An Effective Technique for Reducing the Truncation Error in the Near-Field-Far-Field Transformation with Plane-Polar Scanning

An effective approach is proposed in this paper for estimating the near-field data external to the measurement region in the plane-polar scanning. It relies on the nonredundant sampling representations of the electromagnetic field and makes use of the singular value decomposition method for the extrapolation of the outside samples. It is so possible to reduce in a significant way the error due to the truncation of the measurement zone thus increasing the far- field angular region of good reconstruction. The comparison of such an approach, based on the optimal sampling interpolation expansions, with an existing procedure using the cardinal series has highlighted that the proposed technique works better. Some numerical tests are reported for demonstrating its effectiveness.

[1]  Bede Liu,et al.  On the use of singular value decomposition and decimation in discrete-time band-limited signal extrapolation , 1984 .

[2]  J. Cadzow,et al.  An extrapolation procedure for band-limited signals , 1979 .

[3]  Marco Donald Migliore,et al.  A new strategy to reduce the truncation error in near-field/far-field transformations , 2000 .

[4]  Flaminio Ferrara,et al.  Near-field – far-field transformation techniques , 2006 .

[5]  Ovidio Mario Bucci,et al.  Data Reduction in the Nf-Ff Transformation Technique With Spherical Scanning , 2001 .

[6]  Francesco D'Agostino,et al.  NF-FF transformation with plane-polar scanning: ellipsoidal modelling of the antenna , 1999 .

[7]  Flaminio Ferrara,et al.  NF-FF transformation with cylindrical scanning from a minimum number of data , 2002 .

[8]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[9]  A. Papoulis A new algorithm in spectral analysis and band-limited extrapolation. , 1975 .

[10]  William H. Press,et al.  Numerical recipes , 1990 .

[11]  E. Joy,et al.  Basic theory of probe-compensated near-field measurements , 1978 .

[12]  Paulo Jorge S. G. Ferreira The stability of a procedure for the recovery of lost samples in band-limited signals , 1994, Signal Process..

[13]  Per Christian Hansen,et al.  Rank-Deficient and Discrete Ill-Posed Problems , 1996 .

[14]  Gene H. Golub,et al.  Matrix computations , 1983 .

[15]  Henry J. Landau,et al.  Extrapolating a band-limited function from its samples taken in a finite interval , 1986, IEEE Trans. Inf. Theory.

[16]  W. Steenaart,et al.  An approach to band-limited signal extrapolation: The extrapolation matrix , 1978 .

[17]  A. Jain,et al.  Extrapolation algorithms for discrete signals with application in spectral estimation , 1981 .

[18]  J. Sanz,et al.  Some aspects of band-limited signal extrapolation: Models, discrete approximations, and noise , 1983 .

[19]  Claudio Gennarelli,et al.  Theoretical Foundations of Near-Field-Far-Field Transformations with Spiral Scannings , 2006 .

[20]  Yahya Rahmat-Samii,et al.  FFT applications to plane-polar near-field antenna measurements , 1987 .

[21]  D. Slepian,et al.  Prolate spheroidal wave functions, fourier analysis and uncertainty — II , 1961 .

[22]  O. Bucci,et al.  Representation of electromagnetic fields over arbitrary surfaces by a finite and nonredundant number of samples , 1998 .

[23]  M.D. Migliore,et al.  Reduction of truncation error in near-field measurements of antennas of base-station mobile communication systems , 2004, IEEE Transactions on Antennas and Propagation.

[24]  G. Franceschetti,et al.  On the spatial bandwidth of scattered fields , 1987 .

[25]  Ovidio Mario Bucci,et al.  Near-field-far-field transformation from nonredundant plane-polar data: effective modellings of the source , 1998 .

[26]  O. Bucci,et al.  Optimal interpolation of radiated fields over a sphere , 1991 .

[27]  A. Sano,et al.  Optimally regularized inverse of singular value decomposition and application to signal extrapolation , 1993, Signal Process..

[28]  Claudio Gennarelli,et al.  Data reduction in the NF-FF transformation with bi-polar scanning , 2003 .

[29]  Flaminio Ferrara,et al.  An Efficient Near-field to Far-field Transformation Using the Planar Wide-mesh Scanning , 2007 .