Forming the Radio Image with Multiple Antennas



In the preceding chapter, we discussed image-formation options at radio wavelengths, and we committed ourselves to an array of directional antennas, a “compound eye” architecture. We have seen that the directional sensitivity of individual sensors is essential, and that their fields must be somewhat overlapped. We have also seen (in Sect. 2.2) that every distant radio source produces sensors’ outputs that lie on a lobe shape pointing toward that source; we refer to this shape as the rotated lobe.

The crux of radiolocating the sources lies in accurately determining the direction of the rotated lobe, on the basis of somewhat sparse data points, which are the antenna signals. Optimizing the fit between the antenna signals and the rotated lobe synthesizes the “image” of the source, i.e., its direction, and we see that the overlap and directional sensitivity of the individual sensors are essential for that synthesis. We entrusted the optimization to a straightforward iterative minimization algorithm, and while this approach was successfully implemented and proved reliable in a networking device, we explore in this chapter an alternative method of image synthesis.


Discrete Fourier Transform Spherical Harmonic Input Function Image Spectrum Directional Sensitivity 


  1. Antolovic, D. An Algorithm for Simultaneous Radiolocation of Multiple Sources, Proceedings of 2009 IEEE International Conference on Portable Information Devices, Anchorage, AK, September 2009, (2009)Google Scholar
  2. Byron, F.W., Fuller, R.W. Mathematics of Classical and Quantum Physics, Dover, New York (1992)Google Scholar
  3. Davis, P.J. Circulant Matrices, Wiley-Interscience, New York (1979)MATHGoogle Scholar
  4. Gantmacher, F.R. The Theory of Matrices, Chelsea, New York (1959)MATHGoogle Scholar
  5. Golub, G.H., Van Loan, C.F. Matrix Computations, 3rd edition, Johns Hopkins University Press, MD (1996)MATHGoogle Scholar
  6. Gradshteyn, I.S., Ryzhik, I.M. Table of Integrals, Series and Products, 7th edition, Academic Press, New York (2007)Google Scholar
  7. Gray, R.M. Toeplitz and Circulant Matrices: A Review, now Publishers, The Netherlands, (2006)
  8. Hamming, R.W. Digital Filters, 3rd edition, Dover, New York (1998)Google Scholar
  9. Jackson, J.D. Classical Electrodynamics, 3rd edition, Wiley, New York (1998)Google Scholar
  10. Messiah, A. Quantum Mechanics, Dover, New York (1999)Google Scholar
  11. Morse, P.M., Feshbach, H. Methods of Theoretical Physics, McGraw- Hill, New York (1953)MATHGoogle Scholar
  12. Smith, S.W. The Scientist and Engineer’s Guide to Digital Signal Processing, California Technical Publishing, CA (1997)Google Scholar

Copyright information

© Springer-Verlag US 2010

Authors and Affiliations

  1. 1.University Information Technology ServicesIndiana UniversityBloomingtonUSA

Personalised recommendations