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.

Identification of Linear and Bilinear Systems: A Unified Study

In applications involving system identification problems, some characteristics of the impulse response of the system to be identified are usually exploited to design adaptive algorithms with improved performance. In this context, this paper focuses on the identification of systems that own intrinsic symmetric or antisymmetric properties, which can be further formulated by using a combination of bilinear forms. Based on such an approach, the least-mean-square (LMS) and normalized LMS (NLMS) algorithms with symmetric/antisymmetric properties (termed here LMS-SAS and NLMS-SAS) are proposed. Simulation results are shown confirming the improved convergence speed achieved by the proposed algorithms as compared to the conventional LMS and NLMS counterparts for different operating scenarios.

LMS and NLMS Algorithms for the Identification of Impulse Responses with Intrinsic Symmetric or Antisymmetric Properties

In linear system identification problems, it is important to reveal and exploit any specific intrinsic characteristic of the impulse responses, in order to improve the overall performance, especially in terms of the accuracy and complexity of the solution. In this paper, we focus on the nearest Kronecker product decomposition of the impulse responses, together with low-rank approximations. Such an approach is suitable for the identification of a wide range of real-world systems. Most importantly, we reformulate the system identification problem by using a particular symmetric filter within the development, which allows us to efficiently design two (iterative/recursive) algorithms. First, an iterative Wiener filter is proposed, with improved performance as compared to the conventional Wiener filter, especially in challenging conditions (e.g., small amount of available data and/or noisy environments). Second, an even more practical solution is developed, in the form of a recursive least-squares adaptive algorithm, which could represent an appealing choice in real-time applications. Overall, based on the proposed approach, a system identification problem that can be conventionally solved by using a system of L=L1L2 equations (with L unknown parameters) is reformulated as a combination of two systems of PL1 and PL2 equations, respectively, where usually P≪L2 (i.e., a total of PL1+PL2 parameters). This could lead to important advantages, in terms of both performance and complexity. Simulation results are provided in the framework of network and acoustic echo cancellation, supporting the performance gain and the practical features of the proposed algorithms.

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Efficient Algorithms for Linear System Identification with Particular Symmetric Filters

The recently proposed tensor-based recursive least-squares dichotomous coordinate descent algorithm, namely RLS-DCD-T, was designed for the identification of multilinear forms. In this context, a high-dimensional system identification problem can be efficiently addressed (gaining in terms of both performance and complexity), based on tensor decomposition and modeling. In this paper, following the framework of the RLS-DCD-T, we propose a regularized version of this algorithm, where the regularization terms are incorporated within the cost functions. Furthermore, the optimal regularization parameters are derived, aiming to attenuate the effects of the system noise. Simulation results support the performance features of the proposed algorithm, especially in terms of its robustness in noisy environments.

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Tensor-Based Recursive Least-Squares Adaptive Algorithms with Low-Complexity and High Robustness Features

In this paper, we address the problem of constant-beamwidth beamforming using nonuniform planar arrays. We propose two techniques for designing planar beamformers that can maintain different beamwidths in the XZ and YZ planes based on constant-beamwidth linear arrays. In the first technique, we utilize Kronecker product beamforming to find the weights, thus eliminating matrix inversion. The second technique provides a closed-form solution that allows for a tradeoff between white noise gain and directivity factor. The second technique is applicable even when only a subset of the sensors is used. Since our techniques are based on linear arrays, we also consider symmetric linear arrays. We present a method that determines where sensors should be placed to maximize the directivity and increase the frequency range over which the beamwidth remains constant, with a minimal number of sensors. Simulations demonstrate the advantages of the proposed design methods compared to the state-of-the-art. Specifically, our method yields a 1000-fold faster runtime than the competing method, while improving the wideband directivity factor by over 8 dB without compromising the wideband white noise gain in the simulated scenario.

Constant-Beamwidth Kronecker Product Beamforming With Nonuniform Planar Arrays

A Kronecker product CLMS algorithm for adaptive beamforming

On the behavior of a combination of adaptive filters operating with the NLMS algorithm in a nonstationary environment

This paper deals with the stochastic modeling of the normalized least-mean-square algorithm for bilinear forms (NLMS-BF), which is defined from the temporal and spatial impulse responses of a multiple-input single-output (MISO) spatiotemporal system. Specifically, considering a system identification problem with stationary plant and Gaussian input data, model expressions are derived describing the mean weight behavior of the temporal, spatial, and spatiotemporal adaptive filters, the learning curve, as well as some correlation-like matrices required. Simulation results are shown confirming that the model predicts satisfactorily the algorithm behavior for both transient and steady-state phases.

On the Stochastic Modeling of the NLMS Algorithm Operating with Bilinear forms

Keyword spotting (KWS) is one of the speech recognition tasks most sensitive to the quality of the feature representation. However, the research on KWS has traditionally focused on new model topologies, putting little emphasis on other aspects like feature extraction. This paper investigates the use of the multitaper technique to create improved features for KWS. The experimental study is carried out for different test scenarios, windows and parameters, datasets, and neural networks commonly used in embedded KWS applications. Experiment results confirm the advantages of using the proposed improved features.

Khaled Jamal Bakri

Papers

A Kronecker product CLMS algorithm for adaptive beamforming

LMS and NLMS Algorithms for the Identification of Impulse Responses with Intrinsic Symmetric or Antisymmetric Properties

On the behavior of a combination of adaptive filters operating with the NLMS algorithm in a nonstationary environment

On the Stochastic Modeling of the NLMS Algorithm Operating with Bilinear forms

Multitaper-Mel Spectrograms for Keyword Spotting