Pipelined Architectures for Transform Domain LMS Adaptive Filtering

Abstract

In this paper, efficient pipelined architectures for the implementation of the Transform Domain LMS (TD-LMS) adaptive filter are considered. Pipelining of the TD-LMS algorithm is achieved by introducing an amount of time delay into the original adaptive scheme. The resulting algorithm, called thereafter the delayed TD-LMS, performs adaptive filtering with delayed coefficients adaptation. A statistical performance analysis of the proposed delayed TD-LMS adaptive algorithm is presented, both for the mean error and the mean squared error of the filter coefficients. A closed form expression is derived for the estimation of the steady state excess mean squared error, in terms of the adaptation delay and the input signal characteristics. The adaptation delay introduced to the delayed TD-LMS algorithm is subsequently utilized for the development of pipelined architectures. By retiming the delays existing in the error signal feedback loop, efficient pipelined implementations of the delayed TD-LMS algorithm are developed. The proposed architectures are suitable for parallel implementation on a general-purpose parallel machine, or on dedicated hardware, integrated on ASIC or ASIP VLSI processors.

A Study on a Novel Inverted Ultra-Short Baseline Positioning System and Phase Difference Estimation

“…The least mean square (LMS) adaptive algorithm [18] does not require prior knowledge of the signal; it also has simple calculations and is easy to implement. It is widely used in the fields of adaptive filtering, frequency tracking, and delay estimation [19][20][21][22][23].…”