Distributed user selection scheme for uplink multiuser MIMO systems in a multicell environment

Transcription

1 Lee et al. EURASIP Journal on Wreless Communcatons and Networkng 212, 212:22 RESEARCH Dstrbuted user selecton scheme for uplnk multuser MIMO systems n a multcell envronment Byong Ok Lee 1, Oh-Soon Shn 2* and Kwang Bok Lee Open Access Abstract We propose an nterference-aware user selecton scheme for uplnk multuser multple-nput multple-output systems n a multcell envronment. he proposed scheme works n a dstrbuted manner. Each moble staton determnes ts transmt beamformng vector based on the locally avalable channel state nformaton, and nforms the assocated base staton (BS) of the amount of potental nterference caused to adacent cells along wth the resultng beamformng vector. hen, the BS selects a set of users to be served smultaneously wth consderaton of ntercell nterference. he user selecton scheme s devsed ether to maxmze the sum rate or to acheve proportonal farness among users. For each case, we derve an optmal user selecton crteron and propose a suboptmal dstrbuted user selecton algorthm wth low complexty. Smulaton results confrm that the proposed scheme offers sgnfcant throughput enhancement due to reducton of the ntercell nterference n a multcell envronment. Introducton Multuser multple-nput multple-output (MU-MIMO) s wdely accepted as a key technology for enablng hghspeed wreless access. In the uplnk MU-MIMO systems, multple moble statons (MSs) are allowed to smultaneously transmt ther sgnals to the base staton (BS) to ncrease the system capacty. Under ths scenaro, the system performance may depend on the set of transmttng users and ther transmt beamformng vectors [1-]. In [1], a general framework for transmt beamformng and user selecton was developed based upon general convex utlty functons. In [2], successve user selecton algorthms were proposed along wth optmzaton of transmt beamformng vectors. In [], varous lowcomplexty beamformng and user selecton schemes were proposed. All these works, however, have dealt wth only a sngle cell envronment where the ntercell nterference does not exst. Intercell nterference s one of the most crtcal factors that lmt the performance of cellular systems, especally for low-frequency reuse factor. here have been several * Correspondence: osshn@ssu.ac.kr 2 School of Electronc Engneerng, Soongsl Unversty, Seoul 1-7, South Korea Full lst of author nformaton s avalable at the end of the artcle works on MIMO that account for the ntercell nterference n a multcell envronment [-7]. In [], t was reported that the performance of spatal multplexng MIMO scheme s sgnfcantly degraded n an nterference-lmted multcell envronment. In [], an optmal MIMO transmsson strategy was studed when the channel state nformaton (CSI) s not avalable at the transmtter. For the case when the CSI s avalable at the transmtter, a centralzed precodng scheme that maxmzes the total sum rate was proposed n []. In [7], a precodng scheme was proposed to maxmze the total sum rate n a dstrbuted manner. However, these works have been based on a sngle user MIMO system where only one MS s served at a tme. MU-MIMO systems were only recently nvestgated n a multcell envronment [8-1]. In [8], downlnk multcell MU-MIMO systems were dscussed from the aspects of tradeoffs, overhead, and nterference control. In [9], schedulng schemes were developed for the downlnk multcell MIMO systems. Uplnk MU-MIMO systems were analyzed n [1] n the case that the adacent BS s are allowed to cooperate. In ths artcle, we develop an nterference-aware user selecton scheme for uplnk MU-MIMO systems n a 212 Lee et al.; lcensee Sprnger. hs s an Open Access artcle dstrbuted under the terms of the Creatve Commons Attrbuton Lcense ( whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal work s properly cted.

2 Lee et al. EURASIP Journal on Wreless Communcatons and Networkng 212, 212:22 Page 2 of 1 multcell envronment. he scheme comprses of two steps and works n a dstrbuted manner. In the frst step, each MS determnes ts transmt beamformng vector. By utlzng the prevous result on the nterferenceaware beamformng proposed n [7], we can effectvely reduce the nterference caused to adacent cells. In the second step, each BS selects a set of users to be served smultaneously to realze multuser dversty wth consderaton of nterference caused to adacent cells as well as the desred lnk performance. he user selecton scheme s developed so to maxmze the sum rate or to acheve proportonal farness among users. For each obectve, we derve an optmal user selecton crteron and propose a suboptmal dstrbuted user selecton algorthm wth low complexty. Smulaton results are provded to show the throughput enhancement of the proposed scheme. he rest of ths artcle s organzed as follows. Secton 2 descrbes the system model. In Secton, we explan dstrbuted beamformng schemes. In Secton, we propose an uplnk user selecton algorthm based on the beamformng vectors. Smulaton results are presented n Secton, and conclusons are drawn n Secton. We defne here some notaton used throughout ths artcle. We use boldface captal letters and boldface small letters to denote matrces and vectors, respectvely, () and () H to denote transpose and conugate transpose, respectvely, det() to denote determnant of a matrx, tr() to denote trace of a matrx, () 1 to denote matrx nverson, to denote Eucldean norm of a vector, I N to denote the N N dentty matrx. System model We consder the uplnk of an MU-MIMO system comprsed of L cells where there are K users n each cell. Each MS and each BS are equpped wth N t transmt antennas and N r receve antennas, respectvely. he kth MS n the th cell s assumed to communcate wth the BS n the th cell by usng a transmt beamformng vector w kþ. he receved sgnal vector y at the BS n the th cell can be expressed as y ¼ k2s þ L qffffffffffffff ¼1;¼ k2s ρ kþ H kþ ; w kþ qffffffffffffff x kþ η kþ ; H kþ ; w kþ x kþ þ n ; 1Þ where S denotes the set of selected users to be smultaneously served n the th cell. We assume that the maxmum number of selected users per cell s N r. x kþ denotes the nput symbol transmtted from the kth MS n the th cell, H kþ denotes an N r N t channel matrx ; between the kth MS n the th cell and the BS n the th cell. We assume a flat fadng channel n both tme and frequency. he elements of H kþ ; and x kþ are assumed to be ndependent and dentcally dstrbuted (..d.) crcularly symmetrc complex Gaussan random varables wth zero mean and unt varance. In (1), n denotes the addtve whte Gaussan nose (AWGN) vector at the BS n the th cell wth each element havng unt varance, ρ kþ denotes the sgnal-to-nose rato (SNR) of the kth MS n the th cell, and η kþ ; denotes the nterference-tonose rato (INR) for the nterference that the kth MS n the th cell causes to the BS n the th cell. We assume that each BS performs a lnear mnmum mean-square error (MMSE) detecton to suppress the resdual nterference and detect the desred sgnal. he MMSE combnng vector g kþ used n recevng the kth MS s sgnal n the th cell s expressed as qffffffffffffff H 1; g kþ ¼ ρ kþ H kþ ; w kþ K ;kþ NI 2Þ where K ;kþ NI denotes the covarance matrx of the nose plus receved nterference sgnal whch s gven as K ;kþ NI ¼ I Nr þ ρ k Þ H k Þ ; w k Þ k 2S ;k ¼k þ L η k Þ ; H k Þ ; w k Þ ¼1;¼ k 2S H k Þ ; w k Þ H H: H k Þ ; w k Þ Þ In (), the frst term s due to the AWGN, and the second and thrd terms represent the ntracell nterference and ntercell nterference, respectvely. he post processng SINR of the kth MS s sgnal n the th cell s represented as qffffffffffffff H SINR kþ ¼ ρ kþ H kþ ; w kþ K ;kþ 1 qffffffffffffff NI ρ kþ H kþ ; w kþ : Þ hen, the achevable rate of the kth MS n the th cell s calculated as ¼ log 1 þ SINR kþ : Þ r kþ Snce the achevable rate s affected by the ntercell nterference, the optmal desgn for transmt beamformng and user selecton needs a system-wde centralzed optmzaton, whch requres a lot of feedback and huge sgnalng overhead among cells, makng the algorthm mpractcal. Instead of a centralzed approach, we take a

3 Lee et al. EURASIP Journal on Wreless Communcatons and Networkng 212, 212:22 Page of 1 dstrbuted approach for determnng transmt beamformng vectors and the correspondng set of users, as llustrated n Fgure 1. In the frst step, each MS determnes ts transmt beamformng vector based on the locally avalable CSI and calculates the amount of potental nterference caused to adacent cells. hen, each MS nforms the assocated BS of the amount of nterference to adacent cells along wth the determned beamformng vector. In the second step, each BS selects a set of users to be smultaneously served based on the nformaton receved from MSs. he BS then broadcasts the ndces of selected users wth approprate modulaton and codng schemes level. Fnally, the selected users transmt ther own data to the BS. It must be noted that the proposed approach based on the local CSI wll provde a more practcal soluton than the centralzed optmzaton from the vewpont of feedback overhead and computatonal complexty, although t may not guarantee the optmalty. We explan detals of the transmt beamformng and user selecton scheme n the followng two sectons. ransmt beamformng In ths secton, we explan transmt beamformng schemes that were proposed n [7] for the case of sngle user MIMO n a multcell envronment. We assume that each MS ndependently determnes ts transmt beamformng vector based on the locally avalable CSI. We defne the desred channel H ;kþ D and nterference generatng channel H ;kþ for the kth MS n the th cell as qffffffffffffff H ;kþ D ¼ ρ kþ H kþ ; ; Þ 2 qffffffffffffff η kþ 1; H kþ 1;.. qffffffffffffffffffff H ;kþ η kþ 1;H kþ 1; ¼ qffffffffffffffffffff : 7Þ η kþ þ1;h kþ þ1;. 7 qffffffffffffff η kþ L; H kþ L; H ;kþ We assume that the kth MS can obtan D and H ;kþ H H ;kþ by explotng the channel recprocty. hs s possble for tme dvson duplex systems. For example, the MS n the th cell can estmate H ;kþ D through downlnk sgnal that comes from the BS n the th cell. Smlarly, the MS can determne H ;kþ H H ;kþ by estmatng the covarance matrx of aggregate nterference sgnals that come from adacent cells durng the downlnk perod. Based on the above assumptons, we ntroduce two dstrbuted transmt beamformng schemes proposed n [7]: MA-SNR beamformng and MA-SNR beamformng. Fgure 1 he proposed approach for dstrbuted transmt beamformng and user selecton.

4 Lee et al. EURASIP Journal on Wreless Communcatons and Networkng 212, 212:22 Page of 1 MA-SNR beamformng he MA-SNR beamformng vector s constructed to maxmze the desred sgnal power wthout consderaton on the ntercell nterference. he MA-SNR beamformng vector of the kth MS n the th cell can be expressed as w kþ SNR w kþ H ;kþ D w kþ 2 s:t:w kþ 2 ¼ 1: 8Þ he soluton of (8) can be obtaned as the egenvector correspondng to the largest egenvalue of H ;kþh H ;kþ D D. MA-SNR beamformng he MA-SNR beamformng vector s determned consderng not only the desred sgnal power, but also the ntercell nterference caused to adacent cells. he metrc called sgnal to generated nterference plus nose rato (SNR) at the kth MS n the th cell s defned as SNR kþ ¼ ;kþ HD w kþ 2 Þ w kþ 1 þ H ;k 2 ; 9Þ where the numerator corresponds to the desred sgnal power and the denomnator represents the nose plus nterference caused to adacent cells by the kth MS n the th cell. he MA-SNR beamformng vector maxmzes the SNR at each MS as arg max kþ SNR ¼ w 1 þ H ;k ¼ 1: w kþ H ;kþ D Þ w kþ w kþ 2 2 s:t:w k Þ 2 1Þ he soluton of (1) can be obtaned as the egenvector correspondng to the largest egenvalue of 1H I Nt þ H ;kþ H H ;kþ ;kþ D H H ;kþ D. he MA-SNR beamformng effectvely reduces the nterference to adacent cells whle mantanng the desred sgnal power. It s shown n [7] that the MA-SNR beamformng approxmately maxmzes the total sum rate for multplenput sngle-output systems n a two-cell envronment. After determnng a transmt beamformng vector, each MS calculates the amount of nterference caused to adacent cells as β kþ ¼ H ;k Þ w kþ 2 ; 11Þ where β kþ denotes the amount of nterference caused to adacent cell by the kth MS n the th cell. Note that β kþ depends on the transmt beamformng vector. Each MS nforms the assocated BS of w kþ selecton. and β kþ for user User selecton In ths secton, we develop user selecton schemes wth two dfferent obectves: sum rate maxmzaton, and proportonal farness (PF). For each obectve, we frst derve an optmal user selecton crteron and then propose a suboptmal dstrbuted algorthm wth low complexty. Sum rate maxmzaton We begn wth a conventonal user selecton algorthm for sum rate maxmzaton, whch was proposed for a sngle cell envronment. In ths case, each BS selects users to maxmze only the sum rate of ts own cell as S CONV S r k Þ k2s for ¼ 1; 2;...; L: 12Þ However, ths soluton s not optmal n a multcell envronment due to the ntercell nterference. In order to maxmze the total sum rate of the L cells, we modfy the formulaton of (12) as S opt1 ; S opt2 ;...; S optl L r k Þ S 1 ;S 2 ;::S L Þ ¼1 k2s : 1Þ he soluton of (1) can only be obtaned through centralzed optmzaton among cells, whch requres perfect CSI, a lot of sgnalng overhead among cells, and very hgh computatonal complexty. As a more practcal soluton, we propose a suboptmal dstrbuted user selecton algorthm wth low complexty. he algorthm s descrbed as n the followng steps. Step 1. Intalzaton: S ¼ fg: Step 2. k new k ΔCk Þ. Step. If ΔCk new Þ >, then S ¼ S [ fk new g and go back to the Step 2; otherwse termnate the algorthm. Each BS ndependently selects users to be served by usng the above algorthm. In Step 1, the set S of selected users s ntalzed. In Step 2, the BS chooses one user among the users not n S so as to maxmze the amount of the change n the total sum rate. Note that ΔCkÞ denotes the amount of the change n the total sum rate when the kth user s added to S. In Step, f the addton of the selected user n Step 2 ncreases the total sum rate, then the BS adds the user to S and goes back to Step 2. Otherwse, the algorthm termnates and the fnal set of selected users s gven by S. he most challengng part of the above algorthm s to calculate ΔCkÞ wthout sharng nformaton among

5 Lee et al. EURASIP Journal on Wreless Communcatons and Networkng 212, 212:22 Page of 1 neghborng cells. We can splt ΔCkÞ nto two components as From (1) and (1), the estmated obtaned as ΔCkÞ can be ΔCkÞ ¼ ΔC gan kþδc loss kþ; 1Þ where ΔC gan kþ denotes the sum rate ncrement n the th cell by addng the kth user to S, and ΔC loss kþ denotes the sum rate decrement n adacent cells by addng the kth user to S due to the ncreased nterference. he BS can easly calculate ΔC gan kþ as ΔC gan kþ ¼ : 1Þ k 2S k 2S [ fkg However, t s dffcult to calculate ΔC loss kþ n the dstrbuted manner, snce ΔC loss kþ s dependent on the set of selected users n adacent cells. Instead of drectly calculatng ΔC loss kþ, we propose to estmate ΔC loss kþ based on β kþ whch s fed back from the kth MS n the th cell. Note that β kþ represents the amount of nterference caused to adacent cells by selectng the kth user n the th cell. he man dea s to estmate ΔC loss kþ by calculatng the sum rate decrement n the th cell to whch the BS belongs, wth addtonal nterference wth the power β kþ. hen the estmated sum rate decrement Δ~C loss kþ n adacent cell can be expressed as Δ~C loss kþ ¼ ~ β kþ ; 1Þ k 2S [ fkg k 2S [ fkg where ~r k Þ β kþ denotes the achevable rate of the k th user n the th cell wth addtonal nterference of the power β kþ, and t can be calculated as ~r k Þ β kþ ¼ log 1 þ SINR k Þ β kþ ; 17Þ where k SINR Þ ~K ;k NI Þ β kþ β kþ ¼ qffffffffffffffff H ¼ ρ k Þ H k Þ ; w k Þ K ~ ;k Þ NI qffffffffffffffff ρ k Þ H k Þ Þ ; β kþ ; w k 1 β kþ H k ; w k 18Þ 1 þ N r I Nr þ P k 2S ;k ¼k ρ k Þ Þ Þ H H k Þ Þ þ L ; w k Þ Þ Þ η k ; H k ; w k ¼1;¼ k 2S H H k Þ Þ : 19Þ ; w k Δ~C kþ ¼ ΔC gan kþδ~c loss kþ ¼ ~ β kþ k2s : 2Þ k 2S [ fkg he proposed algorthm requres at most KN r computatons of Δ ~C kþ per cell, snce users are successvely selected. Proportonal farness he proportonal farness (PF) schedulng effectvely provdes a trade-off between the average throughput and farness among users [11]. he conventonal PF schedulng was orgnally proposed for a sngle cell envronment. In ths case, each BS selects users as S CONV K S k¼1 ¼ 1; 2;...; L; log R kþ for 21Þ where R kþ denotes the average throughput estmate of the kth user n the th cell. We assume that R kþ s calculated as 8 >< R kþ Þ¼ t >: 1 1 R kþ t 1Þþ 1 r kþ Þ; t c c 1 1 R kþ t 1Þ; c f served at t f not served at t 22Þ where c s the tme constant of the averagng wndow. he soluton of (21), however, does not guarantee the system-wde PF due to the ntercell nterference. We consder an optmal user selecton crteron for the system-wde PF, whch can be expressed as S opt1 ; S opt2 ;...; S optl Þ; 2Þ S 1 ;S 2 ;::S L where U 1 s the system-wde PF utlty functon expressed as U 1 ¼ L K ¼1 k¼1 log R k Þ Þ U 1 : 2Þ As n (1), the optmal soluton of (2) needs centralzed optmzaton among cells. Here, we also propose a suboptmal dstrbuted algorthm. Instead of U 1 n (2), we use another utlty functon U 2 gven as U 2 ¼ YL Y 1 þ 1 r kþ : 2Þ ¼1 k2s c 1 R kþ

6 Lee et al. EURASIP Journal on Wreless Communcatons and Networkng 212, 212:22 Page of 1 As provded n the Appendx, the optmzaton problem (2) remans the same even though U 1 s replaced wth U 2. he use of U 2 enables the user selecton algorthm to work n a dstrbuted fashon wth low computatonal complexty. Based on the newly defned utlty functon U 2, the proposed algorthm works as follows. Step 1. Intalzaton: S ¼ fg. Step 2. k new k ΔU 2 kþ. Step. If ΔU 2 k new Þ >, then S ¼ S [ fk new g and go back to the Step 2, otherwse termnate the algorthm. Note that the above algorthm s the same as the dstrbuted algorthm developed n Secton.1, except that ΔCkÞ s replaced by ΔU 2 kþ, whch denotes the amount of the change n U 2 when the kth user s added to S. As n (1), ΔU 2 kþ can be expressed as ΔU 2 kþ ¼ ΔU 2gan kþδu 2loss kþ; 2Þ where ΔU 2gan kþ denotes the ncrement of U 2 n the th cell by addng the kth user to S, whch can be expressed as ΔU 2gan kþ ¼ Y 1 þ 1 k 2S [ fkg c 1 Y 1 þ 1 k 2S c 1 R k Þ R k Þ : 27Þ ΔU 2loss kþ n (2) denotes the decrement of U 2 n adacent cells by addng the kth user to S due to the ncreased nterference. Lke the approach used for the total sum rate maxmzaton, we propose to estmate ΔU 2loss kþ as Δ ~U 2loss kþ ¼ Y 1 þ 1 k 2S [ fkg c 1 R k Þ 1 Y 1 þ 1 ~ β A: c 1 Þ k 2S [ fkg R k 28Þ hen, by usng (27) and (28), the estmaton of ΔU 2 kþ can be found as 1 Δ ~U 2 kþ ¼ Y k 2S [ 1 þ 1 c 1 Y 1 þ 1 k 2S c 1 ~ β kþ R k Þ R k Þ : A 29Þ hs algorthm also requres at most KN r computatons of Δ ~U 2 kþ per cell. Smulaton results In ths secton, we evaluate the performance of the transmt beamformng and user selecton algorthms dscussed n Sectons and usng computer smulatons. We consder a wrap-around hexagonal model wth seven cells as shown n Fgure 2. here are K users per cell who are assumed to be unformly dstrbuted over the cell. Each channel between the MS and BS s assumed to experence an ndependent long-term fadng comprsed of the path loss and log-normal shadow fadng. Correspondngly, ρ kþ and η kþ n (1) can be expressed as ρ kþ ¼ 1 η kþ ; ¼ 1 ; s kþ ; αp 1 d kþ kþ ; ; s kþ ; αp 1 d kþ kþ ; ; Þ where d kþ ; s the dstance between the BS n the th cell and the kth MS n the th cell, α s the path loss exponent, and s kþ ; s a zero-mean Gaussan random varable that stands for the shadow fadng. It s assumed that the long-term power control perfectly compensates for the long-term fadng so that a gven target SNR s satsfed at the BS. In the followng smulaton, the path loss exponent, log standard devaton of the shadow fadng, and the target SNR are set to.7, 8 db, and 1 db, respectvely. We frst consder user selecton for the sum rate maxmzaton. Fgures and depct the average achevable sum rate per cell versus the number of users for Fgure 2 Wrap-around hexagonal model wth seven cells. 1 2

7 Lee et al. EURASIP Journal on Wreless Communcatons and Networkng 212, 212:22 Page 7 of 1 Average achevable rate (bps/hz) centralzed user selecton wth MA-SNR BF proposed user selecton wth MA-SNR BF proposed user selecton wth MA-SNR BF conventonal user selecton wth MA-SNR BF conventonal user selecton wth MA-SNR BF conventonal user selecton wthout BF Number of users Fgure he average achevable sum rate per cell versus the number of users for N t = N r =2. N t = N r = 2 and N t = N r =, respectvely. he performance of the centralzed user selecton derved from an exhaustve search s plotted together as an upper bound. However, the results are provded only up to eght users due to very hgh computatonal complexty. It s shown that the MA-SNR beamformng outperforms the MA-SNR beamformng, and the proposed user selecton scheme outperforms the conventonal one. It must be noted that the proposed user selecton gan ncreases wth the number of users, and that the gan s more dstngushed than the beamformng gan. For the case of K = 1 and N t = N r = 2, for example, the proposed user selecton scheme s shown to provde as much as 2.72 bps/hz mprovement over the conventonal user selecton scheme, when the MA-SNR beamformng s adopted. Under the same condtons, the gan of the Average achevable rate (bps/hz) centralzed user selecton wth MA-SNR BF proposed user selecton wth MA-SNR BF proposed user selecton wth MA-SNR BF conventonal user selecton wth MA-SNR BF conventonal user selecton wth MA-SNR BF conventonal user selecton wthout BF Number of users Fgure he average achevable sum rate per cell versus the number of users for N t = N r =.

8 Lee et al. EURASIP Journal on Wreless Communcatons and Networkng 212, 212:22 Page 8 of 1 Average amount of generated nterference (db) proposed user selecton wth MA-SNR BF proposed user selecton wth MA-SNR BF conventonal user selecton wth MA-SNR BF conventonal user selecton wth MA-SNR BF conventonal user selecton wthout BF Number of users Fgure he average amount of generated nterference per cell versus the number of users for N t = N r =2. MA-SNR beamformng over the MA-SNR beamformng s. bps/hz, when the proposed user selecton scheme s appled. Fgure depcts the average amount of generated nterference per cell for N t = N r =2. It s shown that the proposed user selecton scheme consderably reduces the generated nterference especally for a large number of users. Now we consder the case of the PF utlty. Fgures and 7 depct the system-wde PF utlty U 1 and the average achevable sum rate per cell, respectvely, versus tme for K = 1, N t = N r =2, and c = 2 slots. As n the case of the sum rate maxmzaton, the MA-SNR beamformng outperforms the MA-SNR beamformng, and the proposed user selecton scheme outperforms the conventonal one. he results n Fgure also mply that the proposed scheme mproves the farness among users as compared to the conventonal scheme. Correspondngly, the proposed user selecton scheme -1-1 proposed user selecton he System-wde PF Utlty conventonal user selecton proprosed user selecton MA-SNR BF proprosed user selecton wth MA-SNR BF conventonal user selecton wth MA-SNR BF conventonal user selecton wth MA-SNR BF conventonal user selecton wthout BF 1 2 me Fgure he system-wde PF utlty versus tme for K = 1 and N t = N r =2.

9 Lee et al. EURASIP Journal on Wreless Communcatons and Networkng 212, 212:22 Page 9 of 1 Average Achevable Rate (bps/hz) proprosed user selecton MA-SNR BF proprosed user selecton wth MA-SNR BF conventonal user selecton wth MA-SNR BF conventonal user selecton wth MA-SNR BF conventonal user selecton wthout BF proposed user selecton conventonal user selecton me Fgure 7 he average achevable sum rate per cell versus tme for K = 1 and N t = N r =2. wth the MA-SNR beamformng provdes the best performance. Concluson In ths artcle, we have developed an nterference-aware dstrbuted user selecton scheme for uplnk MU-MIMO systems n a multcell envronment. Multple transmt antennas at each MS are utlzed for transmt beamformng to reduce the nterference caused to adacent cells. Multple receve antennas at each BS are utlzed for recevng the sgnals from the selected users and suppressng ntercell nterference. We have derved system-wde optmal user selecton crtera and proposed dstrbuted user selecton algorthms wth low complexty. Smulaton results have shown that the proposed user selecton scheme provdes sgnfcant performance mprovement n a multcell envronment. Appendx S opt1 ; S opt2 ;::S optl L K S 1 ;S 2 ;::S L Þ ¼1 S 1 ;S 2 ;::S L Þ L ¼1 k2s S 1 ;S 2 ;::S L logr kþ Þ t Þ U 1 logr k Þ Þþ t L Þ 1 logr k Þ Þ t A ¼1 S 1 ;S 2 ;::S L Þ B S 1 ;S 2 ;::S L Þ@ L ¼1 L log 1 1 R kþ t 1Þþ 1 r kþ þ L k2s c c log 1 1 R kþ t 1 c 1 1 R kþ t 1Þ c ¼1 k2s þ L ¼1 k=2s Þþ L ¼ R kþ t 1ÞA c ¼1 k=2s log 1 þ 1 r kþ 1 k2s c 1 R kþ t 1Þ C A S 1 ;S 2 ;::S L Þ L K ¼1 k¼1 log 1 1 R kþ t 1 c Þþ L ¼1 log 1 þ 1 r kþ k2s c 1 R kþ t 1Þ

10 Lee et al. EURASIP Journal on Wreless Communcatons and Networkng 212, 212:22 Page 1 of 1 L S 1 ;S 2 ;::S L Þ ¼1 Y L S 1 ;S 2 ;::S L Þ ¼1 Þ: U 2 S 1 ;S 2 ;::S L Þ log 1 þ 1 r kþ k2s c 1 R kþ t 1Þ Y 1 þ 1 r kþ k2s c 1 R kþ t 1Þ 11. A. Jalal, R. Padovan, R. Panka, Data throughput of CDMA-HDR a hgh effcency-hgh data rate personal communcaton wreless system, n Proceedng of IEEE Vehcular echnology Conference-Sprng (, okyo, Japan, 2), pp vol. do:1.118/ Cte ths artcle as: Lee et al.: Dstrbuted user selecton scheme for uplnk multuser MIMO systems n a multcell envronment. EURASIP Journal on Wreless Communcatons and Networkng :22. Competng nterests he authors declare that they have no competng nterests. Acknowledgment hs work was supported n part by the Natonal Research Foundaton of Korea (NRF) grant funded by the Korea government (MES) (No. 29 8), and n part by the KCC (Korea Communcatons Commsson), Korea, under the R&D program supervsed by the KCA (Korea Communcatons Agency) (KCA ). Author detals 1 Modem System Lab, Samsung Electroncs, Suwon -72, South Korea. 2 School of Electronc Engneerng, Soongsl Unversty, Seoul 1-7, South Korea. School of Electrcal Engneerng & Computer Scence, Seoul Natonal Unversty, Seoul 11-72, South Korea. Receved: February 212 Accepted: 12 May 212 Publshed: 21 June 212 References 1. K.N. Lau, Analytcal framework for multuser uplnk MIMO space-tme schedulng desgn wth convex utlty functons. IEEE rans. Wrel. Commun. (9), (2) 2. Y. Hara, L. Brunel, K. Oshma, Uplnk spatal schedulng wth adaptve transmt beamformng n multuser MIMO systems, n Proceedng of IEEE Internatonal Symposum on Personal, Indoor and Moble Rado Communcatons, Helsnk, Fnland, September 2.. do:1.119/ PIMRC.2.2. S. Serbetl, A. Yener, Beamformng and schedulng strateges for tme slotted multuser MIMO systems, n Proceedng of Aslomar Conference on Sgnals, Systems, and Computers, Pacfc Grove, CA USA, 1st edn., 2, pp S. Catreux, P.F. Dressen, L.J. Greensten, Smulaton results for an nterference-lmted multple-nput multple-output cellular system. IEEE Commun. Lett. (11), (2). R.S. Blum, MIMO capacty wth nterference. IEEE J. Sel. Areas Commun. 21 (), (2). S. Ye, R.S. Blum, Optmzed sgnalng for MIMO nterference systems wth feedback. IEEE rans. Sgnal Process. 1(11), (2) 7. B.O. Lee, H.W. Je, O.S. Shn, K.B. Lee, A novel uplnk MIMO transmsson scheme n a multcell envronment. IEEE rans. Wrel. Commun. 8(1), (29) 8. S.A. Ramprashad, H.C. Papadopoulos, A. Benebbour, Y. Kshyama, N. Jndal, G. Care, Cooperatve cellular networks usng mult-user MIMO: tradeoffs, overheads, and nterference control across archtectures. IEEE Commun. Mag. 9(), 7 77 (211) 9. M. Kobayash, M. Debbah, J. Belfore, Outage effcent strateges for network MIMO wth partal CSI, n Proceedng of IEEE Internatonal Symposum on Informaton heory (, Seoul, Korea, 29), pp do:1.119/ ISI J. Hoyds, M. Kobayash, M. Debbah, Optmal channel tranng n uplnk network MIMO systems. IEEE rans. Sgnal Process. 9(), (211) Submt your manuscrpt to a ournal and beneft from: 7 Convenent onlne submsson 7 Rgorous peer revew 7 Immedate publcaton on acceptance 7 Open access: artcles freely avalable onlne 7 Hgh vsblty wthn the feld 7 Retanng the copyrght to your artcle Submt your next manuscrpt at 7 sprngeropen.com