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VI INTERNATIONAL TELECOMMUNICATIONS SYMPOSIUM (ITS2006), SEPTEMBER 3-6, 2006, FORTALEZA-CE, BRAZILAdding Diversity to Multi-User DownlinkBeamforming by using BER ConstraintsDanilo Zanatta Filho, Luc Féty and João Marcos Travassos RomanoAbstract— In this work, we propose a novel structure andcriterion for joint transmit diversity and multi-user downlinkbeamforming. The proposed structure can be seen as an extensionof the purely spatial downlink beamforming and is atransformation that, for each user, transforms K real antennasinto L virtual antennas, with L≤K. Classical transmit diversityis then applied to these virtual antennas. We propose a designcriterion to optimize the precoders in order to find the best tradeoffbetween minimizing the interference generated towards theother users and maximizing the channel diversity for the desireduser. This criterion is based on the minimization of the totaltransmit power subjected to a target BER constraint for eachuser. Applied to a multiple-antenna transmitter, the proposedtechnique outperforms the purely-spatial downlink beamformerby about 5 dB for a target BER of 10 −2 and by 9 dB for 10 −3in a simple scenario.Index Terms— Minimum BER, Multi-User, Multiple antennas,Smart antennas, MIMO, downlink beamforming, transmit diversity,channel correlation, antenna correlation.I. INTRODUCTIONThis work investigates the use of multiple antennas at theBase Station (BS) and a single antenna at the mobile usersand concerns downlink transmission. By using a multi-userapproach, the multiple transmit antennas at the BS can be usedto spatially separate the co-channel users, adding the spacedimension to the system’s resources. The addition of this newdimension increases the system capacity [1].Based on the knowledge of the Downlink Channel CovarianceMatrix (DCCM) for all users, the works [2] and [3]propose to use a purely spatial filter to beamform the signal ofeach user towards the desired user and to mitigate the interferencegenerated towards all the other co-channel users withinthe cell. This is called multi-user downlink beamforming (MU-DB) and is done by minimizing the transmitted power subjectto Signal-to-Interference-plus-Noise Ratio (SINR) constraintsfor each user [3]. The use of these constraints aims to assurethe desired BER for each user. The minimization of thetransmit power increases the system capacity due to one ofthe following two factors: either the BS has more power leftto accept other users within the same cell or the interferencegenerated on the other cells are reduced. The criterion pro-Danilo 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.frJoão Marcos Travassos Romano is with the Signal Processing Laboratoryfor Communications (DSPCom), State University of Campinas (UNICAMP),Campinas-SP, Brazil. email: romano@decom.fee.unicamp.brposed in [3] leads thus to the joint optimization of downlinkbeamforming and transmit powers.However, the use of a purely spatial filter is not well suitedfor flat-fading channels since the composite channel seen byeach user remains flat-fading. Then, despite of the possibleexistence of channel space diversity, the overall transmissionsystem does not take profit from this diversity to mitigate thefading effect and further minimize the transmission power fora given target BER. On the other hand, there are the classicalTransmit Diversity (TD) schemes [4]–[7], which exploit thechannel diversity to mitigate the fading and minimize thetransmit power for a given BER. The TD techniques, however,assumes a single-user scenario and uncorrelated antennas.Thus, these techniques present a omnidirectional radiationpattern and are not directly applicable in a multi-user scenario.In [8], an optimal mono-user transmitter design is proposedto minimize the Symbol Error Rate (SER) for Rayleighchannels. We have extended this result to any channel typein [9] by proposing a criterion based on the minimization ofthe BER, for the mono-user case.In this paper, we formulate a general criterion to designoptimal transmitter precoders for the multi-user case basedonly on the DCCM. The main contribution of this work isto propose a design criterion to optimize the precoders ω i inorder to find the best trade-off between maximum channeldiversity and minimum pollution. Therefore, our aim is tominimize the total transmit power while respecting a targetBER for each user within the considered cell. The resultingprecoders are thus applicable to any modulation scheme andchannel types (e.g., Rayleigh, Rician, Nakagami [10]).The rest of this paper is organized as follows. Section IIdescribes the multi-user system model The proposed constrainedcriterion of minimum transmit power is presentedin Section III and an iterative algorithm to find the optimumsolution is presented. Performance is analyzed in Section IV.Conclusions are then drawn on Section V.The following notations are used throughout the paper. Boldlower letters denote column vectors, bold upper letters denotematrices; (·) T , (·) H and (·) ∗ denote transpose, conjugatetranspose, and conjugate, respectively. ‖x‖ is the 2-normof vector x, defined as ‖x‖ = √ x H x, and E{·} denotesmathematical expectation.II. SYSTEM MODELWe consider the downlink of a wireless communicationsystem, where the BS is equipped with K antennas andcommunicates with U mobile users, each one with a singleantenna. The transmit processing is done by means of aprecoder for each user, as depicted in Fig. 1 for transmission