Partitioned Block Frequency-domain Adaptive Filter Research Articles

Diffusion Partitioned-Block Frequency-Domain Adaptive Filter Over Multitask Networks

As a generalization of the frequency-domain adaptive filter (FDAF) algorithm, partitioned-block frequency-domain adaptive filter (PBFDAF) results in minimal signal path delay. In this brief, we propose the diffusion normalized PBFDAF algorithm based on an unsupervised clustering strategy to address the low complexity implementation issues in multitask networks. Each node adaptively adjusts the combination weight coefficients by minimizing the instantaneous mean square deviation (MSD) in frequency-domain. The simulation results demonstrate that the proposed algorithm achieves superior performance.

Analysis of Unconstrained Partitioned-Block Frequency-Domain Adaptive Filters

Previously, we have presented a performance analysis of the unconstrained partitioned-block frequency-domain adaptive filter (PBFDAF) with 50% overlap. It was found that the unconstrained PBFDAF always converges to a biased solution, and hence the mean-square deviation (MSD) learning curve does not match the mean-square error (MSE) learning curve. To deal with this problem, we present an alternative theoretical model of the unconstrained PBFDAF by introducing a modified time-domain weight vector. We show that the new weight vector can converge to the true system impulse response in the mean sense. We also derive the analytical expressions for the MSD and the MSE. The analysis here is equivalent to that in our previous work, but the former is much simpler and easier to handle. Also, the MSD learning curve calculated from the new weight vector is in good agreement with the MSE learning curve. Computer simulations support the analytical results well.

On the Convergence Behavior of Partitioned-Block Frequency-Domain Adaptive Filters

Partitioned-block frequency-domain adaptive filter (PBFDAF) algorithms have become very popular, in particular, for acoustic signal processing. However, the stochastic behavior of PBFDAFs has not been extensively examined. This paper presents a comprehensive statistical analysis for a family of the overlap-save PBFDAF algorithms with 50% overlap, including the transient and steady-state performance. The frequency-domain equations of the PBFDAFs are transformed into the time-domain counterparts, which allows us to carry out the analysis completely in the time domain. By means of the independence assumption and vectorization operation, theoretical models for the mean and mean-square behavior of the PBFDAF algorithms are established without restricting the distribution of the inputs to being Gaussian. Specifically, the mean weight behavior and corresponding steady-state solution are provided. Closed-form expressions for the mean-square deviation (MSD) and mean-square error (MSE) are derived. The upper bound on the step size for the mean and mean-square stability of the PBFDAFs is specified. The theoretical model presents new insights into the convergence properties of the PBFDAFs with a sufficient number of coefficients. It was revealed that both the constrained and unconstrained PBFDAFs converge to the Wiener solution. However, the mean weight vector of the unconstrained PBFDAF algorithms cannot converge to the true solution for any inputs, while that of the constrained version can. The presented theory explains why the steady-state MSD of the unconstrained PBFDAF algorithm is larger than that of the constrained version but their minimum MSE is the same. Monte Carlo simulations provide very good support for our theory.

Optimal Step-Size Control of the Partitioned Block Frequency-Domain Adaptive Filter

The partitioned block frequency-domain adaptive filter (PBFDAF) is appealing in echo cancellation due to its computational efficiency and good convergence property. However, the choice of the step size should comprise between the convergence rate and the final misalignment. Several variable step-size schemes were proposed, but this problem was not resolved entirely. In this brief, a robust optimal control approach to the PBFDAF algorithm is presented. We carry out a statistical convergence analysis for the PBFDAF, which is then used to derive the optimal step size and estimate the system distance. Simulation results demonstrate that the proposed method achieves an improved performance than the other variable step-size PBFDAF algorithms in the context of echo cancellation.

An improved block adaptive system for effective feedback cancellation in hearing aids

The hearing aid being a battery operated, portable device requires short processing delay, low computational complexity, with appreciable acoustic feedback cancellation effect. The prediction error method (PEM) and PEM with shadow filter (PEM-SH) based adaptive feedback canceller (AFC) referred as PEMAFC and PEMAFC-SH respectively reduces the amount of bias present in the estimate of feedback path. The available partitioned block frequency domain adaptive filter (PBFAF) based implementation of PEMAFC (PBFAF-P) and PEMAFC-SH (PBFAF-PS), offers a potential option for modelling an adaptive filter with many taps along with short block processing delay. However, the PBFAF suffers from large computational load because of the involvement of computationally expensive gradient constraints in each partition. Though removing or alternately applying the gradient constraint saves some computations but it results in significant performance degradation. With an objective of substantially reducing the computational burden and simultaneously retaining the performance, this paper develops an improved partitioned block Hartley domain adaptive filter (IPBHAF) and then employs it for effective feedback cancellation in hearing aids. Further, the IPBHAF with modified step size (IPBHAF-M) is proposed to achieve both fast convergence and better steady state performance. The simulation based experiments demonstrate the superior performance of IPBHAF-M based implementations of PEMAFC (IPBHAF-MP) and PEMAFC-SH (IPBHAF-MPS) over the PBFAF-P and PBFAF-PS in terms of both computational complexity and feedback cancellation performance.

A Computationally Efficient Delayless Frequency-Domain Adaptive Filter Algorithm

In acoustic echo cancellation (AEC) systems, the partitioned block frequency-domain adaptive filter (PBFDAF) algorithm is commonly adopted to improve the computational efficiency and convergence rate. However, the PBFDAF algorithm introduces an inherent delay. Delayless PBFDAF algorithms have been proposed to tackle this issue. However, the complexity of the existing delayless PBFDAF algorithms is high. Some have high average complexity, but others have high peak complexity. A computationally efficient delayless PBFDAF algorithm is proposed in this letter to reduce both the average and peak complexity. Moreover, a delay compensation method is presented to compensate the error path delay and thus speed up the convergence rate. Simulation results demonstrate that the convergence and tracking performance of the new algorithm with delay compensation is comparable with that of the PBFDAF algorithm.

A Time/Frequency-Domain Unified Delayless Partitioned Block Frequency-Domain Adaptive Filter

In this letter, a delayless counterpart of the partitioned frequency-domain adaptive filter algorithm is straightforwardly derived from the block least-mean-square (BLMS) algorithm. To improve its tracking capability, a time/frequency-domain unified (TFU) adaptation scheme is proposed. It is further shown that other delayless realizations can be seen as simplified implementations of the TFU technique. Simulations are presented to support the analyses and demonstrate the good convergence and tracking performance of the proposed algorithm.

Iterated partitioned block frequency-domain adaptive filtering for acoustic echo cancellation

For high quality acoustic echo cancellation long echoes have to be suppressed. classical LMS-based adaptive filters are not attractive as they are suboptimal from a computational point of view. Multirate adaptive filters such as the partitioned block frequency-domain adaptive filter (PBFDAF) are good alternatives and are widely used in commercial echo cancellers nowadays. In this paper the PBFDRAP is analyzed, which combines frequency-domain adaptive filtering with so-called row action projection. Fast versions of the algorithm are derived and it is shown that the PBFDRAP outperforms the PBFDAF in a realistic echo cancellation setup.

New constraining method for partitioned block frequency-domain adaptive filters

For adaptive filters with many taps, a short processing delay, and relative low computational complexity, the partitioned block frequency-domain adaptive filter (PBFDAF) is a good choice. The computational complexity of this algorithm is significantly reduced by using the alternated constrained PBFDAF. This particular algorithm applies gradient constraints in an alternating manner. In this paper, a serious problem in performance of the alternated constrained PBFDAF is described. Furthermore, a modification is proposed that effectively alleviates this problem. By using this modification together with a gradient constraint approximation, a new efficient alternated constrained PBFDAF is developed. Compared with the fully constrained PBFDAF, this new constraining method does not show any significant performance loss and still has a much smaller computational complexity.

On the implementation of a partitioned block frequency domain adaptive filter (PBFDAF) for long acoustic echo cancellation

The growing demand of communication systems incorporating hands-free audioterminals has multipled the efforts of developing efficient and reduced size acoustic echo cancellers. This work deals with the implementation of a wideband acoustic echo canceller using only a single DSP chip. The complete implementation takes advantage of two interesting features of a partitioned block frequency technique for the filtering operation:its good computational burden, and reduced and user-bounded delay. Essentially, this technique makes a sequential partition of the impulse response in the time domain prior to a frequency domain implementation of the filtering operation. Furthermore, this time segmentation allows to set up individual coefficient updating strategies concerning to different sections of the adaptive canceller, thus avoiding the need of disabling the adaption in the complete filter. The adaptive algorithm is based on the known frequency domain adaptive filter (FDAF) for every section of the filter, but the adaptation step computation procedure differs from other usual ones because it introduces an additional measure of the input spectral uniformity. Finally, a real time prototype is implemented with the help of a commercial floating-point DSP board. It is able to satisfy the needs of any wideband hands-free audioterminal working in reverberant environments with acoustic echoes of length up to 200 ms (≈3000 filter coeffients).