Abstract
The Newton adaptive filtering algorithm in its original form is computationally very complex as it requires inversion of the input-signal autocorrelation matrix at every time step. Also, it may suffer from stability problems due to the inversion of the input-signal autocorrelation matrix. In this paper, we propose to replace the inverse of the input-signal autocorrelation matrix by an approximate one, assuming that the input-signal autocorrelation matrix is Toeplitz. This assumption would help us in replacing the update of the inverse of the autocorrelation matrix by the update of the autocorrelation matrix itself, and performing the multiplication of R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> x in the update equation by using the Fourier transform. This would increase the stability of the algorithm, in one hand, and decrease its computational complexity, on the other hand. Since the objective of the paper is to enhance the stability of the Newton algorithm, the performance of the proposed algorithm is compared to those of the Newton and the improved quasi-Newton (QN) algorithms in noise cancellation and system identification settings.
Highlights
The least-mean-squares (LMS) algorithm is used in many applications that vary from single-input/single-output (SISO) to multiple-input/multiple-output (MIMO) systems [1]–[9]
We provide a detailed description of our algorithm proposed in [28] which is mainly a new approximate inverse quasi-Newton (AIN) algorithm that replaces the inverse of the input-signal autocorrelation matrix by an approximate one, assuming that the input-signal’s instantaneous autocorrelation matrix is Toeplitz
SIMULATION RESULTS To test the performance of the proposed algorithm, we compare its performance to the original Newton and the improved QN [14] algorithms in additive white Gaussian noise (AWGN) and additive white impulsive noise (AWIN) [30], [31] for noise cancellation and system identification settings
Summary
The least-mean-squares (LMS) algorithm is used in many applications that vary from single-input/single-output (SISO) to multiple-input/multiple-output (MIMO) systems [1]–[9]. More sophisticated algorithms such as Newton based algorithms provide improved performance [10]–[13] These algorithms, which are usually computationally very complex, suffer from stability problems since they require the inverse of the input-signal autocorrelation matrix in the weight vector update. We provide a detailed description of our algorithm proposed in [28] which is mainly a new approximate inverse quasi-Newton (AIN) algorithm that replaces the inverse of the input-signal autocorrelation matrix by an approximate one, assuming that the input-signal’s instantaneous autocorrelation matrix is Toeplitz This assumption replaces the update of the inverse autocorrelation matrix by the update of the autocorrelation matrix itself, and allows performing the multiplication of R−1x in the update equation by using the Fourier transform.
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