Dynamically Regularized Fast RLS with Application to Echo Cancellation

This paper introduces a dynamically regularized fast recursive least squares (DR-FRLS) adaptive filtering algorithm. Numerically stabilized FRLS algorithms exhibit reliable and fast convergence with low complexity even when the excitation signal is highly self-correlated. FRLS still suffers from instability, however, when the condition number of the implicit excitation sample covariance matrix is very high. DR-FRLS, overcomes this problem with a regularization process which only increases the computational complexity by 50%. The benefits of regularization include: (1) the ability to use small forgetting factors resulting in improved tracking ability and (2) better convergence over the standard regularization technique of noise injection. Also, DR-FRLS allows the degree of regularization to be modified quickly without restarting the algorithm. The application of DR-FRLS to stabilizing the fast affine projection (FAR) algorithm is also discussed

An Efficient, Fast Converging Adaptive Filter for Network Echo Cancellation

This paper discusses a fast efficient adaptive filtering algorithm for network echo cancellers PNLMS++ (proportionate normalized least mean squares ++). Compared to the conventional normalized least mean squares (NLMS) algorithm, PNLMSI++ converges much more quickly when the echo path is sparse. When the echo path is dispersive, the convergence rate is the same as NLMS. In addition, the new algorithm diverges at the same rate and to the same misalignment level as NLMS during periods of undetected double-talk. PNLMS++ is only 50% more computationally complex than NLMS and requires no additional memor

A Multiple Principal Components Based Adaptive Filter

Proportionate normalized least mean squares (PNLMS) is an adaptive filter that has been shown to provide exceptionally fast convergence and tracking when the underlying system parameters are sparse. A good example of such a system is a network echo canceller. Principal components based PNLMS (PCP) extends this fast convergence property to certain nonsparse systems by applying PNLMS while using the principal components of the underlying system as basis vectors. An acoustic echo canceller is a possible example of this type of nonsparse system. Simulations of acoustic echo paths and cancellers indicate that PCP converges and tracks much faster than the classical normalized least mean squares (NLMS) and fast recursive least squares (FRLS) adaptive filters. However, when a basic parameter, like room temperature, changes, the underlying acoustic structure of the room changes as well and principal components of the room responses at one temperature are very different from those at another. This paper addresses this problem by using multiple sets of principle components as basis vectors and performing PNLMS in each basis set. Each set of principle components are derived from the room at a different temperature. The new algorithm, multiple principal components PNLMS (MPCP) is a generalization of PNLMS++. Simulations show the potential effectiveness of the approach

A Fast Converging, Low Complexity Adaptive Filtering Algorithm

This paper introduces a new adaptive filtering algorithm called fast affine projections (FAP). Its main attributes include RLS (recursive least squares) like convergence and tracking with NLMS (normalized least mean squares) like complexity. This mix of complexity and performance is similar to the recently introduced fast Newton transversal filter (FNTF) algorithm. While FAP shares some similar properties with FNTF it is derived from a different perspective, namely the generalization of the affine projection interpretation of NLMS. FAP relies on a sliding windowed fast RLS (FRLS) algorithm to generate forward and backward prediction vectors and expected prediction error energies. Since sliding windowed FRLS algorithms easily incorporate regularization of the implicit inverse of the covariance matrix, FAP is regularized as well

The Fast Affine Projection Algorithm

This paper discusses a new adaptive filtering algorithm called fast affine projections (FAP). FAP\u27\u27s key features include LMS like complexity and memory requirements (low), and RLS like convergence (fast) for the important case where the excitation signal is speech. Another of FAP\u27\u27s important features is that it causes no delay in the input or output signals. In addition, the algorithm is easily regularized resulting in robust performance even for highly colored excitation signals. The combination of these features make FAP an excellent candidate for the adaptive filter in the acoustic echo cancellation problem. A simple, low complexity numerical stabilization method for the algorithm is also introduced

A Fast and Efficient Frequency-Domain Method for Convolutive Blind Source Separation

In this paper, the problem of blind separation of a convolutive mixture of audio signals is considered. A fast and efficient frequency-domain blind source separation (BSS) method using Independent component analysis (ICA) is investigated. The main difficulties of this approach lie in the so called permutation and amplitude problems. In order to solve the permutation ambiguity, the final value of the ICA derived separation matrix of one frequency bin, is used to initialize the ICA iterations in the next frequency bin. The amplitude problem is addressed by utilizing the elements in the inverse of the separation matrix. Experimental results demonstrate that successful separation is achieved and compared with conventional frequency-domain BSS methods, it is less computationally complex and has faster convergence

An Improved PNLMS Algorithm

The proportionate normalized least mean square (PNLMS) algorithm was developed for use in network echo cancelers. In comparison to the normalized least mean square (NLMS) algorithm, PNLMS has a very fast initial convergence and tracking when the echo path is sparse. Unfortunately, when the impulse response is dispersive, the PNLMS converges much slower than NLMS. This implies that the rule proposed in PNLMS is far from optimal. In many simulations, it seems that we fully benefit from PNLMS only when the impulse response is close to a delta function. We propose a new rule that is more reliable than the one used in PNLMS. Many simulations show that the new algorithm (improved PNLMS) performs better than NLMS and PNLMS, whatever the nature of the impulse respons