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In this paper, we consider the block conjugate gradient (BCG) algorithm as a robust and reduced-rank implementation of the matrix Wiener filter (MWF). Stopping the BCG iterations before the algorithm converges, reduces the computational complexity as well as the performance loss due to channel estimation errors which is especially a problem in low sample support scenarios. We investigate the inherent robustness of the BCG method by deriving the corresponding filter factor matrix which is a well-known tool in the theory of ill-posed problems to describe and analyze regularizing effects. Moreover, we present a robust BCG algorithm where we applied the regularization method of diagonal loading in order to increase both robustness against estimation errors and flexibility in choosing the number of BCG iterations without decreasing performance. Finally, we use quasi-optimal loading instead of common heuristic choices. Simulation results of a frequency-selective multi-user single-input multiple-output (MU-SIMO) system show the improved performance of the robust BCG filter compared to the conventional MWF despite of the enormously reduced computational complexity.