Beam Selection and Antenna Selection: A Hybrid Transmission Scheme over MIMO Systems Operating with Vary Antenna Arrays

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1 It. J. Commuicatios, Network ad System Scieces, 2, 4, doi:.4236/ijcs Published Olie October 2 ( Beam Selectio ad Atea Selectio: A ybrid Trasmissio Scheme over MIMO Systems Operatig with Vary Atea Arrays Feg Wag, Marek E. Bialkowski School of Iformatio Techology ad Electrical Egieerig, Uiversity of Queeslad Brisbae, Brisbae, Australia {fwag, meb}@itee.uq.edu.au Received July 3, 2; revised August 24, 2; accepted September 5, 2 Abstract I this paper, we have proposed a hybrid trasmissio scheme which ivolves beam selectio ad atea selectio techiques over a MIMO system operatig with vary atea array. Optimal subset of trasmit ateas are selected via fast successive selectio scheme desiged to optimize the target eigebeam. Optimal eigebeams correspodig to the largest sigular values of the ew MIMO chael formed by the selected ateas are exploited for data trasmissio. To evaluate the performace of the proposed scheme, differet array structures, icludig uiform liear array (ULA) ad icludig uiform circular array (UCA) are employed i the simulatios. The trasmitter is assumed to be surrouded by scatterig objects while the receiver is postulated to be free from scatterig objects. The Laplacia distributio of agle of arrival (AoA) of a sigal reachig the receiver is postulated. The results preseted by this paper idicate that the proposed scheme ca sigificatly improve the performace of data trasmissio i term of symbol error rate (SER). Keywords: MIMO, Beam Selectio, Atea Selectio, ULA, UCA. Itroductio I recet years, wireless multiple-iput multiple-output (MIMO) systems featured by employig multiple ateas at the trasmitter ad receiver have attracted costat attetio. Research has revealed that MIMO is capable of improvig system capacity ad lik robustess sigificatly i a rich scatterig eviromet without costig extra trasmit power ad badwidth [-3]. The data trasmissio schemes over a MIMO chael ca be categorized ito three types. The first oe is multiplexig gai maximizig schemes, which are exploited to trasmit idepedet data streams i parallel through multiple spatial chaels. Bell Labs Layered space-time (BLAST) techiques [4,5] are typical multiplexig schemes to icrease the data rate. The secod oe is diversity gai maximizig schemes, which are exploited to combat the fadig effect of wireless chael ad improve the biterror-rate (BER) performace. To obtai the diversity gai, the sigals carryig the same iformatio are trasmitted through redudat idepedet fadig chaels. As a result, the data trasmissio reliability is assured. Space-time codig techiques [6,7] are typical schemes of exploitig spatial diversity. owever, maximizig multiplexig gai may ot ecessarily maximize diversity gai ad vice versa. Cosequetly, scholars also tried to achieve trade-off betwee the multiplexig ad diversity gai [8]. With the perfect chael state iformatio (CSI), the optimal desig, i terms of maximum data rate is multichael beamformig (MB) [9]. This strategy trasmits data o the eigemodes (or eigebeams) of the MIMO chael usig liear trasmit-receive processig [,2]. It has bee well oted that the eigemodes correspodig to the small sigular values are showig a poor performace. Targetig at this problems, power allocatig ad bit-loadig schemes were proposed i []. By allocatig differet power ad costellatios amog a subset of available eigemodes, a sigificatly improved performace ca be achieved. The complexity of such a scheme is sigificat sice each chael eigemode requires a differet combiatio of sigal costellatio ad codes, depedig o the allocated power [3]. For this reaso, equal power ad bit allocatio scheme is still a popular trasmissio scheme. With equal power ad bit allocatio, a improved performace ca also be obtaied by

2 F. WANG ET AL. 639 selectig the optimal eigemodes (which are correspodig to the largest sigulars) [9]. Atea selectio (AS) has bee proposed for ehaces performace i correlated fadig [4,5]. By selectig a small umber of optimal ateas from a large set of ateas, AS is capable of capturig a large portio of the chael capacity of MIMO [9]. AS also results i a reduced hardware cost ad computatioal complexity [7]. AS have received a plety of attetios. A couple of atea selectio criteria have bee studied i [4]. To avoid the theory-optimal exhaustive search scheme, fast ateas selectio schemes have bee proposed [7-9]. I this paper, we proposed a hybrid trasmissio scheme over a MIMO system, i where, the optimal eigemodes for the optimal atea subset are employed to trasmit data. To achieve this goal, a fast atea selectio scheme desiged for the eigebeam selectio is proposed. The performace of the proposed scheme is evaluated i a spatial correlatio fadig eviromet. Previous researches show that spatial correlatio always has a egative impact o the MIMO performace [2,22]. It ca be expected that differece cofiguratios of atea arrays will result i differet spatial correlatios of trasmitted ad received sigals. As a result, the chael properties betwee the trasmitter ad receiver could be differet. I this paper, we select uiform liear array (ULA) ad uiform circular array (UCA) as the objects. owever, it is worthwhile oticig that we ca reach similar coclusios by reasoig the similarity betwee UCA ad other alike structures such as triagular, square, petagoal or hexagoal arrays. This paper is orgaised as follows. I Sectio 2, we briefly itroduce the sigal model ad chael model which are used i the rest of the paper. I Sectio 3, the hybrid scheme is preseted by itroducig the eigebeam selectio scheme with LMMSE receiver ad the fast atea selectio scheme desiged for the eigebeam selectio scheme. I Sectio 4, we provide error rate results to show the performace of the proposed scheme i spatial correlated fadig chaels. Coclusios are give i Sectio Sigal Model 2.. System Model Cosider a wireless MIMO system employig N trasmit ad M receiver ateas, The impulse respose for the MIMO chael ca be modeled by a M N matrix with the (m,) th elemet cotaiig the complex fadig parameter betwee the th trasmit ad m th receive atea. The basebad equivalet sigal model ca be represeted by r X () M N r is the received sigal vector, X M represets the trasmitted sigal vector, is the additive white Gaussia oise vector with covariace matrix give by E 2 I M (2) We assume that perfect Chael State Iformatio (CSI) is available for both the receiver ad trasmitter sides. The trasmitted sigal vector ca be writte as X ws (3) where N w L, L mi N, M is the trasmit adaptive switchig matrix which maps the L modulated data symbols s i ( i L ) oto the N trasmit ateas. The symbol s i is the elemets of s, with E {ss } = I L, ad chose from all possibly sigal costellatios. X is subject to the power costrait, which is give by 2.2. Chael Model 2 E X tr ww E (4) 2 s We assume that the wireless MIMO lik betwee the trasmitter ad receiver is udergoig a flat-fadig arrow-bad fadig. The Kroecker model [2] is utilized, i where the spatial correlatios at the trasmitter ad receiver are idepedet ad separable. As a result, the complex chael matrix ca be give as R GR (5) 2 2 R T where R R is the spatial correlatio matrix at the receiver ad RT represets the spatial correlatio at the trasmitter. I a scatterig rich sigal propagatio eviromet, the atea array is surrouded by scatterig objects. Based o the assumptio that these scatterig objects are uiformly distributed i a circle, the correlatio experieced by a pair of ateas with large iter-ateas spacig i a array ca be writte as R ( m, ) J [2 ( m ) ] (6) O the other had, if the atea array is free from ay surroudig objects, the correlatios matrices at the trasmitter ad receiver sides are subjective to the array structure. Figure demostrates the model uder cosidered, where the receiver are surrouded by uiformly distributed scatterers ad trasmitter equipped with ULA or UCA is located high above groud where there are o scatterig objects. All the atea elemets at receiver ad trasmitter have a omi-directioal radiatio patter i the azimuth plae. The θ is the cetral Agle of Departure (AoD) or Agle of Arrival (AoA), we assume

3 64 F. WANG ET AL. Figure. Sigal model of a dowlik MIMO multiuser system. that θ follows the Laplacia distributio. For the case of ULA, the real ad imagiary compoets of the spatial correlatio parameter betwee the m th ad th elemets are give as [23] 2 a a a e Re R J Z 2 J Z cos(2 k ) Im m, l 2 2 2k l k a 4k R m, l 2 2 2k l k a (2k) a a a e 4C J Z si2k Similarly, for the case of UCA, the real ad imagiary compoets of spatial correlatio parameter betwee the m th ad th elemets are give as [23] Re R m, 2 a a a e J Z 2 J Z cos k c 2 2 2k c k a 4k 2 (7) (8) (9) Im R m, l 2 2 2k c k a (2k ) a a a e 4C J Z si 2k ( ) () I the expressios (7)-(), a is the decay factor related to the agle spread, specifically, as a icreases, the agle spread decreases. It also decides the ormalizig costat [23] a Cl () a 2e J represets the th order Bessel fuctio of the first kid. The parameter α is the relative agle betwee the m th ad th elemets i a UCA. Let φ m ad φ represet the agle of the m th ad th elemets i a azimuth plae, the we have si cos cos cos 22 cos m si si m 22 cos m m (2) Z l ad Z c are related to the atea spacig i ULA ad UCA, they ca be expressed as 2d Zl m (3) 2R Zc 22cosm (4) The formulas (7)-() show that the spatial correlatios betwee two atea elemets i a ULA ad UCA are characterized by a couple of parameters, icludig iter-elemet spacig (d/λ or d/lambda), AoA ad decay factor. Figure 2 shows the spatial correlatio betwee the atea ad 2 i regards to iter-elemet spacig with differet decay factors. We ca see from Figure 2 that for both ULA ad UCA, large decay factors result i a icreased spatial correlatio. Figure 3 ad Figure 4 are the correlatio surface i regards to the iter-elemet spacig ad AoA. Oe ca see from Figure 3 ad Figure 4 that for a give iter-elemet spacig, the spatial correlatio i a ULA icrease sigificatly with AoA (it becomes more apparet whe iter-elemet spacig is larger tha.5), while i a UCA the spatial correlatio remais almost costat i regards to AoA. 3. Beam Selectio ad Atea Selectio: A ybrid Scheme I this sectio, we preset the ideal of the hybrid tras-

4 F. WANG ET AL. 64 Spatial Correlatio UCA a=3 UCA a=.2 UCA a=3 ULA a=3. ULA a= ULA a = d/lambda Figure 2. Spatial correlatio betwee atea ad 2 (four-atea ULA ad UCA, AoA = ). Spatial Correlatio AoA(degrees) 2 d/lambda 2 3 Figure 3. Spatial correlatio betwee atea ad 2 (four-atea ULA, decay factor = 5). Spatial Correlatio d/lambda AoA(degrees) Figure 4. Spatial correlatio betwee atea ad 2 (four-atea UCA, decay factor = 5).

5 642 F. WANG ET AL. missio scheme by itroducig beam selectio scheme ad atea selectio scheme respectively. Logically, the desig of atea selectio scheme ad performace metrics is based o beamformig ad beam selectio scheme. The beamformig ad beam selectio scheme are based o the curret chael statio iformatio, ad the atea selectio scheme is goig chage the MIMO chael matrix. Cosequetly, beamformig ad beam selectio is carried out after atea selectio. I our scheme, beamformig ad beam selectio is performed at trasmitter side, ad atea selectio ca be implemeted at either trasmitter or receiver side. 3.. Beam Selectio Scheme We assume that atea selectio scheme has fiished. The output of the atea selectio scheme is a ew chael matrix betwee the trasmitter ad receiver with smaller dimesios (smaller umber of colums for trasmits atea selectio ad smaller umber of rows for receives atea selectio). We represet the ew complex matrix as ca be give as ˆ ( P M, Q N PQ ). Without loss of geerality, we assume that P Q. As a result, by applyig SVD techique, the complex chael ca be give as ˆ UΣV PQ d uu P vvq U d P V (5) where( ) deotes the hermitia operatio ad d p is the p th o-egative sigular values with d d 2 d P ad U ad V are the left ad right uitary matrices, respectively. We have PP U U I QQ (6) VV I I fact, V is the matrix with all the colums are the eigevectors of ˆ ˆ, which is related to the eige-modes of the MIMO commuicatio chael. The equatio (5) ca be writte i a differet way, which is give as ˆ ˆ V VΣ Σ (7) For trasmit beamformig, the optimal beam directios are alog the eigevectors of the ˆ ˆ [2]. I other words, eige-beamformig [9,2] utilized the eige-modes of the auto-correlated ˆ Ĥ to trasmit sigal symbols. By assumig that there are L (L mi (P, Q)) data streams are beig trasmitted to the receiver, the L colums of V correspodig to the L largest eige-values are selected as the trasmittig beamformig matrix. Cosequetly, the received sigal vector is give as Es r V ˆ Ls N (8) By weightig the received sigal vector, the estimated data at the receiver ca be defied as s F r (9) The error vector the ca be give as e s s (2) The mea squared error (MSE) matrix will be the defied as the covariace matrix of the error vector, which ca be preseted as E E ˆ ˆ ee F R F r I F V L V F L (2) where ˆ ˆ Rr VLVL R (22) The MSE of the l th symbol trasmitted to the receiver is the l th diagoal elemet of E. Give the trasmit beamformig matrix V L, the optimal receive matrix F opt is obtaied such that diagoal elemets of E are miimized. This is equivalet to the solve mi c Ec mi Tr( Ecc ), c (23) F F By settig the gradiet of (23) to zero, ad particularizig c for all the vectors of the caoical base, it follows that ˆ ˆ F ˆ opt VLVL R V L (24) which is the liear miimum MSE (LMMSE) receiver (Wieer solutio). With this choice of liear receive ad trasmit filterig, the MIMO chael is decomposed ito L parallel eigemode sub-chaels, with each ca be expressed as s ˆ,,, l l dl plsl l l L (25) where l is a costat, which does ot affect the received sub-chael SNR, p l is the trasmit power allocated to the l th subchael ad d l is the l th largest sigular value of ˆ ( P M, Q N PQ ). The istataeous received SNR via the l th suchael is give by 2 dl pl l, l,, L 2 (26) Clearly, the overall received SNR ca be lower bouded by 2 dl pl SNRoverall 2 (27) 3.2. Atea Selectio Scheme Equatio (27) shows that the received SNR for the MIMO system with the choice of trasmits ad receives

6 F. WANG ET AL. 643 matrices is lower bouded by a mootoically icreasig fuctio of the L th largest sigular value of Ĥ. I the case that all the sigulars are exploited for data trasmissio, the received SNR the will be lower bouded by a mootoically icreasig fuctio of the smallest sigular value of Ĥ, which is cofirmed i [4,6]. As a result, to match the aforemetioed beam selectio scheme, the atea selectio scheme i this paper is to seek the subset of trasmit ateas ad receive ateas with the largest L th largest sigular value. A optimal selectio ca be achieved by exhaustively searchig over all possible combiatios trasmit ad receive ateas. owever, such a exhaustive search is hardly suitable for real-time implemetatio because of prohibitively log computatioal time. A umber of complexity reduced atea selectio schemes [7-9] have bee proposed, however these atea selectio schemes are targetig at maximizig the chael Shao capacity. I this paper, we utilize the successive selectio approach which was firstly described i [8] i the cotext of chael capacity. owever, i this paper, the target of the atea selectio has chaged to maximizig the L th largest sigular value of Ĥ. Without loss of geerality, we assume that the subset of atea selectio is performed at the receiver side. The receive atea selectio approach begis with full set of receive ateas available ad the removes oe of receive atea per step. I each step, the atea with the smallest cotributio to the L th largest sigular value of the updated chael matrix is removed. This process is repeated util the required umber of ateas remaied. This approach ca also be straightforwardly applied to the trasmitter atea selectio. Assume that we select O (M O L) out of M available receive ateas. The selectio algorithm ca be preseted as follows Set G MN, Pt for i to ( M O), for j to ( M Pt) T T T T UpdateG: [ g,, g j, g j,, gmpt]; Calculate SVD over updated G ed th fid pˆ : argmi L Largest sigular of G jpˆ ( MPt) T T T T pˆ pˆ MPt UpdateG: [ g,, g, g,, g ]; Update Pt : Pt ed let ˆ : G (28) The strategy requires M-O iteratios, ad the i th iteratio requires M-I + space searches. As a result, the size of the search space is give as MO S M i (29) i which is far less tha the oe obtaied from the exhaustive search scheme. For istace, the total search space for the exhaustive search scheme amouts to 82 whe O = 4 ad M = 6, while for the fast search employed i this paper oly 26 iteratios are used. 4. Numerical Results Moto-carol simulatios are performed to evaluate the performace of the proposed scheme i term of symbol-error-rate (SER). QPSK modulatio with Gray codig is used for the data streams. By assumig that a Gray ecodig is employed to map the bits ito the costellatio poit, the bit-error-rate (BER) ca be approximately obtaied from SER by BER SER R (3) where R = log 2 K is the umber of bits per symbol ad K is the costellatio size. Figure 5 shows the SER performace of trasmit atea selectio without beam selectio. We assume that LMMSE receiver is employed. For simplicity reaso, the complex Rayleigh chael is utilized i the simulatios. The receiver is equipped with 2 ateas. The umber of RF chais at trasmitter is 2, which meas 2 optimal ateas out of all the available ateas will be activated durig data trasmissio. We ca see from Figure 5 that for a give SNR, the SER performace improved sigificatly with the trasmit atea pool. Whe SNR = db, the system without atea selectio (2 2/2) achieves SER approximately at 6.5 2, however whe we icrease the size of trasmit atea pool to 4 ad 8, the SER the are decreased to ad 6.5 4, respectively. Figure 6 shows the SER performace of beam selectio without atea selectio. We assume that LMMSE receiver is employed. Both the receiver ad trasmitter are equipped with 4 elemets ULA array with iter-elemet spacig equals to.5 λ. Uder Rayleigh chael, there are 4 eigebeams at most ca be exploited for data trasmissio. We ca see from Figure 6 that for a give SNR, the SER performace improved sigificatly by beam selectio. Whe SNR = 5 db, the system without beam selectio achieves SER approximately at.7. owever whe we block the worst beams ad select the best beams for data trasmissio, the SER performace is sigificatly improved. The SER is decreased to whe the worst eigebeam is blocked

7 644 F. WANG ET AL. - SER X (2/2) MIMO 2 X (2/4) MIMO 2 X (2/6) MIMO 2 X (2/8) MIMO SNR(dB) Figure 5. SER performace of Trasmit atea selectio with LMMSE receiver uder Gaussia Chael SER Eigebeams 3 Eigebeams 2 Eigebeams Eigebeam SNR(dB) Figure 6. SER performace of beam selectio with LMMSE receiver uder Rayleigh Chael. from data trasmissio, to whe the worst 2 eigebeams are blocked ad to.7 5 whe the worst 3 eigebeams are blocked. Figure 7 shows a compare of the SER performaces of proposed scheme with beam selectio. The receiver is equipped with 4 ateas. The trasmitter has 4 RF braches. The results cofirm the observatios from Figure 6 that the performace is sigificatly improved whe the worst beams are deactivated from data trasmissio. The MIMO system employs all the 4 eigebeams show a poor SER performace (stared ad dotted curves). Whe the 2 optimal eigebeams out of 4 available eigebeams are exploited, the SER is improved dramatically (circled ad up-triagled curves). The improved performace is achieved by sacrificig data rate. Whe the umber of available ateas (i Figure 7, the umber is 8) is larger tha the umber of RF braches, the proposed fast atea selectio scheme ca be utilized together with beam selectio, thus rederig a hybrid scheme. It ca be see from Figure 7 that the proposed scheme is capable of achievig a better BER without sacrificig data rate. Whe SNR = db, the SER is further icreased by the proposed scheme from to.7 2 for UCA ad.6 3 to.3 3 for ULA. Figure 8 ad Figure 9 show the SER performace of hybrid scheme i where beam selectio ad atea selectio are both employed. We assume that there are 2 data streams to be trasmitted. As a result, oly 2 eigebeams are exploited for data trasmissio. The receiver is equipped with a 4-elemet ULA or UCA. The trasmitter has 4 RF chais ad is equipped with a ULA with

8 F. WANG ET AL Eigebeams expoited - 2 optimal eigebeam exploited 4 optimal ateas ad 2 optimal eigebeams exploited SER -2 UCA 4x4 MIMO w/o BS ULA 4x4 MIMO w/o BS UCA 4x4 MIMO BS ULA 4x4 MIMO BS UCA Proposed Scheme ULA Proposed Scheme SNR(dB) Figure 7. SER performace of the hybrid scheme with LMMSE receiver (AoA = π/6, a = 5). - ULA UCA SER -2 UCA 4X4/4 MIMO 2 Eigebeams UCA 4X4/6 MIMO 2 Eigebeams UCA 4X4/8 MIMO 2 Eigebeams ULA 4X4/4 MIMO 2 Eigebeams ULA 4X4/6 MIMO 2 Eigebeams ULA 4X4/8 MIMO 2 Eigebeams SNR(dB) Figure 8. SER performace of the hybrid scheme with LMMSE receiver with vary array structures (AoA = π/6, a = 5). ULA 4X4/4 2 eigebeams ULA 4X4/6 2 eigebeams ULA 4X4/8 2 eigebeams UCA 4X4/4 2 eigebeams UCA 4X4/6 2 eigebeams UCA 4X4/8 2 eigebeams SER SNR(dB) Figure 9. SER performace of the hybrid scheme with LMMSE receiver with vary array structures (AoA = π/3, a = 5).

9 646 F. WANG ET AL. iter-elemet spacig equals to.5 λ. Trasmit atea selectio ad beam selectios are performed at trasmitter side. We ca see from these figures that with extra ateas the hybrid scheme is capable of improvig the SER performace further. Oe ca see from Figure 8, the system employig ULA shows a much better performace whe AoA = π/6. owever, whe AoA icreased to π/3, the system employig UCA takes domiat positio (as show i Figure 9). By comparig Figure 8 ad Figure 9, it is easy to be oted that the icreased AoA leads to a sigificat decrease i the SER performace for ULA. This observatio cofirms the results show i Figures 3 ad 4 that a UCA receiver is robust to AoA. The chage of AoA results i little chage of SER performace for UCA receievr. O the cotrary, the receiver equipped with ULA is sesitive to AoA. A icreased AoA could result i a sigificat decrease i the SER performace. 5. Coclusios I this paper, we have proposed a hybrid trasmissio scheme which ivolves beam selectio ad atea selectio techiques over a MIMO system operatig with vary atea array. Optimal subset of trasmit ateas are selected via fast successive selectio scheme desiged to optimize the target eigebeam. Optimal eigebeams correspodig to the largest sigular values of the ew MIMO chael formed by the selected ateas are exploited for data trasmissio. We also evaluated the performace of the proposed scheme with differet array structures. I our simulatios, the trasmitter is assumed to be surrouded by scatterig objects while the receiver is postulated to be free from scatterig objects. The Laplacia distributio of agle of arrival (AoA) of a sigal reachig the receiver is postulated. The results show that the proposed scheme is capable of achievig a improved SER performace. I regards to the array structure, we ca coclude that ULA is preferred whe AoA is small the costat while UCA is favoured whe AoA is varyig sigificatly. 6. Refereces [] G. J. Foschii ad M. G. Gas, O Limits of Wireless Commuicatios i a Fadig Evirmoet Whe Usig Multiple Ateas, Wireless Persoal Commuicatios, Vol. 6, No. 3, 998, pp doi:.23/a: [2] E. Telatar, Capacity of Multi-Atea Gaussia Chaels, Europea Trasactios o Telecommuicatios, Vol., No. 6, 999, pp doi:.2/ett [3] A. Goldsmith, S. A. Jidal ad S. Vishwaash, Capacity Limits of MIMO Chaels, IEEE Joual o Selected Areas i Commuicatios, Vol. 48, No. 3, 2, pp [4] G. J. Foschii, Layered Space-Time Architecture for Wireless Commuicatio i a Fadig Eviromet Whe Usig Multiple Ateas, Bell Labs Techical Joural, Vol., No. 2, 996, pp doi:.2/bltj.25 [5] G. J. Foschii ad M. J. Gas, Capacity Whe Usig Multiple Ateas at Trasmit ad Receive Sites ad Rayleigh-Faded Matrix Chael Is Ukow to the Trasmitter, The Kluwer Iteratioal Series i Egieerig ad Computer Sciece, Vol. 435, No. 4, 22, pp doi:.7/ _7 [6] V. Tarokh, N. Seshadri ad A. R. Calderbak, Space-Time Codes for igh Data Rate Wireless Commuicatio: Performace Criterio ad Code Costructio, IEEE Trasactio o Iformatio Theory, Vol. 44, No. 3, 998, pp doi:.9/ [7] S. Alamouti, A Simple Trasmitter Diversity Scheme for Wireless Commuicatios, IEEE Joural o Selected Areas i Commuicatios, Vol. 6, No. 8, 998, pp doi:.9/ [8] L. Zhag ad D. N. Tse, Diversity ad Multiplexig: A Fudametal Tradeoff i Multiple Atea Chaels, IEEE Trasactio o Iformatio Theory, Vol. 49, No. 5, 23, pp doi:.9/tit [9] S. Ji, R. McKay, X. Gao ad I. B. Colligs, MIMO Multichael Beamformig: SER Outage Usig New Eigevalue Distributios of Complex Nocetral Wishart Matrices, IEEE Trasactio o Commuicatios, Vol. 56, No. 3, 28, pp []. Busche, A. Vaaev ad. Rohlig, SVD-Based MIMO Precodig ad Equalizatio Scheme for Realistic Chale Kowledge: Desig Criteria ad Performace Evaluatio, Wireless Persoal Commuicatios, Vol. 48, No. 3, 29, pp [] D. P. Palomar ad S. Bararossa, Desigig MIMO Commuicatio Systems: Costelatio Choise ad Liear Trasceiver Desig, IEEE Trasactio o Iformatio Theory, Vol. 53, No., 25, pp [2] S. Zhou ad G. B. Giaakis, Optimal Trasmitter Eige- Beamformig ad Space-Time Block Codig Based o Chael Mea Feedback, IEEE Trasactios o Sigal Processig, Vol. 5, No., 22, pp doi:.9/tsp [3] M. Codreau, A. Tolli ad M. Jutti, Joit Desig of Tx- Rx Beamformers i MIMO Dowlik Chael, IEEE Trasctio o Sigal Processig, Vol. 55, No. 9, 27. [4] R. W. eath, Jr., S. Sadhu ad A. J. Paulraj, Atea Selectio for Spatial Multiplexig Systems with Liear Recievers, IEEE Commuicatios Letters, Vol. 5, No. 4, 2, pp doi:.9/ [5] D. Gore, R. Nabar ad A Paulraj, Selectig a Optimal seo of Trasmit Ateas for a Low Rak Matrix Chael, Proceedigs of ICASSAP, Salt Lake City, 7- May 2, pp

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