Two Distributed Arithmetic Based High Throughput Architectures of Non-Pipelined LMS Adaptive Filters

Distributed arithmetic (DA) is an efficient look-up table (LUT) based approach. The throughput of DA based implementation is limited by the LUT size. This paper presents two high-throughput architectures (Type I and II) of non-pipelined DA based least-mean-square (LMS) adaptive filters (ADFs) using two’s complement (TC) and offset-binary coding (OBC) respectively. We formulate the LMS algorithm using the steepest descent approach with possible extension to its power-normalized LMS version and followed by its convergence properties. The coefficient update equation of LMS algorithm is then transformed via TC DA and OBC DA to design and develop non-pipelined architectures of ADFs. The proposed structures employ the LUT pre-decomposition technique to increase the throughput performance. It enables the same mapping scheme for concurrent update of the decomposed LUTs. An efficient fixed-point quantization model for the evaluation of proposed structures from a realistic point-of-view is also presented. It is found that Type II structure provides higher throughput than Type I structure at the expense of slow convergence rate with almost the same steady-state mean square error. Unlike existing non-pipelined LMS ADFs, the proposed structures offer very high throughput performance, especially with large order DA base units. Furthermore, they are capable of performing less number of additions in every filter cycle. Based on the simulation results, it is found that
$256^{\mathrm {th}}$
order filter with
$8^{\mathrm {th}}$
order DA base unit using Type I structure provides
$9.41 \times $
higher throughput while Type II structure provides
$16.68 \times $
higher throughput as compared to the best existing design. Synthesis results show that
$32^{\mathrm {nd}}$
order filter with
$8^{\mathrm {th}}$
order DA base unit using Type I structure achieves 38.76% less minimum sampling period (MSP), occupies 28.62% more area, consumes 67.18% more power, utilizes 49.06% more slice LUTs and 3.31% more flip-flops (FFs), whereas Type II structure achieves 51.25% less MSP, occupies 21.42% more area, consumes 47.84% more power, utilizes 29.10% more slice LUTs and 1.47% fewer FFs as compared to the best existing design.