In this work, we present some asymptotic results on the maximum likelihood multi-rank processor for passive wavefront curvature ranging systems using large-scale distributed arrays. We assume that the operation environment for the distributed arrays is subject to a spatial coherence loss. Under an exponential coherence model, analytical expressions for the multi-rank combiners are derived. The results provide a simple guideline for choosing inter-module spacing according to the spatial coherence length for formulating multi-rank mode filters and weights used in the combiner. The general framework and the numerical procedures of designing a multi-rank combiner can be applied to other coherence models.