Statistical modal analysis applied to near-field measurements of random emissions

The problem of near-field to far-field transformation of narrow-band incoherent electromagnetic fields is analyzed. The coherence matrix of signals sampled in the time domain on a surface enclosing incoherent sources is derived. Two equivalent formulations based on the processing of the coherence matrix are introduced: The signal subspace analysis and the bimodal transformation. In the signal-subspace approach, the coherence matrix is processed using a method based on singular value decomposition, giving rise to a set of functions on the surface enclosing the incoherent sources. Each of these functions is individually transformed to the far field via a modal decomposition and the sum of the transformed functions gives the total far field. In the second formulation, the bimodal transformation is used to transform the near field coherence matrix into the far field coherence matrix from which the far-field pattern is derived. The applications of the proposed transformations in the presence of noise are illustrated. A numerical example using incoherent radiating dipoles inside a leaking wire-grid enclosure validates the two formulations of near-field to far-field transformation. The proposed methodology gives the mathematical foundation for designing a compact time domain measurement facility well suited to incoherent electromagnetic radiation.