Flexible Coordinated Beamforming (FlexCoBF) Algorithm for the Downlink of Multi-User MIMO Systems Bin Song, Florian Roemer, and Martin Haardt Communications Research Laboratory Ilmenau University of Technology P. O. Box 100565, D-98694 Ilmenau, Germany, http://www.tu-ilmenau.de/crl Email: { bin.song, florian.roemer, martin.haardt }@tu-ilmenau.de Abstract—We propose a Flexible Coordinated Beamforming (FlexCoBF) algorithm for the Multi-User MIMO downlink in the case where the total number of receive antennas exceeds the number of transmit antennas at the base station. This case is relevant for many scenarios that have been discussed recently. For instance, for coordinated multipoint (CoMP) transmissions, which play a significant role in LTE to achieve the IMT-Advanced requirements [1], we have to consider users across cell borders jointly and hence a large total number of receive antennas is present. FlexCoBF is significantly more flexible compared to previous approaches, since the linear transmit as well as receive strategies can be chosen arbitrarily. Moreover, we achieve the same sum rate as the best known coordinated beamforming (CBF) algorithm with significantly fewer iterations. Index Terms—Multi-user MIMO, coordinated beamforming I. I NTRODUCTION In the multi-user MIMO broadcast channel, a high capacity can be achieved by coordinating the transmissions to multiple users simultaneously. As an optimal transmit strategy, dirty paper coding (DPC) has been shown to achieve the capacity region of Gaussian MIMO broadcastchannels in [2]. However, deploying DPC in real systems is impractical due to the prohibitive complexity at both transmitter and receiver. Non- linear precoding [3], [4], as a sub-optimal transmit strategy, is proposed to approach the sum capacity and enhance the link quality. However, non-linear precoding techniques are sensitive to erroneous channel state information (CSI) and still suffer from a high complexity at the transmitter side. Another alternative sub-optimal transmit strategy is given by linear precoding which is a promising approach due to a lower complexity and an enhanced robustness to erroneous CSI while being able to achieve the same multiplexing gain as DPC. For instance, Zero Forcing (ZF) and Block Diagonalization (BD) [5] are well-known linear precoding techniques. Both ZF and BD enforce zero interference between different users. However, their application is constrained by the dimensional- ity restriction which states that the total number of receive antennas must be smaller than or equal to the number of transmit antennas. This condition is usually not fulfilled in many scenarios that have been studied recently. For example, the users across cell borders have to be considered jointly for coordinated multipoint (CoMP) transmission [1]. Therefore, a large total number of receive antennas is present. Furthermore, a relay-assisted communication scenario discussed in [6] con- tains a larger total number of receive antennas than the number of transmit antennas, when the assisting relay simultaneously serves groups of users belonging to different operators. A related linear precoding technique is Regularized Block Diagonalization (RBD) [7]. RBD has an improved sum rate and diversity order compared to BD and ZF and releases the dimensionality restriction. However, it has been shown that the performance of RBD degrades heavily with an increasing aggregate number of receive antennas [8]. Coordinated beamforming (CBF) algorithms have been pro- posed to transmit a number of data streams that is smaller than the total number of receive antennas [5], [7], [9], [10], [11]. The methods in [5], [7], [9] compute the transmit- receive beamformers by jointly optimizing the beamforming vectors at the transmitter and the receiver in an iterative fashion. The coordinated transmission strategy in [9] is a low complexity approach, and the sum rate performance is closest to the sum capacity of the MIMO broadcast channel compared to the other CBF algorithms [5], [7]. However, only a single data stream to each user is considered in [9] and the receive beamforming strategy is fixed to maximum ratio combining (MRC) matched filtering. Furthermore,the transmit beamformers are found by a matrix inversion, which imposes further constrains on the dimensionality and is sensitive to the conditioning of the matrix (e.g., it suffers from spatial correlation). Closed-form expressions for CBF were proposed in [10] and [11], in order to avoid iterative computations while achieving the same sum rate performance as the iterative CBF in [9]. In [10], the transmit beamformers are designed as the generalized eigenvectors of the channel correlation matrices of the users when a MRC matched filter is used at each user side. However, this algorithm is only valid for a two transmit antennas system with two users. In [11], a closed- form coordinated beamforming algorithm for an arbitrary number of transmit antennas was proposed. The coordinated transmit-receive beamformers are directly calculated by using 2010 International ITG Workshop on Smart Antennas (WSA 2010) 978-1-4244-6072-4/10/$26.00 ©2010 IEEE 414