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Achieving probabilistic robustness for multiuser SIMO uplink with Gaussian channel uncertainty

This paper studies the robust receive beamforming design and power control for a multiuser single-input multiple-output (SIMO) antenna system in the uplink with imperfect channel state information at the base station receiver (CSIR). The objective of the robust design is to minimize the total transmit power while ensuring the users' target signal-to-interference plus noise ratios (SINR) to be achieved for some given probabilities. Using Gaussian approximation to characterize the distribution of the interference, an optimization algorithm which optimizes the power allocation and beamforming vectors iteratively to obtain a robust solution is presented. The proposed algorithm is proved to be the global optimum for the Gaussian approximated problem, though it is not convex. Simulation results validate the robustness of the proposed algorithm and illustrate a significant gain when compared to a zero-forcing (ZF) solution.