Efficient recursive least-squares algorithms for the identification of bilinear forms

Elisei-Iliescu, Camelia; Stanciu, Cristian; Paleologu, Constantin; Benesty, Jacob; Anghel, Cristian; Ciochină, Silviu

doi:10.1016/j.dsp.2018.09.005

Cited by 33 publications

(25 citation statements)

References 27 publications

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“…For the corresponding term from (56), we use the dual expression for e(n) (see (14)), which leads to…”

Section: Discussionmentioning

confidence: 99%

“…Let us consider the two estimated impulse responses h(n) and g(n), such that the estimated signal is given by (13). As a consequence, the a priori error signal between the desired signal and the estimated one can be defined following (14), i.e.,…”

Section: Optimized Lms Algorithm For Bilinear Formsmentioning

confidence: 99%

“…More recently, a new approach was studied in [11], where the bilinear term was defined in the context of a multiple-input/single-output (MISO) system, with respect to the impulse responses of a spatiotemporal model. In [11], the Wiener filter solution for the identification of such bilinear forms was proposed, and then, in [12][13][14], some adaptive solutions based on different basic algorithms were provided. Similar frameworks can be found in [15][16][17][18], in conjunction with specific applications, such as channel equalization and nonlinear acoustic echo cancellation; however, these works were not associated with the identification of bilinear forms or analyzed in this context.…”

Section: Introductionmentioning

confidence: 99%

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A Connection Between the Kalman Filter and an Optimized LMS Algorithm for Bilinear Forms

et al. 2018

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The system identification problem becomes more challenging when the parameter space increases. Recently, several works have focused on the identification of bilinear forms, which are related to the impulse responses of a spatiotemporal model, in the context of a multiple-input/ single-output system. In this framework, the problem was addressed in terms of the Wiener filter and different basic adaptive algorithms. This paper studies two types of algorithms tailored for the identification of such bilinear forms, i.e., the Kalman filter (along with its simplified version) and an optimized least-mean-square (LMS) algorithm. Also, a comparison between them is performed, which shows interesting similarities. In addition to the mathematical derivation of the algorithms, we also provide extensive experimental results, which support the theoretical findings and indicate the good performance of the proposed solutions.

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“…For the corresponding term from (56), we use the dual expression for e(n) (see (14)), which leads to…”

Section: Discussionmentioning

confidence: 99%

Section: Optimized Lms Algorithm For Bilinear Formsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Connection Between the Kalman Filter and an Optimized LMS Algorithm for Bilinear Forms

et al. 2018

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“…Equation (7) reveals that the choice of δ determines the minimum of the objective function. Therefore, to minimize (7) with respect to δ, one has to simply select δ as the index of the largest diagonal element of R ss H H u R −1 xx H u R ss . The a priori knowledge of R xx and p is hardly practical, and, thus, the statistics need to be estimated.…”

Section: A Linear Mmse Filtermentioning

confidence: 99%

Low-Rank Tensor MMSE Equalization

Ribeiro

Almeida

Mota

2019

2019 16th International Symposium on Wireless Communication Systems (ISWCS)

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New-generation wireless communication systems will employ large-scale antenna arrays to satisfy the increasing capacity demand. This massive scenario brings new challenges to the channel equalization problem due to the increased signal processing complexity. We present a novel low-rank tensor equalizer to tackle the high computational demands of the classical linear approach. Specifically, we propose a method to design a canonical polyadic tensor filter to minimize the mean square error criterion. Our simulation results indicate that the proposed equalizer needs fewer calculations and is more robust to short training sequences than the benchmark.

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“…In [11], the method of [10] is extended to cope with low-rank Kronecker separable systems, allowing for the identification of more intricate acoustic responses. In [12], fast recursive least squares methods for identifying second-order Kronecker separable (bilinear) systems are presented. Analytical and simulation results confirm the low computational costs and the identification performance of the proposed bilinear methods.…”

Section: Introductionmentioning

confidence: 99%

Low‐Complexity separable beamformers for massive antenna array systems

Ribeiro

Almeida

Nossek

et al. 2019

IET signal process.

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Future cellular systems will likely employ massive bi-dimensional arrays to improve performance by large array gain and more accurate spatial filtering, motivating the design of low-complexity signal processing methods. We propose optimising a Kroneckerseparable beamforming filter that takes advantage of the bi-dimensional array geometry to reduce computational costs. The Kronecker factors are obtained using two strategies: alternating optimisation, and sub-array minimum mean square error beamforming with Tikhonov regularization. According to the simulation results, the proposed methods are computationally efficient but come with source recovery degradation, which becomes negligible when the sources are sufficiently separated in space.

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Efficient recursive least-squares algorithms for the identification of bilinear forms

Cited by 33 publications

References 27 publications

A Connection Between the Kalman Filter and an Optimized LMS Algorithm for Bilinear Forms

A Connection Between the Kalman Filter and an Optimized LMS Algorithm for Bilinear Forms

Low-Rank Tensor MMSE Equalization

Low‐Complexity separable beamformers for massive antenna array systems

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