动态选择子带的可变步长改进多带自适应滤波算法

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"本文提出了一种新的可变步长改进的多带结构子带自适应滤波器算法，该算法能够在动态选择子带滤波器的同时降低计算复杂性。通过比较稳态子带均方误差（SMSE）与子带误差功率，设计了一种子带选择策略，用于识别有意义的子带。同时，通过估计均方偏差（MSD）来控制步长，以优化稳态性能。模拟结果显示，该提案算法在稳态MSD更低且计算复杂度更小的情况下，优于现有的子带算法。关键词：归一化子带自适应滤波器，改进的多带结构自适应子带滤波器，可变步长（VSS），动态选择" 本文研究的是子带自适应滤波器领域，特别关注于提高算法的收敛速度和降低计算复杂性。传统的子带自适应滤波器通过预白化处理输入信号以改善其收敛行为。然而，该过程可能会导致较高的计算负载。为了应对这一挑战，作者提出了一个新的算法——VSS-DS-IMASF（可变步长、动态选择的改进多带结构子带自适应滤波器）。在VSS-DS-IMASF算法中，一个关键创新是动态子带选择策略。这个策略基于比较稳态子带均方误差与子带误差功率，以识别哪些子带的滤波器已达到稳态。只有当子带滤波器达到稳态时，才会继续处理，从而减少了不必要的计算。这种选择机制有助于在保持滤波器性能的同时降低整体的计算复杂性。此外，该算法还引入了步长控制机制，通过估计均方偏差（MSD）来优化算法的稳态性能。MSD的估计使得滤波器可以调整其更新步长，从而更快地收敛到最优状态，并且在稳态下提供更好的性能。模拟结果验证了VSS-DS-IMASF算法的优势，表明它在稳态均方误差（MSD）上显著低于现有子带算法，而且计算复杂度更低。这意味着该算法在实际应用中，如音频处理、通信系统噪声消除或图像处理等领域，可能有更高的效率和效果。这项研究为子带自适应滤波器领域提供了一个新的、高效的解决方案，其动态子带选择和步长控制策略有望推动该领域的技术进步，同时降低计算资源的需求。

Abstract—Subband adaptive filter algorithms are able to improve

the convergence behavior by performing the pre-whitening procedure

on the input signals. In this paper, we propose a new variable step size

improved multiband-structured subband adaptive filter algorithm

which dynamically selects subband filters (VSS-DS-IMASF) in order

to reduce the computational complexity. The subbband selection

scheme which is designed to select the meaningful subbands is based

on comparing the steady state subband mean square error (SMSE) with

the subband error power throughout the algorithm execution, checking

whether the subband filters converge to the steady state. In addition,

the step size is controlled by the estimated mean square deviation

(MSD) in order to achieve better steady state performance. Simulation

results show that the proposed algorithm has lower steady state MSD

and less computational complexities compared with the existing

subband algorithms.

Keywords—

Normalized subband adaptive filter, Improved

multiband-structured adaptive subband filter, Variable step size (VSS),

Dynamic selection

I. I

NTRODUCTION

ubband adaptive filtering has been received much attention

in recent years, due to its capability of improved

convergence performance for highly correlated input signals.

For the conventional subband adaptive filters(SAFs), the

adaptive subfilter coefficients are updated independently in

each subband, and thus the convergence performance is

degraded by the band-edge and aliasing effects [1]. To

overcome this drawback, several subband structures have been

presented [2-6]. Pradhan-Peddy subband model [2] is designed

by use of the polyphase decomposition and noble identity.

Furthermore, combining the characteristics of the affine

projection (AP) algorithm [7] with Pradhan-Peddy subband

model, a subband AP (SAP) algorithm has been reported in [3],

which improves the convergence rate and reduce the

computational complexity of the AP algorithm. Lee and Gan [4]

presented a normalized subband adaptive filter (NSAF)

algorithm which made use of all the subband signals,

This work was supported in part by the National Natural Science

Foundation of China under Grant 61501119.

Chang Liu, Zhi Zhang are with School of Electronic Engineering,

Dongguan University of Technology, No.1, DaXue Avenue, Songshan Lake

district, Dongguan, 523808, People’s Republic of China (

chaneaaa@163.com,

ellon_zhang@sina.com

normalized by their respective subband input variance, to

update the full-band adaptive filter coefficients. Recently, to get

better convergence performance, an improved multiband struct

-ured subband adaptive filter (IMASF) algorithm has been

proposed [5-6]. It applies the most recent P input signal vectors

(projection orders) to participate in the full-band filter updating.

The IMSAF algorithm can be considered as a generalized form

of normalized least mean square (NLMS), AP and NSAF

algorithms. However, it encounters higher computational

complexity with the increased projection orders and long

unknown system.

For SAFs, the convergence rate, steady state performance and

computational complexity have been intensively investigated

for many years. It is known that the fixed step size in SAFs

reflects a tradeoff between fast convergence rate and low steady

state misadjustment. To address this problem, several variable

step size (VSS) subband algorithms have been proposed such as

set-member NSAF (SM-NSAF)[8], VSS matrix for NASF [9],

VSS-NASF [10-11], etc. The computational complexity is

another subject for SAFs, it is showed that the computational

complexity of SAF is depends on the number of subband [13].

Although the VSS subband algorithms mentioned above

achieve both better steady state performance and the faster

convergence simultaneously, their computational complexity

remains invariant throughout the convergence process.

Especially, they suffer from huge complexity for some

applications such as acoustic echo cancellation (AEC)

involving extremely long unknown system. Abadi and Husϕy

have presented the simplified selective partial-update subband

adaptive filter (SSPU-SAF) algorithm [12] with a lower

computational complexity compared with the NSAF algorithm.

The dynamic selective NSAF (DS-NSAF) presented in [13]

adopts the subband filters dynamically based on the maximum

mean square deviation (MSD) decrease principle, which retains

the convergence performance and reduce the computational

complexity. Song’s selective subband scheme [14] is derived

from the larger ratio of the squared error to an input power for

each subband. It has better convergence performance and lower

complexity. Yang [15] makes an analyses on the computational

complexity of the IMSAF algorithm and proposes several

simplified computation approaches to reduce its complexity.

These simplified variants for IMSAF acquire the decrease of the

complexity.

A variable step size improved

multiband-structured subband adaptive filter

algorithm with subband input selection

Chang Liu, Zhi Zhang

INTERNATIONAL JOURNAL OF CIRCUITS, SYSTEMS AND SIGNAL PROCESSING

Volume 11, 2017

ISSN: 1998-4464

202

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