A Residue Number System Implementation of the LMS Algorithm Using Optical Waveguide Circuits

A detailed design of a real-time data processor based on the residue number system is presented which uses near-term optical waveguide devices and concepts. The optical computational units consist of cascaded, mask-programmable arrays of total internal reflection electrooptic switches arranged on a LiNbO3 substrate in a serpentine configuration. This paper describes these computational units and then concentrates on the computational and residue-related aspects of the processor. A new scaling algorithm is presented which is based on the Chinese remainder theorem and performs scaling during a single clock period. The least-mean-square adaptive filter algorithm with eight weights is tailored to the optical waveguide residue arithmetic format and requires only three computational stages per iteration. Detailed computer simulations of the processor have verified the design and representative output is included. An envisioned 8 ns clock period corresponds to 2.5 × 109 operations/s ( 2.5 G operations/s) using the equivalent of 23 bit internal precision, which compares favorably to expected rates using established technologies.