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Complex independent component analysis is formulated for ultrawideband (UWB) incoherent fields, based on maximum-likelihood estimation with iterative natural gradient searching. It can be applied to measurements of complex power separated in contributions by propagating and reactive near-fields. A set of novel nonlinear asymmetric score functions is derived that are asymptotically matched to skewed probability density functions of incoherent energy sources departing from ideal chi-square ensemble distributions. The source decomposition is applied to two analog and digital integrated circuits. Based on the measured intensity of the emitted magnetic field, the technique is shown to enable nonlinear extraction of a set of independent spatially separated UWB sources, without knowledge of neither the detailed circuit geometry nor its on-board signals. Overcompleteness of the data set is found to have a relatively small effect on the accuracy of the estimated magnitude and location of the emission hot spots, but has a major influence on the global spatial maps and nature of the extracted sources.