Project info
Project Title: New Decomposition-Based Algorithms for Sparse System Identification
Code: TE 144/2020
Program name and purpose: Research projects to stimulate young independent teams - Supporting young researchers, PhDs, to create or strengthen their own research team and an independent research program.
Funding Institution: Executive Unit for Higher Education, Research, Development and Innovation Funding (UEFISCDI)
Project code: PN-III-P1-1.1-TE-2019-0529
Project abstract & goals
Sparsity represents a key feature in system identification scenarios where only a small percentage of the impulse response components have a significant magnitude. Many important applications can be formulated in terms of sparse system identification problems, e.g., network/acoustic echo cancellation, satellite-linked communications, radar systems, underwater communications, microphone arrays, etc. In these frameworks, adaptive filters represent some of the most popular solutions for real-world/real-time applications. The current state-of-art algorithms used in sparse system identification scenarios are mainly based on the proportionate approach, i.e., each coefficient of the filter is updated independently of the others (in proportion to its magnitude). However, in most applications, a major limitation is the high length of the impulse response (e.g., hundreds/thousands of coefficients), which poses significant challenges in terms of complexity, convergence, and accuracy of the solution. In this project, we focus on a new approach that exploits the impulse response decomposition based on the nearest Kronecker product and low-rank approximations, which fits very well for sparse system identification problems. The basic idea is to transform a high-dimension system identification problem into smaller problems (i.e., shorter filters) that are connected to match the original purpose. The gain is twofold, in terms of both performance and complexity. The new family of decomposition-based adaptive algorithms involves fast converging techniques, like least-squares methods, which are usually prohibitive due to their high complexity. Also, we exploit these decomposition-based structures in the context of multichannel and multidimensional adaptive algorithms, which broaden the applicability of the developed solutions from a system identification perspective.
The team's work focuses on four representative goals:
- Developing the convergence analysis of the decomposition-based algorithms.
- Developing multidimensional decomposition-based algorithms.
- Developing computationally efficient versions of the RLS-NKP algorithms.
- Developing multichannel decomposition-based algorithms.
Estimated results
The target is to create a new direction and address the system identification problem using adaptive systems by exploiting the impulse response decomposition based on the nearest Kronecker product, together with low-rank approximations. In this framework, the identification of sparse systems will be reformulated using multiple low-rank techniques, so that a high dimension system identification problem will be transformed into “smaller” problems (i.e., shorter filters) that can be further connected to match the original purpose. The main feature of the decomposition-based algorithms (mostly developed for the RLS family) will be their ability to work with smaller structures, which further involves many related advantages. First, the convergence rate and tracking of these new algorithms will outperform the capabilities of their classical counterparts (which work with a single high-length adaptive filter). Second, a better accuracy of the solution (in terms of system identification) is expected, since the mi sadjustment of the adaptive filter (i.e., a measure of accuracy of the solution) is highly influenced by the length of the impulse response. Besides, the computational complexity of the decomposition-based algorithms will be much lower as compared to the classical versions. Additionally, we will exploit the decomposition-based structures in the context of multichannel and multidimensional adaptive algorithms, which broaden the applicability of the proposed solutions from a system identification perspective. We will mainly focus on the acoustic echo cancellation applications, where an important goal is to find the best solutions for real-time implementations.