Adaptive

Overall results (2011 - 2016)

6 published and accepted papers in ISI journals with cumulated ISI Article Influence Score (according to Thomson Reuters 2012 Journal Citation Reports) = 7.28.

49 papers published in conference proceedings indexed by ISI, and other international databases (IEEE Xplore, DBLP and Google Scholar) These papers have received over 70 citations (excluding self-citations).

Three special sessions on adaptive filtering issues have been organized by the PI at EUSIPCO 2012 and ECAI 2015 and APSIPA 2015.

Two awards: Best paper award at IEEE SPA 2014 and best presentation award at IEEE ICCAS 2014.

S. Ciochina, C. Paleologu and J. Benesty, An optimized NLMS algorithm for system identification, Signal Processing, vol. 118, pp. 115-121, Jan. 2016, Website

Abstract: The normalized least-mean-square (NLMS) adaptive filter is widely used in system identification. In this paper, we develop an optimized NLMS algorithm, in the contest of state variable model. The proposed algorithm follows a joint-optimization problem on both the normalized step-size and regularization parameters, in order to minimize the system alignment. Consequently, it achieves a proper compromise between the perfomance criteria, i.e., fast convergence/tracking and low misadjustment. Simulations performed in the context of acoustic echo cancellation indicate the good features of the proposed algorithm

F. Albu, P.S.R. Diniz,Improved Set-Membership Partial-Update Pseudo Affine Projection Algorithm, accepted at IEEE ICCACI 2016 Website

Abstract: In this paper, an improved set-membership partial-update pseudo affine projection (I-SM-PUPAP) algorithm is presented. An approximation that leads to solving a linear system with a direct method is used. It is proved that I-SM-PUPAP algorithm has a much lower numerical complexity and memory requirements than recently proposed I-SM-PUAP algorithm. Simulation results identify an inherent compromise between the convergence rate, complexity reduction and the number of updates.

Y. Li, Y. Wang, F. Albu, Sparse Channel Estimation Based on a Reweighted Least-Mean Mixed-Norm Adaptive Filter Algorithm, in Proc. of Eusipco 2016, Budapest, Hungary, pp. 2380 – 2384. Website

Abstract: A sparsity-aware least-mean mixed-norm (LMMN) adaptive filter algorithm is proposed for sparse channel estimation applications. The proposed algorithm is realized by incorporating a sum-log function constraint into the cost function of a LMMN which is a mixed norm controlled by a scalar mixing parameter. As a result, a shrinkage is given to enhance the performance of the LMMN algorithm when the majority of the channel taps are zeros or near-zeros. The channel estimation behaviors of the proposed reweighted sparse LMMN algorithm is investigated and discussed in comparison with those of the standard LMS and the least-mean square/fourth (LMS/F) and previously sparse LMS/F algorithms. The simulation results show that the proposed reweighted sparse LMMN algorithm is superior to aforementioned algorithms with respect to the convergence speed and steady-state error floor.

F. Albu, J. Liu, S.L. Grant, Approximated Proportionate Affine Projection Algorithms for Block Sparse Identification, ECTI-CON 2016, Chiang Mai, Thailand, 9-11 July 2016. Website

Abstract: In this paper two block-sparse approximated memory improved proportionate affine projection algorithm are proposed for block sparse system identification. An approximation is used for a recently proposed family of block-sparse proportionate affine projection algorithms. It is shown that the proposed algorithms have close convergence performance to the original ones and they are less numerically complex. An investigation of the influence of their parameters is also presented.

C. Stanciu, C. Anghel, C. Paleologu, S. Ciochina, On the Numerical Properties of an Optimized NLMS Algorithm, Communications 2016, Bucharest, 9-11 June 2016. Website

Abstract: In this paper, we analyze the numerical properties of the recently proposed joint-optimized normalized least-mean square (JO-NLMS) algorithm. This algorithm was developed in the context of a time-variant system model, using an iterative procedure for adjusting the system model parameter. Due to these features, the JO-NLMS algorithm behaves like a variable step-size adaptive filter, leading to both fast convergence/tracking and low misadjustment. Simulations performed in the context of acoustic echo cancellation indicate that this algorithm could be a strong and reliable candidate for real-world applications where adaptive identification is required.

F. Albu, Block-Sparse Fast Recursive Approximated Memory Improved Proportionate Affine Projection Algorithm, AES 140, June 2016. Website

Abstract: A new approximated memory improved proportionate affine projection algorithm for block sparse echo cancellation is proposed. This contribution presents a fast recursive implementation combined with the use of dichotomous coordinate descent iterations. It is shown that the proposed algorithm has good convergence speed and tracking abilities for echo path changes in the context of acoustic and network echo cancellation applications. Also it is proved that these achievements are obtained while having a reduced numerical complexity than competing algorithms.

F. Albu, K. Nishikawa, New Iterative Kernel Algorithms for Nonlinear Acoustic Echo Cancellation, in Proc. of APSIPA 2015, Hong Kong, December 2015 Website

Abstract: Recently, a nonlinear acoustic echo cancellation algorithm based on the framework of kernel methods has been proposed by modeling the echo path as a Hammerstein system. However, it requires a large amount of computation to be implemented. In this paper, we propose to use iterative methods for solving linear systems in order to reduce the numerical complexity of identifying the nonlinear and linear parts of the echo path. Also we investigate the effect on performance of the parameters of the methods for both iterative batch and online versions. Simulation results confirm the complexity reduction and good performance of the proposed methods for clipping nonlinearity and room impulse response variation.

C. Stanciu, C. Anghel, L. Stanciu, Efficient FPGA implementation of the DCD-RLS algorithm for stereo acoustic echo cancellation, in Proc. of IEEE ISSCS 2015, July 2015, Iasi, Romania Website

Abstract: The development of teleconferencing systems has allowed the communication using two acoustic channels (stereo configuration). The corresponding standard acoustic echo cancellation process requires four adaptive filters with a considerable usage of hardware resources. In this context, the dichotomous coordinate descent (DCD) - recursive least-squares (RLS) algorithm, using the widely linear (WL) model, was proposed as an efficient alternative to the classical RLS solution. In this paper, an efficient Field Programmable Gate Array (FPGA) implementation of the DCD-RLS method is presented, with attractive numerical properties and good performance.

S. Ciochina, C. Paleologu, J. Benesty and S.L. Grant, An optimized NLMS algorithm for acoustic echo cancellation, in Proc. of IEEE ISSCS 2015, July 2015, Iasi, Romania Website

Abstract: In order to improve the overall performance of the normalized least-mean-square (NLMS) algorithm, there is the need to control its main parameters, i.e., the normalized stepsize and regularization terms. In this context, the variable stepsize and variable regularized versions of the NLMS algorithm are designed to address the conflicting requirement of fast convergence and low misadjustment. In this paper, we propose an optimized NLMS algorithm for acoustic echo cancellation (AEC). This algorithm is based on a joint-optimization on both the normalized step-size and regularization parameters, in the context of a state variable model (similar to Kalman filtering). The simulation results indicate that the proposed algorithm can be a reliable choice for AEC applications, since it achieves fast convergence and tracking, low misadjustment, and double-talk robustness.

F. Albu, Fast recursive AMIPAP algorithm, IEEE ECAI 2015, Bucharest, Romania, June 2015 Website

Abstract: The approximate memory improved proportionate affine projection algorithm has been proposed for sparse system identification. This paper presents a fast recursive implementation of this algorithm. Three ideas used previously for other affine projection variants are used: auxiliary coefficients vectors, periodically update of the proportionate coefficients and recursive filtering of the error vector. Simulation results are made in order to show the performance of the algorithm for network echo cancellation example.

S. Ciochina, C. Paleologu, J. Benesty, R. Caramalau, On the performance of the joint-optimized NLMS algorithm, IEEE ECAI 2015, Bucharest, Romania, June 2015 Website

Abstract: The recently proposed joint-optimized normalized least-mean-square (JO-NLMS) algorithm was developed in the context of a state variable model. Moreover, following the minimization of the system misalignment and using an iterative procedure for adjusting the system model parameter, this algorithm is able to achieve a proper compromise between the performance criteria (i.e., fast convergence/tracking and low misadjustment). In this paper, we present a performance analysis of the JO-NLMS algorithm, outlining some relations between its main parameters and indicating its good behavior.

F. Albu,The Proportionate APL-I algorithm, IEEE ICTRC 2015, May 2015 Website

Abstract: A proportionate affine projection like (PAPL-I) adaptive filtering algorithm is proposed that incorporates the proportionate feature to affine projection like (APL-I) algorithm. Simulation results show that the proposed PAPL-I algorithm provides improved steady state performance than the APL-I and affine projection algorithms (APA) in case of an acoustic echo cancellation application with a very sparse echo path. In addition, the PAPL-I algorithm also offers improved performance over the APL-I algorithm for adaptive feedback cancellation for hearing aids systems.

C. Paleologu, J. Benesty, S. Ciochina, Widely linear general Kalman filter for stereophonic echo cancellation, Signal Processing, vol. 94, pp. 570-575, January 2014 Website

Abstract: The stereophonic acoustic echo cancellation (SAEC) problem is usually modeled as a two-input/two-output system with real random variables. Recently, the SAEC scheme was recast as a single-input/single-output system with complex random variables, thanks to the widely linear (WL) model. In this paper, we motivate the use of a more general form of the Kalman filter with the WL model for SAEC. Simulation results indicate that this algorithm outperforms the recursive least-squares (RLS) algorithm, which is usually considered as a benchmark for SAEC.

F. Albu, K. Nishikawa, A fixed budget implementation of a new variable step size kernel proportionate NLMS algorithm, accepted at IEEE ICCAS 2014, Seoul, South Korea, October 2014 Website

Abstract: In this paper, a fixed-budget implementation of the kernel proportionate normalized least mean square (KPNLMS) algorithm using a variable step size scheme is proposed. The similarity between the equations of the NLMS algorithm and those of the kernel proportionate NLMS algorithm with coherence criterion is emphasized and the reason of using the proportionate coefficients for the KPNLMS algorithm is given. It is shown that applying the proportionality principle to the kernel outputs leads to better convergence properties than applying it to the weights of the nonlinear filter. The effect of the step size on the convergence properties of KPNLMS is exemplified. Also, and the effect of SNR on the dictionary size of the KPNLMS algorithm is proved for channel equalization and forward prediction examples. The influence of the dictionary size on the performance of the fixed budget KPNLMS algorithm is demonstrated. Therefore, a simple variable step size scheme is proposed in order to improve the convergence properties of fixed-budget KPNLMS algorithm for channel equalization of a multi-path Rayleigh fading channel and forward prediction applications. It is also proved that the additional computational complexity burden of the proposed algorithms is very small.

F. Albu, H. Coanda, A fast filtering proportionate affine projection sign algorithm, accepted at IEEE SPA 2014, Poznan, Poland, September 2014 Website

Abstract: In this paper, a new proportionate affine projection sign algorithm using the - law proportionality idea is proposed. It has an efficient implementation because it uses a fast recursive filtering procedure. Simulation results indicate that the proposed algorithm has slightly better performance than a competing algorithm in a network echo cancellation system in impulsive environments and adaptive feedback cancellation for hearing aids systems.

Award Diploma

Award Poznan

C.R.C. Nakagawa, S. Nordholm, F. Albu, W. -Y. Yan, Closed-loop feedback cancellation utilizing two microphones and transform domain processing, in Proc. of IEEE ICASSP 2014, Florence, Italy, pp. 3673-3677, May 2014 Website

Abstract: In this paper we are studying the use of two microphones for acoustic feedback cancellation in hearing aids. With the two microphones approach, an additional microphone is employed to provide added information about the signals which is then utilized to obtain an incoming signal estimate. This estimate is removed from the error signal prior to adapting the canceler, thus removing the undesired signal correlation. In this paper, we propose to use orthogonal transforms with the two microphones approach. The discrete Fourier transform and the discrete cosine transform are implemented to transform the adaptive filter signals. Also, a bank of adaptive filters is employed, each adapting to different portions of the spectrum for a finer control of the adaptation process. Simulation results based on real measured feedback paths and speech signals show improved convergence rates and stable solutions.

C. Paleologu, J. Benesty, S. Ciochina, A practical solution for the regularization of the affine projection algorithm, in Proc. of IEEE COMM 2014, May 2014, Bucharest, Romania. Website

Abstract: The regularization of the affine projection algorithm (APA) is of great importance in echo cancellation applications. The regularization parameter, which depends on the level of the near-end signal, is added to the main diagonal of the input signal correlation matrix to ensure the stability of the APA. In this paper, we propose a practical way for evaluating the power of the near-end signal or, equivalently, the signal-to-noise ratio that is explicitly related to the regularization parameter. Simulation results obtained in the context of acoustic echo cancellation support the appealing performance of the proposed solution.

C. Stanciu, C. Anghel, Numerical properties of the DCD-RLS algorithm for Stereophonic Acoustic Echo Cancellation, in Proc. of IEEE COMM 2014, May 2014, Bucharest, Romania. Website

Abstract: Modern teleconferencing systems have been developed in recent years to use multiple acoustic channels (stereo communication). This feature improves the quality of communication (e.g., in terms of spatial localization), but the classic problem of the acoustic echo cancellation becomes more complicated. In this context, the dichotomous coordinate descent (DCD) - recursive least-squares (RLS) algorithm can be an attractive choice for hardware implementation. In this paper, the numerical properties of the DCD-RLS parameters will be analyzed, related to finite precision implementations.

C. Paleologu, J. Benesty, S. Ciochina, Widely linear general Kalman filter for stereophonic echo cancellation, Signal Processing, vol. 94, pp. 570-575, January 2014 Website

F. Albu, H. Coanda, D. Coltuc, M. Rotaru, Intermittently Updated Simplified Proportionate Affine Projection Algorithm, in Proc. of ADAPTIVE 2014, Venice, Italy, pp. 42-47, May 2014 Website

Abstract: In this paper, an intermittent update interval for filter coefficients and a simplified output error vector computation is proposed for a proportionate affine projection algorithm. It is shown that the proposed algorithm has good convergence performance and much smaller computation complexity than other proportionate-type APAs. Also, the accuracy of its implementation using the logarithmic number system was investigated. We demonstrated the performance of the proposed algorithm for echo cancellation and adaptive feedback cancellation applications

F. Albu, K. Nishikawa, The kernel proportionate NLMS algorithm, accepted at EURASIP EUSIPCO 2013, Marrakech, Morocco, September 2013 Website

Abstract: In this paper, the kernel proportionate normalized least mean square algorithm (KPNLMS) is proposed. The proportionate factors are used in order to increase the convergence speed and the tracking abilities of the kernel normalized least mean square (KNLMS) adaptive algorithm. We confirm the effectiveness of the proposed algorithm for nonlinear system identification and forward prediction using computer simulations.

F. Albu, D. Coltuc, K. Nishikawa, M. Rotaru An efficient implementation of the kernel affine projection algorithm, accepted at IEEE ISPA 2013, Trieste, Italy Website

Abstract: In this paper an efficient kernel affine projection algorithm using dichotomous coordinate descent iterations is proposed. The effectiveness of the proposed algorithm for nonlinear system identification and forward prediction is confirmed by computer simulations.

M. Rotaru, S. Ciochina, F. Albu, An efficient GSC VSS-APA Beamformer with integrated log-energy based VAD for noise reduction in speech reinforcement systems, accepted at IEEE ISSCS 2013, Iasi, Romania, July 2013 Website

Abstract: This paper presents an efficient time-domain Generalized Sidelobe Canceller GSC) with low signal distortion capabilities using the variable step size affine projection algorithm (VSS-APA) and a log-energy based voice activity detector (VAD). The performance of the proposed VSS-APA based GSC method with integrated log-energy VAD, is illustrated in the context of speech reinforcement application using different signals with low signal-to-noise ratio and different types of noise.

F. Albu,H.K.Kwan, Memory Improved Proportionate Affine Projection Sign Algorithm, in IET Electronics Letters, volume 48, issue 20, October 2012 Page(s): 1279-1281, 27 September 2012, Website

Abstract: A new proportionate affine projection sign algorithm is proposed for network echo cancellation. It uses a recursive procedure and takes into account the previously computed proportionate coefficients. It is shown that the proposed algorithm can obtain a lower steady-state misalignment than other affine projection sign algorithms for different echo paths, impulsive interferences and step sizes.

M. Rotaru, C. Stanciu, S. Ciochina, F. Albu, H. Coanda, A FPGA Implementation of Prediction Error Method for Active Feedback Cancellation using Xilinx System Generator, ADAPTIVE 2013, Valencia,Spain, pp. 26-29. Website

Abstract: This paper describes a real-time, field programmable gate array (FPGA) implementation of Feedback Cancellation(FC) system to improve the intra-cabin communication among the driver and passengers, which is typically degraded by the noisy environment and by the distance in between them. The feedback canceller, used to reduce the acoustic coupling the loudspeaker and the microphone, is based on the continuously adaptive filtering technique, implementing the prediction error method (PEM) for closed loop system identification. The adaptive algorithm implements the modified least mean square algorithm (MLMS)while for the linear prediction a fix-order linear predictor has been selected. The implementation was done using Xilinx System GeneratorTM.

F. Albu, M. Rotaru, R. Arablouei, and K.Dogancay,Intermittently-updated affine projection algorithm, in Proc. of IEEE ICASSP 2013, Vancouver, Canada, 26-31 May 2013, pp.585-589 Website

Abstract: Acoustic echo cancellation and feedback cancellation systems require robust and computationally efficient adaptive filtering techniques. In this paper, a new affine projection algorithm with intermittent update of the filter coefficients is proposed where the update interval is determined according to the adaptation state. Simulation results show that the proposed algorithm provides improved performance and reduced average computational complexity compared with other similar algorithms for acoustic echo cancellation and acoustic feedback cancellation applications.

F. Albu,H.K.Kwan,New proportionate affine projection sign algorithms, in Proc. of IEEE ISCAS 2013, Beijing, China,19-23 May 2013, pp. 1789-1793. Website

Abstract: In this paper, two proportionate affine projection sign algorithms are introduced. The performance of the proposed algorithms is compared with that of other proportionate affine algorithms under impulsive interference environment of a network echo cancellation system. It is shown that one of the proposed algorithms, termed memory improved proportionate affine projection sign algorithm (MIP-APSA), is the most robust to impulsive interferences and colored inputs. It is proved that MIP-APSA is a good candidate for network echo cancellation, because of its low complexity, good convergence speed and tracking abilities for echo paths with different sparseness measures, and projection orders.

F. Albu,Improved Variable Forgetting Factor Recursive Least Square Algorithm, in Proc. of IEEE ICARCV 2012, Guangzhou, China, 5-7 December 2012, Website

Abstract: In this paper an improved variable forgetting factor recursive least square (IVFF-RLS) algorithm is proposed. The forgetting factor is adjusted according to the square of a time-averaging estimate of the autocorrelation of a priori and a posteriori errors. The proposed algorithm has fast convergence, and robustness against variable background noise, near-end signal variations and echo path change. The simulation results indicate the superior performances of IVFF-RLS when compared to the RLS and VFF-RLS algorithms.

F. Albu,Leading Element Dichotomous Coordinate Descent Exponential Recursive Least Squares Algorithm for Multichannel Active Noise Control, in Proc. of AAS ACOUSTICS 2012, Fremantle,Australia, 21-23 November 2012, 4 pages, Website

Abstract: In this paper, a new multichannel modified filtered-x (MFX) recursive least square (RLS) algorithm for active noise control (ANC) based on leading element dichotomous co-ordinate descent(LEDCD) iterations is proposed. It is shown that the proposed algorithm has less than half of the complexity of MFX fast transversal filter (FTF) algorithm with good performance for ideal plant models and improved robustness for noisy plant models.

F. Albu,D. Coltuc, D. Comminiello, M. Scarpiniti,The variable step size regularized block exact affine projection algorithm,in Proc. of IEEE ISETC 2012, Timisoara, Romania, 15-16 November 2012, pp.283-286, Website

Abstract: This paper presents several block exact affine projection algorithms (BEAPA) with a variable regularization factor and/or variable step size. The performance of the algorithms is investigated for the acoustic echo cancellation (AEC) and noise reduction applications. It is shown that the variable step size regularized BEAPA whose regularization factor and variable step size are adjusted according to the square of a time-averaging estimate of the autocorrelation of a priori and a posteriori errors is a possible choice for AEC and noise reduction systems.

M. Rotaru, F. Albu, H. Coanda,A Variable Step Size Modified Decorrelated NLMS Algorithm for Adaptive Feedback Cancellation in Hearing Aids,in Proc. of IEEE ISETC 2012, Timisoara, Romania, 15-16 November 2012, pp. 263-266, Website

Abstract: This paper presents a new algorithm for adaptive feedback cancellation (AFC) suitable for hearing aids. A variable step size scheme is added to a step size decorrelated NLMS algorithm. It is shown that the proposed algorithm has increased robustness and stability for both fixed and variable gain cases.

A. Gonzalez, M. Ferrer, F. Albu, and M. de Diego, Affine projection algorithms: evolution to smart and fast multichannel algorithms and applications, in Proc. of EUSIPCO 2012,Bucharest, Romania, August 2012, pp. 1965-1969 Website

Abstract: Affine projection algorithm encompasses a family of configurable algorithms designed to improve the performance of other adaptive algorithms, mainly LMS based ones, especially when input data is highly correlated. The computational cost of the affine projection algorithm depends largely on the projection order, which in turn conditions the speed of convergence, thus high speed of convergence implies usually high computational cost. Some real-time applications(especially multichannel) using the affine projection algorithm can not be implemented in the existing general-purpose hardware, because of this several improvements of the affine projection algorithm have been proposed to make it more computationally efficient and more versatile in terms of performance. This paper outlines the evolution of the affine projection algorithm and its variants, in order to get an efficient and self-reconfigurable algorithm. Furthermore new improvements over the existing low cost and variable step size and projection order versions are proposed to give examples of the new generation of affine projection algorithms.

C. Stanciu, C. Paleologu, J. Benesty, T. Gänsler,S. Ciochina, and F. Albu, Variable-Forgetting Factor RLS for Stereophonic Acoustic Echo Cancellation with Widely Linear Model, in Proc. of EUSIPCO 2012, Bucharest, Romania, pp. 1960-1964. Website

Abstract: A widely linear (WL) model was recently proposed for stereophonic acoustic echo cancellation (SAEC). In this framework, the classical two-input/two-output SAEC scheme with real random variables is recasted as a single-input/single output system with complex random variables. The main advantage of this approach is that instead of handling two (real) output signals separately, we only handle one (complex) output signal. In general, due to their good convergence features, recursive least-squares (RLS) algorithms are preferable for SAEC applications. However, the performance of RLS-based algorithms is governed by the forgetting factor, whose value leads to a compromise between convergence rate/tracking capabilities on the one hand and misadjustment/stability on the other hand. In this paper, we develop a variable-forgetting factor RLS (VFF-RLS) algorithm for SAEC with the WL model. Simulation results indicate the good performance (in terms of tracking and robustness) of the proposed algorithm.

F. Albu, New proportionate affine projection algorithm, INTERNOISE 2012, New York, U.S.A., pp. 417-424. Website

Abstract: A new proportionate-type affine projection algorithm with intermittent update of the weight coefficients is proposed. It takes into account the “history” of the proportionate factors and uses a fast recursive filtering procedure. Also, the effect of using dichotomous coordinate descent iterations is investigated. Simulation results indicate that the proposed algorithm has improved performance and much lower computational complexity than other proportionate affine projection algorithms. Therefore it represents a practical solution for acoustic echo cancellation systems.

F. Albu, C. Paleologu, S. Ciochina, New variable step size affine projection algorithms, in Proc. of IEEE COMM 2012, Bucharest, Romania, pp. 63-66. Website

Abstract: In this paper, we propose new variable step size affine projection algorithms whose step sizes are adjusted according to the square of a time-averaging estimate of the autocorrelation of a priori and a posteriori errors. The proposed algorithms have fast convergence, robustness against near-end signal variations (including double-talk) and do not require any a priori information about the acoustic environment. The simulation results indicate the good performance of the proposed algorithms when compared to similar algorithms.

F. Albu, Simplified proportionate affine projection algorithms, IEEE IWSSIP 2012, Vienna, Austria, pp. 382-385. Website

Abstract: In this paper, new efficient proportionate affine projection algorithms are proposed. They use a simplified way of com-puting the output error vector. It is shown that the simplified approximated memory improved proportionate affine projection algorithm (SAMIPAPA) offers the best compromise between complexity and performance if compared with other proportionate-type APAs. Also, it is shown that, if the logarithmic proportionate scheme is integrated in SAMIPAPA, the convergence speed and tracking abilities are worsened.

C. Paleologu, J. Benesty, F. Albu, Regularization of the improved proportionate affine projection algorithms, IEEE ICASSP 2012, Kyoto, Japan, pp. 169-172. Website

Abstract: In sparse adaptive ﬁlters, the adaptation gain is “proportionately” redistributed among all the coefﬁcients, emphasizing the large ones in order to speed up their convergence. The improved proportionate afﬁne projection algorithm (IPAPA) is a very attractive choice for echo cancellation,since it combines the good convergence features of the afﬁne projection algorithm (APA) and the gain factors of the improved proportionate normalized least-mean-square (IPNLMS) algorithm. Similar to the APA, a matrix inversion is required within the IPAPA. For practical reasons, the matrix needs to be regularized before inversion, i.e., a positive constant is added to the elements of its main diagonal. In this paper, we propose a formula for choosing the regularization parameter of the IPAPA, aiming at attenuating the effects of the noise in the adaptive ﬁlter estimate. Simulation results indicate the validity of this approach in both network and acoustic echo cancellation scenarios

This work was supported by CNCS-UEFISCDI, PN-II-ID-PCE-2011-3-0097 project