Adaptive filtering in subbands using a weighted criterion

Abstract

Abstract-Transform-domain adaptive algorithms have been proposed to reduce the eigenvalue spread of the matrix governing their convergence, thus improving the convergence rate. However, a classical problem arises from the conflicting requirements between algorithm improvement requiring rather long transforms and the need to keep the input/output delay as small as possible, thus imposing short transforms. This dilemma has been alleviated by the so-called "short-block transform domain algorithms" but is still apparent. This paper proposes an adaptive algorithm compatible with the use of rectangular orthogonal transforms (e.g., critically subsampled, lossless, perfect reconstruction filter banks), thus allowing better tradeoffs between algorithm improvement, arithmetic complexity, and input/output delay.The method proposed here makes a direct connection between the minimization of a specific weighted least squares criterion and the convergence rate of the corresponding stochastic gradient algorithm. This method leads to improvements in the convergence rate compared with both LMS and classical frequency domain algorithms.

The Novel Proportionate Normalized Subband Adaptive Filter Algorithms for Sparse System Identification

“…The filter update equation proposed in [7] is similar to what proposed in [8] and [9], where the fullband filters are updated instead of subfilters as in the conventional SAF structure [10] and [11]. In this paper the concept of proportionate adaptation is extended to the normalized subband adaptive filter (NSAF), and three proportionate normalized subband adaptive filter algorithms are established.…”

“…Updating rules of PNLMS++ are based on switching between PNLMS and NLMS weight vector equations with n as index parameter. Consequently, PNLMS and NLMS are used alternately at odd and even sample instants n , respectively [5], [7].…”

“…In [7], the subband adaptive algorithm called normalized subband adaptive filter (NSAF) was developed based on a constrained optimization problem. The filter update equation proposed in [7] is similar to what proposed in [8] and [9], where the fullband filters are updated instead of subfilters as in the conventional SAF structure [10] and [11].…”

The New Normalized Subband Adaptive Filter Algorithms with Variable Step-Size

“…In the presence of colored input signals, the LMS and NLMS algorithms have extremely slow convergence rates. Adaptive filtering in subbands has been proposed to improve the convergence behavior of the LMS algorithm [6]. The normalized subband adaptive filter (NSAF) was proposed in [7].…”

A Family of Variable Step-Size Affine Projection Adaptive Filtering Algorithms

“…In the presence of colored input signals, the LMS and NLMS algorithms have extremely slow convergence rates. To solve this problem a number of adaptive filtering structures based on affine subspace projections [3], [4], [5], data reusing adaptive algorithms [6], [7], [8], Block adaptive filters [2] and multirate techniques have been proposed in the literature [9], [10], [11]. In all these algorithms the selected fixed step-size can change the convergence speed and the steady-state mean square error.…”