Uplink User Selection Scheme for Multiuser MIMO Systems in a Multicell Environment

Transcription

1 Uplnk User Selecton Scheme for Multuser MIMO Systems n a Multcell Envronment Byong Ok Lee School of Electrcal Engneerng and Computer Scence and INMC Seoul Natonal Unversty leebo@moble.snu.ac.kr Oh-Soon Shn School of Electronc Engneerng Soongsl Unversty osshn@ssu.ac.kr Kwang Bok Lee School of Electrcal Engneerng and Computer Scence and INMC Seoul Natonal Unversty klee@snu.ac.kr Abstract We propose an nterference-aware user selecton scheme for uplnk multuser multple-nput multple-output MU- MIMO systems n a multcell envronment. The proposed scheme works n a dstrbuted manner. Each moble staton MS determnes ts transmt beamformng vector based on the locally avalable channel state nformaton CSI, and nforms the assocated base staton BS of the amount of potental nterference caused to adjacent cells along wth the resultng beamformng vector. Then, the BS selects a set of users to be served smultaneously wth consderaton of ntercell nterference. The 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. I. INTRODUCTION Multuser multple-nput multple output MU-MIMO s wdely accepted as a key technology for enablng hgh speed wreless access. In the uplnk MU-MIMO systems, multple moble statons MS s 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]-[3]. 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 [3], varous low-complexty 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. Recently, there have been several works on MIMO that account for the ntercell nterference n a multcell envronment [4]-[7]. In [4], t was reported that the performance of spatal multplexng MIMO scheme s sgnfcantly degraded n an nterference-lmted multcell envronment. In [5], 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 [6]. 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. In ths paper, we develop an nterference-aware user selecton scheme for uplnk MU-MIMO systems n a multcell envronment. The 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 nterference-aware beamformng proposed n [7], we can effectvely reduce the nterference caused to adjacent 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 adjacent cells as well as the desred lnk performance. The user selecton scheme s developed so to maxmze the sum rate or to acheve proportonal farness among users. For each objectve, 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. To the best of our knowledge, ths s the frst work to come up wth a dstrbuted uplnk MU-MIMO transmsson scheme n a multcell envronment. The rest of ths paper s organzed as follows. Secton II descrbes the system model. In Secton III, we explan dstrbuted beamformng schemes. In Secton IV, we propose an uplnk user selecton algorthm based on the beamformng vectors. Smulaton results are presented n Secton V, and conclusons are drawn n Secton VI. We defne here some notaton used throughout ths paper. We use boldface captal letters and boldface small letters to denote matrces and vectors, respectvely, T and H to denote transpose and conjugate 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.

2 II. 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. The k-thmsnthe-th cell s assumed to communcate wth the BS n the -th cell by usng a transmt beamformng vector. The receved sgnal vector y atthebsnthe-th cell can be expressed as y = ρ k H k x k k S + L j=1,j k S j, wk η k,j Hk,j wk j x k j + n, 1 where S denotes the set of selected users to be smultaneously served n the -th cell, x k denotes the nput symbol transmtted from the k-thmsnthe-th cell, H k,j denotes an N r N t channel matrx between the k-thmsnthej-th cell and the BS n the -th cell. We assume a flat fadng channel n both tme and frequency. The elements of H k,j and xk 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 k denotes the sgnal-to-nose rato SNR of the k-thmsnthe-th cell, and η k,j denotes the nterference-to-nose rato INR for the nterference that the k-thmsnthej-th cell causes to the BS n the -th cell. We assume that each BS performs a lnear mnmum meansquare error MMSE detecton to detect the desred sgnal. The MMSE combnng vector g k used n recevng the k-th MS s sgnal n the -th cell s expressed as H 1 g k = ρ k H k, wk K,k NI, 2 where K,k NI denotes the covarance matrx of the nose plus receved nterference sgnal whch s gven as K,k NI =I Nr + + L k S,k k η k,j j=1,j k S j H ρ k H k, w k H k, w k H H k,j wk j H k,j wk j.3 In 3, the frst term s due to the AWGN, and the second and thrd terms represent the ntracell nterference and ntercell nterference, respectvely. The post processng SINR of the k-th MS s sgnal n the -th cell s represented as H SINR k = ρ k H k, wk K,k NI 1 ρ k H k, wk. 4 Select users to be served Determne transmt beamformng vector Calculate the amount of nterference to adjacent cells Feed back transmt beamformng vector and the amount of nterference caused to adjacent cells The ndces of selected users wth MCS levels Data transmsson Fg. 1. The proposed approach for dstrbuted transmt beamformng and user selecton. Then, the achevable rate of the k-thmsnthe-th cell s calculated as r k = log1 + SINR k. 5 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 dstrbuted approach for determnng transmt beamformng vectors and the correspondng set of users, as llustrated n Fg. 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 adjacent cells. Then, each MS nforms the assocated BS of the amount of nterference to adjacent 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 MS s. The BS then broadcasts the ndces of selected users wth approprate modulaton and codng schemes MCS level. Fnally, the selected users transmt ther own data to the BS. We explan detals of the transmt beamformng and user selecton scheme n the followng two sectons. III. TRANSMIT BEAMFORMING 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,k D

3 and nterference generatng channel H,k for the k-thmsn the -th cell as H,k D = ρ k H k,, 6 η k 1, Hk 1,. H,k η k = 1, Hk 1, η k. 7 +1, Hk +1,. η k L, Hk L, We assume that the k-th MS can obtan H,k D and H,kH H,k by explotng the channel recprocty. Ths s possble for tme dvson duplex TDD systems. For example, the MS n the -th cell can estmate H,k D through downlnk sgnal that comes from the BS n the -th cell. Smlarly, the MS can determne H,kH H,k by estmatng the covarance matrx of aggregate nterference sgnals that come from adjacent cells durng the downlnk perod. Based on the above assumptons, we ntroduce two dstrbuted transmt beamformng schemes proposed n [7]: MAX-SNR beamformng and MAX-SNR beamformng. A. MAX-SNR Beamformng The MAX-SNR beamformng vector s constructed to maxmze the desred sgnal power wthout consderaton on the ntercell nterference. The MAX-SNR beamformng vector of the k-thmsnthe-th cell can be expressed as SNR =arg max H,k D 2 s.t. 2 =1. 8 The soluton of 8 can be obtaned as the egenvector correspondng to the largest egenvalue of H,kH D H,k D. B. MAX-SNR Beamformng The MAX-SNR beamformng vector s determned consderng not only the desred sgnal power but also the ntercell nterference caused to adjacent cells. The metrc called sgnal to generated nterference plus nose rato SNR at the k-th MS n the -th cell s defned as SNR k = H,k D 1+ H,k 2 2, 9 where the numerator corresponds to the desred sgnal power and the denomnator represents the nose plus nterference caused to adjacent cells by the the k-thmsnthe-th cell. The MAX-SNR beamformng vector maxmzes the SNR at each MS as SNR =arg max H,k D 2 1+ H,k 2 s.t. 2 =1. 10 The soluton of 10 can be obtaned as the egenvector correspondng to the largest egenvalue of 1 I Nt + H,kH H,k,kH H D H,k D. The MAX-SNR beamformng effectvely reduces the nterference to adjacent cells whle mantanng the desred sgnal power. It s shown n [7] that the MAX-SNR beamformng approxmately maxmzes the total sum rate for multple-nput sngle-output MISO systems n a two cell envronment. After determnng a transmt beamformng vector, each MS calculates the amount of nterference caused to adjacent cells as β k = H,k 2, 11 where β k denotes the amount of nterference caused to adjacent cell by the k-th MS n the -th cell. Note that β k depends on the transmt beamformng vector. Each MS nforms the assocated BS of and β k for user selecton. IV. USER SELECTION In ths secton, we develop user selecton schemes wth two dfferent objectves: sum rate maxmzaton and proportonal farness PF. For each objectve, we frst derve an optmal user selecton crteron and then propose a suboptmal dstrbuted algorthm wth low complexty. A. 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 =arg max S r k k S for =1, 2,..., L. 12 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 L S opt1, S opt2,..s optl = arg max. 13 r k S 1,S 2,..S L =1 k S The soluton of 13 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. The algorthm s descrbed as the followng steps. Step 1 Intalzaton: S = {}. Step 2 k new = arg max ΔCk. k Step 3 If ΔCk new > 0, then S = S {k new } 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 the Step 1, the set S of

4 selected users s ntalzed. In the 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 ΔCk denotes the amount of the change n the total sum rate when the k-th user s added to S. In the Step 3, f the addton of the selected user n the Step 2 ncreases the total sum rate, then the BS adds the user to S and goes back to the Step 2. Otherwse, the algorthm termnates and the fnal set of selected users s gven by S. The most challengng part of the above algorthm s to calculate ΔCk wthout sharng nformaton among neghborng cells. We can splt ΔCk nto two components as ΔCk =ΔC gan k ΔC loss k, 14 where ΔC gan k denotes the sum rate ncrement n the -th cell by addng the k-th user to S, and ΔC loss k denotes the sum rate decrement n adjacent cells by addng the k-th user to S due to the ncreased nterference. The BS can easly calculate ΔC gan k as ΔC gan k = k S {k} k S {k} r k r k k S k S {k}. 15 However, t s dffcult to calculate ΔC loss k n the dstrbuted manner, snce ΔC loss k s dependent on the set of selected users n adjacent cells. Instead of drectly calculatng ΔC loss k, we propose to estmate ΔC loss k based on β k whch s fed back from the k-th MS n the -th cell. Note that β k represents the amount of nterference caused to adjacent cells by selectng the k-th user n the -th cell. The man dea s to estmate ΔC loss k by calculatng the sum rate decrement n the -th cell to whch the BS belongs, wth addtonal nterference wth the power β k. Then the estmated sum rate decrement Δ C loss k n adjacent cell can be expressed as Δ C loss k = r k r k β k, 16 where r k β k denotes the achevable rate of the k -th user n the -th cell wth addtonal nterference of the power β k. From 15 and 16, the estmated ΔCk can be obtaned as Δ Ck=ΔC gan k Δ C loss k = k S {k} r k β k r k k S. 17 The proposed algorthm requres at most KN r computatons of Δ Ck per cell, snce users are successvely selected. B. Proportonal Farness The proportonal farness PF schedulng effectvely provdes a trade-off between the average throughput and farness among users [8]. The conventonal PF schedulng was orgnally proposed for a sngle cell envronment. In ths case, each BS selects users as S CONV =arg max S K k=1 k log R for =1, 2,..., L, 18 R k denotes the average throughput estmate of the s calculated where k-th user n the -th cell. We assume that Rk as R k t = 1 1 Rk T c t T c r k t 1 1 Rk T c t 1, f served at t, f not served at t 19 where T c s the tme constant of the averagng wndow. The soluton of 18, 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 = arg max S 1,S 2,..S L U 1, 20 where U 1 s the system-wde PF utlty functon expressed as U 1 = L K =1 k=1 k log R. 21 As n 13, the optmal soluton of 20 needs centralzed optmzaton among cells. Here, we also propose a suboptmal dstrbuted algorthm. Instead of U 1 n 20, we use another utlty functon U 2 gven as U 2 = L =1 k S 1+ 1 r k R k. 22 The optmzaton problem 20 remans the same even though U 1 s replaced wth U 2. The proof s omtted due to space lmtatons. The 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 = {}. Step 2 k new = arg max ΔU 2 k. k Step 3 If ΔU 2 k new > 0, then S = S {k new } 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 IV-A, except that ΔCk s replaced by ΔU 2 k, whch denotes the amount of the change n U 2 when the k-th user s added to S. As n 14, ΔU 2 k can be expressed as ΔU 2 k =ΔU 2gan k ΔU 2loss k, 23 where ΔU 2gan k denotes the ncrement of U 2 n the -th cell by addng the k-th user to S, whch can be expressed as ΔU 2gan k= 1+ 1 r k k S {k} R k 1+ 1 r k. 24 R k k S

5 Fg. 2. The average achevable sum rate per cell vs. the number of users for N t = N r =2. ΔU 2loss k n 23 denotes the decrement of U 2 n adjacent cells by addng the k-th user to S due to the ncreased nterference. Lke the approach used for the total sum rate maxmzaton, we propose to estmate ΔU 2loss k as ΔŨ2lossk= 1+ 1 r k k S {k} R k 1+ 1 r k j β k. 25 k S {k} R k Then, by usng 24 and 25, the estmaton of ΔU 2 k can be found as ΔŨ2k= k S {k} k S r k j β k r k j R k R k. 26 Ths algorthm also requres at most KN r computatons of ΔŨ2k per cell. V. SIMULATION RESULTS In ths secton, we evaluate the performance of the transmt beamformng and user selecton algorthms dscussed n Sectons III and IV usng computer smulatons. We consder a wrap-around hexagonal model wth 7 cells. There 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 k and η k,j n 1 can be expressed as ρ k =10 s k, 10 d k, α k P, 27 Fg. 3. The average achevable sum rate per cell vs. the number of users for N t = N r =4. η k,j =10s k,j 10 d k,j α k P j, 28 where d k,j s the dstance between the BS n the -th cell and the k-th MS n the j-th cell, α s the path loss exponent, and s k, 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 3.7, 8dB, and 10dB, respectvely. We frst consder user selecton for the sum rate maxmzaton. Fgs. 2 and 3 depct the average achevable sum rate per cell vs. the number of users for N t = N r = 2 and N t = N r =4, respectvely. It s shown that the MAX-SNR beamformng outperforms the MAX-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 =16and 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 MAX-SNR beamformng s adopted. Under the same condtons, the gan of the MAX-SNR beamformng over the MAX-SNR beamformng s 0.65 bps/hz, when the proposed user selecton scheme s appled. Now we consder the case of the PF utlty. Fgs. 4 and 5 depct the system-wde PF utlty U 1 and the average achevable sum rate per cell, respectvely, vs. tme for K =16, N t = N r = 2, and T c = 200 slots. As n the case of the sum rate maxmzaton, the MAX-SNR beamformng outperforms the MAX-SNR beamformng, and the proposed user selecton scheme outperforms the conventonal one. Cor-

6 MAX-SNR beamformng provdes the best performance. Fg. 4. The system-wde PF utlty vs. tme for K =16and N t = N r =2. VI. CONCLUSIONS In ths paper, 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 adjacent 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. ACKNOWLEGDEMENT Ths work was supported by the Natonal Research Foundaton of KoreaNRF grant funded by the Korea governmentmest No REFERENCES Fg. 5. The average achevable sum rate per cell vs. tme for K =16and N t = N r =2. respondngly, the proposed user selecton scheme wth the [1] K.-N. Lau, Analytcal framework for multuser uplnk MIMO spacetme schedulng desgn wth convex utlty functons," IEEE Trans. Wreless Commun., vol. 3, pp , Sept [2] Y. Hara, L. Brunel, and K. Oshma, Uplnk spatal schedulng wth adaptve transmt beamformng n multuser MIMO systems," n Proc. IEEE Inter. Symp. Personal, Indoor, and Moble Rado Commun. 2006, Helsnk, Fnland, Sept [3] S. Serbetl and A. Yener, Beamformng and schedulng strateges for tme slotted multuser MIMO systems," n Proc. Aslomar Conf. Sgnals, Systems and Computers, pp , Nov [4] S. Catreux, P. F. Dressen, and L. J. Greensten, Smulaton results for an nterference-lmted multple-nput multple-output cellular system," IEEE Commun. Lett., vol. 4, pp , Nov [5] R. S. Blum, MIMO capacty wth nterference," IEEE J. Select. Areas Commun., vol. 21, pp , June [6] S. Ye and R. S. Blum, Optmzed sgnalng for MIMO nterference systems wth feedback," IEEE Trans. Sgnal Processng, vol. 51, pp , Nov [7] B. O. Lee, H. W. Je, I. S. Sohn, O.-S. Shn, and K. B. Lee, Interferenceaware decentralzed precodng for multcell MIMO TDD systems," n Proc. IEEE Global Commun. Conf. 2008, New Orleans, USA, Nov [8] A. Jalal, R. Padovan, and R. Pankaj, Data throughput of CDMA- HDR a hgh effcency-hgh data rate personal communcaton wreless system," n Proc. IEEE Veh. Technol. Conf. 2000, Tokyo, Japan, May 2000, pp