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Application of Distributed Arithmetic to Adaptive Filtering Algorithms: Trends, Challenges and Future

Mohd. Tasleem Khan

TL;DR

The paper investigates applying distributed arithmetic (DA) to adaptive filtering (AF) to reduce multiply-accumulate cost and hardware resources in real-time implementations. It surveys DA-based architectures for LMS and its fast variants, detailing Type TC and OBC encodings, conjugate DA, and block/sliding-block approaches, and it formulates LMS AF using DA with explicit IPC and coefficient-update rules. The analysis highlights trends toward LUT-based precomputation, pipelining, and LUT sharing, while noting challenges from memory growth, precision loss, and adaptation complexity; future work envisions hybrid DA with approximate computing and machine learning, plus specialized hardware for edge/6G deployments. Overall, DA-based AFs promise higher throughput and lower hardware complexity, enabling real-time, energy-efficient adaptive filtering in resource-constrained environments and guiding future extensions to more advanced AFs like APA and RLS.

Abstract

The utilization of distributed arithmetic (DA) in AF algorithms has gained significant attention in recent years due to its potential to enhance computational efficiency and reduce resource requirements. This paper presents an exploration of the application of DA to adaptive filtering (AF) algorithms, analyzing trends, discussing challenges, and outlining future prospects. It begins by providing an overview of both DA and AF algorithms, highlighting their individual merits and established applications. Subsequently, the integration of DA into AF algorithms is explored, showcasing its ability to optimize multiply-accumulate operations and mitigate the computational burden associated with AF algorithms. Throughout the paper, the critical trends observed in the field are discussed, including advancements in DA-based hardware architectures. Moreover, the challenges encountered in implementing DA-based AF is also discussed. The continued evolution of DA techniques to cater to the demands of modern AF applications, including real-time processing, resource-constrained environments, and high-dimensional data streams is anticipated. In conclusion, this paper consolidates the current state of applying DA to AF algorithms, offering insights into prevailing trends, discussing challenges, and presenting future research and development in the field. The fusion of these two domains holds promise for achieving improved computational efficiency, reduced hardware complexity, and enhanced performance in various signal processing applications.

Application of Distributed Arithmetic to Adaptive Filtering Algorithms: Trends, Challenges and Future

TL;DR

The paper investigates applying distributed arithmetic (DA) to adaptive filtering (AF) to reduce multiply-accumulate cost and hardware resources in real-time implementations. It surveys DA-based architectures for LMS and its fast variants, detailing Type TC and OBC encodings, conjugate DA, and block/sliding-block approaches, and it formulates LMS AF using DA with explicit IPC and coefficient-update rules. The analysis highlights trends toward LUT-based precomputation, pipelining, and LUT sharing, while noting challenges from memory growth, precision loss, and adaptation complexity; future work envisions hybrid DA with approximate computing and machine learning, plus specialized hardware for edge/6G deployments. Overall, DA-based AFs promise higher throughput and lower hardware complexity, enabling real-time, energy-efficient adaptive filtering in resource-constrained environments and guiding future extensions to more advanced AFs like APA and RLS.

Abstract

The utilization of distributed arithmetic (DA) in AF algorithms has gained significant attention in recent years due to its potential to enhance computational efficiency and reduce resource requirements. This paper presents an exploration of the application of DA to adaptive filtering (AF) algorithms, analyzing trends, discussing challenges, and outlining future prospects. It begins by providing an overview of both DA and AF algorithms, highlighting their individual merits and established applications. Subsequently, the integration of DA into AF algorithms is explored, showcasing its ability to optimize multiply-accumulate operations and mitigate the computational burden associated with AF algorithms. Throughout the paper, the critical trends observed in the field are discussed, including advancements in DA-based hardware architectures. Moreover, the challenges encountered in implementing DA-based AF is also discussed. The continued evolution of DA techniques to cater to the demands of modern AF applications, including real-time processing, resource-constrained environments, and high-dimensional data streams is anticipated. In conclusion, this paper consolidates the current state of applying DA to AF algorithms, offering insights into prevailing trends, discussing challenges, and presenting future research and development in the field. The fusion of these two domains holds promise for achieving improved computational efficiency, reduced hardware complexity, and enhanced performance in various signal processing applications.
Paper Structure (14 sections, 16 equations, 4 figures, 1 table)

This paper contains 14 sections, 16 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Literature review of DA-based architecture for LMS and its variants
  3. DA-based LMS AFs
  4. DA-based DLMS AFs
  5. DA-based BLMS AFs
  6. Formulation of LMS AF using DA
  7. IPC using TC DA
  8. IPC using OBC DA
  9. Coefficient Update using TC and OBC DA
  10. Trends, Challenges, and Future Prospects
  11. Trends
  12. Challenges
  13. Future
  14. Conclusion

Figures (4)

  • Figure 1: An overview of applications of AF algorithms.
  • Figure 2: Comparison of error performance, computational cost, and real-time efficiency across LMS, APA, RLS with different implementation approaches such as multipliers-based, DA and AC, where $E_0 < E_1 < E_2$.
  • Figure 3: Block diagram of LMS AF with a system identification problem.
  • Figure 4: LUT contents of an IPC with (a) TC DA and (b) OBC DA for $N=4$.