An implementation of the LMS algorithm in the residue number system

The Residue Arithmetic Adaptive Filter (RAAF) processor performs the least mean square (LMS) algorithm using 60 ns discrete PROM-latch combinations for the residue operations. Parallel and pipeline techniques are used throughout. Since the LMS algorithm is recursive, scaling is required between filter iterations. The scaling penalty has been eliminated by the use, of a new residue scaling technique and an increased parallelism made possible by a reformulation of the LMS equations. The scaling algorithm is based on the mixed radix conversion process and permits scaling by a fixed but arbitrary scale factor in clock periods, where is the number of moduli used. The reformulated LMS equations permit the scaling to proceed in parallel with other filter operations so that the scaling requirement does not increase the number of clock periods per filter iteration. Throughputs of 2 MHz are attained, and the processor performance as a noise canceller agrees well with computer simulations.