IEEE 6th CAS Symp. on Emerging Technologies: Mobile and Wireless Comm Shanghai, China, May 31-June 2,2004

Transmit Processing in MIMO Wireless Systems

Josef A. Nossek, Michael Joham, and Wolfgang Utschick Institute for Circuit Theory and Signal Processing, Munich University of Technology, 80333 Munich, Germany Phone: +49 (89) 289-28501, Email: [email protected]

Abstract-By restricting the receive filter to he scalar, we weighted by a scalar in Section IV. In Section V, we compare derive the optimizations for linear transmit processing from the linear transmit and receive processing. respective joint optimizations of transmit and receive filters. We A popular nonlinear transmit processing scheme is Tom- can identify three filter types similar to receive processing: the nmamit matched filter (TxMF), the transmit zero-forcing filter linson Harashima precoding (THP) originally proposed for (TxZE), and the transmil Menerfilter (TxWF). The TxW has dispersive single inpur single output (SISO) systems in [IO], similar convergence properties as the receive Wiener filter, i.e. [Ill, but can also be applied to MlMO systems [12], [13]. it converges to the matched filter and the zero-forcing Pter for THP is similar to decision feedback equalization (DFE), hut low and high signal to noise ratio, respectively. Additionally, the contrary to DFE, THP feeds back the already transmitted mean square error (MSE) of the TxWF is a lower hound for the MSEs of the TxMF and the TxZF. symbols to reduce the interference caused by these symbols The optimizations for the linear transmit filters are extended at the receivers. Although THP is based on the application of to obtain the respective Tomlinson-Harashimp precoding (THP) nonlinear modulo operators at the receivers and the transmitter, solutions. The new formulation of the THP optimizations directly similar optimizations as for the linear transmit filters can be leads.10 an algorithm to compute the precoding order. We used to find the THP filters. In Section VI, we show how also discuss the reasons why the lincar transmit filters are outperformed by the respective THP schemes. the optimizations of Section IV for linear transmit processing have to be extended to get the respective optimizations for I. INTROOUCTION THP, where we incorporate the precoding order into the system The most general approach to multiple input multiple output model. Consequently, we end up with an algorithm to find the (MIMO) communication systems is the application of jointly precoding order directly resulting from the THP optimization. optimized transmit and receive filters (see e.g. [I], [2], [3], In Section VII, we compare the linear transmit filters to THP. [4], [SI, [6],[7], [SI). Since the joinr optimization oftransmit Note that we assume that the channel and the statistics and receivefilters is usually based on the assumption that the of the received noise are perfectly known to the receiver transmitters but also the receivers cooperate, it can neither be and the transmitter. Generally, these parameters bave to he applied to the uplink (non-cooperating transmitters) nor to the signaled from the receiver to the transmitter, but in rime downlink (non-cooperating receivers) of a multi-user wireless division duplex systems, the transminer can reuse the channel communication system. estimate obtained during the reception in the other link to In a system with receive pmcessing (e.g. [9]). the trans- design the transmit filter. Since the channel is time varying, mitter utilizes an a priori defined signal processing and the the performance deteriorates [14], [IS] and the applicability receiver has to equalize the channel. Obviously, this approach of transmit processing is limited. A mbust design (see [16]) leads to simple transmitters and the transmitters can be non- reduces the negative effect of outdated channel knowledge and cooperative. Thus, receive processing is well suited for the therefore enhances the applicability of transmit processing. uplink of wireless MIMO systems. However, the receivers have Notation: Vectors and matrices are denoted by lower case to be cooperative for optimum receive processing. Therefore, bold and capital bold letters, respectively. We use E[.], tr (e), receive processing is not appropriate for the downlink. (e)*, and (a)" for expectation, trace of a matrix, com- To end up with simple non-cooperaring receivers. transmit plex conjugation, transposition. and conjugate transposition, pmcessing has to be employed for the downlink. The receive respectively. All random processes are assumed to be zero- filter is n priori defined and known to the transmitter, whereas mean and stationary. The covariance matrix of the vector the transmitfilter is applied to equalize the channel. process x is denoted by R, = E(xxH]and the variance of Contrary to receive processing, the optimizations for trans- the scalar process y is = E[IY~~].The I<-dimensional zero mit processing are not well established. We show in Section I11 vector is OK, the K x L zero matrix is'OrCx[,, and the Z x L that the well known optimizations for receive processing identity matrix is 1~.whose e-th column is er. evolve from the respective joint optimizations of transmit and receive filters (see Section 11) by restricting the transmit filter 11. JOINT OPTIMIZATION OF TRANSMITAND RECEIVE to be an identity matrix weighted by a scalar. Motivated by FILTERS this result, we obtain the optimizations for transmit processing As depicted in Fig. I, the data signal s E CR is passed from the respective joint optimizations of transmit and receive through the transmit filter P E CMxeto form the transmit filters by restricting the receive filter tn be an identity matrix signal y = Pa E @", where M denotes the number of /d

0-7803-7938-1104l920.00 0 2004 IEEE 1-18 Fig. I. MIMO System with Linear Transmit and Receive Filtcn Fig. 2. MlMO System with Linear Receivc Filter scalar channel inputs. After propagation over the channel With the same restriction on the transmit filter to be equal H E CNynrand perturbation by the noise q E CN,the to ple, we obtain the well known optimizations for receive resulting received signal x = Hy + rj E CN is transformed processing from (2), (3), and (4). by the receive filter G E CSxN to get the estimate The optimization for the receive mnlcked Jib- (RxMF) follows from the eigenprecoder optiiniratioii (2): s^ = GHPS+ GQ E a?. (1) 11.1 (PHGRJ' (p~~.GMF)= argrnax Here, denotes the number of scalar channel outputs and in M {P.CI tr (R,)tr (GR,G") Fig. I, Q(.) denotes quantization. (6) Although also other joint optimizations have been proposed s.t.: Ipl*tr(RB)= .htr. (e.g. in IS]), we concentrate on the following three criteria, A of above RxMF optilnizationis: because they are a generalization of the most often used criteria for receive processing. PMF = GMF=purR,HnR;'. (7) The eigrnprecoder [ 171, [ IS] was originally proposed for tr (R.1' CDMA systems, but can also be derived for the more general system of F;~,1 by maximizing the desired signal portion in By setting P = ple in the joint zero-forcing optimization (3), the estimate under a mean transmit energy constraint: we obtain the receive zero-fixingfiller (RxZF) optimization:

With the restriction p E R+. the RxZF of (8) is unique:

The join( zero-forcing oplintira[ion is based on the mini- -1 HHR-L H)-' HI'R;'. (9) P~F&;, G~~.= p,F ( 71 inizatioti or the MSE together with a zero-forcine~ ~ ~~ constraint and a transmil energy constraint (e.g. [19], [ZO],[Zll): The receive FF'ienerf//er (RxWF) for the system in Fig. 2 can be found with (cf. Eq. 4): {P~~tG~~?']= argminE[(js - SI(;] {PWF;GWF)= urgiIlinE[~ls - {CGI (3) .?I[:] s.1.: Il,,=oN= s and E[\\y\\;] = E,,. (,'.GI (10) s.1.: (PI' tr (R.) = B,. We call the minimization of the MSE with a mean transmit The resulting RxWF for p E R+ can be expressed as

.. (PG) Obviously, GWF-+ GMF for low and GWF GZFfor (4) SNR - high Note that the optimizations for receive processing Note that the solutionfor ,he joint wiener (4) SNR. converges to the eigenprecoder (2) and the solution of the joint are usuab' formulated the energy constraint zero.forcing optimization (3) for low and high sig,,ai lo and the Scalar weight P at the transmitter (e.g. PI). Sitice ralin (SNR). respectively. p = ,/- is only necessary to fulfill the transmit energy constraint and the receiver Cannot distinguish between 111. LINEARRECEIVE PROCESSING p and H, the receiver assumes Is,, = tr(R,) (p' = 1) and bases the receive filter on the total channel H' = pH. By restricting the transmit filter to he an identity matrix weighted by a scalar, that is P = pl~with p E @, we obtain IV. LINEAR TRANSMITPROCESSING Fig. 2 from Fig. 1. The resulting system in Fig. 2 is appropriate When the receive filter in ~i~.1 to be an identity for receive processing, since the channel H E CNxBcan only weighted by a scalar, i.e. G = gle E c, we be equalized by the receive filter G E 'CeXN.The estimate end up with the system for transniit processing in Fig. 3. The can be written as (cc Eq. I) estimate reads as (cf. Eq. I) s^ =pGHs + Gq E 62". (5) d=gHPs+qqt 6'. 02)

1-19 Fig. 3. MIMO System with Linear Transmit Filter

The channel H E CBxMhas to be equalized by the transmit filter P E Similar to receive processing in the previous section, the optimizations for transmit processing evolve from (Z), (3), and (4) with the restriction that G = 918. The frunsmit mutchedjlter (TxMF) was first proposed by McIntosh et al. [22] and became especially popular in CDMA applications asprerake (see e.g. [23], [24], [25]). The TxMF -10 -5 0 5 10 15 20 25 30 maximizes the received signal power [ZZ]: Es/N0 in dB

Fig. 4, QPSK Transmission over MIMO Channel with Two Transmining and Two Receiving Antenna Elements Uncoded BER vs. SNR for Linear Receive and Transmit Processing s. I.: tr (PR.P") = G,.

The 'TxMF For ~WFE R+, the TxWF can he written as 1 PWF= 9,: H"H cwt:lnd)- H" and PYF HH and ~MPE@ (14) ( + tr (HHRJI) (I8) is thus advantageous for systems with low transmit energy or SWF = high received noise power. Since the TxMF does not lake into Et, account interference, its performance is poor for interference where &F Kariini et al. introduced this limited scenarios. = tr(h),/Eu. [31] filter in an intuitive way, whereas Choi et al. [32] and Joham This property of the TxMF motivates the lrunsmit zem- et al. [33] published above optimization to obtain the TxWF. forcingfilfer (TxZF) which completely suppresses the inter- Interestingly, the TxWF converges to the TxMF for low SNR ference at the receive filter output (cf. Eq. 3): and to the TxZF for high SNR:

PWF-+ PM~:for Etr/!3[ll~\\;]+ 0 and PWF- PZF for Etr/E[ll~ll~]- m. Note that the TxWF PWFdepends on the average received With gZF E R+, we find for the TxZF: noise power E[//TJ~/~]contrary to the TxMF and the TxZF. Since the transmitter caniiot estimate this parameter, the PZF= g;:HH (WHH)-l and receiver has to signal the noise power to the transmitter. Fortunately, the TxWF is very robust against wrong values for E[11q11'$ (see e.g. [33]). Consequently, the transmitter only needs a rough estimate of this value.

COMPARISON OF LINEARTRANSMIT FILTERS Most publications on the TxZF (e.g. [2h], [27], [ZS], [291, V. [30], (141) focus on CDMA systems, but the TxZF can also Obviously, the MSEs of the TxMF and the TxZF are always be applied to MIMO systems [31]. Due to the interference lower bounded by the MSE of the TxWF, as the TxWF suppression, the TxZF outperforms the TxMF in interference minimizes the MSE. Moreover, it can he shown analytically limited scenarios, but the TxZF is worse than the TxMF, if the that the MSE of the TxZF is higher than the MSE of the transmit energy is low or the received noise power is high. TxMF for low SNR, but the MSE of the TxZF is smaller for The transmif Wiener filter (TxWF) minimizes the MSE high SNR (see [34]). We have also shown that the MSEs of the under the average transmit energy constraint (cf Eq. 4): transmit filters are equal to the MSEs of the respective receive filters, if the symbols s and the noise q are white [34]. The same relations are true for the BERs of the trans- mit filters, but cannot be shown analytically. To illustrate this statement, we present the uncoded BER results for the

1-20 Fig. J. Linear Representation of Madulo Operation at Transminer Fig. 5. Tomlinson-Harushima Precader with Modulo Operator M(.) and Permutation Matrix ll

Fig. 8. Linear Representation of Modulo Operation at Receiver Fig. 6. Channel and Receiver with Qwntizer Q(.)

for the THP ovtimizations instead of 8 and 1. because the auxiliary signals and -h are added automatically by the discussed transmit filters and the respective receive filters a modulo operator M(*). The estimate depending on the modulo applied to a MtMO system with two transmit and two receive output reads as antenna elements in Fig. 4. We see that the TxWF is superior U compared to the TxMF and the TxZF. The BER of the TxMF d= gHPu+ gu E CB, (19) is smaller than the BER of the TxZF for low SNR, but the BER ofthe TxMF saturates for high SNR due to the remaining whereas we get for the desired value for the estimate: interference. d = 17'0)'T(le - F)U E CB. (20) VI. TOMLINSON-HARASHLMAPRECODLNG Since the modulo operator M(o) is applied element-wise, The interference suppressing linear transmit filters, i.e. the the feedback filter F has to be lower triangular with zem TxZF and the TxWF (see Section IV), depend on the pseudo main diagonal. Thereby, delay-free loops are avoided ensuring inverse of the channel H.Therefore, the power of the received realizability, because only already precoded data streams are signal can be small, if the channel is ill-conditioned, because fed hack by F. Including this constraint, we can rewrite the the transmit energy is fixed. To overconle this difficulty, TxWF optimization (17) to obtain'the Mener THP (WF-THP) a feedback loop with the feedback filter F E CBxBis optimization [36],[37]: introduced (see Fig. 5). Inside the loop, the nonlinear element- {pTl[P, FTHP THP THP - wise modulo operator WF .SWF :%F } - awlill E[lld- d^ll:] (21) iP.F,B,Ot s.t.: E[l(y(lz]=E,, and F : lower triang., zero diagonal. ~(s)=x- I?+ 7- 1- Im (x) + 7 Under the common assumption of uncarrelated modulo out- applied to ensure that the amplitude the OUtpt U € is of @ puts v, that is & = diag(,,;, , , . . , r:B), the WF-THP filters is limited. The modulo constant r is chosen according to the depending on the ordering 0 be as modulation alphabet (see e. E. 1351)... To counteract this modulo - . B operator at the transmitter, the receiver also has to apply a pTHPwF - -,',,CHHT~, (n,~~~n;+

before it is passed through the precoder, i.e. the b;-th scalar Y data stream is precoded i-th. This reordering represents a where we introduced

1-21 10- d m 10

A ZF-THP --C ZF-THP -8- unitary ZF-THP . .. 10 -10 -5 0 5 10 15 20 -10 -5 0 5 10 15 20 Es/NUin dB &/Nu in dB

Fig. 9. QPSK Transmission over MIMO Channel with Four Tmnsmining Fig. 10. 16QAM Transmission over MlMO Channel with Four Transinitling and Four Receiving Antenna Elcmcnts: Uncoded BER vs. SNR for Linear and Four Receiving Antenna Elcmenir: Uncoded BER YS. SNR for Linear and Nonlinear Transmit Processing and Nonlinear Transmit Processing

Plugging the result of (22) into the cost function of (21), mit and four receive antenna elements and QPSK transmission. we find for the optimum WF-THP ordering: Additionally, we include the uncoded BER results for iinilor)? B ZF-THP [38], a variant of ZF-THP with unitary feedforward ObF = argmin~o~,e~(n,HHHn;+iwFi~)-leb,. filter and a weighting with a diagonal matrix at the receiver 0 i=, different from a weighted identity matrix. We observe that (23) the THP approaches clearly outperform the respective linear To avoid the high complexity O(B!B3)of this optimization, transmit filters for high SNR as expected, but are worse for we suggest following suboptimum approach instead: ' low SNR due !o the additional allowed constellation points introduced by the modulo operation at the receiver. Note that HHHni + eb' (24) the BERs of the two ZF-THP types have the same slope as the btO, CWFiB)-' linear transmit filters for high SNR, since the last column of for 7 = R, . . . , 1, i.e. instead of minimizing the whole sum, P:FP is the weighted bB-th column of the linear TxZF PZF. each summand is minimized separately for fixed succeeding Thus, the diversity order of the data stream precoded last is the indices. Here, 0, = [I,.. . ,B}\{b&;y,+l,. . . ,bTHP wF,a} is the same as the diversity order of the TxZF data streams. As the set of possible indices for the i-th precoded data stream. lowest diversity order is dominatit, the ZF-THP approaches The zem-forcing THp (ZF-THP) optimiz:tion =an be found have the Same diversity order as the transmit filters. by including the zero-forcing constraint dl,=orr = d into Not unexpected, the unitary ZF-THP outperforms the ZF- the WF-TW optimization (21). The WF-THP filters in (22) THP approach discussed in this paper, because the diagonal converge to the ZF-THP filters for the limit EU/ t'r(%) * weighting at the receiver offers more deg of freedom, + Note that we get for ZF-THP (tWF 0). [36]: For 16QAM (see Fig. IO), the negative effect of the modulo nT1+P.THp~l+PZF ZF - B - FBp, operation at the receiver can be neglected. Therefore, the THP approaches are superior in the whole depicted SNR range. where the ZF-THP feedback filter FZF is a lower triangular Note that WF-THP needs dB less SNR than ZF-THP matrix with zero main diagonal. We can conclude that the feed- for a uncoded BER of 10 %. forward filter P:F* removes the interference of data streams In Fig, we show the uncoded BER results for QPSK, preceded later, whereas the lower triangular feedback filter four transmit and three receive antenna Obviously, FIFp suppresses the interference by already preceded all approaches have an improved performance compared to data Since the THP feedforward 'Iter p:FP has to Fig. 9. However, the advantage or the linear transmit filters suppress less interference lhan the TxZF PZF (cf. Eq. 16), for lowSNR is pronounced and the unitary ZF.THP is more degrees Of are le' to maximize the received than the ZF-THP with scalar weight at the receiver, We signal power. Hence, THP outperforms the respective linear can conclude that the inhlitively designed unitary ZF-TH~is transmit filter. suboptimum. VII. COMPARISON OF LINF.ARAND NONLINEAR REFERENCES TRANSMITPROCESSING [I] R. 1. Pilc, '7he Optimum Linear Modulator for a Gausinn Source Used 111 Fig. 9, we compare the linear TxZF and TxWF with the with a Gaussian Channel:' Be// ~j~.~rcmTec/u+/ Journnl, VOI. 48. no. 9, nonlinear ZF-THP and WF-THP for a system with four trans- pp. 3075-3089. November 1969.

1-22 Wiener Filter for Time Division Dudex SVsIems." in Pioa. ISSPIT2003. December 2W3. 1171 J. Wang. M. Zhao. S. Zhau, and Y. Yao, "A Novel Multipath Transmis- sion Diversity Scheme in TDD-CDMA Syrtm"' IEICE Tmnsocrioar on Communicntions. vol. E82-B. no. IO, pp. 1706-1709. October 1999. (181 R. Inner, A. Noll Barreto, and G. Fenwek. Tmnsminec Precodiog for Soread-Socctrum Sienals in Freaucncv-Selective Fadine Channels." in Pmc. 3G wireless. iay 2001. &. 936..-944. 1191 J. W. Smith, 'The Joint Optimization of Transmined Signal and Re- ceiving Filter for Data TraiismiSsion Systems:' Bell Spmn Technical Journal, vol. 44, no. IO, pp. 2363-2392, December 1965. [20] C. D. Golden, J. E. Mso, and J. Salz, "Transminer Design far Data Transmission in the Presence of a Data-Like laerfercr:' IEEE 7i"uclionr on Cummunicoliom, vol. 43, no. 2314. pp. 837-850. Feb"yIMarchIApri1 1995. (211 A. Scaglione, G. E. Giannakis, and S. Bwbrbarossa. "Redwdmt Filttr- bank PRcodcrs and Equalizers Pan I: Unification and @lima1 Desips," IEEE Pomocriom on Sign"/ Pmcensinp, vol. 47, no. 7, pp. 1988-ZW6, &/No in dB July 1999. [22] R. E. McIntosh and S. E. El-Khamy. "Optimum Pulse Transmission Through a Plasma Medium," IEEE Tronsoclions Antennos ond Fig. I I. QPSK Transmission mer MIMO Channel with Four Transmining on Pmpagulion, vol. AP-18, no. 5, pp. 666671, September 1970. and 'I" Receiving Antenna Elements: Uncoded Linear EER VI. SNR for [23] R. Esmaihdeh and M. Xakagawa. "Pre-RAKE Divenity Combination and Nonlinear Transmit Proceriing far Direct Sequence Spread Specvum Mobile Communications Sys- tems," EKE Tmenerions on Communicolio,w, vol. E76-B. no. 8. pp. IWR-1015, August 1993. 1241 R. Esmailzadeh, E. Saumur. and M. Nakagaws. "*rake Diversity [2] 1. Salz, "Dipibl Transmission Over Cmss-Coupled Linear Channels:' Combining in Time-Division Duplex CDMA MobilC Communications." AT&T Terhnicvi Jolournul. vol. 64. no. 6. pp. 1147-1159, July-Augun IEEE Trmrocliom on Rhiculor %dnolo~,.vol. 4R. no. 3, pp, 7YS-801, 19S5. May 1999. (31 H. S. Malm and D. H. Staelin, "Optimal Prc- and Postfiltcrr for Mul- I251 R. L. C.hoi. K. E. Letaief, 2nd R. D. Murch. "MISO CDMA Transmis- tichanncl Signal Processing:' IEEE Trumucrionr on Acouticr. Speed. sion with Simplified Rcceivcr for Wireless Communication Handsets:' und sigd pmcrssing. YO!. 36, no. 2. pp. 287-289, February 1988. IEEE Trunsmliuns on Communicotiom, vol. 49. no. 5. May 2001 141 M. Honiz. Cresoo. and K. SteieliQ. "Suooression of Near- andi .1 1. P. .. (261 U. Liu and G. Xu. "Multiuser Blind Channel Estimation and SpaUal Far-End Cm&k by Linear Pre- andbos;-Filt&g; IEEE Joumol on Channel Pre-Equalization:' in Pmc. ICASSP'95. vol. 3. May 1995, pp. Sdecwd Area in Commu-liu~is, vol. 10. no. 3, pp. 614429, Apd 1756-1759. $00,.,,-. [27] G. Montalbano and D. T. M. Slock. "SpatirSTemponl Amy Pmessing 1.51 1. Yang and S.Roy, "On Joint Transminer and Receiver Optimization for for Matched Filter Bound Optimization in SDMA Downlink Transmis- Multiple-lnput-Multiplc-Output (MIMO) Transmission Sptems." IEEE sion:' in Pmc. ISSSE'98. Scptcmber 1998. pp. 416-421. Tmnroctionr on Communicotiom, vol. 42. no. 12. pp. 3221-3231. [28] B. R. Vojfif and W. M. Jang, "Transminer Pwecding in Synehmnous Dccembecr 1994. MuWium Communications:' IEEE Tronroctions on Communications. [6] W. M. Jang, B. R. Vojfi6, and R. L. Pickhholtr. "Joint Transminer- vol. 46. no. IO. pp. 13461355. October 1998. Receiver Optimization in Synchronous Multiuser Communications over [29] P. W. Baier, M. Meurer, T. Weber. and H. TrLiger, "Joint Transmission Multipath Channels:' IEEE Tr~nroclionron Communicorionr. vol. 46. (IT),an alternative rationale far the dnwnlink Of Time Division CDMA no. 2. pp. 269-278. February 1998. using multi-element "nit antennas," in PNC ISSSTA 2000, vol. I, 171 H. Smpth, P. Stoica, and A. Paulrdj, '%enmlizd Liner Precodn September 2003, pp. 1-5. and Decoder Design for M[MO Channels Using the Weighted MMSE [30] M. Joham and W. Utachick, "Domilink Proeasing for Mitigation of Crite&m:' IEEE Pomocliom on Commlmicoriom, vol. 49, no. 12. pp. lntracell Interference in DS-CDMA Systems:' in Pmc. ISSSTA 2000. 219B-2206, December 2W1. vol. I, September 20W, pp. 15--19. [8] A. Scaglione, P. Stoia, S. Barbarossa, G. B. Ciannrkis, and H. Snmpath, 1311 H. R. Karimi. M. Sandell. and J. Sa4 '"Compan'son betweer transmitter "Optimal Designs for Space-Time Linear Prccdm and Decoden:' and receiver amy proeessing to achieve interference ding and diver- IEEE Tronsudiom on Signal Pmcwing, vol. 50. no. 5. pp. 1051-1064, sity," in PNC. PIMRC99, vol. 3, September 1999. pp. 997-1001 May 2002. I321 R. L. Choi and R. D. Much. 'Transmit MMSE Pre-Rae Pre-processing (91 S. VudG, Mdtiwrr LWrctiun. Cambridge University Press, 1998. with Simplifid Receivers for thc Downlink of MISO TDD-CDMA [IO] M. Tamlinson. "Nrw automatie equaliser employing modulo arithmetic," Systems," in Pmc. Globecm 2002, vol. I, November 2W2. pp. 429- Eleclmnics Lelterr. vol. 7, no. 516, pp. 138-139, Manb 1971 433. [I I] H. Hamhima and H. Miyakawu, "Matchcd-Transmission Technique 1331 M. Joham, K. Kusume. M. H. Gzam, W. Utschick, md J. A. Noss for Channels With lntrnymbol Intcrfercnce." IEEE Pomacrions on "Transmit Wicnsr Filter forthe Downlink ofTDD DS-CDMA System Cummunicutiom, vol. 20, no. 4, pp. 774-780. August 1972. in Pmc. ISSTA 1002, vol. I. September 2W2, pp. 9-13. [IZ] G. Ginis and I. M. Cioffi, "A Multi-user Prccoding Scheme achieving [34] M. Joham, W. Uschick. and J. A. Nossek, "Linear Transmit Processing Crosstalk Cancellation with Application to DSL Systems:' in Pmc. in MIMO Communications Systsmr." 2004, Accepted for publiention in Asilumvr Cunfereacu on Sigmais. System. and Computers. vol. 2, IEEE Trmmclionr w Signal Pmceming. Oetok 2000. pp. 1627-1631. (351 R. F. H. Fischer. Precaling ondSigngnalShopingfor Digilul Tmnrmiision. [I31 R. F. H. Fischer, C. Windpassinger, A. Lampe, and 1. E. Huber, "Space- John Wily &Sons, 2002. Time Tcansmission "ring Tomlinsan-Harmhima Precoding:' in Pmc. 136) M. Joham, J. Brehmer, and W, Utschick. "MMSE Appmaches to 41h ITG Conference on Source and Channel Codins, January 2002, pp. Multiuser SpatieTemporal Tomlinson-Harashima FTecding," in Pmc 139-147. ITG SCC'l4. January 2W4, pp. 387-394. 1141 F. Kowalnvski and P. Mangold, "Joint Prcdinonion and Transmit 1371 M. loham. I. Erehmer, A. Voulgarelis, md W. Uschick, "Multiwei Diversity," in Pmc. Globemm '00, w1. I, November 2000, pp. 245- Spatic-Tempd Tomlinson-Harashhns Precding for Frequency Selec- 249. tive Vector Channels:' in Pmc. ITG U'orkrhap on Smnn Anrenno,t, March (151 F. Dietneh, R. Hunger, M. Jaham. and W. Utsehick, "Linear Preeoding 2004. over Time-Varying Channels in TDD systems:' in pmc. ICASSP 2003. (381 R. F. H. Fischer. C. Windpasringer, A. Lamp, and 1. E. Huber, "MLMO vol. V. April 2003, pp. 117-120. Prccding for Decentallzed Reecivcn:' in Pme ISIT 2002, JundJuly [I61 F. A. Dietrich, R. Hunger, M. Joham. and W. Utschick, "Robust Transmit 2W2. P- 49b.

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