Linear system identification is a key problem in many important applications, among which echo cancellation is a very challenging one. Due to the long length impulse responses (i.e., echo paths) to be identified, there is always room (and needs) to improve the performance of the echo cancellers, especially in terms of complexity, convergence rate, robustness, and accuracy. In this paper, we propose a new way to address the system identification problem (from the echo cancellation perspective), by exploiting an optimal approximation of the impulse response based on the nearest Kronecker product decomposition. Also, we make a first step toward this direction, by developing an iterative Wiener filter based on this approach. As compared to the conventional Wiener filter, the proposed solution is much more attractive, since its gain is twofold. First, the matrices to be inverted (or, preferably, linear systems to be solved) are smaller as compared to the conventional approach. Second, as a consequence, the iterative Wiener filter leads to a good estimate of the impulse response, even when a small amount of data is available for the estimation of the statistics. Simulation results support the theoretical findings and indicate the good results of the proposed approach, for the identification of different network and acoustic impulse responses.

The recursive least-squares (RLS) adaptive filter is an appealing choice in many system identification problems. The main reason behind its popularity is its fast convergence rate. However, this algorithm is computationally very complex, which may make it useless for the identification of long length impulse responses, like in echo cancellation. Computationally efficient versions of the RLS algorithm, like those based on the dichotomous coordinate descent (DCD) iterations or QR decomposition techniques, reduce the complexity, but still have to face the challenges related to long length adaptive filters (e.g., convergence/tracking capabilities). In this paper, we focus on a different approach to improve the efficiency of the RLS algorithm. The basic idea is to exploit the impulse response decomposition based on the nearest Kronecker product and low-rank approximation. In other words, a high-dimension system identification problem is reformulated in terms of low-dimension problems, which are combined together. This approach was recently addressed in terms of the Wiener filter, showing appealing features for the identification of low-rank systems, like real-world echo paths. In this paper, besides the development of the RLS algorithm based on this approach, we also propose a variable regularized version of this algorithm (using the DCD method to reduce the complexity), with improved robustness to double-talk. Simulations are performed in the context of echo cancellation and the results indicate the good performance of these algorithms.

In this letter, the identification problem of bilinear forms with the Wiener filter is addressed. The contribution is twofold. First, a different approach is introduced, by defining the bilinear term with respect to the impulse responses of a spatiotemporal model, in the context of multiple-input/single-output systems. Second, two versions of the Wiener filter (namely direct and iterative) are developed in this context. Moreover, the advantage of the iterative Wiener filter is outlined as compared to the direct solution. The results of the simulations, which are performed from a system identification perspective, support the theoretical findings.

Acoustic echo cancellation represents one of the most challenging system identification problems. The most used adaptive filter in this application is the popular normalized least mean square (NLMS) algorithm, which has to address the classical compromise between fast convergence/tracking and low misadjustment. In order to meet these conflicting requirements, the step-size of this algorithm needs to be controlled. Inspired by the pioneering work of Prof. E. Hänsler and his collaborators on this fundamental topic, we present in this paper several solutions to control the adaptation of the NLMS adaptive filter. The developed algorithms are “non-parametric” in nature, i.e., they do not require any additional features to control their behavior. Simulation results indicate the good performance of the proposed solutions and support the practical applicability of these algorithms.

System identification problems are always challenging to address in applications that involve long impulse responses, especially in the framework of multichannel systems. In this context, the main goal of this review paper is to promote some recent developments that exploit decomposition-based approaches to multiple-input/single-output (MISO) system identification problems, which can be efficiently solved as combinations of low-dimension solutions. The basic idea is to reformulate such a high-dimension problem in the framework of bilinear forms, and to then take advantage of the Kronecker product decomposition and low-rank approximation of the spatiotemporal impulse response of the system. The validity of this approach is addressed in terms of the celebrated Wiener filter, by developing an iterative version with improved performance features (related to the accuracy and robustness of the solution). Simulation results support the main theoretical findings and indicate the appealing performance of these developments.

There are different strategies to improve the overall performance of the recursive least-squares (RLS) adaptive filter. In this letter, we focus on the data-reuse approach, aiming to improve the convergence rate/tracking of the algorithm by reusing the same set of data (i.e., the input and reference signals) several times. First, we present a computationally efficient data-reuse RLS algorithm, which is the result of a low complexity implementation of the data-reuse process. Moreover, we extend the idea to the fast RLS algorithm. Simulations performed in the context of echo cancellation support the performance gain.