and interference temperature constraints,” IEEE Trans. Mobile Comput., vol. 6, no. 4, pp. 423–433, Apr. 2007. [13] J. Tadrous, A. Sultan, M. Nafie, and A. El-Keyi, “Power control for constrained throughput maximization in spectrum shared networks,” in Proc. 2010 IEEE Global Telecommun. Conf., pp. 1–6. [14] I. F. Akyildiz, W.-Y. Lee, M. C. Vuran, and S. Mohanty, “Next generation/dynamic spectrum access/cognitive radio wireless networks: a survey,” Comput. Network J., vol. 50, no. 13, pp. 2127–2159, 2006. [15] M. Wellens, J. Wu, and P. Mahonen, “Evaluation of spectrum occupancy in indoor and outdoor scenario in the context of cognitive radio,” in Proc. 2007 IEEE Int. Conf. on Cognitive Radio Oriented Wireless Networks and Commun., pp. 420–427. [16] D. West et al., Introduction to Graph Theory. Prentice Hall, 2001. [17] B. Blaszczyszyn and M. Karray, “Quality of service in wireless cellular networks subject to log-normal shadowing,” IEEE Trans. Commun., vol. 61, no. 2, pp. 781–791, 2013. [18] A. Gjendemsjo, D. Gesbert, G. Oien, and S. Kiani, “Optimal power allocation and scheduling for two-cell capacity maximization,” in Proc. 2006 IEEE Int. Symp. on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks, pp. 1–6. Daquan Feng received his B.S. degree in communication engineering in 2008 from Henan University, Kaifeng, China. He is currently puring his Ph.D. degree at National key Laboratory of Science and Technology on Communications, University of Electronic Science and Technology of China, Chengdu, China. Since August 2011, he is working as a visiting student in the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, USA. His research interests include device-to-device communications, energyefficient wireless network design, and heterogeneous network. Lu Lu received her B.S.E degree and M.S.E degree from the University of Electronic Science and Technology of China (UESTC), Chengdu, China, in 2007 and 2010, respectively. She then got her licentiate degree from Royal Institute of Technology (KTH) in 2011. She is currently working toward the Ph.D. degree with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, USA. Her research interests include MIMO, cooperative communications, and cognitive radio networks.

Yi Yuan-Wu received the Engineer degree in electronic from Huazhong University, Wuhan, China, in 1982, the Master of Sciences degree in 1983 and Ph.D. in 1987 in signal processing and telecommunication from Rennes University, Rennes, France. Between 1983 and 1987, she done the Ph.D. research on the systems of digital diffusion to mobile (DAB) at CCETT of Rennes. Between 1989 and 1991, she worked in Thomson-LGT on video diffusion networks. Since 1992, she joined FranceTelecom R&D (todays Orange Labs), Issy-les-Moulineaux France. Her working domains are the signal detection, channel estimation, broadcast channel and D2D communications underlaying cellular network for the mobile systems. Between 1992 and 1996, she was in charged of the studying and specifying a CDMA Modem with variable flows. Between 1996 and 2000, she studied the DECT and PHS radio link systems for the 64 kbits/s and 2 Mbits/s data transmission. Between 2000 and 2003, she was in charge of studying on the UMTS-TDD physical layer performance. Between 2003 and 2005, she worked on the MC-CDMA system within the European Matrice and 4More projects. Now she is working for the European Metis and Sharing projects on the multiuser MIMO and the D2D subjects. She is a senior research expert of Orange Labs since 2004. Geoffrey Ye Li received his B.S.E. and M.S.E. degrees in 1983 and 1986, respectively, from the Department of Wireless Engineering, Nanjing Institute of Technology, Nanjing, China, and his Ph.D. degree in 1994 from the Department of Electrical Engineering, Auburn University, Alabama. He was a Teaching Assistant and then a Lecturer with Southeast University, Nanjing, China, from 1986 to 1991, a Research and Teaching Assistant with Auburn University, Alabama, from 1991 to 1994, and a Post-Doctoral Research Associate with the University of Maryland at College Park, Maryland, from 1994 to 1996. He was with AT&T Labs - Research at Red Bank, New Jersey, as a Senior and then a Principal Technical Staff Member from 1996 to 2000. Since 2000, he has been with the School of Electrical and Computer Engineering at Georgia Institute of Technology as an Associate and then a Full Professor. He is also holding the Cheung Kong Scholar title at the University of Electronic Science and Technology of China since March 2006. His general research interests include statistical signal processing and telecommunications, with emphasis on cross-layer optimization for spectraland energy-efficient networks, cognitive radios, and practical techniques in LTE systems. In these areas, he has published over 300 referred journal and conference papers in addition to 20 granted patents. His publications have been cited about 14,000 times and he is listed as a highly cited researcher by Thomson Reuters. He once served or is currently serving as an editor, a member of editorial board, and a guest editor for over 10 technical journals. He organized and chaired many international conferences, including technical program vice-chair of IEEE ICC’03 and co-chair of IEEE SPARC’11. He has been awarded an IEEE Fellow for his contributions to signal processing for wireless communications since 2006, selected as a Distinguished Lecturer for 2009 - 2010 by IEEE Communications Society, and won 2010 Stephen O. Rice Prize Paper Award in the field of communications theory by IEEE Communications Society and 2013 James Evans Avant Garde Award by IEEE Vehicular Society. Gang Feng (M’01–SM’06) received his BEng. and MEng degrees in Electronic Engineering from the University of Electronic Science and Technology of China (UESTC), in 1986 and 1989, respectively, and the Ph.D. degrees in Information Engineering from The Chinese University of Hong Kong in 1998. He joined the School of Electric and Electronic Engineering, Nanyang Technological University in December 2000 as an assistant professor and was promoted as an associate professor in October 2005. At present he is a professor with the National Laboratory of Communications, University of Electronic Science and Technology of China. Dr. Feng has extensive research experience and has published widely in computer networking and wireless networking research. His research interests include resource management in wireless networks, wireless network coding, energy efficient wireless networking, etc. Dr. Feng is a senior member of IEEE.


Shaoqian Li received his M.E. degree in Information and Communication Systems from University of Electronic Science and Technology of China (UESTC), Chengdu, China, in 1984 and his B. Eng in Wireless Engineering from Northwest Institute of Telecommunication Engineering (current Xidian University), Xi’an, China, in 1981. He joined University of Electronic Science and Technology of China in 1984. Currently, he is Professor of UESTC and Director of National Key Laboratory of Science and Technology on Communications (formerly National Key Lab of Communications) of UESTC. His research interest include mobile and wireless communications, anti-jamming techniques for wireless communications, frequency-hopping techniques, cognitive radio and spectrum sharing technologies. He has co-authored two books and published more than 40 referred journal papers and 200 conference papers. He is inventor of more than 20 issued patents and more than 50 filed Chinese Patents. He has received the 2nd class

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National Award for Technological Invention of China in 2008 and the 2nd class National Award for Science and Technology Progress of China in 2007. He received the Innovation and Excellent Award for contribution to National Information Industrial, by Ministry of Industry and Information Technology of P. R. China and Excellent Award for personal contribution to National HighTech Development Program (863) of P. R. China from 2001-2005. Since 1990s, he has served for many domestic academic conferences as Senior member of China Institute of Communications(CIC) and Chinese Institute of Electronics(CIE). And since 2001, he as served for Intl. Conf. on Commun., Circuits, and Systems (ICCCAS), in 2007, in 2008, in 2009, in 2010, in 2012, as Chair of Steering Committee, and/or General (co-) Chair, respectively. He also served as consultant Member of Board of Communications and Information Systems of Academic Degrees committee of the State Council, P. R. China, and Member of expert group of Key Project on Next-Generation Mobile Broadband Wireless Communications Systems towards 2020, Ministry of Industry and Information Technology of P. R. China. He is now IEEE Senior Member.