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Beam-space data preprocessing is a powerful tool commonly used in array processing to reduce the computational burden and improve the performance of high-resolution direction-finding algorithms. However, currently used beam-space techniques appear to lack robustness in the presence of sources that are located outside the beam-space angular sectors-of-interest. In this paper, a new approach to beam-space preprocessing with an improved robustness against such out-of-sector interfering sources is developed. Our techniques design the beam-space matrix filter based on proper tradeoffs between the in-sector (passband) source distortion and out-of-sector (stopband) source attenuation. Computationally efficient convex formulations for these beam-space matrix filter design problems are derived using second-order cone (SOC) programming.