Learning to Beamform for Minimum Outage

Acquiring channel state information (CSI) at the base station (BS) is a critical requirement for successfully employing transmit beamforming in multiantenna systems. In practice, channel estimation/quantization errors, feedback delays, and fast fading can make it difficult to obtain accurate CSI at the BS. In this paper, we consider an outage-based approach for transmit beamforming in order to deal with the channel uncertainty at the BS. Our formulation is applicable to both point-to-point transmit beamforming as well as single-group multicasting scenarios. A key difference from prior works is that we do not assume knowledge of the underlying channel distribution; instead, stochastic approximation is used for computing approximate solutions of a nonconvex stochastic optimization problem via simple first-order methods (FOMs). We evaluate the performance of our FOMs in two settings: First) where we design a beamformer at the BS based on historical channel realizations collected over a relatively long time window before deployment, and second) in a post-deployment phase where we perform incremental updates of our beamformer based on intermittent, delayed, or peer feedback. Simulation results reveal the effectiveness of FOMs for our problem compared to other alternatives.