Fast RLS Research Articles

The fast normalized cross-correlation double-talk detector

In this paper, we present a method for handling double-talk. This approach uses a robust fast recursive least-squares algorithm (FRLS) and the normalized cross-correlation double-talk detector (NCC DTD). The NCC DTD is developed into a fast version, called FNCC, by reusing computational results from the FRLS algorithm. The major advantage of this detector is that it is much less dependent on the actual echo path attenuation than, e.g., the Geigel DTD. This makes it much more suitable for the acoustic application.

Subband transforms for adaptive, RLS direct sequence spread spectrum receivers

Adaptive Direct Sequence Spread Spectrum (DSSS) receivers have advantages over their fixed matched filter counterparts including interference cancellation capabilities and simplification of PN code acquisition. However, convergence using the LMS algorithm will be very slow in situations with relatively high SNR and/or a large number of users. The use of the RLS algorithm will improve convergence speed but at significantly increased computational cost, especially for long PN codes. Unfortunately, computationally efficient, fast RLS algorithms cannot be used because the filter is updated at the symbol rate rather than at every sample. In this paper, we propose a subband version of the RLS-based receiver that utilizes multiple, shorter length adaptive filters. This approach significantly reduces computation and introduces architectural parallelism into the system implementation. We design an optimal subband transform and provide simulation results demonstrating the improved convergence properties as compared with the fullband system.

Multichannel parallelizable sliding window RLS and fast RLS algorithms with linear constraints

This paper presents new sliding window (SW) recursive least squares (RLS) and fast RLS algorithms for adaptive filtering with linear constraints. The algorithms are formulated for the general case of multichannel adaptive filters with complex-valued weights, and are based on Papaodysseus's matrix inversion lemma. The lemma is used for SW correlation matrix inversion and for the inversion of some other matrices that appear in constrained SW RLS algorithms. The algorithms have a form that can be implemented by means of at least two parallel processors. The proposed algorithms can be used for time-domain adaptive filtering of non-stationary signals, whilst restricting the frequency response of the filter to specific values at particular frequencies. In addition, the algorithms can be used in linearly constrained adaptive beamforming, dealing with non-stationary interference.

Efficient fast recursive least-squares adaptive complex filtering using real valued arithmetic

In this paper, a novel implementation of the fast recursive least squares (FRLS) algorithm for complex adaptive filtering, is presented. Complex signals are treated as pairs of real signals, and operations are re-organized on a real arithmetic basis. A new set of signals and filtering parameters is introduced, which are expressed either as the sum, or as the difference between the real and the imaginary part of the original variables. The algorithmic strength reduction technique is subsequently applied, resulting in significant computational savings. In this way, an efficient, FRLS algorithm is derived, where only two real valued filters are propagated, based on novel three-terms recursions for the time updating of the pertinent parameters. The proposed algorithm is implemented using real valued arithmetic only, whilst reducing the number of the required real valued multiplication operations by 23.5%, at the expense of a marginal 2.9% increase in the number of the real valued additions. The performance of the proposed FRLS algorithm is investigated by computer simulations, in the context of adaptive system identification and adaptive channel equalization.

Using a fast RLS adaptive algorithm for efficient speech processing

In this paper, a new method is presented that offers efficient computation of Linear Prediction Coefficients (LPC) via a new Recursive Least Squares (RLS) adaptive filtering algorithm. This method can be successfully used in speech coding and processing. The introduced algorithm is numerically robust, fast, parallelizable and has particularly good tracking properties. By means of this scheme, Linear Prediction Coefficients are obtained that offer an improvement in the reconstruction of the speech signal before coding, as compared to the signal obtained by various classical algorithm. An analogous improvement is observed in speech coding experiments too, while a subjective test confirms the improvement of the quality of synthesized speech. The overall processing time of the proposed method of speech coding is a bit greater, but comparable to the time the classical methods need.

Extended rls lattice adaptive filters

This paper solves the problem of developing exact fast weighted RLS lattice adaptive filters for input signals induced by general orthonormal filter models. The resulting algorithm can be viewed as a counterpart of the extended fast fixed-order RLS adaptive filters previously derived.

Fast QR Algorithms Based on Backward Prediction Errors: A New Implementation and Its Finite Precision Performance

QR decomposition techniques are well known for their good numerical behavior and low complexity. Fast QRD recursive least squares adaptive algorithms benefit from these characteristics to offer robust and fast adaptive filters. This paper examines two different versions of the fast QR algorithm based on a priori backward prediction errors as well as two other corresponding versions of the fast QR algorithm based on a poste- riori backward prediction errors. The main matrix equations are presented with different versions derived from two distinct deployments of a particular matrix equation. From this study, a new algorithm is derived. The discussed algorithms are compared, and differences in computational complexity and in finite-precision behavior are shown. Ke yw ords: Adaptive system, fast RLS algorithm, QR decomposition.

Adaptive linearly constrained inverse QRD-RLS beamforming algorithm for moving jammers suppression

A general, linearly constrained (LC) recursive least squares (RLS) array-beamforming algorithm, based on an inverse QR decomposition, is developed for suppressing moving jammers efficiently. In fact, by using the inverse QR decomposition-recursive least squares (QRD-RLS) algorithm approach, the least-squares (LS) weight vector can be computed without back substitution and is suitable for implementation using a systolic array to achieve fast convergence and good numerical properties. The merits of this new constrained algorithm are verified by evaluating the performance, in terms of the learning curve, to investigate the convergence property and numerical efficiency, and the output signal-to-interference-and-noise ratio. We show that our proposed algorithm outperforms the conventional linearly constrained LMS (LCLMS) algorithm, and the one using the fast linear constrained RLS algorithm and its modified version.

Equalization techniques based on fast RLS algorithms to improve mobile reception performance of 8-VSB receivers

This paper presents fast and robust equalization techniques to improve ATSC DTV reception for fixed, portable, pedestrian, and mobile receivers. There are many strong and dynamic echoes affecting portable, pedestrian, and mobile reception. The conventional decision feedback equalizer using least mean square algorithm is stable and shows good performance in handling the static multipath channel. The equalizer however has difficulty in handling strong echoes and shows poor performance in tracking high Doppler frequencies. To combat strong and dynamic echoes, a fast converging equalizer using a fast transversal decision feedback algorithm combined with the least mean square method is proposed and investigated.

A real-time implementation of a stereophonic acoustic echo canceler

Teleconferencing systems employ acoustic echo cancelers to reduce echoes that result from the coupling between loudspeaker and microphone. To enhance the sound realism, two-channel audio is necessary. However, stereophonic acoustic echo cancellation (SAEC) is more difficult to solve because of the necessity to uniquely identify two acoustic paths, which becomes problematic since the two excitation signals are highly correlated. In this paper, a wideband stereophonic acoustic echo canceler is presented. The fundamental difficulty of stereophonic acoustic echo cancellation is described and an echo canceler based on a fast recursive least squares (FRLS) algorithm in a subband structure, with equidistant frequency bands, is proposed. The structure has been used in a real-time implementation, with which experiments have been performed. In this paper, simulation results of this implementation on real life recordings, with 8 kHz bandwidth, are studied. The results clearly verify that the theoretic fundamental problem of SAEC also applies in real-life situations. They also show that more sophisticated adaptive algorithms are needed in the lower frequency regions than in the higher regions.

Extended fast fixed-order RLS adaptive filters

The existing derivations of conventional fast RLS adaptive filters are intrinsically dependent on the shift structure in the input regression vectors. This structure arises when a tapped-delay line (FIR) filter is used as a modeling filter. We show, unlike what original derivations may suggest, that fast fixed-order RLS adaptive algorithms are not limited to FIR filter structures. We show that fast recursions in both explicit and array forms exist for more general data structures, such as orthonormally based models. One of the benefits of working with orthonormal bases is that fewer parameters can be used to model long impulse responses.

Inverse filter design for immersive audio rendering over loudspeakers

Immersive audio systems can be used to render virtual sound sources in three-dimensional (3-D) space around a listener. This is achieved by simulating the head-related transfer function (HRTF) amplitude and phase characteristics using digital filters. In this paper, we examine certain key signal processing considerations in spatial sound rendering over headphones and loudspeakers. We address the problem of crosstalk inherent in loudspeaker rendering and examine two methods for implementing crosstalk cancellation and loudspeaker frequency response inversion in real time. We demonstrate that it is possible to achieve crosstalk cancellation of 30 dB using both methods, but one of the two (the Fast RLS Transversal Filter Method) offers a significant advantage in terms of computational efficiency. Our analysis is easily extendable to nonsymmetric listening positions and moving listeners.

A frequency domain stereophonic acoustic echo canceler exploiting the coherence between the channels

Stereophonic acoustic echo cancellation (AEC) is typically intended for use in high quality teleconferencing systems and multiparticipant desktop conferencing that implement sound transmission through two channels. Because of the high correlation between the two channel signals, rapidly converging adaptive filter algorithms (such as the two-channel fast recursive least-squares—FRLS) are required. In this paper, we propose a new and efficient frequency domain adaptive algorithm that achieves this goal.

V-vector algebra and its application to Volterra-adaptive filtering

In this paper, we describe a new algebraic structure called V-vector algebra, which is a formal basis for the development of Volterra-adaptive filter algorithms as an extension of linear-adaptive techniques. In this way, fast and numerically stable adaptive Volterra filtering algorithms can be easily derived from the known linear theory. V-vector algebra can also be applied to deal with linear multichannel filters with channels of different memory lengths. A reformulation of the Lee-Mathews fast recursive least squares (RLS) algorithm and a new fast and stable Givens rotation-based square root RLS algorithm, both derived using V-vector algebra, are finally presented.

Active noise control of higher-order modes in a rectangular duct using stabilized fast transversal filters

For active noise control of sound propagating down a duct in the fundamental mode commercial systems are available. Cancellation of sound also propagating in higher-order modes adds the requirement of higher computational power for the signal processing unit, and stability problems due to source coupling effects. The widely used LMS algorithms need little computational effort, are very stable, but also have a slow tracking behavior to changes in the input signal. Depending on the eigenvalue spread of the input signal’s autocorrelation matrix they lead to slow convergence. One method to overcome this problem is to use stabilized fast RLS algorithms which are independent of the statistics of the input signal. A multi-channel stabilized fast transversal filter algorithm has been investigated experimentally in a rectangular duct with respect to its stability, convergence, and performance.

A fast recursive-least-squares adaptive notch filter and its applications to biomedical signals.

A fast recursive-least-squares (FRLS) adaptive notch filter (ANF) for cancellation of sinusoidal interference from recorded biomedical signals is investigated. The FRLS ANF is derived by making an approximation to the conventional recursive-least-squares (RLS) ANF for computation economy. It outperforms the commonly adopted least-mean-squares (LMS) ANF, demonstrating a rapid and bandwidth-insensitive initial convergence. A novel application of the FRLS ANF is for the elimination of the tonal artefact in distortion product otoacoustic emission (DPOAE) signals.

Algorithmically engineered fast multichannel adaptive filter based on QR-RLS

A fast version of the multichannel QR algorithm for RLS adaptive filtering, with channel filters of unequal length, is derived. This is achieved by applying the techniques of algorithmic engineering to a signal flow graph representation of the basic QR RLS algorithm. By virtue of this graphical approach, the derivation is relatively straightforward and circumvents the complex and notationally verbose matrix algebra usually involved in the derivation of fast RLS algorithms in general and the previously published, unequal-length, multichannel RLS lattice algorithm in particular.

A numerically stable fast RLS algorithm for adaptive filtering and prediction based on the UD factorization

The use of UD factorization in adaptive RLS algorithms is interesting for its numeric robustness and because no square-root operations at all are involved. We describe a square root free fast RLS algorithm based on the UD factorization of the autocorrelation matrix. Numerous finite precision simulations tend to indicate that this algorithm is numerically stable. The algorithm requires /spl Oscr/(/spl Nscr/) operations, where /spl Nscr/ is the linear filter order.

Stabilizing fast RLS algorithms by leakage

In this paper a new stabilization method for the problem of numerical instability of fast recursive least-squares algorithms is introduced. The new approach arose from implementation aspects of common stabilized fast transversal filters (SFTF) algorithms in the compensation of acoustical echoes. Real-time situations are characterized by non-persistent excitation and time-variant systems. Analysing these cases we found out insufficiencies in the performance of SFTF algorithms that exploit redundancy by feedback of numerical errors. Out of these results arose a new concept to cope with stabilization problems: A leakage in the prediction part of the FTF algorithm turned out to make the algorithm very stable and robust. The new found Leaky FTF (LFTF) algorithm, first derived in Binde, IEEE Signal Process. Lett. 2(6) (June 1995) 114–116, is analysed in this article. It has proven to be stable given an appropriate value for the leakage factor.

Adaptive filter bank reconstruction using fast multichannel RLS algorithms

The recursive least-squares (RLS) algorithm has been used in the adaptive synthesis filter bank for fast convergence. However, because of interpolation operations involved in the synthesis process, fast RLS algorithms cannot be applied. In this Letter, an approach is proposed that can formulate subband signal reconstruction as a multichannel filtering problem. This formulation allows the application of fast multichannel RLS algorithms and substantial reduction in computational complexity.