An Enhanced Affine Projection Algorithm Based on the Adjustment of Input-Vector Number.

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.

Fast exact variable order affine projection algorithm

Subband affine projection (SAP) algorithm which combines the advantages of the affine projection algorithm (APA) and subband adaptive filtering (SAF) has been proposed for achieving the improved convergence performance. In this paper, the family of SAP algorithms is presented. Following this, the mean-square performance for this family of SAP algorithms is derived. The derivation process is based on energy conservation arguments and does not limit the regressors to being a specific random distribution. Simulation results illustrate the efficiency for this analysis.

Affine projection algorithms (AP) are widely used to implement active noise control (ANC) systems, due to their fast convergence speed and robustness, nevertheless their high computational cost could restringe their use in real-time applications. For that reason several low cost AP algorithms have been proposed, such as the Error Coded Affine Projection (ECAP) algorithm; however, in order to implement the algorithm in an ANC system is necessary to perform some modifications. In this paper, we present a version of the ECAP algorithm for single-channel ANC systems. The proposal is done using the conventional filtered-x scheme; furthermore, we use an evolutionary method to reduce the projection order of the algorithm during the computation process. Simulation results show a similar convergence speed to the AP algorithm, a lower final residual error and significant computational savings.

The adaptive algorithms have been widely studied in Gaussian environment. However, the impulsive noise and other non-Gaussian noise may largely deteriorate the performance of algorithm in practical applications. To address this problem, in this paper, we propose two novel adaptive algorithms for system identification problem with mixed noise scenarios. Both proposed algorithms are based on the framework of the affine projection (AP) algorithm. The first proposed algorithm, termed as VS-APMCCA, combines variable step-size (VS) strategy and maximum correntropy criterion (MCC) to obtain improved performance. For further performance improvement, the VC-VS-APMCCA is developed, which is based on the variable center (VC) scheme of MCC. The convergence analysis of the VC-VS-APMCCA is conduced. Finally, simulation results demonstrate the superior performance of the VS-APMCCA and VC-VS-APMCCA.

Based on affine projection algorithm (APA) in adaptive filtering and the technique of parallel computing, we propose a novel algorithm called ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -APA with its parallel implementation for sparse system identification and sparse signal recovery. For sparse system identification, parallel ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -APA can serve as an effective approach for practical hardware implementation, since it lowers the requirement on the processors' clock speed. For sparse signal recovery, it can significantly reduce the convergence time. Prior algorithms such as ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -LMS and ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -ZAP can be seen as special cases of ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -APA. Finally the performance of the proposed algorithm is analyzed and verified by numerical experiments.

Affine projection (AP) algorithms have demonstrated faster convergence speed than conventional least mean square (LMS) algorithms, thus providing an attractive solution in the active noise control (ANC) field. However, the AP algorithms demand high computational cost, restricting their practical use in real-time ANC applications. Recently, a multichannel filtered-x error-coded affine projection-like (FXECAP-L) algorithm with evolving order has been proposed to reduce the computational burden by maintaining the convergence speed of AP algorithms. In order to obtain an efficient and robust FXECAP-L algorithm with evolving order, the scaling factor and encoder resolution need to be adjusted manually, which is a time-consuming and costly effort that must be carried out by expert designers. To reduce these costs and efforts, we introduce, for the first time, a strategy for automatic adjustment of the scaling factor and encoder resolution that benefits the rapid development of practical ANC applications. To demonstrate its practical use, we applied the proposed strategy for controlling the noise in an acoustic duct. The practical results demonstrate the automatic adjustment of the FXECAP-L algorithm which maintains high convergence speed at the expense of a small compromise in terms of processing time.

Improved variable step-size least mean square algorithm based on Sigmoid function

Publication in the conference proceedings of EUSIPCO, Bucharest, Romania, 2012

Hypotheses made about the behavior of the affine projection algorithm (APA) are investigated by means of carefully designed comparative experiments. These experiments lead us to the properties of the direction vector used in APA. Experiments also show that APA converges faster than NLMS in the case of white noise input, leading us to question that whitening of the direction vector is the explaining factor for the convergence acceleration observed with APA. An alternative hypothesis is offered for why APA may yield faster convergence than NLMS.

A simplified forms of adaptive set-membership affine projection based on least mean fourth algorithm is proposed. Least mean fourth (LMF) algorithm is defined by taking the fourth power of error to against the non-Gaussian environment. A set-membership adaptive filtering is described firstly. Then, an affine projection algorithm is based on LMF algorithm. A simplified set-membership affine projection algorithm based on LMF is introduced. Adaptive threshold parameter and learning rate are presented for improvement of convergence rate. Numerical simulations show that the proposed algorithm can provide significantly to the conventional affine projection algorithm.

This paper introduces a space-time decision feedback equalizer whose coefficients are recursively renewed on the basis of the modified affine projection algorithm (APA). Despite its effectiveness against a rank-deficiency problem, the complexity of the conventional APA utilizing the sample matrix inversion is considerable. Furthermore, the shift invariance property could not be exploited in the case of a space-time decision-directed equalizer (STDE) application. To overcome such challenges, this paper introduces an APA employing a hyperplane projection scheme to reduce computational complexity without any degradation in its convergence characteristic and tracking capability. The performance of the proposed equalization methodology is verified by showing its superior bit error rate behaviors, fast convergence property, and reduced computational complexity by performing adaptive STDE under the single-input-multiple-output wireless multipath fading channel.

Affine projection algorithms (APA) have been widely employed for acoustic echo cancellation (AEC) since they provide a natural trade-off between convergence speed and computational complexity. However, their application in Acoustic Feedback Cancellation (AFC) in hearing aids so far has been limited due to lack of performance improvement in one microphone settings. A two microphone technique was recently proposed to provide an improved cancellation for a larger class of input signals. This paper proposes to use APA in the two microphone closed-loop feedback cancellation. It is shown that APA has significantly improved the misalignment and maximum stable gain of the system. Moreover, a new variable Gaussian step-size control (VGSS) for APA is also proposed. The simulation results indicate an improvement in convergence speed of the proposed algorithms as compared to previously suggested methods.

Based on the variable step-size afiine projection algorithm, the idea of multiple forgetting factors and variable projection order is proposed. On the one hand, the accurate estimation of error energy is realized in order to achieve faster convergence rate and lower final misalignment. On the other hand, the reduction of computational complexity can be achieved. The simulation results show that the proposed algorithm achieves significant improvement in the convergence rate, misalignment and computational complexity compared with variable step-size affine projection algorithm, variable projection order affine projection algorithm and variable step-size and rojection order affine projection algorithm without multiple forgetting factors.

We present a novel affine projection algorithm (APA) which automatically determines its projection order by an evolutionary method. The evolutionary method increases or decreases the projection order by comparing the output error with a threshold. The experimental results show that the proposed algorithm has fast convergence speed and small steady-state error compared to the conventional APA.