Marcus Zeller

Adaptive Combination of Volterra Kernels and Its Application to Nonlinear Acoustic Echo Cancellation

The combination of filters concept is a simple and flexible method to circumvent various compromises hampering the operation of adaptive linear filters. Recently, applications which require the identification of not only linear, but also nonlinear systems are widely studied. In this paper, we propose a combination of adaptive Volterra filters as the most versatile nonlinear models with memory. Moreover, we develop a novel approach that shows a similar behavior but significantly reduces the computational load by combining Volterra kernels rather than complete Volterra filters. Following an outline of the basic principles, the second part of the paper focuses on the application to nonlinear acoustic echo cancellation scenarios. As the ratio of the linear to nonlinear echo signal power is, in general, a priori unknown and time-variant, the performance of nonlinear echo cancellers may be inferior to a linear echo canceller if the nonlinear distortion is very low. Therefore, a modified version of the combination of kernels is developed obtaining a robust behavior regardless of the level of nonlinear distortion. Experiments with noise and speech signals demonstrate the desired behavior and the robustness of both the combination of Volterra filters and the combination of kernels approaches in different application scenarios.

Adaptive Volterra Filters With Evolutionary Quadratic Kernels Using a Combination Scheme for Memory Control

This paper proposes a new paradigm for adaptive Volterra filtering using a time-variant size of the quadratic kernel memory in order to optimally identify any unknown transversal second-order nonlinear system. To this end, competing Volterra structures of different sizes are employed in a hierarchical combination scheme so as to find the best configuration of the second-order kernel memory, using the already known diagonal-coordinate representation. The length and number of required quadratic kernel diagonals can be concurrently estimated by monitoring the combination performance. Subsequently, the memory size of the involved models is dynamically increased or decreased, following a set of intuitive rules. Since this automatic memory adaptation is performed along with the coefficient updates, an efficient Volterra filter is realized, offering great flexibility and minimizing the risk of under- or overmodeling any given quadratic nonlinearity. Besides the straightforward scheme, a simplified version is presented, greatly reducing the algorithmic demands. This efficient version is based on a virtualization of the competing Volterra filters by jointly using common coefficients and hence exhibits a computational complexity suitable for practical implementations. The robust estimation performance of the approach is demonstrated by various examples for a nonlinear acoustic echo cancellation scenario, involving stationary noise, real speech signals and realistic Volterra kernels.

Enhanced Adaptive Volterra Filtering by Automatic Attenuation of Memory Regions and Its Application to Acoustic Echo Cancellation

This paper presents a novel scheme for nonlinear acoustic echo cancellation based on adaptive Volterra Filters with linear and quadratic kernels, which automatically prefers those diagonals contributing most to the output of the quadratic kernel with the goal of minimizing the overall mean-square error. In typical echo cancellation scenarios, not all coefficients will be equally relevant for the modeling of the nonlinear echo, but coefficients close to the main diagonal of the second-order kernel will describe most of the nonlinear echo distortions, such that not all diagonals need to be implemented. However, it is difficult to decide the most appropriate number of diagonals a priori, since there are many factors that influence this decision, such as the energy of the nonlinear echo, the shape of the room impulse response, or the step size used for the adaptation of kernel coefficients. Our proposed scheme incorporates adaptive scaling factors that control the influence of each group of adjacent diagonals contributing to the quadratic kernel output. An appropriate selection of these factors serves to emphasize or neglect diagonals of the model as required by the present situation. We provide adaptation rules for these factors based on previous works on combination of adaptive filters, and comprehensive simulations showing the reduced gradient noise reached by the new echo canceller.

Fast and Robust Adaptation of DFT-Domain Volterra Filters in Diagonal Coordinates Using Iterated Coefficient Updates

This paper presents a novel data-reusing technique for implementing adaptive discrete Fourier transform (DFT) domain Volterra filters in diagonal coordinates having arbitrary nonlinear order. In general, a major drawback of such nonlinear filters is the large number of parameters. Thus, a weak excitation of higher-order kernels results in a slow convergence for system identification tasks. In order to exploit the available innovation of the signals more effectively, each data frame is processed for a specified number of iterations in an overlap-save scheme, thereby enhancing the convergence performance. Due to inherent recursions of the repeated filtering and updating steps, this concept also lends itself to a fast algorithm, requiring only a moderate increase in algorithmic complexity over a baseline implementation. A detailed comparison of the required number of multiplications is given for several different algorithm versions. Despite the relatively simple concept, the outlined iteration algorithm exhibits significant gains in both adaptation speed and steady-state convergence. This is demonstrated by various experiments for both stationary noise and speech input considering an application of nonlinear acoustic echo cancellation. Finally, investigations on the tracking behavior for time-variant nonlinearities and robustness against misdetection of double-talk situations confirm the promising benefits and good trade-off of the proposed iterated coefficient updates Volterra filters approach.

Online estimation of the optimum quadratic kernel size of second-order Volterra filters using a convex combination scheme

This paper presents a method for estimating the optimum memory size for identification of an unknown second-order Volterra kernel. As these structures may imply considerable computational demands, it is highly desirable to design adaptive realizations with a minimum number of coefficients. Therefore, we propose a combination scheme comprising two Volterra filters with time-variant sizes of the actually used quadratic kernels. By following some simple rules, the number of diagonals in the quadratic kernels is increased or decreased in order to find the optimum memory configuration in parallel to the coefficient adaptation. Thus, the arbitrary choice of the nonlinear system size is overcome by a dynamically growing/shrinking system. Experimental results for various signals and nonlinear scenarios demonstrate the effectiveness of the proposed method.

Novel schemes for nonlinear acoustic echo cancellation based on filter combinations

Nonlinear acoustic echo cancellers (NLAEC) are becoming increasingly important in hands-free applications. However, in some situations, an NLAEC is inferior to a linear AEC, especially when the channel generates a negligible (or no) nonlinear echo. In general, the ratio of the linear to nonlinear echo signal power is unknown a priori, and will vary over time, thus making it difficult to know if an NLAEC would improve or degrade the cancellation. In this paper, we present two novel solutions to this problem based on the adaptive combination of linear and nonlinear echo cancellers. Both solutions perform efficiently regardless of the level of nonlinear echo. The benefits and robustness of both schemes are illustrated by experiments using Laplacian colored noise and speech input signals.

Adaptive fir filters with automatic length optimization by monitoring a normalized combination scheme

This paper presents a novel strategy of adaptive filtering which provides an automatic self-configuration of the filter structure in terms of memory length. By monitoring the adaptive mixing of a normalized combination of two competing filters with a different number of coefficients, an online estimate of the optimum filter length is obtained and used to dynamically scale the size of the employed filters. Furthermore, a more efficient, simplified version of this approach is proposed and shown to be equally effective while significantly reducing the required complexity. Experimental results for high-order real-world systems as well as stationary noise and speech signals demonstrate the good performance and the robust tracking behaviour of the outlined algorithms in the context of realistic system identification scenarios.

Least-squares adaptation of affine combinations of multiple adaptive filters

Adaptive combinations of adaptive filters are gaining popularity as a flexible and versatile solution to improve adaptive filters performance. In the recent years, combination schemes have focused on two different approaches: Convex and affine combinations, developing principally practical implementations with just two component filters. However, combinations of a higher number of adaptive filters can offer additional advantages, mainly in tracking environments. In this paper, we introduce a practical adaptation scheme for the affine combination of an arbitrary number of filters, including a steady-state analysis where the proposed rule is compared with the optimal combination. Several experiments both in tracking and stationary scenarios serve to demonstrate the appropriate performance of this approach.

Iterated Coefficient Updates of Partitioned Block Frequency Domain Second-Order Volterra Filters for Nonlinear AEC

This paper presents the benefits of iterated coefficient updates for the adaptation of partitioned block frequency domain second-order Volterra filters when applied to nonlinear acoustic echo cancellation. In order to increase the convergence speed of an NLMS algorithm with separate kernel normalization, each input frame is used for several coefficient updates. This procedure effectively accelerates the convergence of the employed adaptive Volterra filters and is shown to be superior to processing with increased data overlap. The advantages of this novel approach are illustrated by experimental results for noise and speech input and guidelines for determining suitable numbers of iterations for the filter kernels are given.

Efficient adaptive DFT-domain Volterra filters using an automatically controlled number of quadratic kernel diagonals

This paper presents a method for estimating the optimum number of second-order kernel diagonals of an adaptive Volterra filter in system identification tasks. To this end, a recently proposed time-domain mechanism is carried over to the very efficient partitioned-block DFT-domain Volterra filtering technique. The size of the nonlinear memory is controlled by monitoring the performance of an adaptive combination scheme with two differently-sized quadratic kernels. Subsequently, an efficient version is derived, requiring only minor additional computations as compared to a single Volterra filter. The effectiveness of the outlined estimation procedure is demonstrated by various simulations with real nonlinear systems and both noise and speech inputs in an acoustic echo cancellation scenario.