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VI INTERNATIONAL TELECOMMUNICATIONS SYMPOSIUM (ITS2006), SEPTEMBER 3-6, 2006, FORTALEZA-CE, BRAZILJoint Transmit Diversity and DownlinkBeamforming by using a Minimum BER CriterionDanilo Zanatta Filho and Luc FétyAbstract— In this work, we propose a novel criterion to findthe optimum precoder for joint transmit diversity and downlinkbeamforming. This precoder is an extension of the purely spatialdownlink beamforming and can be seen as a transformationthat transforms K real antennas into L virtual antennas, withL≤K. The proposed criterion is based on the minimization ofthe received BER and extends the previous technique [1] (Eigen-Beamforming) to any type of channel distribution, not onlyRayleigh. Simulation results show that the proposed techniqueis equivalent to Eigen-Beamforming for Rayleigh channel, butoutperforms the latter for Rician channels, providing substantialimprovement. This makes the proposed technique an attractivesolution for the general application, where the channel type isnot known a priori.Index Terms— Minimum BER, smart antennas, multiple antennas,MIMO, downlink beamforming, precoder, transmit diversity,channel correlation, antenna correlation, STBC.I. INTRODUCTIONThe evolution of the wireless communication systems towards3GB (3 rd Generation and beyond) is propelled byInternet access and increasing demand for data-based services.Most of these services, such as internet surfing, are downlinkintensive,in opposition to voice services, which demand thesame data rate in both directions. These factors lead to anincreasing demand for higher data rates in the downlink, whichcan only be achieved by a better link quality. This better linkquality reflects in a lower Bit Error Rate (BER) at the physicallayer and in a greater system capacity.This work investigates the use of multiple antennas at theBase Station (BS) and a single antenna at the Mobile User(MU) and concerns downlink transmission. Exploiting themultiple antennas at the BS, which has much more resourcesthan the MU, keeps the MU receiver simple and it can yettake profit from the multiple-antenna performance gain. In thiscontext, the multiple transmit antennas at the BS can be usedeither to perform downlink beamforming or to achieve transmitdiversity.In the classical Transmit Diversity (TD) scheme, the antennasare assumed to be uncorrelated and no channel informationis required at the BS [2]–[5]. Maybe the most known techniquefor TD is Space-Time Block Codes (STBC) [4], with theAlamouti scheme [2] being the most popular one. The TDschemes exploit the channel diversity to mitigate the fadingDanilo Zanatta Filho is with the Signal Processing Laboratory for Communications(DSPCom), State University of Campinas (UNICAMP), Campinas-SP, Brazil and with the Laboratory of Electronics and Communications,Conservatoire National des Arts et Métiers (CNAM), Paris, France. email:daniloz@decom.fee.unicamp.brLuc Féty is with the Laboratory of Electronics and Communications,Conservatoire National des Arts et Métiers (CNAM), Paris, France. email:fety@cnam.frand achieve lower BER. However, they radiate the transmitpower in a omnidirectional way, wasting power.On the other hand, there is the classical Downlink Beamforming(DB) scheme [6], which uses a purely spatial filter. Inthis scheme, the antennas are assumed to be strongly correlatedand some kind of channel information is available at theBS, e.g., Direction Of Arrival (DOA) or Channel CovarianceMatrix (CCM). The primary aim of DB is to maximize thereceived power at the MU for a given transmit power at theBS. This approach however is not well suited for flat-fadingchannels since the composite channel seen by the MU remainsflat. Even if the channel has more than one path, these pathshave the same propagation delay and are seen by the MU as asingle composite path. So, even if there is a power gain due tobeamforming (array gain), the MU does not take profit fromthe channel space diversity to mitigate the fading effect andfurther lower the BER.The performance of TD systems can be further enhancedwhen perfect or partial Channel State Information (CSI)is available at the transmitter [7]. In [8], the problem ofpower allocation among different antennas in a TD schemeis addressed, in opposition to equal power transmission. Itis shown that, if the transmitter knows the power of eachdiversity branch linking one transmit antenna and the mobilereceiver, then optimized power allocation can be realized inorder to minimize the BER of a BPSK differential-encodedsignal over a Rayleigh channel, for a given transmit power.The author shows that, when the branch powers have a greatdispersion, in the low-SNR regime, allocating power to theantennas corresponding to weak branches leads to a waste oftransmit power and no diversity gain. On the other hand, inthe high-SNR regime, these weak branches can contribute tothe system diversity. So, allocating power to the correspondingantennas provides a significant performance enhancement, interms of BER. Moreover, it is shown in [8], that the problem ofcorrelated antennas can be solved by whitening the channel.This is done by means of a precoder that converts the realantennas into virtual antennas, which are uncorrelated butpresent different gains. Then, the optimum power allocation iscarried out on the virtual antennas in the same way as before.In order to compute the precoder, the Downlink ChannelCovariance Matrix (DCCM) must be known at the BS.The work of [1] extends [8] by using the DCCM informationto optimize the TD precoder to minimize the Symbol ErrorRate (SER) for any modulation. The authors show that theoptimum solution in this case is to use the eigenvectors ofthe DCCM as a precoder. These eigenvectors are furthermorescaled according to a spatial water-filling principle, similarto [8]. This optimum solution, called Eigen-Beamforming,minimizes the SER for the Rayleigh flat-fading channel case.