A Probabilistic Constraint Approach for Robust Transmit Beamforming with Imperfect Channel Information

Technical Report.

P.-J. Chung, H. Du and J. Gondzio

Transmit beamforming (or precoding) is a powerful technique for enhancing performance of wireless multi-antenna communication systems. Standard transmit beamformers require perfect channel state information at the transmitter (CSIT) and are sensitive to errors in channel estimation. In practice, such errors are inevitable due to finite feedback resources, quantization errors and other physical constraints. Hence, robustness has become a crucial issue recently. Among two popular robust designs, the stochastic approach exploits channel statistics and optimizes the average system performance while the maximin approach considers errors as deterministic and optimizes the worst case performance. The latter usually leads to a very conservative design against extreme (but rare) conditions which may occur at a very low probability. In this work, we propose a more flexible approach that maximizes the average signal-to-noise ratio (SNR) and takes the extreme conditions into account using the probability with which they may occur. Simulation results show that the proposed beamformer offers higher robustness against channel estimation errors than several popular transmit beamformers.

Key words: Robust Transmit Beamforming, Imperfect Channel Information, MIMO Communications, Probabilistic Constraints, Convex Optimization.

Written: 2009, revised 21 Feb, 2011.
IEEE Transactions on Signal Processing 59 (2011) No 6, 2773-2782.