Abstract
In this letter, we propose techniques for joint transmit and receive beamforming in downlink multi-user MIMO systems under Rayleigh fading channels using knowledge of the second-order statistics. The contribution of our work is twofold. First, we derive a closed-form expression for the outage probability for a general channel model using a recent covariance shaping method and for the conventional Kronecker structured model. Second, we present an outage minimization technique obtained by designing the transmit and receive beamformers. The transmit beamformers maximize the statistics of the signal-to-leakage-plus-noise ratio, while the receive beamformers minimize the cross-covariance of all users. Our techniques are "blind" in the sense that they do not require the transmission of pilot symbols, nor the estimation of the instantaneous state of the channel, making them bandwidth efficient. The derived theoretical results are validated via Monte Carlo simulations and show significant reduction in the outage probability by employing the proposed statistical beamforming techniques.