Can. J. Elect. Comput. Eng., Vol. 36, No. 2, Spring 2013 Manuscript received January 28, 2013; accepted April 1, 2013 * Yi Zheng and Steven D. Blostein are with the Department of Electrical and Computer Engineering Queen’s University, Kingston, Ontario, K7L3N6, Canada; steven.blostein@queensu.ca and zyimister@gmail.com This research has been supported by Defence R&D Canada through the Defence Research Program at the Communications Research Centre Canada. This was presented in part at IEEE PIMRC, Toronto, Sept. 2011. Associate Editor managing this paper’s review: S. Yousefi Downlink beamforming through relays: imperfect CSI and coordinated transmission Formation de faisceau pour liaison descendante par relais: CSI imparfait et transmissions coordonnées Yi Zheng and Steven D. Blostein * Future wireless systems face challenges in supporting high-rate multimedia streaming with wide coverage area and at low power. Cooperative relaying is investigated in the following context: a single base station with multiple antennas simultaneously transmits different data streams to single-antenna destina- tions through a set of single-antenna fixed relays, with no direct link transmission between base stations and destinations. Transmission is via space-division multiple access with per-user quality-of-service constraints. The base station performs transmit beamforming (precoding) and relays cooperatively perform distributed beamforming. To address minimum-power source precoding and relay beamforming, the source precoder design with a fixed relay beamformer is first considered. Precoding is also generalized to multiple cooperating base stations. Next, the relay beamformer is optimized for a given source precoder and the process is iterated. The formulation is generalized to account for CSI estimates obtained from pilot symbol training. Simulation results quantify tradeoffs, including numbers of base station antennas and relays, effect of CSI quality on performance, as well as the impact of cooperating base stations. Les systèmes sans fil font face à un défi, celui d’assurer, avec un minimum de puissance, une diffusion multimédia haut débit sur une grande aire géo- graphique. Le relais coopératif est examiné dans le contexte suivant : Une station de base unique constituée de plusieurs antennes transmet simultanément des flux de données différents vers une unique antenne réceptrice par le biais d’une série d’antennes relais fixes. Aucun lien direct n’existe entre la station de base et l’antenne réceptrice. La transmission se fait par SDMA (Space Division Multiple Access) avec contraintes de qualité de service par utilisateur. La station de base produit le faisceau (pré-codage) et les antennes relais distribuent le faisceau de façon coopérative. Pour satisfaire l’usage d’un minimum de puissance, nous concevons d’abord un pré-codeur source avec un relais formateur de faisceau. Le pré-codage est aussi généralisé à plusieurs stations de base coopératives. Ensuite, le relais formateur de faisceau est optimisé pour une source pré-codeur donnée et le processus est itéré. La formulation est généralisée pour représenter des évaluations de CSI obtenues de la formation de symboles pilotes. Les résultats de simulation quantifient les différences au regard du nombre de stations de base du nombre d’antennes et du nombre de relais, de l’effet de la qualité du CSI sur la performance, ainsi que l’impact des stations de base coopératives. Keywords: MIMO, cooperative systems, beamforming, channel estimation, semi-definite relaxation, multi-cell communications. I Introduction Providing cellular coverage and links that stream high-rate multimedia leads to increased transmission power, which in turn increases inter- cell interference. Alternatively, cell-splitting leads to frequent hand- overs. A recent approach to increase coverage and capacity that limits transmission power is cooperative communication involving relaying. While orthogonal subcarriers and careful network planning can be used to accommodate relay systems as proposed with LTE Advanced [1] [2] [3], spectrum is scarce and in-band interference cannot be com- pletely eliminated. Thus, limiting transmission power at both base sta- tions and relays is critical, which is the topic addressed in this paper. A variety of relaying technologies have been proposed. For example, diversity can be introduced [4] [5] through cooperation of spatially separated communication nodes, via relaying, to improve communica- tions. Relaying protocols [4] [6] include amplify and forward (AF), which has also been shown to achieve full diversity. To date, the design problems concerning relay assignment have been examined mainly for single-user scenarios with focus on the outage probability analysis of the best relay for transmission or for reception and bottleneck link [7] [8]. Multi-user multi-relay wireless networks with single-carrier fre- quency division multiple access (SC-FDMA) at the terminals is stud- ied in [9]. Joint relay selection and power allocation for cooperative systems has been studied in [10]. In [11], the design of linear precoders broadcasting to fixed MIMO receivers using signal-to-noise plus inter- ference (SINR) constraints is considered. Transceiver design that takes imperfect channel state information into account has also been studied [12] [13] [14]. However, these approaches apply to MIMO transceiv- ers. In this paper, we address imperfect CSI for cooperative systems. Transmission techniques for broadcast channels have been extended to cooperative networks, where relays cooperatively transmit to a re- ceiver [15], which is an instance of distributed beamforming, where amplitudes and phases of transmitted signals are coherently combined. In [16], rate maximization for a parallel relay network with noise cor- relation is studied. In [17], a distributed beamforming system with a single transmitter and receiver and multiple relay nodes is studied, and second order statistics of the channel are employed to design the optimal distributed relay beamformer (DRBF). In [18], single-antenna source-destination pairs that communicate peer-to-peer through a relay network are considered, and the DRBF problem is formulated in terms of semi-definite programming (SDP) and solved through semi-definite relaxation. Unfortunately, the requirement for accurate channel state information (CSI) and the distributed nature of wireless sensor/relay