Statistical signal analysis for the inverse source problem of electromagnetics

A statistical signal analysis for the inverse source problem of electromagnetics is given. This correspondence considers the problem of estimating either the near field or the radiating current distribution from a measurement of the far field. The solution is derived via a linear operator formalism, and the ill-posedness of the reconstruction is quantified by using the Cramer-Rao lower bound, which is explicitly given in terms of the multipole expansion of the electromagnetic field. A numerical study is included to illustrate the theoretical results.

[1]  George W. Kattawar,et al.  Scattering theory of waves and particles (2nd ed.) , 1983 .

[2]  Mats Gustafsson,et al.  Reconstruction of equivalent currents using a near-field data transformation - with radome applications , 2004 .

[3]  A. Karlsson,et al.  Physical limitations of antennas in a lossy medium , 2004, IEEE Transactions on Antennas and Propagation.

[4]  M. Brereton.  Classical Electrodynamics (2nd edn) , 1976 .

[5]  S. Kay.  Fundamentals of statistical signal processing: estimation theory , 1993 .

[6]  A. Devaney,et al.  Inverse source problem with reactive power constraint , 2004, IEEE Transactions on Antennas and Propagation.

[7]  A. Yaghjian.  An overview of near-field antenna measurements , 1986 .

[8]  Mats Gustafsson,et al.  On the spectral efficiency of a sphere , 2004 .

[9]  Mats Gustafsson,et al.  Fundamental Limitations for DOA Estimation by a Sphere , 2004 .

[10]  G. Arfken.  Mathematical Methods for Physicists , 1967 .

[11]  R.M. Jha,et al.  Tuning of EM performance for streamlined aircraft radomes , 2004, IEEE Antennas and Propagation Society Symposium, 2004..

[12]  R. Collin.  Field theory of guided waves , 1960 .

[13]  Steven Kay,et al.  Fundamentals Of Statistical Signal Processing , 2001 .

[14]  D. A. Dunnett.  Classical Electrodynamics , 2020, Nature.

[15]  A. Devaney,et al.  The inverse source problem of electromagnetics: linear inversion formulation and minimum energy solution , 1999 .

[16]  R. Newton.  Scattering theory of waves and particles , 1966 .

[17]  Richard W. Ziolkowski,et al.  Nonradiating and minimum energy sources and their fields: generalized source inversion theory and applications , 2000 .

[18]  Mats Gustafsson,et al.  Multichannel broadband Fano theory for arbitrary lossless antennas with applications in DOA estimation , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[19]  R. Hansen,et al.  Fundamental limitations in antennas , 1981, Proceedings of the IEEE.

[20]  R. Fano.  Theoretical limitations on the broadband matching of arbitrary impedances , 1950 .

[21]  L. J. Chu.  Physical Limitations of Omni‐Directional Antennas , 1948 .

[22]  R. Collin,et al.  Evaluation of antenna Q , 1964 .