General RNS - Optical Adaptive Processing For Large Systems

P. R. Beaudet; J. C. Bradley; E. C. Malarkey; Brian M. Hendrickson

doi:10.1117/12.946947

22 August 1988 General RNS - Optical Adaptive Processing For Large Systems

P. R. Beaudet, J. C. Bradley, E. C. Malarkey, Brian M. Hendrickson

Proceedings Volume 0936, Advances in Optical Information Processing III; (1988) https://doi.org/10.1117/12.946947
Event: 1988 Technical Symposium on Optics, Electro-Optics, and Sensors, 1988, Orlando, FL, United States

Abstract

In a Residue Number System, Second Factorization reduces modular multiplication, addition and subtraction to several miniature look up tables (LUT's). Optical implementation of Second Factorization for parallel matrix processing is investigated for large adaptive phased array radar applications. It is shown that a modified Sherman-Morrison method can be used with Second Facorization in a Quadratic Residue Number System, QRNS, to solve the adaptive beam forming problem. Second Factorization techniques are invoked to implement Quadratic RNS and General RNS arithmetic with small optical LUT's. Properties of the complex primes in QRNS/GRNS are discussed. It is shown that non-Archimedean primes as well as the complex factors of Archimedean primes can be used in a general residue number system (GRNS). Optical architectures for multiplication and addition (subtraction) are presented. Examples of these operations are illustrated. A photograph of a preliminary Mod (6+5i) matrix-vector processor is shown.

Citation Download Citation

P. R. Beaudet, J. C. Bradley, E. C. Malarkey, and Brian M. Hendrickson "General RNS - Optical Adaptive Processing For Large Systems", Proc. SPIE 0936, Advances in Optical Information Processing III, (22 August 1988); https://doi.org/10.1117/12.946947

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