Steady‐state mean‐square deviation analysis of the sign subband adaptive filter

Numerous various step size normalized least mean square (VSS-NLMS)Algorithms have been derived to solve the problem of fast convergence rate and low mean square error.Here we find out the ways to control the step size. A normalized subband adaptive filter algorithm uses a fixed and variable step size, which is chosen as a trade-off between the steady-state error and the convergence rate. A variable step size for normalized subband adaptive filter is derived by minimizing the mean-square deviation between the optimal weight vector and the estimated weight vector at each instant of time. The variable step size is presented in terms of error variance. Therefore, we verify thedifferentÂ algorithmseither they are capable of tracking in stationary and non-stationary environments. The results show good tracking ability and low misalignment of the algorithm in system identification. Parameters are tracking, steady state errors, and misalignment, environment, step size.

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Steady-State Mean-Square Deviation Analysis of the Zero-Attracting CLMS Algorithm With Circular Gaussian Input

IEEE Access ◽

10.1109/access.2019.2911957 ◽

2019 ◽

Vol 7 ◽

pp. 52331-52338 ◽

Cited By ~ 2

Author(s):

Yifan Wu ◽

Jingen Ni

Keyword(s):

Steady State ◽

Mean Square ◽

Mean Square Deviation ◽

Deviation Analysis ◽

Gaussian Input ◽

Zero Attracting

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Statistical-mechanical analysis of adaptive filter with clipping saturation-type nonlinearity

10.36227/techrxiv.16801336 ◽

2021 ◽

Author(s):

Seiji Miyoshi

Keyword(s):

Steady State ◽

Differential Equations ◽

Asymptotic Analysis ◽

Adaptive Filter ◽

Adaptive System ◽

Adaptive Signal Processing ◽

Mean Square ◽

Mean Square Stability ◽

Statistical Mechanical ◽

The Mean

Adaptive signal processing is used in broad areas. In most practical adaptive systems, there exists substantial nonlinearity that cannot be neglected. In this paper, we analyze the behaviors of an adaptive system in which the output of the adaptive filter has the clipping saturation-type nonlinearity by a statistical-mechanical method. To represent the macroscopic state of the system, we introduce two macroscopic variables. By considering the limit in which the number of taps of the unknown system and adaptive filter is large, we derive the simultaneous differential equations that describe the system behaviors in the deterministic and closed form. Although the derived simultaneous differential equations cannot be analytically solved, we discuss the dynamical behaviors and steady state of the adaptive system by asymptotic analysis, steady-state analysis, and numerical calculation. As a result, it becomes clear that the saturation value S has the critical value SC at which the mean-square stability of the adaptive system is lost. That is, when S > SC, both the mean-square error (MSE) and mean-square deviation (MSD) converge, i.e., the adaptive system is mean-square stable. On the other hand, when S < SC, the MSD diverges although the MSE converges, i.e., the adaptive system is not mean-square stable. In the latter case, the converged value of the MSE is a quadratic function of S and does not depend on the step size. Finally, SC is exactly derived by asymptotic analysis.<br>

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Robust Normalized Subband Adaptive Filter Algorithm with a Sigmoid-Function-Based Step-Size Scaler and Its Convex Combination Version

Mathematical Problems in Engineering ◽

10.1155/2021/9924179 ◽

2021 ◽

Vol 2021 ◽

pp. 1-11

Author(s):

Zijie Shen ◽

Lin Tang ◽

Li Yang

Keyword(s):

Steady State ◽

Cost Function ◽

Adaptive Filter ◽

Convex Combination ◽

Sigmoid Function ◽

Function Structure ◽

Step Size ◽

Subband Adaptive Filter ◽

Norm Constraint ◽

Normalized Subband Adaptive Filter

In this paper, by inserting the logarithm cost function of the normalized subband adaptive filter algorithm with the step-size scaler (SSS-NSAF) into the sigmoid function structure, the proposed sigmoid-function-based SSS-NSAF algorithm yields improved robustness against impulsive interferences and lower steady-state error. In order to identify sparse impulse response further, a series of sparsity-aware algorithms, including the sigmoid L0 norm constraint SSS-NSAF (SL0-SSS-NSAF), sigmoid step-size scaler improved proportionate NSAF (S-SSS-IPNSAF), and sigmoid L0 norm constraint step-size scaler improved proportionate NSAF (SL0-SSS-IPNSAF), is derived by inserting the logarithm cost function into the sigmoid function structure as well as the L0 norm of the weight coefficient vector to act as a new cost function. Since the use of the fix step size in the proposed SL0-SSS-IPNSAF algorithm, it needs to make a trade-off between fast convergence rate and low steady-state error. Thus, the convex combination version of the SL0-SSS-IPNSAF (CSL0-SSS-IPNSAF) algorithm is proposed. Simulations in acoustic echo cancellation (AEC) scenario have justified the improved performance of these proposed algorithms in impulsive interference environments and even in the impulsive interference-free condition.

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Normalized Combinations of Proportionate Affine Projection Sign Subband Adaptive Filter

Scientific Programming ◽

10.1155/2021/8826868 ◽

2021 ◽

Vol 2021 ◽

pp. 1-12

Author(s):

Tong An ◽

Tao Zhang ◽

Yanzhang Geng ◽

Haiquan Jiao

Keyword(s):

Steady State ◽

Adaptive Filter ◽

Future Research ◽

L1 Norm ◽

Power Normalization ◽

Affine Projection ◽

Mixing Parameter ◽

Subband Adaptive Filter ◽

Accelerated Gradient ◽

The Cost

The proportionate affine projection sign subband adaptive filter (PAP-SSAF) has a better performance than the affine projection sign subband adaptive filter (AP-SSAF) when we eliminate the echoes. Still, the robustness of the PAP-SSAF algorithm is insufficient under unknown environmental conditions. Besides, the best balance remains to be found between low steady-state misalignment and fast convergence rate. In order to solve this problem, we propose a normalized combination of PAP-SSAF (NCPAP-SSAF) based on the normalized adaption schema. In this paper, a power normalization adaptive rule for mixing parameters is proposed to further improve the performance of the NCPAP-SSAF algorithm. By using Nesterov’s accelerated gradient (NAG) method, the mixing parameter of the control combination can be obtained with less time consumed when we take the l1-norm of the subband error as the cost function. We also test the algorithmic complexity and memory requirements to illustrate the rationality of our method. In brief, our study contributes a novel adaptive filter algorithm, accelerating the convergence speed, reducing the steady-state error, and improving the robustness. Thus, the proposed method can be utilized to improve the performance of echo cancellation. We will optimize the combination structure and simplify unnecessary calculations to reduce the algorithm’s computational complexity in future research.

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