Tensor-Based Adaptive Filtering Algorithms

Laura-Maria Dogariu,Cristian-Lucian Stanciu,Jacob Benesty,Silviu Ciochină,Constantin Paleologu,Camelia Elisei-Iliescu

doi:10.3390/sym13030481

Abstract

Tensor-based signal processing methods are usually employed when dealing with multidimensional data and/or systems with a large parameter space. In this paper, we present a family of tensor-based adaptive filtering algorithms, which are suitable for high-dimension system identification problems. The basic idea is to exploit a decomposition-based approach, such that the global impulse response of the system can be estimated using a combination of shorter adaptive filters. The algorithms are mainly tailored for multiple-input/single-output system identification problems, where the input data and the channels can be grouped in the form of rank-1 tensors. Nevertheless, the approach could be further extended for single-input/single-output system identification scenarios, where the impulse responses (of more general forms) can be modeled as higher-rank tensors. As compared to the conventional adaptive filters, which involve a single (usually long) filter for the estimation of the global impulse response, the tensor-based algorithms achieve faster convergence rate and tracking, while also providing better accuracy of the solution. Simulation results support the theoretical findings and indicate the advantages of the tensor-based algorithms over the conventional ones, in terms of the main performance criteria.

Highlights

Nowadays, adaptive filtering algorithms represent powerful signal processing tools, which are widely used in many important applications [1]
In the second case (SISO scenario in the framework of echo cancellation), the input signal is either a highly-correlated AR(1) process or a speech sequence, while the measurement noise is generated such that the echo-to-noise ratio (ENR) is 20 dB
We have presented a family of tensor-based adaptive filtering algorithms, targeting an efficient way to solve high-dimension MISO system identification problems

Summary

Introduction

Adaptive filtering algorithms represent powerful signal processing tools, which are widely used in many important applications [1] Due to their capabilities to work in nonstationary environments and to process real-time data, these algorithms can provide efficient solutions for system identification problems [2], interference cancellation scenarios [3], and adaptive control processes [4]. The main advantage of the LMS-based algorithms consists of a lower computational complexity, as compared to their counterparts from the RLS family. The latter ones are able to provide a faster convergence rate. The LMS algorithms are more sensitive to the character of the input data, e.g., when dealing with nonstationary or highly correlated inputs

Objectives

Results

Conclusion