EUROPEAN TRANSACTIONS ON TELECOMMUNICATIONS Eur. Trans. Telecomms. 2007; 18:605–615 Published online 8 June 2007 in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/ett.1229 Enhanced opportunistic beamforming scheme for practical broadcast systems † R. Bosisio 1* , J. L. Vicario 2 , U. Spagnolini 1 and C. Anton-Haro 3 1 Dipartimento Elettronica e Informazione, Politecnico di Milano, Piazza L. da Vinci 32, I-20133 Milano, Italy 2 Departament de Telecomunicacions i Enginyeria de Sistemes, Universitat Auton` oma de Barcelona, 08193 Bellaterra, (Cerdangola del Vall` es), Spain 3 Centre Tecnol` ogic de Telecomunicacions de Catalunya, Av. Canal Ol´ ımpic S/N, 08860 Castelldefels, Barcelona, Spain SUMMARY In multiantenna systems the optimisation of linear spatial precoding is severely hampered by the amount of feedback. A practical solution consists in the opportunistic beamforming (OB), which randomly generates the beamforming and schedules the user with the largest signal-to-noise ratio (SNR). In this paper we investigate the benefits that can be provided by the knowledge of the users spatial covariance at the transmitter. We enhance the OB scheme by matching the beamforming generation to the users channels spatial patterns. We analytically assess the performance of the proposed scheme, referred to as Cluster-Eigenbeamforming (Cluster-EB), both in ideal (perfect feedback) and in practical scenario (imperfect feedback). Cluster-EB is shown to outperform the conventional schemes and the performance gain increases in practical systems as Cluster-EB capitalises on the spatial covariance knowledge to reduce the sensitivity with respect to the feedback imperfections. Copyright © 2007 John Wiley & Sons, Ltd. 1. INTRODUCTION Opportunistic beamforming (OB) [1, 2] has been recently proposed to exploit multiuser diversity (MUD) in broadcast wireless communication systems. OB is effective when an antenna array is employed at the base station (BS) and reduced feedback is mandatory as compared to other optimal strategies that require full channel state information (CSI) at the transmitter. The main idea is to generate a random beamforming at the BS and to schedule the users ac- cording to the signal-to-noise ratio (SNR) and some fairness requirements. A low-rate feedback channel is needed as the users have to report only the instantaneous SNR (I-CSI). The OB scheme can be enhanced by capitalising on the knowledge at the BS of the channels spatial covariance, also known as long term CSI (LT-CSI) [3–5]. Since the channel spatial covariance can be assumed stationary over large time scale, it can be acquired by the transmitter either directly *Correspondence to: Roberto Bosisio, Dipartimento Elettronica e Informazione, Politecnico di Milano, Piazza L. da Vinci 32, I-20133 Milano, Italy. E-mail: rbosisio@elet.polimi.it † A Previous edition of this paper has been presented in the 12th European Wireless Conference (EW 2006), Athens, Greece. from measurements on the opposite link or from limited feedback. The LT-CSI permits to match the beamforming generation to the spatial patterns of the users. To this aim, the eigenbeamforming (EB) technique [3] generates the beamforming vectors from the set of leading eigenvectors of the users’ covariance matrices. Following the approach in Reference [4], we say that users i and j are spatially similar when they have spatial co- variance matrices R i and R j so that range(R i )  range(R j ). The Cluster-Eigenbeamforming (Cluster-EB) scheme in Section 2 proposes to group the spatially similar users and to assign to each group one beamforming tailored on the spatial covariances of the clustered users. In each time slot the BS selects one cluster and transmits the corresponding beamforming. Then, the scheduler selects the user within the selected cluster that reports the largest SNR. We point out that the knowledge of the spatial covariance grants the spatial matching between the transmission beamforming Copyright © 2007 John Wiley & Sons, Ltd. Accepted 1 December 2006