A linearly constrained minimum variance (LCMV) beamformer aims to completely remove interference and optimize the signal-to-noise ratio (SNR). We examine an array geometry consisting of multiple sub-arrays. Our analysis shows that the increased intersensor distance typical of such setups is beneficial for the task of signal separation. Another unique feature of distributed arrays is the necessity of sharing information from different locations, which may pose a burden in terms of power and bandwidth resources. We discuss a scheme with minimalistic transmission requirements involving a preprocessing operation at each sub-array node. Expressions for the penalties due to preprocessing with local parameters are derived and corroborated with computer simulations.