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A diffuse spectrum estimation method is presented that is suitable for direction finding for channels with diffuse electromagnetic scattering. The diffuse channel may be the result of physical phenomena (e.g., rough-surface scattering) or limited angular and temporal discrimination of the channel probing equipment. The method decomposes the ideal noncoherent spectrum into a sum of power-weighted basis functions. The basis function coefficients are obtained through a linear programming solution. The method is applied to recent radio channel data collected on the Vienna University of Technology campus. Parameters for a path-based model are extracted using the technique. Site-specific spectra and global capacity comparisons indicate the utility of this new method.