Critical-Path Analysis and Low-Complexity Implementation of the LMS Adaptive Algorithm

In order to derive its architectures for high-speed and low-complexity implementation, this study gives a rigorous analysis of the least-mean-square (LMS) adaptive filter's critical path. It is demonstrated that the direct-form LMS adaptive filter offers substantially faster convergence and smaller register complexity while having almost the same critical path as its transpose-form equivalent. From the critical-path evaluation, it is further demonstrated that, in most practical circumstances, no pipelining is needed to build a direct-form LMS adaptive filter. In contrast, cases where a very high sampling rate is required can be realised with a very tiny adaptation delay. This paper suggests three topologies for the LMS adaptive filter in light of these findings:

There are three different designs: (i) Design 1 has no adaptation delays, (ii) Design 2 has just one adaptation delay, and (iii) Design 3 has two adaptation delays. Design 1 utilises the smallest area and the EPS, or minimum energy per sample. The best direct-form structures now in use require 41.9% more EPS and 80.4% more area than Design 1. While offering nearly twice and three times the MUF at a cost of 55.0% and 60.6% more area, Designs 2 and 3 use a little bit more EPS than Design 1 does.

Index Terms—Adaptive filters, critical-path optimization, least mean square algorithms, LMS adaptive filter