Joint user clustering and resource allocation for device-to-device communication underlaying MU-MIMO cellular networks

Transcription

1 Wang et al. EURASIP Journal on Wireless Counications and Networking (2015) 2015:145 DOI /s RESEARCH Joint user clustering and resource allocation for device-to-device counication underlaying MU-MIMO cellular networks Qiang Wang *, Conglin Lai, Yue Dong, Yuquan Shu and Xiaodong Xu Open Access Abstract In this paper, ultiple device-to-device (D2D) counication underlaying cellular ultiuser ultiple inputs ultiple outputs (MU-MIMO) systes is investigated. This type of counication can iprove spectral efficiency to address future deand, but interference anageent, user clustering, and resource allocation are three key probles related to resource sharing. Interference alignent (IA) is proposed to better itigate in-cluster interference copared with a ultiplex schee, and user clustering and resource allocation are jointly investigated using binary-integer prograing. In addition to an exhaustive search for a axiu throughput, we propose a two-step suboptial algorith by reducing the search space and applying branch-and-bound searching (BBS). To further obtain a good trade-off between perforance and coplexity, we propose a novel algorith based on distance-constrained criteria for user clustering. The siulation results show that the IA and ultiplex schees acquiring user clustering gains outperfor the orthogonal schee without user clustering. Besides, the proposed two-step and location-based algoriths achieve little losses copared with the optial algorith under low coplexities. Keywords: D2D counication; Multiuser MIMO; Interference alignent; Location-based; Resource allocation 1 Introduction In recent years, device-to-device (D2D) counication underlaying cellular infrastructures has attracted considerable attention on both acadeia and industry. This infrastructure perits peer-to-peer counication without base station (BS) relays but should be under the control of the BS. With the increasing use of local applications, such as short-distance data transission in social networks, D2D counication which is an effective proxiity transission schee has seen substantial deand. D2D counication has great potential to iprove spectru efficiency and syste perforance by reusing cellular resources [1,2]. Multiuser ultiple inputs ultiple outputs (MU-MIMO), which is regarded as a very iportant technology, has been applied in nuerous systes, including long-ter * Correspondence: wangq@bupt.edu.cn Wireless Technology Innovation Institute, National Engineering Laboratory for Mobile Network Security, Beijing University of Posts and Telecounications, No. 10, Rd. Xitucheng, Dist. Haidian, Beijing, China evolution (LTE) uplink and other cooperative networks, to obtain higher ultiuser diversity gain [3]. To address future increased deand, the cobination of MU-MIMO networks and D2D underlaying counications, as a novel research field, can further iprove spectral efficiency and increase the nuber of access users [4,5]. The relatively sparse literature only focuses on a single D2D pair reusing a cellular user equipent (CUE) resource, and the scenario where ultiple D2D pairs reuse resources with CUEs in the MU-MIMO uplinks has not been widely investigated. In this work, we divide CUEs and D2D pairs into several clusters. Each cluster has a certain nuber of CUEs and D2D pairs. For axiizing the syste rate, there are three key issues related to the syste optiization proble, i.e., 1) how to itigate the serious in-cluster interference, 2) how to deterine which D2D pairs and CUEs are clustered together, and 3) how to allocate appropriate resources to the clusters. The investigated counication pattern will cause excessive and serious interference in the network, including D2D links to cellular links and cellular links to 2015 Wang et al. This is an Open Access article distributed under the ters of the Creative Coons Attribution License ( which perits unrestricted use, distribution, and reproduction in any ediu, provided the original work is properly credited.

2 Wang et al. EURASIP Journal on Wireless Counications and Networking (2015) 2015:145 Page 2 of 17 D2D links [6]. To obtain a better syste or personal perforance, the effective ethods of interference anageent in D2D counication underlaying cellular networks include power control [7-10], resource allocation [11-18], interference awareness [19-21], and precoding [22]. Xing and Hakola [8] eploy LTE open-loop and closed-loop power control schees in a D2D scenario. The resource allocation proble is solved by an iterative cobinatorial auction ethod in [14]. By identifying interference, Min et al. [21] propose interferenceliited areas of D2D pairs to prohibit the fro reusing resources with CUEs if the interference at D2D receivers is greater than a threshold. In MIMO transission, the interference alignent (IA) technique, which is an effective precoding echanis that can align the interference at the receiver together to iprove receiving signal-to-interference-plus-noise ratio (SINR), has attracted substantial attention in recent years [23-25]. As the earliest research about IA, Cadabe and Jafar [23] provide a linear precoding codebook design in K-user interference channels. Furtherore, the second issue in clustering and the third issue in resource allocation are coupled with each other. It is thus necessary to jointly study the. Recently, increasingly ore works about jointly considering various optiization issues have been discussed [11,17,26-28] and have been shown to further iprove syste perforances. In [27], the authors analyze optiu power control and resource allocation with different sharing odes between CUEs and D2D pairs in a single-cell scenario. Generally, these types of probles are too hard to directly solve, i.e., NP-hard probles [29,30]. An optial and direct solution to these probles is exhaustive searching, which is used as a benchark in our paper. In this work, we attept to design low-coplexity suboptial algoriths for joint user clustering and resource allocation optiization prograing. Heuristic greedy algoriths [26], reverse iterative cobinatorial auction approaches [14,28], and D2D pair association vector search algoriths [5] are soe exaples of effective solutions to the NP-hard proble. The inspiration of Xu et al. [28] coes fro gae theory. The study sets the resources and D2D links as bidders and goods and then conducts a price iteration process. Its result can converge in a finite nuber of rounds and is better than rando allocation, but it exhibits soe perforance loss. 1.1 Our contribution According to the studies entioned above, we perfor the contributions as following: (1)We consider ultiple D2D pairs reusing resources with CUEs in the MU-MIMO uplink syste and forulate the joint user clustering of CUEs and D2D pairs and resource allocation optiization prograing. (2)We eploy a linear IA technique in the scenario to eliinate interference inside clusters, and we then propose evaluation coparisons between the schees with IA and without IA which is the traditional ultiplex schee. (3)A two-step optiization algorith is designed to first reduce the search space, thereby decreasing the search difficulty, and then obtain the solution using a branch-and-bound searching (BBS) algorith. To further reduce the coplexity for practical counications, we propose a location-based algorith that divides a single cell into an inner round eploying the IA schee and an outer circle eploying the ultiplex schee. The siulation results first show that the IA and ultiplex schees acquiring user clustering gains outperfor the orthogonal schee without eploying user clustering. The IA schee outperfors the ultiplex schee in a large range of the D2D user equipent transit (DUE-TX) power. Second, the two-step algorith exhibits inial losses copared to the optial exhaustive search. The proposed location-based algorith, whose perforance is near optial under low practical coplexity, exhibits a good trade-off between perforance and coplexity. Third, it is better to keep the distance between D2D users sufficiently sall to obtain a better syste perforance. Finally, the appropriate inner round radius r 0 of the location-based algorith onotonously increases with increasing DUE-TX power. With high DUE-TX power, a large r 0 is ore suitable. The reainder of this paper is organized as follows. Section 2 generalizes the scenario s syste and signal odels in the IA schee and ultiplex schee. We then deduce the SINR expressions. Section 3 proposes the objective and constraint conditions of the joint resource allocation and clustering prograing. In Section 4, a two-step algorith and a location-based algorith are proposed in detail. Section 5 presents the nuerical results, coplexities, and analysis. A further discussion is deonstrated in Section 6. Finally, conclusions are shown in Section Scenario description and sybol notations As shown in Figure 1, our research focuses on uplink transission in a single cell, where a total of K c CUEs and K d D2D pairs share K rb frequency resource blocks (RBs). The BS is equipped with N r antennas, while all users are equipped with N t antennas (N t < N r ). A D2D pair consists of a DUE-TX and a D2D user equipent receiver (DUE- RX). The interference in the investigated scenario is so coplicated, including DUE-TX to BS, CUEs to DUE-RX, and DUE-TX to DUE-RX of other D2D pairs. Power

3 Wang et al. EURASIP Journal on Wireless Counications and Networking (2015) 2015:145 Page 3 of 17 Figure 1 D2D counication underlaying cellular networks in a single-cell uplink scenario, where N c CUEs and N d DUEs siultaneously transit. control is used to satisfy the target CUE SINR. All DUE-TX powers are equal and set to P D. In the clustering course, each user cluster will consist of N c CUEs chosen fro K c CUEs and N d D2D pairs chosen fro K d D2D pairs. The sets of CUEs in user clusters, naed CUE subclusters, are denoted as C k ¼ fðc 1 ; ; C N c Þj1 C 1 C N C K c g. D l ¼ fðd 1 ; ; D N d Þj1 D 1 D N d K d g denotes the sets of D2D pairs, naed DUE subclusters. Here, k 1 k N all:c ¼ C Nc K c ; l 1 l N all:d ¼ C N K d d are the indices of CUE subclusters and DUE subclusters, respectively, where C p q ¼ q!= ð p! ð q p Þ! Þ. The users in the sae cluster are assigned the sae resources. Each RB consists of M subcarriers. We assue that each cluster can occupy any nuber of RBs fro 0 to K rb, and its occupied RBs ust be adjacent. Thus, there are N all. rb = K rb (K rb +1)/2+1 different resource patterns eeting the requireent [31]. R n (1 n N all. rb ) denotes the n-th resource pattern, where R 1 is the epty resource pattern. Moreover, none of the resources are peritted to be assigned ore than one cluster, and we define that the clusters that are assigned resources cannot contain the sae user. The channel we consider includes large-scale path loss related to user position and sall-scale path loss related to subcarrier and antenna. Uppercase boldface letters denote atrices and lowercase boldface letters denote vectors. Siilarly, span(x), rank(x), and vec(x) denote the colun space, rank, and vector obtained by stacking the coluns of atrix X, respectively. The superscripts, ( ) T, ( ) H, and ( ) -1 denote the Kronecker product, transpose, Heritian transpose, and atrix inversion, respectively. ( ) + sets the negative eleents of a vector to 0, and I n denotes the identity atrix. Other key atheatical notations used in the paper are listed in Table 1. 2 Syste odel In this section, we first introduce a traditional D2D underlaying MU-MIMO uplink scenario eploying a ultiplex schee. After deducing a cluster s received SINRs with iniu ean-square error (MMSE) frequency-doain equalization, we calculate its su throughput. Then, we forulate the precoding and decoding process of the scenario using IA and give soe feasibility conditions and derive the total throughput. 2.1 D2D underlaying MU-MIMO systes using a ultiplex schee In this schee, each antenna transits an independent data strea. With regard to the BS, all CUE signals are target signals. The BS eploys MMSE frequency-doain equalization [31] for ultiuser receiving to distinguish different target signals. Copared to the zero-forcing (ZF) ethod for ultiple user detection, MMSE is able to obtain a good trade-off between the perforance of interference itigation and noise aplification. There is no interference between CUEs. The transit sybol vector of CUEs can be estiated. The received signals at the -th subcarrier of the BS and DUE-RX antenna front-ends are written as y BS ¼ XN c H BS;Ci i¼1 pffiffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffi s Ci þ XNd L BS;Ci E Ci H BS;Dj j¼1 qffiffiffiffiffiffiffiffiffiffiffiqffiffiffiffiffiffi s þ n Dj BS ; L BS;Dj E Dj ð1þ

4 Wang et al. EURASIP Journal on Wireless Counications and Networking (2015) 2015:145 Page 4 of 17 Table 1 Matheatical notations Notation Physical interpretation K rb K c, K d N c, N d Denotes the nuber of all available tie-frequency RBs Denote the nuber of CUEs or D2D pairs in a cell Denote the nuber of CUEs in a CUE subcluster and the nuber of D2D pairs in a DUE subcluster C i D j s ; Ci s Dj E Ci ; E Dj H i;j L i,j r i,j n BS ; n Dj Denotes the label of CUE in a CUE subcluster, where i varies fro 1 to N c Denotes the label of D2D pairs in a DUE subcluster, where j varies fro 1 to N d, and each D2D pair includes a D j T x and D j R x Denote the transitted signal transitted at the -th subcarrier, and the subscript indicates the source of the signal Denote the diagonal atrix of the ultiantenna transit power, where the subscript indicates the source of the signal Denotes the Rayleigh channel atrix fro node j to node i over the -th subcarrier, with 0 ean and unit variance Denotes the diagonal atrix of the path loss fro node j to node i Denotes the distance between node j and node i Denote the additive white Gaussian noise (AWGN) on the -th subcarrier qffiffiffiffiffiffiffiffiffiffiffiqffiffiffiffiffiffi y D j ¼ H D j;d j s D j þ XN d þ XNc H D j;c i k¼1 L Dj;D j L Dj;C i E Dj j 0 ¼1;j 0 i qffiffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffi E Cis Ci þ n D j : H D j;d j 0 qffiffiffiffiffiffiffiffiffiffiffiffiqffiffiffiffiffiffiffi L Dj;D j 0 E Dj 0 s D j 0 ð2þ For BS receiving, for conciseness, the cobined target channel gain and the cobined CUE transit signals are h H BS pffiffiffiffiffiffiffip ffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffii H BS;C 1 L C1 E C1 H BS;CNc L CNc E CNc ; ð3þ T T T S s C 1 s : ð4þ CNc Then, the received signal at the BS at the -th subcarrier is rewritten as y BS ¼ H BS S þ XN d H BS;D j j¼1 qffiffiffiffiffiffiffiffiffiffiffiqffiffiffiffiffiffi s D j þ n BS : L BS;Dj E Dj ð5þ The MMSE equalization atrix is written as W BS ¼ H 1; H BS H BS H H BS þ Z BS I ð6þ N rn r where I N r N r is denoted as the unit diagonal atrix and Z BS ¼ σ2 BS I N rn r þ XNd H; H BS;D j L Dj E Dj ð7þ j¼1 H BS;D j where σ 2 Bs is the average power of n BS. Then, the SINR of the p-th data strea (p =1, N t N c ) at the -th subcarrier after MMSE equalization can be obtained as where the target receive signal after MMSE is D BS ¼ diag W BS H BS ð9þ and its corresponding received power is in the nuerator of (8). In the denoinator, the generated noise is coposed of white noise, the interference fro the other data streas of the CUEs, and the interference fro D2D data streas. The interference fro the other data streas of the CUEs is shown below Y BS ¼ W BS H BS D BS : ð10þ Siilarly, for DUE-RX receiving, we write the target channel gain between DUEs as The equalization atrix is W D j ¼ H D j qffiffiffiffiffiffiffiffiffiffiffiqffiffiffiffiffiffi H D j H D j ;D j L Dj ;D j E Dj : ð11þ H H 1 H Dj H Dj þ Z I Dj N t N ; ð12þ t where I N t N t is denoted as the unit diagonal atrix and h i diag D H γ BS;p ¼ BS D BS p diag σ 2 H BS W BS W BS þ Y BS Y H X Nd H BS þ j¼1 W BS Η BS;D j L BS;Dj E Dj H BS;D j W BS H p ; ð8þ

5 Wang et al. EURASIP Journal on Wireless Counications and Networking (2015) 2015:145 Page 5 of 17 Z D j ¼ σ 2 D j I N t N t þ XN d H D j ;D L j 0 D j ;D j 0 E Dj 0 H D j ;D j 0 j 0 ¼1;j 0 j þ XN c H: H D j ;C i L Dj ;C i E Ci k¼1 H D j ;C i H ð13þ (13) presents the cobination of noise and interference that originate fro CUEs and other D2D pairs in ters of DUE-RX. Subsequently, the SINR of the q-th data strea (q =1,,N t ) of the j-th DUE-RX at the -th subcarrier after MMSE equalization can be obtained as diag D D Dj Dj γ Dj;q ¼ h H diag σ 2 Dj W W Dj Dj þ YDj Y H Dj H þ X Nd H H j 0 ¼1;j 0 j W Dj H Dj;D L j 0 Dj;D j 0 E Dj 0 H Dj;D j 0 W Dj þ X N c H k¼1 W Dj H L Dj;Ci Dj;CiE Ci H Dj;Ci W Hq Dj where the target receive signal after MMSE is D D j h ¼ diag W D j H D j q i ð14þ ð15þ and its corresponding received power is in the nuerator of (14). In the denoinator, the generated noise is coposed of white noise, the interference fro the other data strea of the sae D2D pair, the interference fro the data streas of the other D2D pairs, and the interference fro CUE data streas. The interference fro the other data streas of the sae D2D pair is shown below: Y Dj ¼ W D j H D j D D j : ð16þ Because there exist M continuous subcarriers in an RB, the post-processing SINR of the p-th data strea (p =1, N t N c ) at the BS is γ BS;p ¼ 1 M X M 1 ¼0! þ γ BS;p 1; ð17þ and the post-processing SINR of the q-th data strea (q =1,,N t )atthej-th DUE-RX is N t k;l;rb ¼ X tn c log 2 1 þ γ BS;p p¼1 þ X j D l X N t q¼1 log 2 1 þ γ Dj ;q : ð19þ 2.2 D2D underlaying MU-MIMO systes using the IA schee Signal odel through IA This ultiplex schee is siple and can be easily ipleented without channel state inforation (CSI) feedback, but it has no interference itigation echanis and thus results in a degraded perforance. We utilize a linear IA echanis for the clusters. To provide successful receiving, we assue each transitter only sends a data strea to its corresponding receiver. Thus, each receiver can see N c + N d independent data flows. DUE- RX should align N c + N d 1 interfering flows to a certain space to enlarge the space of the target flow. In ter of the BS, N c independent spaces are required to receive N c target flows. The receiving signal at the -th subcarrier of BS and DUE-RX before decoding can be written as where y BS ¼ XN c G BS;C i Q C i s C i þ XN d G BS;D j Q D j s D j y D j i¼1 þ n BS ; j¼1 ¼ G D j ;D j Q D j s D j þ XN c G D j ;C i Q C i s C i þ XN d j 0 ¼1;j 0 j j ¼ 1; ; N d ; i¼1 G D j ;D j 0 Q D j 0 s D j 0 þ n D j ; ð20þ ð21þ G a;b ¼ H a;b qffiffiffiffiffiffiffiffi L a;b; ð22þ Q b ¼ p ffiffiffiffiffiffi E b P b ; ð23þ a fbs; D 1 ; ; D Nd g; b fc 1 ; ; C N c ; D 1 ; ; D Nd g; ð24þ where P represents the IA-noralized precoding atrix. Subsequently, by applying a ZF algorith for decoding, the interference spaces will be set to 0 and the target spaces will be preserved. We can obtain γ Dj ;q ¼ 1 M X M 1 ¼0! þ γ D j ;q 1: ð18þ y BS ¼ U BS X N c i¼1 G BS;C i Q C i s C i þ U BS n BS ; ð25þ Hence, the throughput of the k-th CUE subcluster and l-th DUE subcluster in the rb-th resource is given as y D j ¼ U D j G D j ;D j Q D j s D j þ U D j n D j ; j ¼ 1; ; N d ; ð26þ

6 Wang et al. EURASIP Journal on Wireless Counications and Networking (2015) 2015:145 Page 6 of 17 where U BS and U D j ðj ¼ 1; ; N d Þ are the interferencenulling atrices at the BS and DUE-RX. The precoding and decoding atrix designs will be described later. After ZF decoding, the post-processing SINR of the j-th DUE-TX (j =1,, N d ) can be obtained as where γ D j γ Dj ¼ 1 M X M 1 ¼0! þ γ D j 1; ð27þ U D j H pffiffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffi D j ;D j L Dj ;D j E Dj ¼ σ 2 D j P Dj 2 The SINR of the i-th CUE (i =1,, N c )is γ Ci ¼ 1 M X M 1 ¼0 ð28þ! þ γ C i 1; ð29þ where the MMSE is added at the BS receiver after decoding to distinguish different CUE flows [31] as γ C i ¼ σ 2 BS H BS 1 HH BS þ σ 2 BS I N c N c 1 i;i 1: ð30þ The throughput of the k-th CUE subcluster and the l-th DUE subcluster in the rb-th resource is expressed as t k;l;rb ¼ X log 2 1 þ γ Ci þ X log 2 1 þ γ Dj : ð31þ i C k j D l Liitation and feasibility of the scenario using IA The basic condition of feasible IA is shown in [25]. The feasibility is ainly related to the user nuber, antenna nuber, and data strea nuber which prefor interaction to each other. In this scenario, it can be transfored as U þ a H a;bq b ¼ 0; a b 0 ; ð32þ rank U þ b 0H b 0 ;bq b ¼ DOFb ; ð33þ a; b 0 fbs; D 1 ; ; D N d g; b fc 1 ; ; C N c ; D 1 ; ; D Nd g: ð34þ where b denotes the target of b and a is not the target of b. DOF is the degree of freedo representing the nuber of data streas in the b-th link. Yetis et al. [25] utilize Bezout s theore to deterine whether the syste is feasible. It presents that if the syste is feasible, the nuber of equations ust be less than or equal to the nuber of variables. In future, the BS has enough ability to possess ore antennas. Thereby, there can be ore spaces to store interference at the BS. In this first analysis, we assue the BS uses N b spaces to align N d interference, while each DUE-RX uses one space to align N c + N d 1 interference. The interference aligning to the D2D receivers can be expressed as span H a1 ;b 1 Q b1 span H a2 ;b 1 Q b1 span H and ;b 1 Q b1 ¼ ¼ span Ha1 ;b β Q bβ ¼ span H a1 ;b NcþNd Q bncþnd ¼ ¼ span Ha2 ;b β Q bβ ¼ span H a2 ;b NcþNd Q bncþnd ¼ ; a 1 b 0 β ; ¼ ; a 2 b 0 β ; ¼ ¼ span H and ;b β Q bβ ¼ ¼ span H and ;b NcþNd Q bncþnd ð35þ ; a N d b 0 β ; where β represents the subscript of the user set of the transit side. The nuber of precoding atrix is N c + N d, and the nuber of uncorrelated equations for D2D receivers is N d (N c + N d 2). In ters of BS, there are N d N b uncorrelated equations. The overall syste is solvable if and only if N c + N d N d (N c + N d 2) + N d N b. Since N b 0, N d being set to 1 can acquire feasible cases no atter which N c is. If N d denotes larger than 1, then " # 2 N d ðn d Þ 2 þ N b N c 0; N d 1 ð36þ ðn d 1ÞðN c þ N d Þ N d N b : ð37þ As (36) and (37) show, if N b = 1, the feasible cobinations do not exist. If N b = 2, then the only two feasible cases are N c =1,N d = 2 and N c = N d = 2. In noralization, a relatively lower bound of N b will be satisfied when N c = N d which is without loss of generality. Then, (37) is transfored into N c = N d N b. That eans BS ust use at least N d spaces to align interference. Besides, BS acquires N c target signals. Cobining the target and interference spaces, the total antenna nuber of BS, N r,ustbeat least N c + N d for a feasible syste. It can be inferred that the ore antenna nuber is, the ore users the syste can contain. If we assue D2D receivers have ore spaces to align interference, the iniu ipleentation needs to be figured out for a feasible syste. In the second analysis, we use a ethod siilar to [25] to evaluate the relation between N t and N d. We add the influence of antenna. The nuber of equation is

7 Wang et al. EURASIP Journal on Wireless Counications and Networking (2015) 2015:145 Page 7 of 17 N e ¼ X d a d b ; a; b 0 fbs; D 1 ; ; D N d g; b fc 1 ; ; C N c ; D 1 ; ; D N d g: a b 0 ð38þ We assue each user transits a data strea at one tie. That eans its DOF is 1. Also, BS receives N c data streas siultaneously so its DOF is N c. The equation nuber is N e ¼ N c N d þ N c N d þ ðn d 1ÞN d ; ð39þ where the ters are respectively DUE-TX to BS, CUE to DUE-RX, and DUE-TX to the other D2D pairs DUE-RX in a cluster. Next, after reoving the superfluous variables, the effective variable nuber for each user is N u = N t 1, while the BS s isn v = N c (N r N c ). The inequality ust be satisfied which is shown below N e ðn c þ N d ÞN u þ N d N u þ N c ðn r N c Þ; N c N d þ N c N d þ ðn d 1ÞN d ðn c þ 2N d ÞðN t 1ÞþN c ðn r N c Þ; ðn c þ N d Þ 2 þ N c þ N d ðn c þ 2N d ÞN t þ N c N r : ð40þ The deriving result of (40) is the general restricted relation between user nuber and antenna nuber in the investigated scenario. If N r = N c + N d and N c = N d, then " 2N d þ 2 3 # N t : ð41þ As (41), the feasible user antenna nuber increases linearly with D2D user nuber. As long as there is enough antenna nuber, the ore satisfied users can be accoodated in the syste. IA has a great potential to increase the nuber of users. The feasible ipleentations for a practical N c = N d syste of the investigated scenario are N r = N c + N d and N t (2N d + 2)/3. It is worth noting that these two conditions are the sufficient but not the necessity conditions of feasible IA in the investigated scenario Precoding and decoding designs The linear precoding and decoding codebook designs are related to specific scenario paraeters, particularly the nuber of users and antennas. Cadabe and Jafar [23] state that each receiver should use at least one antenna to receive a target signal and at least one antenna to receive the interference. We select a group of the feasible ipleentation fro the last section. As the standard ipleentation in 3GPP LTE [32,33] presents, the BS is configured with 4 with antennas, i.e., N r =4, and each user is configured with 2 antennas, i.e., N t =2. As a siple exaple, we assue N c = N d = 2 in a cluster. The paraeters subitting forula (40) are general in practical usage. Using the above paraeter setting, three interference signals seen by each DUE-RX are aligned into a signal space. Thus, the transitter strategy is to select beaforing vectors to satisfy the following constraints: span G D 1 ;C 1 Q C 1 span G D 2 ;C 1 Q C 1 ¼ span G D 1 ;C 2 Q C 2 ¼ span G D 1 ;D 2 Q D 2 ¼ span G D 2 ;C 2 Q C 2 ¼ span G D 2 ;D 1 Q D 1 ; ð42þ ; ð43þ where span(a) stands for the vector space spanned by the colun vectors of the atrix A. Then, Q C 2 ¼ G D 2 ;C 2 1 G D 2 ;C 1 Q C 1 ; ð44þ Q D 1 ¼ G D 2 ;D 1 1 G D 2 ;C 1 Q C 1 ; ð45þ Q D 2 ¼ G D 1 ;D 2 1 G D 1 ;C 2 G D 2 ;C 2 1 G D 2 ;C 1 Q C 1 ; ð46þ span Q C 1 ¼ span G D 1 1;C 1 G D 1;C 2 G D 1 2;C 2 G D 2;C 1 Q C 1 : ð47þ As (47) expresses, Q C 1 can be set as the eigenvector of G D 1 ;C 1 1 G D 1 ;C 2 G D 2 ;C 1 2 G D 2 ;C 1, and then, all precoding atrices Q C 1 ; Q C 2 ; Q D 1 ; Q D 2 can be siilarly deterined. After deriving precoding atrices, the corresponding ZF decoding atrices also need to be derived to preserve the target spaces. Taking y D1 as an exaple, because G D1;C1 Q C1, G D1;C2 Q C2,andG D1;D2 Q D2 have been aligned in the sae space, we select any one of the and then use SVD decoposition, i.e., G D1;C1 Q C1 ¼ ½ U 1ΛV.Wetake the second colun of U 1, which is denoted as U (2) 1. Then, T the ZF atrix at DUE-RX1, D 1,is U D 1 ¼ U ðþ 2 1.Because U 1 is a unitary atrix, U ðþ 2 TG 1 D1;C1 Q C1 can preserve the target signal and eliinate the interference signal. Siilar to D 1, U D 2 can be derived. In ters of the BS receiving the C 1 signal, after using SVD decoposition to obtain G BS;C1 Q C1 ¼ ½ U 2ΛV, we select the second, the third, and the fourth coluns as U (2 4) 2,andU C 1 is (U (2 4) 2 ) T.To obtain the C 2 signal, U C 1 G BS;C2 Q C2 ¼ ½ U 3ΛV,then,we set U C 2 is (U (3 4) 3 ) T. 3 Forulation of joint user clustering and resource allocation proble The prior section presents the cluster throughput calculation of each RB in the ultiplex (19) and IA (31) schees. Regardless of the eployed schee, the objective is to axiize the overall syste throughput via

8 Wang et al. EURASIP Journal on Wireless Counications and Networking (2015) 2015:145 Page 8 of 17 joint user clustering and resource allocation. Before solving the optiization proble, we need to derive the throughput of each resource pattern as t 0 k;l;n ¼ X t k;l;rb ; k; l: ð48þ rb R n The indicator x k,l,n = 1 represents that the n-th resource pattern is assigned to the CUE subcluster C k and DUE subcluster D l ;otherwise,x k,l,n =0. If n = 1 and x k,l,n =1, it eans that there is no resource assigned to this cluster; thus, t ' k,l,1 = 0. Matheatically, the optiization proble can be forulated as subject to ax XN all;c XN all;d XN all;rb fk;l;ng k¼1 l¼1 n¼1 XN all;d XN all;rb l¼1 n¼1 XN all;c XN all;rb k¼1 n¼1 XN all;c XN all;d k¼1 l¼1 x k;l;n 1; k x k;l;n 1; l x k;l;n 1; n 1 C k1 C k2 ¼ ; k1 k2 D l1 D l2 ¼ ; l1 l2 R n1 R n2 ¼ ; n1 n2 x k;l;n t 0 k;l;n The descriptions of constraints (a) to (f) are as follows: ð49þ ðaþ ðbþ ðcþ ðdþ ðeþ (a)indicates that each CUE subcluster can share a resource allocation pattern, including an epty resource pattern, with at ost one DUE subcluster; (b)indicates that each DUE subcluster can share a resource allocation pattern, including an epty resource pattern, with at ost one CUE subcluster; (c) indicates that each resource allocation pattern, except the epty pattern, can only be allocated to at ost one CUE subcluster and one DUE subcluster; (d)guarantees that each CUE can only be selected by one CUE subcluster. k1 and k2 represent the indices of the selected CUE subclusters that are allocated resources; (e)guarantees that each D2D pair can only be selected by one DUE subcluster. l1 and l2 represent the indices of selected DUE subclusters that are allocated resources; (f) guarantees that each RB is only allocated to a cluster. n1 and n2 represent the indices of the eployed resource pattern. ðfþ The joint optiization used to axiize the overall rates of the CUEs and DUEs sharing the sae resources is a typical discrete optiization proble and ust be non-convex. The usual ethod to obtain the optial result of such types of proble is exhaustive searching which is extreely difficult, i.e., NP-hard [29,30]. Because x k,l,n is 0 or 1, the proble can be transfored as a standard binary-integer prograing proble. In this paper, we utilize low-coplexity heuristic algoriths to obtain approxiately optial results that do not have uch loss of perforance copared to the optial one. 4 Joint user clustering and resource allocation algoriths In this section, we first present the standard binaryinteger prograing of the optiization proble and subsequently develop a two-step algorith to solve it. Finally, a location-based algorith is provided to obtain a good trade-off between perforance and coplexity. 4.1 Standard binary-integer prograing for Define a N all. c N all. d K all. rb 1 user clustering and resource allocation vector and a N all. c N all. d K all. rb 1 noralized throughput vector whose eleents are calculated by (48) as x ¼½x 1;1;1 ; ; x 1;1;Nall;rb ; ; x 1;N all;d ;1; ; x 1;Nall;d ;N all;rb ; x 2;1;1 ; ; x 2;1;N all;rb ; ; x 2;N all;d ;1; ; x 2;N all;d ;N all;rb ; x N all;c ;1;1; ; x Nall;c ;1;N all;rb ; ; x N all;c ;N all;d ;1; ; x N all;c ;N all;d ;N all;rb T ð50þ t ¼½t 0 1;1;1; ; t 0 1;1;N all;rb ; ; t 0 1;N all;d ;1; ; t 0 1;N all;d ;N all;rb ; t 0 2;1;1; ; t 0 2;1;N all;rb ; ; t 0 2;N all;d ;1; ; t 0 2;N all;d ;N all;rb ; t 0 N all;c ;1;1; ; t 0 N all;c ;1;N all;rb ; ; t 0 N all;c ;N all;d ;1; ; t 0 N all;c ;N all;d ;N all;rb T Reforulate the optiization as in t T x x subject to ð51þ ð52þ Rx 1ð Nc N d N rb þk c þk d Þ1 ð53þ where R is a (N c N d K rb + K c + K d ) N all. c N all. d N all. rb constraint atrix containing only 0 and 1. This atrix can be expressed as

9 Wang et al. EURASIP Journal on Wireless Counications and Networking (2015) 2015:145 Page 9 of ð Nall;c N all;d Þ J 3 R ¼ 4 F 1 1Nall:d 1 1Nall;rb 5: ð54þ 1 1N all:c N 1 1Nall;rb The first bar represents the extended resource constraint atrix used to ensure the constraints (c) and (f) of (49), where J is a (N c N d K rb ) N all. rb resource pattern atrix for each cluster. Because there are N c CUEs and N d D2D pairs in a cluster utilizing the sae resource pattern, J can be expressed as J ¼ 1ð Nc N d Þ1 T; ð55þ where T is a K rb N all. rb basic resource pattern atrix used to list all types of adjacent resources, including an epty pattern. The second bar represents the extended CUE constraint atrix used to ensure the constraints (a) and (d) of (49), where F is a K c N all. c CUE subcluster atrix for a fixed resource allocation pattern and a fixed DUE subcluster. The third bar represents the extended DUE constraint atrix used to ensure the constraints (b) and (e) of (49), where N is a K d N all. d DUE subcluster atrix for a fixed resource allocation pattern and a fixed CUE subcluster. For exaple, N c = N d =2, K rb = 6, and K c = K d = 12 is a group of exaple paraeters in this paper; thus, there are N all. c = K c (K c 1)/2 different types of CUE subcluster and N all. d = K d (K d 1)/2 different types of DUE subcluster. Then, F ¼ N ¼ K cn all:c ð56þ An exhaustive search is a straightforward and basic algorith used to find the optial solution of binaryinteger prograing probles. However, it is overly coplex and ipractical in real-world scenarios. 4.2 Two-step algorith To reduce the coplexity, we propose a two-step optiization algorith. In this algorith, an exhaustive search algorith is first used to find the optial user cluster at each RB. Then, we reserve the eleents in (51) that contain the users in RBs optial clusters and abandon the reainder. Based on such a reduceddiension CUE subcluster subset and DUE subcluster subset, we ipleent the BBS algorith [31] to realize the joint optiization. Let us use an exaple to illustrate the advantage of reducing the search space by utilizing a two-step algorith. When K c = K d = 12 and K rb = 6, the extree case is that 6 CUE and 6 DUE subclusters will be selected to for the reduced-diension CUE subcluster subset and DUE subcluster subset. Clearly, the diension of such a CUE subcluster subset is substantially saller than that of the full CUE subcluster set, i.e., N all. c = 66. The sae effect will occur in the DUE subcluster. Consequently, the search space for the optiization can be reduced, thereby decreasing its coplexity. The pseudo-code of the algorith is shown in Table 2, where k and l denote that the k -th CUE subcluster and l -th DUE subcluster are the ost suitable for rb. K and L denote the CUE subcluster subset and DUE subcluster subset, respectively. S represents the index set of all cobinations between ^k fro K and ^l fro L. ^x S denotes the target vector of user clustering and resource allocation. 4.3 Rando clustering schee based on distance (location-based algorith) When there are a large nuber of CUEs and DUEs in the cell, the coputation is quite coplex when using exhaustive searching or the two-step algorith. Therefore, we propose a novel location-based algorith to randoly T ¼ K rb N all:rb ð57þ

10 Wang et al. EURASIP Journal on Wireless Counications and Networking (2015) 2015:145 Page 10 of 17 Table 2 Low-coplexity suboptial two-step algorith Two-step algorith 1. Initialization: S =, K =, L = 2. Clustering Procedure: 3. For each resource pattern with only one RB rb {1,2,,K rb } 4. Find the CUE sub-cluster and DUE sub-cluster k; l ¼ arg ax 5. K ¼ K k 6. L ¼ L l 7. End 8. Searching Space Reduction Procedure: 9. For each ^k K;^l L sets n 10. s 0 ¼ ij ^k 1 N all;d N all;rb þ ^l 1 N all;rb þ 1 i ^k 1 o N all;d N all;rb þ^l N all;rb 12. S = S s End 14. Joint Solution Procedure: 15. Obtain the reduced-diension optiization proble 16. x s ¼ in t T xs S x S, s.t. R:;S x S ¼ 1ð NcNdNrbþKcþKdÞ1 17. Find its solution based on the BBS algorith 18. Return x s 19. End fk;lg t k;l;rb select CUEs and D2D pairs based on a distance-constrained criterion to asseble a user cluster. The cell is divided into two areas by a circle of radius r 0, as shown in Figure 2. The area inside the circle is denoted as A, and the area outside the circle is denoted as B. Multiplex (Section 2.1) and IA (Section 2.2) schees are eployed in those respective areas. The users are randoly distributed in the cell. Users in area A and area B are independent and are randoly cobined into clusters. In a cluster, N c and N d are equal to 2. Each user is only clustered in one group. We set each user s antenna nuber as N t =2. Each user in area A transits a single data strea, whereas each user in area B transits two data streas. The eployed resource assignent is a rando schee, and the RBs used in different areas are orthogonal. We can suppose that there will be greater opportunity to assign resources for the area that is larger. All the RBs are fully exploited to support as any users as possible. We assue that area B is divided into six equal sections, denoted by B1 to B6, as illustrated in Figure 2. The ain in-cluster interference is between D2D pairs and between CUEs and D2D pairs. Two D2D pairs and two CUEs are randoly located at three non-adjacent sections so that the utual interference can be reduced to a low level. We select two D2D pairs fro two of the three non-adjacent sections and two CUEs fro the reaining section. Then, we cobine these users into a cluster, which is eployed in the ultiplex schee. In area A, the utual interference cannot be neglected because the distance between the CUEs and D2D pairs is not sufficiently large. Therefore, the IA schee is adopted. The area does not need to be divided because the utual interference is nearly non-existent when the IA schee is used. Next, we define r 0 and P D, where P D is the axiu transit power of the D2D transitter. We eploy a type of dynaic power control to adjust the CUE s uplink transit power P c to the target SINR (the sallest SINR satisfying quality of service (QOS) requireents), while all of the D2D counications are being perfored with a fixed transission power P D. The initial P c is set at the axiu 23 db. The location-based algorith s procedure is described in detail in Table 3. 5 Siulation results In this section, we present the perforance of the proposed algoriths and other coparison schees. For siplicity, we consider a single-cell scenario with various siulation paraeters based on the 3GPP LTE standard [32,33], which are listed in Table 4. In this scenario, we eploy IA, ultiplex, and orthogonal schees, each of which considers optial, two-step, and rando algoriths. The location-based algorith is also considered. The orthogonal schee is the echanis whereby each CUE or D2D pair utilizes an independent orthogonal resource, where K rb,c and K rb,d are the nubers of resources for the CUE and D2D pairs. The rando algorith indicates that user clustering and resource allocation are rando. We attept to consider various factors, including

11 Wang et al. EURASIP Journal on Wireless Counications and Networking (2015) 2015:145 Page 11 of 17 Figure 2 Location-based architecture in a single-cell scenario containing two areas using IA and ultiplex schees. the effect of the DUE transit power, D2D pair utual distance, and inner round radius. 5.1 Effect of D2D transit power Figure 3 illustrates the average capacity versus the DUE transit power for various schees, where the distance between D2D pairs is 20 and the inner round radius of the location-based algorith is 300. In the figure, the ultiplex and IA schee siultaneously allocate each RB to two CUEs and two D2D pairs. In addition, the orthogonal schee allocates one third of the RBs to CUEs, whereas the reaining RBs are allocated to the DUEs, and each RB is shared by two CUEs or by one pair of DUEs. Initially, in addition to the location-based algorith, the average capacities of the IA and orthogonal schees onotonously increase with increasing DUE transit power. In regard to the ultiplex schee, although the useful received power increases with increasing DUE transit power, the interference power also increases; therefore, the perforance trend does not vary with the DUE transit power. The IA and ultiplex schees using user clustering outperfor the orthogonal schee, which does not use user clustering. Additionally, when the DUE transit power is higher than 0 db, which eans a large power range in practical ipleentation, the IA schee outperfors the ultiplex and orthogonal schees in both the two-step and optial algoriths. As shown in Table 5, the two-step algorith (polynoial coplexity) is less coplex than the optial algorith (exponential coplexity). For a typical exaple of K rb = K c = K d = 4 and N c = N d = 2, the search coplexity of the two-step algorith is 144, whereas that of the optial algorith is approxiately 1.6E6. When K rb =6 and K c = K d = 12, the search coplexities of the two-step and optial algoriths are 2.6E4 and 6.8E21, respectively. Obliviously, the growth in the optial algorith s coplexity is greater. Figure 3 also shows that regardless of whether the schee is an IA, ultiplex, or orthogonal, the two-step algorith has an average capacity that is siilar to the optial algorith, and both of the outperfor the rando algorith. In suary, the proposed two-step algorith exhibits not only a higher average capacity but also a lower coplexity. Nevertheless, the perforance of the location-based algorith, which eploys a rando algorith, is greater than that of any other schee using a rando algorith, and it is closer to that of the two-step algorith in the ultiplex and IA schees. The coplexity of the location-based algorith is linear, which is considerably lower than that of the two-step algorith and is equal to that of the rando algorith.

12 Wang et al. EURASIP Journal on Wireless Counications and Networking (2015) 2015:145 Page 12 of 17 Table 3 Location-based algorith Location-based algorith 1. Initialization: Randoly distribute CUEs and D2D pairs in a cell and calculate their distances to the center of the BS. Deterine the value of r 0 between 0 and the radius of the cell 2. Divide users into four groups according to r 0,A CUE,A D2D,B CUE,andB D2D 3. In area A or B, users randoly constitute clusters (the clustering in area B ust satisfy the distance criterion), and each cluster consists of two CUE users and two D2D pairs 4. For each RB 5. Randoly choose a cluster in the cell and deterine whether it is in area A or B 6. Calculate the large-scale loss in this cluster 7. Case user to BS: * log 10 (d[k]) 8. Case user to user: * log 10 (d[k]) 9. Set the initial transit power according to area A or B: P C1, P C2, P D1, P D2 10. Do 11. For each subcarrier (SC) 12. Generate sall-scale loss H: ultiplex Gaussian with zero ean unit variance 13. If cluster in area A 14. Interference Alignent - Equations (20)-(26), (42)-(47) 15. Else cluster in area B 16. Multiplex Schee - Equations (1)-(16) 17. End if 18. End SC 19. Calculate SINR in this RB: Equations (27) to(30) for IA 20. Equations (17) and (18)for Multiplex; 21. While SINR does not eet the target, Power Control, then jup End each RB 23. Calculate su throughput Table 4 Siulation paraeters Carrier frequency: 2 GHz Macro cell radius R: 500 Nuber of CUEs per cell K c : 12 Nuber of D2D pairs per cell K d :12 CUE and DUE distribution: unifor Clustering ode: 2 CUEs + 2 D2D pairs IA precoding ode: 1 strea per Multiplex ode: 2 streas per user user K rb : 6 Nuber of subcarriers per RB, M: 12 Syste bandwidth: 1.4 MHz Subcarrier spacing: 15 khz Multiplex equalizer: MMSE Sall-scale channel: coplex Gaussian channel User antenna nuber: 2 BS antenna nuber: 4 Macro UE path loss: log 10 (d[k]) D2D path loss: log 10 (d[k]) CUE target SINR: 5 db Noise power density N 0 : 174 db/hz The perforance and coplexity of the optial or rando algorith cannot becoe optial siultaneously because a conflict always exists between perforance and coplexity. However, the location-based algorith can achieve a good trade-off between these two criteria. 5.2 Effect of distance between D2D pairs Figure 4 presents the average capacity versus the DUE transit power for various schees and for different distances between DUE-TX and DUE-RX in a D2D pair (i.e., 10, 20, and 30 ). In this case, the inner round radius in the location-based algorith is 300. The average capacity increases with increasing DUE transit power. A shorter D2D utual distance results in a superior perforance for all schees because the DUE receivers experience lower interference when the distances between D2D pairs decrease. In addition, the perforance of the location-based algorith is close to that of the IA using the two-step algorith when the D2D utual distance is sall, whereas the perforance reains close to that of the IA schee using the rando algorith if the D2D utual distance is large. These results occur ainly because SINR decreases with increasing path loss resulting fro the increase in the D2D pair utual distance and vice versa (in this scenario, interference reains invariant; however, the signal decreases rapidly copared to the interference variance). The siulation results iply that it is better to keep the distance between D2D users sufficiently sall for the sake of good perforance. 5.3 Effect of the inner round radius Figure 5 presents the average capacity versus the DUE transit power using the location-based algorith for different inner round radii, where the D2D pair utual distance is 20. Different radii lead to different perforances. For exaple, when the DUE transit power is 5 db, r 0 = 300 provides the best perforance, whereas r 0 = 500 provides the worst perforance. This is ainly because the perforance is deterined by the inner part, whose perforance decreases with increasing r 0, and the outer part, whose perforance increases with increasing r 0. Therefore, an appropriate r 0 position can likely be deterined to axiize the perforance, but this position varies when the DUE transit power is varied. The appropriate r 0 position onotonously increases with increasing DUE transit power. With high DUE-TX power, a large r 0 is ore suitable. Figure 6 presents a CDF plot to illustrate the dynaic range and the scale of the throughput. DUE transit power is set as 5 db in the proposed and coparative schees. The location-based algorith and the IA schee using the rando algorith have siilar dynaic ranges, whereas the ultiplex schee using the rando algorith

13 Wang et al. EURASIP Journal on Wireless Counications and Networking (2015) 2015:145 Page 13 of 17 Figure 3 Average overall capacity of different transission schees and corresponding algoriths versus the DUE transit power. produces a larger dynaic range. Thus, copared to the ultiplex schee using the rando algorith, the location-based algorith is fairer to the user. In ters of the scale of the throughput, the location-based algorith with r 0 = 200, 300, and 400 outperfors the IA and ultiplex schees using the rando algorith. One of the reasons for this result is that the throughput of the outer circle in the location-based algorith using a double strea is greater than that in the IA schee using a single strea. Another reason for this is that because the outer circle is divided into six sections, a lower level of utual interference between ultiplex users can occur. The receivers using the ultiplex schee using the rando algorith will receive the coplex interference, which decreases the ultiplex gain. However, the locationbased algorith can be used to iniize this influence. Figure 7 presents a CDF plot analyzing the different locations perforance and distribution situations using the location-based algorith, where the DUE transit power is 5 db. Area A denotes the inner round using IA, whereas area B denotes the outer circle using ultiplex. The inner average capacity is large when r 0 = 200 because the inner CUEs are closer to the BS, i.e., their path losses are saller than those of the outer CUEs. However, in this case, the outer average capacity is iniized when the utual interference is strong. Thus, the inner perforance has a positive overall ipact when r 0 is sall. In contrast, when r 0 = 400, the Table 5 Coplexity coparison Schees IA optial IA two-step IA rando Location-based Coplexity of the throughput calculation K rb C Nc Kc CNd Kd Krb K rbc Nc Kc CNd Kd K rbm K rb M Coplexity of the search C Nc Kc CNd K Kd rb C Nc Kc CNd Kd K rb K rb Schees Orthogonal optial Orthogonal two-step Orthogonal rando Coplexity of the throughput calculation K rb;c C Nc þ K Kc rb;d K d M K rb;c C Nc þ K Kc rb;d K d M K rb M Coplexity of the search K d^k rb;d þ C Nc K d K rb;d þ C Nc Kc ^K rb;c Schees Multiplex optial Multiplex two-step Multiplex rando Coplexity of the throughput calculation K rb C Nc Kc CNd Kd Krb K rbc Nc Kc CNd Kd K rbm Coplexity of the search K rb C Nc C Nc Kc CNd Kd Kc CNd Kd Kc K rb;c K rb K rb

14 Wang et al. EURASIP Journal on Wireless Counications and Networking (2015) 2015:145 Page 14 of 17 Figure 4 Average overall capacity under different schees and D2D pair utual distances ρ versus the DUE transit power. Figure 5 Average overall capacity of the location-based algorith using different inner round radii r 0 versus the DUE transit power.

15 Wang et al. EURASIP Journal on Wireless Counications and Networking (2015) 2015:145 Page 15 of 17 Figure 6 Overall throughput cuulative probability functions in different schees. Figure 7 Average overall throughput cuulative probability functions in different areas in the location-based algorith.

16 Wang et al. EURASIP Journal on Wireless Counications and Networking (2015) 2015:145 Page 16 of 17 outer average capacity is larger than the inner average capacity. This is ainly because the perforance of the outer circle is priarily deterined by that of the outer circle D2D users. The increase in the average distance between CUEs and DUEs leads to the decrease in utual interference; therefore, the D2D SINR increases. As a result, when r 0 is large, the outer perforance is beneficial to the whole. Therefore, to iprove the cell-edge perforance, a larger radius for the inner round can be eployed. Otherwise, the central perforance can be iproved when the radius of the inner round is decreased. 6 Discussions As well as [23,26], our research is based on the assuption of the global CSI known by transitters or central BS. In ters of the IA schee, the global CSI acquisition is an iportant proble and needs significant attention; otherwise, it will cause signals overhead. Jin et al. [34] provided a feedback topology design that can be used to acquire sufficient CSI and reduce signaling overhead. The ethod helps each transitter to easily acquire the knowledge of the CSI. However, if the CSI condition cannot be satisfied, the IA schee will suffer a perforance loss. Once it happens, we can only eploy statistical CSI as a replaceent for instant CSI. The result will ost likely be lower than the ultiplex perforance which does not require CSI knowledge. And this will ake the IA schee no sense. Additionally, the IA schee is to a great extent liited by the nuber of antennas and users. The investigated scenario is regarded as the cobination of ultiple access channel (MAC) [35] and K-user [23]. But to the best of our knowledge, there is no previous research on joint considering of MAC and K-user scenarios. In this paper, we ainly consider whether a feasible IA can iprove the syste perforance besides a feasibility evaluation. The feasible inequality condition (40) is sufficient but not necessary of IA. The condition is not so tight. Furtherore, the algorith convergence is ainly affected by IA and power control in this research. The linear IA [23] is used in this paper which only requires a few calculation steps for precoding and decoding and cannot lead to serious signaling overhead. In order to satisfy the feasibility of linear IA, the nuber of antennas and users should be ipleented appropriately. The iteration ethod is not our concern which has few differences with the linear ethod except for IA precoding and decoding. In ters of power control, the powers are iteratively odified by ΔP for the CUE target SINR. The solution will converge ore quickly if ΔP is bigger, but the syste will be unstable. We eploy an abandon echanis to guarantee convergence. If the nuber of iterations in an RB is ore than a critical value, the corresponding counications are abandoned and reallocated. This echanis can also prevent the syste fro signaling overhead. The CSI acquireent, feasibility, and convergence issues are very iportant but not copletely studied in this paper. In addition to the location-based algorith utilizing fractional frequency reuse (FFR) and soft frequency reuse (SFR) algoriths in ultiple-cell scenarios, they will be considered in our future work. 7 Conclusions In this paper, we consider a single-cell scenario of ultiple D2D counications underlaying MU-MIMO cellular uplink networks. First, we investigate IA and ultiplex schees in user clustering. The IA schee can eliinate interference, and it obtains higher perforance than the ultiplex schee in a large range of DUE-TX power. These two schees can achieve higher perforances copared to the orthogonal schee, which does not eploy user clustering. Second, we generalize a joint optiization proble of user clustering and resource allocation to axiize the overall throughput. To derive the solution, because the global optial ethod is an exhaustive search with very high coplexity, we propose a two-step algorith and a location-based algorith to reduce the coplexities with inial loss of perforance. The location-based algorith, coposed of IA and ultiplex schees, has both the low interference advantage of the IA schee and the easy ipleentation advantage of the ultiplex schee. The siulation results show that the proposed locationbased algorith produces low levels of utual interference for ultiplex users and that its perforance is near optial under low practical coplexity; therefore, it exhibits a good trade-off between perforance and coplexity. Finally, we evaluate the effect of the distance between D2D pairs and the effect of the appropriate inner round radius r 0 of the location-based algorith. The results show that it is better to keep the distance between DUE-TX and DUE-RX sufficiently sall to obtain a better perforance and that it is ore suitable to select a larger r 0 with a higher DUE-TX power condition. Copeting interests The authors declare that they have no copeting interests. Acknowledgeents This work is supported in part by the National Natural Science Foundation of China under Grant and in part by the National High-tech Research and Developent Progra of China under Grant 2014AA01A701. Received: 30 October 2014 Accepted: 11 April 2015 References 1. S Andreev, A Pyattaev, K Johnsson, O Galinina, Y Koucheryavy, Cellular traffic offloading onto network-assisted device-to-device connections. IEEE. Coun. Mag. 52(4), (2014)