Low Steady-state Misalignment Research Articles

Bias-Compensated Normalized Least-Mean Fourth Algorithm for Noisy Input

This paper proposes a bias-compensated normalized least-mean fourth (NLMF) algorithm to compensate for the bias caused by noisy input. In the proposed algorithm, we add a bias-compensation vector to the conventional NLMF algorithm, and the bias-compensation vector is then derived based on the unbiasedness criterion. Simulation results in system identification context show that the proposed algorithm provides lower steady-state misalignment as compared to the conventional NLMF algorithm.

Individual-activation-factor Memory Proportionate Affine Projection Algorithm with Evolving Regularization

The individual-activation-factor memory proportionate affine projection algorithm (IAF-MPAPA) provides a good solution for echo cancelation. However, the IAF-MPAPA with fixed regularization factor requires a tradeoff between fast convergence rate and low steady-state misalignment. In this paper, the mathematical relationship between the regularization factor and the steady-state mean square error (MSE) of the IAF-MPAPA was deduced. The mathematical formula of the steady-state MSE indicates that it is inversely proportional to the value of regularization factor. Then, inspirited by the evolutionary method, the IAF-MPAPA with evolving regularization (ERIAF-MPAPA) was proposed. The ERIAF-MPAPA increases or decreases the regularization factor by comparing the power of output error with a threshold which contains the information of the steady-state MSE. For highly sparse impulse responses, simulation results demonstrate that the proposed ERIAF-MPAPA offers better convergence performance than other proportionate-type APAs in terms of convergence rate and steady-state misalignment.

A block parallel ℓ0-norm penalized shrinkage and widely linear affine projection algorithm for adaptive filter

To improve the identification capability of AP algorithm in time-varying sparse system, we propose a block parallel l 0 -SWL-DCD-AP algorithm in this paper. In the proposed algorithm, we first introduce the l 0 -norm constraint to promote its application for sparse system. Second, we use the shrinkage denoising method to improve its track ability. Third, we adopt the widely linear processing to take advantage of the non-circular properties of communication signals. Last, to reduce the high computational complexity and make it easy to implemented, we utilize the dichotomous coordinate descent (DCD) iterations and the parallel processing to deal with the tap-weight update in the proposed algorithm. To verify the convergence condition of the proposed algorithm, we also analyze its steady-state behavior. Several simulation are done and results show that the proposed algorithm can achieve a faster convergence speed and a lower steady-state misalignment than similar APA-type algorithm. When apply the proposed algorithm in the decision feedback equalizer (DFE), the bite error rate (BER) decreases obviously.

Diffusion least mean square/fourth algorithm for distributed estimation

Proposed is a diffusion least mean square/fourth (LMS/F) algorithm, which is characterized by its fast convergence and low steady-state misalignment for distributed estimation in non-Gaussian noise environments. Instead of the conventional mean square error cost function, the diffusion LMS/F algorithm is derived from the mixed square/fourth error cost function, which is more suitable for non-Gaussian noise environments. Moreover, we incorporate the L1- and L0-norm constraints into the mixed square/fourth error cost function, and then a class of diffusion sparse LMS/F algorithms is developed which is able to exploit the sparsity of the considered system. Simulation results show that the diffusion LMS/F algorithm outperforms the conventional diffusion LMS and LMF algorithms in non-Gaussian noise environments. The improvements of diffusion sparse LMS/F algorithms in terms of steady-state misalignment are also demonstrated relative to the diffusion LMS/F algorithm.

Low-Complexity $$l_0$$ l 0 -Norm Penalized Shrinkage Linear and Widely Linear Affine Projection Algorithms

In this paper, we propose an $$l_0$$l0-norm penalized shrinkage linear affine projection ($$l_0$$l0-SL-AP) algorithm and an $$l_0$$l0-norm penalized shrinkage widely linear affine projection ($$l_0$$l0-SWL-AP) algorithm. The proposed algorithms provide variable step-size by minimizing the noise-free a posteriori error at each iteration and introduce an $$l_0$$l0-norm constraint to the cost function. The $$l_0$$l0-SWL-AP algorithm also exploits noncircular properties of the input signal. In contrast with conventional AP algorithms, the proposed algorithms increase the estimation accuracy for time-varying sparse system identification. A quantitative analysis of the convergence behavior for the $$l_0$$l0-SWL-AP algorithm verifies the capabilities of the proposed algorithms. To reduce the complexity, we also introduce dichotomous coordinate descent (DCD) iterations to the proposed algorithms ($$l_0$$l0-SL-DCD-AP and $$l_0$$l0-SWL-DCD-AP) in this paper. Simulations indicate that the $$l_0$$l0-SL-AP and $$l_0$$l0-SWL-AP algorithms provide faster convergence speed and lower steady-state misalignment than the previous APA-type algorithms. The $$l_0$$l0-SL-DCD-AP and $$l_0$$l0-SWL-DCD-AP algorithms perform similarly to their counterparts but with reduced complexity.

A New Data-Reusing Algorithm Based on Minimum Norm and Minimum Disturbance Principles

Aiming to accelerate convergence speed and reduce steady-state misalignment of adaptive filter, a new data-reusing algorithm is proposed. Different from conventional affine projection algorithm (APA) based on minimum disturbance principle (MDP), the proposed algorithm obtains its cost function based on a convex combination of the minimum norm principle (MNP) and the MDP. Weight factor (named as mixing parameter) used in the combination determines the approach for updating. The proposed algorithm has a performance similar to the APA when the mixing parameter closes to 0 and yields results to the data-reusing algorithm based on the MNP if the mixing parameter closes to 1. By minimizing mean-square deviation, the variable mixing parameter has a large value at initial stage and gradually decreases as iteration number increases. At the initial stage, the proposed algorithm achieves fast convergence since the MNP plays a leading role. At the steady-state, the proposed algorithm obtains a low misalignment since the MDP gives a major impact and the updated results have minimum disturbance from the previous ones. At the transition stage, the proposed algorithm is a combination of the APA and the MNP-based data-reusing algorithm. Simulation results show that the proposed algorithm exhibits faster convergence rate and lower steady-state misalignment than some other derivatives of the APA without significantly increasing computational complexity.

A New Variable Step-Size Affine Projection Sign Algorithm Based on A Posteriori Estimation Error Analysis

In order to accelerate the convergence rate and reduce the steady-state misalignment of the affine projection sign algorithm (APSA), a novel variable step-size APSA based on a posteriori estimation error (APEE) analysis is proposed. The new algorithm modified the iterative process of the APSA in which only sign information of the output error is used. The variable step size is obtained by minimizing the $$L_{2}$$L2-norm of the APEE. And the step size has a large value in the initial stage and a small value in the steady state, which can better reflect the working state of the robust adaptive filter than the APSA with fixed step sizes. Therefore, the proposed algorithm achieves a faster convergence and a lower steady-state misalignment than the APSA and its variable step-size versions. The simulation results provided in the paper confirm that the proposed algorithm retains both the advantages of the APSA with large and small step sizes without significantly increase the computational complexity.

Variable step‐size distributed incremental normalised LMS algorithm

A variable step-size distributed incremental normalised least mean square (DINLMS) algorithm is proposed, in which the time-varying step-size of each node in the distributed network is obtained by minimising a posterior estimation error at that node. It overcomes the drawback that fast convergence rate with high steady-state misalignment or low steady-state misalignment with slow convergence rate, which always exists in the traditional DINLMS. The simulation results show that the proposed algorithm could achieve a better performance.

L 0 norm constraint set‐membership affine projection algorithm with coefficient vector reuse

Proposed is an L 0 norm constraint set-membership affine projection algorithm with coefficient vector reuse, which is derived by minimising a differentiable cost function that utilises the L 0 norm of the updated weight vector as well as the sum of the squared Euclidean norms of the differences between the updated weight vector and past weight vectors. In addition, a power estimate method is introduced to eliminate the effect of the fluctuation of the output error on the step size. Simulations on sparse system identifications demonstrate that the proposed algorithm achieves a lower steady-state misalignment than the existing algorithms in a high background noise environment.

A Signal Decorrelation PNLMS Algorithm for Double-Talk Acoustic Echo Cancellation

Acoustic echo cancellation (AEC) in voiced communication systems is used to eliminate the echo which corrupts the speech signal and reduces the efficiency of signal transmission. Usually, the performance of AEC system based on the adaptive filtering degrades seriously in the presence of speech issued from the near-end speaker (double-talk). In typical AEC scenarios, double-talk detector (DTD) must be added to AEC for improving speech quality. One of the main problems in AEC with DTD is that the DTD errors can result in either large residual echo or distorting the near-end input speech. Considering the strong correlation property of speech signals, this paper presents a novel proportionate decorrelation normalized least-mean-square (PDNLMS) adaptive AEC without DTD for echo cancellation as an interesting alternative to the typical AEC with DTDs. Unlike traditional AEC with a DTD, the proposed PDNLMS uses the difference of near-end speech as the residual error to update adaptive echo channel filter during the periods of double-talk, which can efficiently reduce the double-talk influence on the AEC adaptation process. The experimental results show that not only the proposed PDNLMS without DTD illustrate better stability and faster convergence rate, but it is also of a lower steady-state misalignment and better residual signal than current methods with DTDs at a lower computational cost.

Sparseness-Controlled Proportionate Affine Projection Sign Algorithms for Acoustic Echo Cancellation

In order to reduce the steady-state misalignment of real-coefficient proportionate affine projection sign algorithm (RP-APSA) for sparse impulse responses, a memory RP-APSA is proposed in this paper by exploiting the historical values of proportionate factors, called MP-APSA. Further, to improve the robustness of MP-APSA and the recently proposed memory-improved RP-APSA (MIP-APSA) for impulse responses with mutative sparseness, two sparseness-controlled algorithms (SC-MP-APSA and SC-MIP-APSA) are developed by estimating the sparseness of the impulse response at each iteration. Simulation results in the context of acoustic echo cancellation show that the proposed algorithms retain good robustness against impulsive interferences. More importantly, the proposed sparseness-controlled algorithms can not only obtain low steady-state misalignment in both the sparse and dispersive situations, but also adapt to the variations in the sparseness of the impulse response.

New Steady-State Analysis Results of Variable Step-Size LMS Algorithm With Different Noise Distributions

The step-size in well-known variable step-size least mean square (VSSLMS) is updated as μ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n+1</sub> = αμ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> + γe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> with , γ > 0, and μ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n+1</sub> is set to μ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</sub> or μ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> when it falls below or above these lower and upper bounds, respectively. It provides fast convergence at early stages of adaptation while ensuring small steady-state misalignment. This paper considers the steady-state performance of the VSSLMS in non-Gaussian noise environments. The contribution of the paper to the VSSLMS is threefold; (1) when γ ≪ 1 - α, the VSSLMS has low steady-state misalignment. (2) when α ≪ 1, the VSSLMS achieves different steady-state misalignments for different noise distributions. (3) In theory, there are different optimal values α for different noise distributions, i.e., 0.17 (Gaussian distribution), 0.21 (Student distribution), 0.38 (Laplace distribution), 0 (Binary and Uniform distributions). Analytical results are compared with simulations and are shown to agree well.

APA with Evolving Order and Variable Regularization for Echo Cancellation

Recently APA has become one of most popular algorithms in application of Acoustic Echo Cancellation. Because of the contradictory factors of convergence rate and steady-state misalignment, a new algorithm by the behavior of associating variable regularization and evolving order has been proposed in this paper. Despite of the conventional assumption that the a posteriori error is zero, we take the statistical characteristic of the noise into consideration during the adaptation process. Exact and approximate formulations for the optimal regularization factor are derived. Numerical simulation results show that the proposed algorithm improves the performance of the APA in terms of its faster convergence rate and lower steady-state misalignment compared to existing variable regularization APA and evolving order APA, respectively. Meanwhile it can be seen that near-end speech signal has been restored more effectively

Modified variable step‐size affine projection sign algorithm

A modified variable step-size affine projection sign algorithm (MVSS-APSA) is proposed. Considering the effect of the noise on the steady-state error, the first moment estimation of the noise is utilised to modify the variable step-size update. The test on system identifications under an impulsive noise environment shows that the proposed MVSS-APSA has lower steady-state misalignment than the VSS-APSA.

Variable step-size μ-law memorised improved proportionate affine projection algorithm for sparse system identification

System identification has wide applications in adaptive echo/feedback cancellation, active noise control, adaptive channel equalization, etc. When the system is sparse, recently, a μ-law memorised improved proportionate affine projection algorithm (MMIPAPA) has been proposed to improve the misalignment performance remarkably. However, the MMIPAPA with constant step-size has the conflicting requirement of fast convergence rate and low steady-state error. To solve this problem, a variable step-size version of the MMIPAPA (VSS-MMIPAPA) has been extended by setting each component of the a posterior error energy vector equal the system noise energy. Furthermore, through an alternative method to compute the variable step-size, when the estimated component of the a prior error energy vector is smaller than the system noise energy, further lower steady-state misalignment is achieved. This method leads to an improved VSS-MMIPAPA (IVSS-MMIPAPA). The computational complexity of the IVSS-MMIPAPA is O(P2L), which may ...

Affine projection algorithm with selective projections

In the affine projection adaptive filtering algorithm, convergence is sped up by increasing the projection order but with an unwelcome consequence of increased steady-state misalignment. To address this unfavorable compromise, we propose a new affine projection algorithm with selective projections. This algorithm adaptively changes the projection order according to the estimated variance of the filter output error. The error variance is estimated using exponential window averaging with a variable forgetting factor and a simple moving averaging technique. The input regressors are selected according to two different criteria to update the filter coefficients at each iteration. Simulations, carried out for different adaptive filtering applications, demonstrate that the new algorithm provides fast initial convergence and low steady-state misalignment without necessarily trading off one for the other in addition to a significant reduction in average computational complexity.

Noise-robust normalised subband adaptive filtering

Proposed is a robust normalised subband adaptive filter (NSAF) for identifying a highly noisy system. The proposed NSAF reutilises a number of past weight vectors in adaptation, whereas the classical NSAF relies only on the immediately previous weight vector. A new constrained optimisation criterion is formulated so as to minimise the sum of the squared Euclidean norms of the changes between the weight vectors to be updated and the past weight vectors. The resultant NSAF exhibits robustness to noise in that it prevents the adaptive filter from fluctuating around an optimal solution. Through experiments, the proposed NSAF shows lower steady-state misalignment than the conventional NSAF while retaining comparable convergence rate, especially when noise gets severe.

Proportionate Affine Projection Sign Algorithms for Network Echo Cancellation

Two proportionate affine projection sign algorithms (APSAs) are proposed for network echo cancellation (NEC) applications where the impulse response is often real-valued with sparse coefficients and long filter length. The proposed proportionate-type algorithms can achieve fast convergence and low steady-state misalignment by adopting a proportionate regularization matrix to the APSA. Benefiting from the characteristics of l1-norm optimization, affine projection, and proportionate matrix, the new algorithms are more robust to impulsive interferences and colored input than the proportionate least mean squares (PNLMS) algorithm and the robust proportionate affine projection algorithm (Robust PAPA). The new algorithms also achieve much faster convergence rate in sparse impulse responses than the original APSA and the normalized sign algorithm (NSA). The new algorithms are robust to all types of NEC impulse response with different sparseness without the need to change parameters or estimate the sparseness of the impulse response. The computational complexity of the new algorithms is lower than the affine projection algorithm (APA) family due to the elimination of the matrix inversion.

Adaptive multichannel blind identification using manifold optimization

The multichannel blind identification problem can be formulated as minimizing a cost function based on the cross-relations among different sub-channels, subject to a unit-norm constraint. In this correspondence, this constraint optimization problem is reformulated as an unconstrained one on the Stiefel manifold. Some previously proposed algorithms are also shown to be special cases of this algorithm framework. The convergence and low steady-state misalignment of the proposed algorithms are verified by illustrative computer simulations.