A Robust Beamforming Algorithm for Multiple Access Systems with Multiple-Input Multiple-Output and Single-Carrier Frequency Division

A robust beamforming algorithm for multiple access systems with multiple-input multiple-output (MIMO) and single carrier frequency division (SC-FDMA) is proposed to solve the problems of performance degradation and sensitivity to channel state information (CSI) errors of conventional beamforming algorithms under scenarios of imperfect CSI. The algorithm establishes a model for the imperfect CSI by using a spectral norm, and the beamforming optimization is formulated as a min-max problem based on the criterion of sum of mean-squared errors. Then, the saddle point property of the min-max problem is established and the optimal beamforming structure is obtained by using majorization theory and singular value inequalities. An optimal power allocation algorithm is derived by employing convex optimization. Simulation results and comparisons with the non-robust beamforming and equal power allocation algorithms show that the proposed algorithm has better performance in bit error rate (BER) and spectral efficiency. When the CSI errors increase, a comparison with the non-robust beamforming algorithm in the high SNR regime show that the proposed algorithm obtains 1 dB gain in bit error rate, and the spectral efficiency improves by about 6%.