Optical Adaptive Beamforming Using Residue Number Systems (RNSs) And Gauss Elimination

P R Beaudet; J C Bradley; E C Malarkey

doi:10.1117/12.944186

12 April 1988 Optical Adaptive Beamforming Using Residue Number Systems (RNSs) And Gauss Elimination

P R Beaudet, J C Bradley, E C Malarkey

Proceedings Volume 0886, Optoelectronic Signal Processing for Phased-Array Antennas; (1988) https://doi.org/10.1117/12.944186
Event: 1988 Los Angeles Symposium: O-E/LASE '88, 1988, Los Angeles, CA, United States

Abstract

Optical look-up tables (LUT's) are used for solving the Adaptive Beamforming problem in a quadratic (Complex) Residue Number System, QRNS. It is shown that QRNS is isomorphic to the usual RNS arithmetic so that real moduli implementations can be used. In QRNS, a system of linear equations can appear singular when the determinant is a multiple of one of the moduli used in the representation. It is shown that this apparent singularity can be avoided and that the singular-like system of equation can be solved uniquely in spite of the apparent singularity. An example is given to illustrate the technique of solving singular-like QRNS systems of equations. The optical implementation of QRNS arithmetic uses Second Factorization which is shown to significantly reduce the number of optical components needed in the LUT's.

Citation Download Citation

P R Beaudet, J C Bradley, and E C Malarkey "Optical Adaptive Beamforming Using Residue Number Systems (RNSs) And Gauss Elimination", Proc. SPIE 0886, Optoelectronic Signal Processing for Phased-Array Antennas, (12 April 1988); https://doi.org/10.1117/12.944186

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