The blind multichannel identification is useful in many applications. Although many approaches have been proposed to address this challenging problem, the adaptive filtering-based methods are attractive due to their computational efficiency and good convergence property. The multichannel normalized least mean-square (MCNLMS) algorithm is easy to implement, but it converges very slowly for a correlated input. The multichannel affine projection algorithm (MCAPA) is thus proposed to speed up the convergence. However, the convergence of the MCNLMS and MCAPA is still unsatisfactory in practice. In this paper, we propose a time-domain Kalman filtering approach to the blind multichannel identification problem. Specifically, the proposed adaptive Kalman filter is based on the cross relation method and also uses more past input vectors to explore the decorrelation property. Simulation results indicate that the proposed method outperforms the MCNLMS and MCAPA significantly in terms of the initial convergence and tracking capability.

Affine projection sign algorithm (APSA) is an important adaptive filtering method to combat the impulsive noisy environment. However, the performance of APSA is poor, if its regularization parameter is not well chosen. We propose a variable regularization APSA (VR-APSA) approach, which adopts a gradient-based method to recursively reduce the norm of the a priori error vector. The resulting VR-APSA leverages the time correlation of both the input signal matrix and error vector to adjust the value of the regularization parameter. Simulation results confirm that our algorithm exhibits both fast convergence and small misadjustment properties.

In this Letter, a robust variable step-size affine-projection subband adaptive filter algorithm (RVSS-APSAF) is proposed, whereby a band-dependent variable step-size is introduced to improve convergence and misalignment performances in impulsive noise environments. Specifically, the weight vector is adaptively updated to achieve robustness against impulsive noises. Finally, the proposed RVSS-APSAF algorithm is tested for system identification in an impulsive noise environment.

We propose a novel bias-free adaptive beamformer employing an affine projection algorithm with the optimal regularization parameter. The generalized sidelobe canceller affine projection algorithm suffers from a bias of a weight vectors under the condition of no reference signals for output of an array in the beamforming application. First, we analyze the bias in the algorithm and prove that the bias can be eliminated through a large regularization parameter. However, this causes slow convergence at the initial state, so the regularization parameter should be controlled. Through the optimization of the regularization parameter, the proposed method achieves fast convergence without the bias at the steady-state. Experimental results show that the proposed beamformer not only removes the bias but also achieves both fast convergence and high steady-state output signal-to-interference-plus-noise ratio.

This paper presents an adaptive feedback canceller (AFC) based on a pseudo affine projection (PAP) algorithm that can provide fast and stable adaptation to the time-varying environment. The proposed algorithm utilizes the adaptive linear prediction (LP) to obtain the LP coefficients of input signal model and the inverse gain filter (IGF) to alleviate the effect of compensation gain. As a result, when the input is model as an AR signal, the proposed algorithm satisfies the condition for having an almost unbiased estimatie of the feedback path and then its performance is relatively independent of the gain setting of hearing aids. Simulation results showed that the proposed algorithm is capable of obtaining unbaised feedback path estimates and high speech quality.

We present a low-complexity complementary pair affine projection (CP-AP) adaptive filter which employs the intermittent update of the filter coefficients. To achieve both a fast convergence rate and a small residual error, we use a scheme combining fast and slow AP filters, while significantly reducing the computational complexity. By employing an evolutionary method which automatically determines the update intervals, the update frequencies of the two constituent filters are significantly decreased. Experimental results show that the proposed CP-AP adaptive filter has an advantage over conventional adaptive filters with a parallel structure in that it has a similar convergence performance with a substantial reduction in the total number of updates.

Acoustic feedback is a major complaint of hearing aid users. Adaptive filters are a common method for suppressing acoustic feedback in digital hearing aids. In this letter, we propose a new variable step-size algorithm for normalized least mean square and an affine projection algorithm to combine with a variable step-size affine projection algorithm and global speech absence probability in an adaptive filter. The computer simulation used to test the proposed algorithm results in a lower misalignment error than the comparison algorithm at a similar convergence rate. Therefore, the proposed algorithm suggests an effective solution for the feedback suppression system of digital hearing aids.

A new type of the affine projection (AP) algorithms which incorporates the sparsity condition of a system is presented. To exploit the sparsity of the system, a weighted l1-norm regularization is imposed on the cost function of the AP algorithm. Minimizing the cost function with a subgradient calculus and choosing two distinct weightings for l1-norm, two stochastic gradient based sparsity regularized AP (SR-AP) algorithms are developed. Experimental results show that the SR-AP algorithms outperform the typical AP counterparts for identifying sparse systems.

We present a new framework of the data-reusing (DR) adaptive algorithms by incorporating a constraint on noise, referred to as a noise constraint. The motivation behind this work is that the use of the statistical knowledge of the channel noise can contribute toward improving the convergence performance of an adaptive filter in identifying a noisy linear finite impulse response (FIR) channel. By incorporating the noise constraint into the cost function of the DR adaptive algorithms, the noise constrained DR (NC-DR) adaptive algorithms are derived. Experimental results clearly indicate their superior performance over the conventional DR ones.

We present a new structure for parallel affine projection (AP) filters with different step-sizes. By observing their error signals, the proposed alternating AP (A-AP) filter selects one of the two AP filters and updates the weights of the selected filter for each iteration. As a result, the total computations required for the proposed structure is almost the same as that for a single AP filter. Experimental results show that the proposed alternating selection scheme extracts the best properties of each component filter, namely fast convergence and small steady-state error.

To attain good performance in an acoustic echo cancellation system, it is important to have a variable step size (VSS) algorithm as part of an adaptive filter. In this paper, we are concerned with the development of a VSS algorithm for a recently proposed subband affine projection (SAP) adaptive filter. Two popular VSS algorithms in the literature are the methods of delayed coefficients (DC) and variable regularization (VR). However, the merits and demerits of them are mutually exclusive. We propose a VSS algorithm that is a hybrid of both methods and combines their advantages. An extensive study of the new algorithm in different scenarios like the presence double-talk (DT) during the transient phase of the adaptive filter, DT during steady state, and varying DT power is conducted and reasoning is given to support the observed behavior. The importance of the method of VR as part of a VSS algorithm is emphasized.

Recently, a data-selective method has been proposed to achieve low misalignment in affine projection algorithm (APA) by keeping the condition number of an input data matrix small. We present an improved method, and a complexity reduction algorithm for the APA with the data-selective method. Experimental results show that the proposed algorithm has lower misalignment and a lower condition number for an input data matrix than both the conventional APA and the APA with the previous data-selective method.

This letter presents a new mathematical expression for the excess mean-square error (EMSE) of the affine projection (AP) algorithm. The proposed expression explicitly shows the proportional relationship between the EMSE and the condition number of the input signals.

We propose a gradient-limited affine projection algorithm (GL-APA), which can achieve fast and double-talk-robust convergence in acoustic echo cancellation. GL-APA is derived from the M-estimation-based nonlinear cost function extended for evaluating multiple error signals dealt with in the affine projection algorithm (APA). By considering the nonlinearity of the gradient, we carefully formulate an update equation consistent with multiple input-output relationships, which the conventional APA inherently satisfies to achieve fast convergence. We also newly introduce a scaling rule for the nonlinearity, so we can easily implement GL-APA by using a predetermined primary function as a basis of scaling with any projection order. This guarantees a linkage between GL-APA and the gradient-limited normalized least-mean-squares algorithm (GL-NLMS), which is a conventional algorithm that corresponds to the GL-APA of the first order. The performance of GL-APA is demonstrated with simulation results.

Affine projection algorithms perform well for acoustic echo cancellation and adaptive equalization. Although these algorithms typically provide fast convergence, they are unduly complex when updating the weights of the associated adaptive filter. In this paper, we propose a new subband affine projection (SAP) algorithm and a facile method for its implementation. The SAP algorithm is derived by combining the affine projection algorithm and the subband adaptive structure with the maximal decimation. In the proposed SAP algorithm, the derived weight-updating formula for the subband adaptive filter has a simple form as compared with the normalized least mean square (NLMS) algorithm. The algorithm gives improved convergence and reduced computational complexity. The efficiency of the proposed algorithm for a colored input signal is evaluated experimentally.

This paper introduces an efficient affine projection algorithm (APA) using iterative hyperplane projection. The inherent effectiveness against the rank deficient problem has led APA to be the preferred algorithm to be employed for various applications over other variety of fast converging adaptation algorithms. However, the amount of complexity of the conventional APA could not be negligible because of the accomplishment of sample matrix inversion (SMI). Another issue is that the "shifting invariance property," which is typically exploited for single channel case, does not hold ground for space-time decision-directed equalizer (STDE) application deployed in single-input-multi-output (SIMO) systems. Therefore, fast adaptation schemes, such as fast traversal filter based APA (FTF-APA), becomes impossible to utilize. The motivation of this paper deliberates on finding an effective algorithm on the basis of APA, which yields low complexity while sustaining fast convergence as well as excellent tracking ability. The performance of the proposed method is evaluated under wireless SIMO channel in respect to bit error rate (BER) behavior and computational complexity, and upon completion, the validity is confirmed. The performance of the proposed method is evaluated under wireless SIMO channel in respect to bit error rate (BER) behavior and computational complexity, and upon completion, the validity is confirmed.