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<p>Division is the dominant computational bottleneck in the normalized least-mean-square (NLMS) algorithm. Consequently, several division-approximation techniques have been explored, with their induced errors shown to have a negligible impact on the performance of robust NLMS adaptive filters. This paper presents a binary reciprocal approximation to replace division in an NLMS adaptive infinite impulse response (IIR) filter. Compared with conventional SRT division, Newton-Raphson (NR)–based approximation, canonical signed digit (CSD)-based techniques, and look-up table (LUT) methods, the proposed approach achieves superior efficiency in both power consumption and hardware resource utilization. In terms of the figure of merit (FOM), defined as the consumed energy per data sample, the NLMS adaptive IIR filter employing the proposed method achieves FOM reductions of 39.1%, 6.5%, 14.4%, and 5.6% relative to implementations using 15-bit SRT division, NR-based approximation, CSD-based techniques, and LUT methods, respectively.</p>

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Enhancing the Power Efficiency of the NLMS Adaptive IIR Filter with Fast Binary Reciprocal Approximation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月6日

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  • Yu-Zhe Huang,
  • Chia-Yu Yao

摘要

Division is the dominant computational bottleneck in the normalized least-mean-square (NLMS) algorithm. Consequently, several division-approximation techniques have been explored, with their induced errors shown to have a negligible impact on the performance of robust NLMS adaptive filters. This paper presents a binary reciprocal approximation to replace division in an NLMS adaptive infinite impulse response (IIR) filter. Compared with conventional SRT division, Newton-Raphson (NR)–based approximation, canonical signed digit (CSD)-based techniques, and look-up table (LUT) methods, the proposed approach achieves superior efficiency in both power consumption and hardware resource utilization. In terms of the figure of merit (FOM), defined as the consumed energy per data sample, the NLMS adaptive IIR filter employing the proposed method achieves FOM reductions of 39.1%, 6.5%, 14.4%, and 5.6% relative to implementations using 15-bit SRT division, NR-based approximation, CSD-based techniques, and LUT methods, respectively.