Perforance of Multiuser MIMO Syste Eploying Bloc Diagonalization with Antenna Selection at Mobile Stations Feng Wang, Mare E. Bialowsi School of Inforation Technology and Electrical Engineering The University of Queensland Brisbane, Australia {fwang, eb}@itee.uq.edu.au Abstract This paper reports investigations into capacity of a ultiuser Multiple-Input Multiple-Output (MIMO) syste which uses a bloc diagonalization (BD) schee with antenna selection at obile stations (MSs). It is shown that the antenna selection at MSs iproves capacity while at the sae tie it offers an effective solution to hardware size and cost. Also it is advantageous fro the point of view of siplicity of signal processing at obile stations. Two antenna selection schees are investigated, one is the nor-based selection and the other is project-axiization selection. The siulations results show that the project-axiization selection is superior over the nor-based selection. eywords- MIMO; Bloc Diagonalization; Broadcasting; Antenna Selection I. ITRODUCTIO ) Recent years have shown a considerable shift of research on MIMO fro point-to-point to ultiuser systes [1][4]. The initial studies concerning a point-to-point MIMO syste have shown a linear iproveent in capacity with an increase of iniu nuber of transit and receive antennas in a rich scattering environent. Recent inforation theories on a ultiuser MIMO syste have proved that the su broadcasting capacity can be achieved by Dirty Paper Coding (DPC) [3][4]. owever, the ipleentation of an optial broadcasting schee is coputationally intensive and coplicated. Because of these reasons there has been a continuing search for siple suboptial transission schees. One of the proising schees is a Bloc Diagonalization (BD) schee [5][6]. It enables the base station (BS) to transit the signal to ultiple Mobile Users (MS) by using orthogonal beaforing weights. With BD, each MS bea-foring weights lie in the null space of all other MSs channels. This is equivalent to having orthogonal effective MIMO channels to different MSs. Since BD represents a low coputation intensive broadcasting schee and its perforance is acceptable, BD is under constant research. In [7], a BD algorith that accounts for the presence of other-cell interferences was proposed under the assuption that the transitter has full Channel State Inforation (CSI) in addition to the inforation about the interference plus noise covariance atrix for in-cell users. In [8], the perforance of BD was investigated assuing presence of spatial correlation and utual coupling in transitting and receiving array antennas. More recent trends include concepts of ultiuser grouping and antenna selection for BD [9][10]. owever, the wors accoplished so far proposed on antenna selection schees for BD require the base station having a full nowledge of channel state inforation (CSI) for all the receiving antennas including non-active ones. This creates a heavy load on uplins for obile users when operated in FDD odel. In this letter, our ai is to deonstrate that it is possible to avoid the above-entioned proble by perforing antenna selection at MSs independently. This operation requires uch less feedbac bits and uch lower coputation coplexity at BS. The structure of this letter is as follows. In section II, the signal and channel odels are introduced. Section III describes the receiver structure with antenna selection and BD receiving antenna selection schee. Section IV presents nuerical results deonstrating the perforance of the proposed schee. Finally, section V provides conclusions. II. SIGAL AD CAEL MODEL A. Signal Model We consider a ultiuser MIMO syste consisting of a base station and obile users all equipped with ultiple antennas. Only the downlin case is considered, in which the base station transits signals while obile users receive the. It is postulated that the base station includes transitting antennas and there are L downlin obile users around a base station (BS). At tie t, obile stations (MS) fro L available users are scheduled to be serviced by BS. The th obile station (MS) eploys M antennas. The transitted signal intended for the th obile station is denoted by the Q 1 diensional vector x which is weighted by the Q pre-processing atrix W before transission. Q is the nuber of parallel data sybols transitted siultaneously to the th MS. The MIMO channel between the BS the th MS is described by the coplex atrix, whose (i,j) th entries represent the coplex gains between the j th transit antenna at BS and i th antenna at th MS. It is assued that different MS experience independent fading. The received signal at th MS can be presented by 978-1-444-6893-5/$6.00 C 010 IEEE V1-671
y W E x n 1 WEx WEx n j j j j1, j (1) R MS 1,1 1, M M,1 M, M (4) where trace(e E ) = p is the power transitted to the th MS. n is the additive Gaussian white noise (AWG) vector, whose eleents are independent identical distribution (i.i.d.) zero-ean circularly syetric coplex Gaussian rando variables with variance n. In turn, the correlation atrix for BS can be obtained fro R BS 1,1 1,,1, (5) Figure 1. Signal odel of a downlin MIMO ultiuser syste. B. Channel Model The properties of the channel atrix describing the channel between BS and the th MS are influenced by the transitting and receiving antenna arrays in addition to a signal propagation environent. ere, it is assued that the lins between BS and different MSs do not share the sae scattering environent. This assuption re-confirs the earlier assuption that the signal fading is independent for different MSs. For each lin, the ronecer channel odel [11] is assued. In this odel, the correlations at transitter and receiver sides are independent and the channel atrix is represented as 1/ 1/ R G R () MS BS III. BLOC DIAGOALIZATIO WIT MULTIUSER ATEAS SELECTIO In this section, the ulti-users MIMO syste structure is described. Under the assuption that the obile users do not share the sae scattering environent, obile users perfor the channel estiation independently. Also they independently do antenna selection and feed bac the channel state inforation for the selected antenna subset to the base station. AS a result, the obile user s antenna selection does not ipact the bea-foring at the base station for other obile users. Further, assuing that there is no cooperation between MSs, this schee greatly reduces the feedbac load for uplin. A. Multiuser Antenna Selction In the proposed syste, the obile users perfor antenna selection and feed bac the channel state inforation corresponding to the selected antennas to the base station independently. This eans that the antenna selection schees proposed for point-to-point MIMO systes can be applied [1][13]. Figure shows the bloc diagra of the obile users structure with antenna selection, where the th MS is equipped with M receiving antennas and L RF chains and L is always equal or less than M. where G is a atrix with i.i.d. Gaussian entries with zero ean and unit variance and R MS and R BS are spatial correlation atrices at the th MS and BS, respectively. In a rich scattering environent, the correlation for any pair of dipole eleent with spacing d,n can be obtained using Clar s odel and are given by a Bessel function J ( d ) (3) n, 0 n, Using (3), the correlation atrix for the th generated as MS can be Figure. Receivers structure with antenna selection. Assuing that the perfect channel state inforation is available at obile users via reliable channel estiate techniques, it is always possible to select the best antenna with respect to soe reference standard. The th MS needs to V1-67
select only L receiving antennas out of the M available antennas for the L RF chains and downconverts their signals for further processing. This is equivalent to selecting L rows out of the M rows of the whole channel atrix. The ost straightforward and siple ethod of antenna selection is to select the L rows with the largest Euclidean nor. This ethod is referred to as nor-based selection (BS) ethod [14]. owever, BS does not offer a robust antenna selection algorith. In the case when L > 1, BS ay lead to a reduced capacity in soe scenarios. When the MSs only see the channel state inforation for theselves, the ost straightforward and feasible selection standard for the th MS is related to the axiu channel capacity between the base station and the obile user itself. owever, axiization of the capacity requires the coputation of capacity for any possible cobinations of L receiving antennas. Achieving this goal is coputationally intensive and thus non-feasible for a obile user. This is because a obile unit with liited coputational resources favors a fast near-optial antenna selection schee with low coputational coplexity [14]. Assuing that the th MS selects one antenna at one step, L steps are required to coplete the whole selection procedure. Assuing that at step l+1, the receive antenna corresponding to the th row of is selected, the capacity between the base station and the th MS is given by [1] l 1 l ( ) log 1 l 1 C deti (6) oting that 1 1 h l l l l h (7) and subitting (7) into (6), the capacity can be rewritten as l1 ( ) C log det I h l l h Applying the Sheran-Morrison forula for deterinants, (8) can rewritten as [14] l1 l ( ) ( ) ( ) Capacityincreent C C C h where the capacity increent can be expressed as Ch ( ) logdet 1 1 l l I h h (8) (9) (10) To axiize the capacity, the antenna selection schee needs to select the row of the channel atrix with the largest capacity increent in (10) at step l+1. Fro a geoetrical viewpoint this is equivalent to selecting the row with the largest projection length to the space spanned by the selected coluns. The resulting optiization schee is referred to as project-axiizing selection (PMS). The MS eeps repeating the process, until all the optial L rows are selected. B. Bloc diagonalizaiton with antenna selection Assue that the channel state inforation obtained by the th MS for the selected antennas is fed bac to the base station without any uplin errors, the base station can use the obtained channel atrix for data transission. The channel atrix used e used for data transission between BS and the th MS is given as h h h h h h 11 1 1 1 L h h h L1 L L L (11) This atrix is a sub-atrix of the atrix that appears in (). The rows of atrix is (11) are selected by the th MS fro the rows of (). Therefore, using an antenna selection schee at MSs, the base station can support ore MSs at the sae tie with bloc diagonalization downlin broadcasting schee. This is under the condition Therefore, the previous restriction that L (1) M (13) does not need to be aintained any ore. The base station broadcasts inforation via the assigned MIMO channels by MSs. At the th MS, the received signal is given as y L L j j j j1, j W E x W E x n (14) To enable the users to receive their own data with zero co-channel interference, the base station has to apply the transit bea-foring weights according to the following rule V1-673
ˆ W null L1 1 L 1 1 L 1 1 L ˆ (15) where null (A) denotes the null space of the atrix A. Fro (15) it can be seen that the MSs antenna selection governed by (11) does not ipact the design of the beaforing atrix for the MSs. This is because different antenna selections generate different null spaces. By perforing the eigenvalue decoposition (EVD) over the non-negative eritian Matrix, one obtains ˆ ˆ 0V [ V, V] (16) 0 0 V where ( ) denotes the conjugate transpose operation. It can be seen fro (16) that V is the atrix with the coluns given by the eigenvectors corresponding to the zero eigenvalues. Its diension is O, where O ax 0, L i1, i By letting W = V, a perfect null steering to all the undesired -1 MSs can be achieved. Then the effective channel atrix between BS and the th MS is given by V (18) eff L We can see fro (18) that the effective channel atrix for the th MS is coposed as a product of two ters. The first ter describes the antenna selection obtained by the th MS itself. The second ters coes fro the eigenvalue decoposition of the atrix fored by other MSs antenna selection results. By feeding bac the whole channel state inforation (not the channel state inforation only for the selected antenna); it is possible to optiize the design of bea-foring atrices for all the MSs in a cooperative anner, which can render a further increase in broadcasting capacity. owever, the cooperative ethod requires a uch higher load on uplin resource. Also it requires intensive coputations at BS. Because we assue that the MSs operate independently, the deand on uplin resources is liited and coputational coplexity at BS is relatively low. By repeating the steps shown by expressions (15) and (16), all the bea-foring atrices and effective channel atrices can be obtained. In this way, the ultiuser MIMO i downlin syste is decoposed into independent singleuser MIMO systes with orthogonal effective MIMO channels. IV. UMERICAL RESULTS Monte Carlo siulations are perfored to investigate the perforance of the proposed syste. We select the su rate capacity as the perforance etric for the proposed broadcasting syste. We assue that the transit power is allocated to the users equally. In this case, the su rate capacity can be expressed as C I su I tx eff eff log det I n P (19) In the undertaen siulation, it is assued that the base station is equipped with =10 antenna eleents, and =4 obile users are scheduled and under service of base station. Each obile user is equipped with L = RF chains, which eans the obile user needs to select best antennas fro all the M available antennas which are available. The intereleent distance is fixed to 1.0 for the antenna array at BS and 0.5 for the array at MSs. In the following siulations, this syste is referred to as (L /M ) syste. Figure3 shows the coparison for the su rate capacity obtained for BS and PMS schees. Outage Capacity(C(x)<C) 1 Without 0.9 Antenna Selection 0.8 0.7 0.6 0.5 0.4 0.3 0. 0.1 4X(/4X10) 4X(/4X10) 4X(/6X10) W/O AS PMS BS 0 0 4 6 8 10 1 14 16 Su Rate Capacity (bps/z) Figure 3. The su rate capacity with antenna selection schees at obile users in the proposed syste when SR is 0dB. As seen in Figure 3, the antenna selection techniques iprove the su capacity for the syste with BD broadcasting schee. Also observed in Figure 3 is that PMS outperfors BS. The perforance gap between PMS and BS increases with increasing receiving antenna nubers. Figure 4 shows the siulation results for the su rate capacity as a function of the MSs receive antenna nuber. With respect to the two schees, PMS outperfors BS siilarly as it has been earlier observed for results shown in V1-674
Figure3. The perforance gap increases with increasing the nuber of receiving antennas at MSs. Su Rate Capacity(bps/z) 10 9 8 7 6 5 4 3 PMS 4X(/sX10) BS 4X(/sX10) 4 6 8 10 1 14 16 18 0 Receive Antenna uber at MSs (s) Figure 4. Su rate capacity Vs receive antenna nuber at obile users in the syste of 4(/s10) when SR is 0dB. Figure 5 shows the su rate capacity versus the antenna nuber at BS for BS and PMS selection schees. Su Rate Capacity(bps/z) 1 11 10 9 8 7 6 5 4 3 BS X(/4Xbs) BS X(/6Xbs) PMS X(/4Xbs) PMS X(/6Xbs) 4 6 8 10 1 14 16 18 0 4 6 8 30 Antenna uber at Base Station (bs) Figure 5. Su rate capacity Vs transit antenna nuber at base station in the proposed syste when SR is 0dB. Fro results presented in Figure 5 it is seen that increasing the nuber of transitting antennas brings ore freedo for the bloc diagonalization broadcasting schee. The plots show an increasing su rate capacity with increasing the nuber of transitting antennas. owever, the increent of the su rate capacity is going to be stagnating when increasing the transit antenna nuber at BS. V. COCLUSIOS This paper has reported investigations into capacity of a ultiuser Multiple-Input Multiple-Output (MIMO) syste using a bloc diagonalization (BD) schee with antenna selection at obile stations (MSs). It has been shown that antenna selection at MSs iproves the ulti-user MIMO syste capacity. Two antenna selection schees have been investigated; one being the nor-based selection and the other one project-axiization selection. The siulations results have shown that the project-axiization selection is superior over the nor-based selection. ACOWLEDGMET F. Wang acnowledges the support of University of Queensland in the for International Postgraduate Research Scholarship (IPRS). REFERECES [1] I. E. Telatar, Capacity of ulti-antenna Gaussian channels, Euro Transactions on Telecounications, no.10, pp.585-595, 1999 [] D. Gesbert, M. ountouris, R. W. eath Jr., C Chae,. T. Salzer, Shifting the MIMO paradig, Signal Processing Magazine, Vol. 4, Issue 5, pp.36-46, Sep. 007 [3] W. Weingarten, Y. Steinberg and S. Shaai, The capacity region of the Gaussian ultiple-input ultiple-output broadcast channel, IEEE Trans. on Inforation Theory, vol.5, no.9, pp.3936-3964, Sep. 006 [4] R. Choi, M. T. Ivrlac, R. D. Murch and W. Utschic, On strategies of ultiuser MIMO transit signal processing, IEEE trans. on wireless counications, Vol.3, o.6, pp1936-1941, ov. 004 [5] Q.. Spencer, A. L. Swindlehurst, M. aardt, Zero-forcing ethods for downlin spatial ultiplexing in ulti-user MIMO channels, IEEE Trans. on Inforation Theory,vol.4, no.3, pp.461-471, Feb. 004. [6] L. U. Choi, R. D. Murch, A transit preprocssing technique for ulti-user MIMO systes using a decoposition approch, IEEE Trans. On Wireless Counications, vol.3, no.1, pp.0-4, Jan. 004 [7] S. Shi, J.S. wa, R. W. eath and J. Andrews, Bloc Diagonalization for ulti-user MIMO with other-cell interference, IEEE Trans. on Wireless Counications, vol.7, issue.7, Jul. 008. [8] F. Wang, M. E. Bialowsi and X. Liu, Perforance of Bloc Diagonalization Broadcasting Schee for Multiuser MIMO Syste Operating in Presence of Spatial Correlation and Mutual Coupling International Journal of Counications, etwor and Syste Science, Vol.3, o. 3,pp.66-7, 010 [9] S. Sigdel and W. A. rzyie&nacute, Siplified antenna selection and user scheduling for orthogonal space-division ultiplexing, in Proc. IEEE WCC, pp. 1730-1735, 007. [10] A. Ghaznavi, M. Ardebilipoor, Joint user scheduling and receive antenna selection in ultiuser MIMO downlin with other cell interference, in Proc. TELFOR, pp45-455, 009 [11] C.. Chuah, D.. C. Tse, and J. M. ahn, Capacity scaling in MIMO wireless systes under correlated fading, IEEE Trans. On Inforation Theory, vol. 48, pp. 637-650, Mar. 00 [1] A. F. Molisch, M. Z. Win, MIMO systes with antenna selection, IEEE Microwave Magazine, pp.46-56, Mar. 004 [13] S. Sanayei,A. osratinia, Antenna selection in MIMO systes, IEEE Counications Magazine,Vol.4, Issue 10, pp.68-73, Oct. 004 [14] M. Gharavi- Alhansari, A. B. Gershan, Fast antenna subset selection in MIMO systes, IEEE Trans. On Signal Processing, vol 5, o., pp. 339 347, Feb 004 V1-675