QR Decomposition RLS Research Articles

Adaptive Filtering for the Maternal Respiration Signal Attenuation in the Uterine Electromyogram.

The electrohysterogram (EHG) is the uterine muscle electromyogram recorded at the abdominal surface of pregnant or non-pregnant woman. The maternal respiration electromyographic signal (MR-EMG) is one of the most relevant interferences present in an EHG. Alvarez (Alv) waves are components of the EHG that have been indicated as having the potential for preterm and term birth prediction. The MR-EMG component in the EHG represents an issue, regarding Alv wave application for pregnancy monitoring, for instance, in preterm birth prediction, a subject of great research interest. Therefore, the Alv waves denoising method should be designed to include the interference MR-EMG attenuation, without compromising the original waves. Adaptive filter properties make them suitable for this task. However, selecting the optimal adaptive filter and its parameters is an important task for the success of the filtering operation. In this work, an algorithm is presented for the automatic adaptive filter and parameter selection using synthetic data. The filter selection pool comprised sixteen candidates, from which, the Wiener, recursive least squares (RLS), householder recursive least squares (HRLS), and QR-decomposition recursive least squares (QRD-RLS) were the best performers. The optimized parameters were L = 2 (filter length) for all of them and λ = 1 (forgetting factor) for the last three. The developed optimization algorithm may be of interest to other applications. The optimized filters were applied to real data. The result was the attenuation of the MR-EMG in Alv waves power. For the Wiener filter, power reductions for quartile 1, median, and quartile 3 were found to be −16.74%, −20.32%, and −15.78%, respectively (p-value = 1.31 × 10−12).

SDR Proof-of-Concept of Full-Duplex Jamming for Enhanced Physical Layer Security.

In order to secure wireless communications, we consider the usage of physical-layer security (PLS) mechanisms (i.e., coding for secrecy mechanisms) combined with self-interference generation. We present a prototype implementation of a scrambled coding for secrecy mechanisms with interference generation by the legitimate receiver and the cancellation of the effect of self-interference (SI). Regarding the SI cancellation, four state-of-the-art algorithms were considered: Least mean square (LMS), normalized least mean square (NLMS), recursive least squares (RLS) and QR decomposition recursive least squares (QRDRLS). The prototype implementation is performed in real-world software-defined radio (SDR) devices using GNU-Radio, showing that the LMS outperforms all other algorithms considered (NLMS, RLS and QRDRLS), being the best choice to use in this situation (SI cancellation). It was also shown that it is possible to secure communication using only noise generation by the legitimate receiver, though a variation of the packet loss rate (PLR) and the bit error rate (BER) gaps is observed when moving from the fairest to an advantageous or a disadvantageous scenario. Finally, when noise generation was combined with the adapted scrambled coding for secrecy with a hidden key scheme, a noteworthy security improvement was observed resulting in an increased BER for Eve with minor interference to Bob.

Direction of arrival tracking for signals with known waveforms based on block least squares techniques

In this paper, we address the problem of tracking DOA of multiple moving targets with known signal source waveforms and unknown gains in the presence of Gaussian noise using a nonuniform linear array. Herein, we make use of the fact that the output of each sensor can be described as a linear regression model whose coefficients each contain a pair of DOA and gain information corresponding to one target. These coefficients are determined by solving a linear least squares (LS) problem and then updated recursively based on a block QR decomposition recursive least squares (QRD-RLS) technique or a block regularized LS technique. Since the coefficients from different sensors have the same amplitude but variable phase information for the same signal, along with simple algebraic manipulations the well-known generalized least squares (GLS) are used to obtain an asymptotically-optimal DOA estimate without requiring a search over a large region of the parameter space. Computer simulations show that the proposed DOA tracking techniques when applied to a sparse antenna array can provide a better tracking performance than some of the existing methods do.

Fixed-Point Implementation of Fast QR-Decomposition Recursive Least-Squares Algorithms (FQRD-RLS): Stability Conditions and Quantization Errors Analysis

The fast QR-decomposition based recursive least-squares (FQRD-RLS) algorithms offer RLS-like convergence and misadjustment at a lower computational cost, and therefore are desirable for implementation on a fixed-point digital signal processor (DSP). Furthermore, the FQRD-RLS algorithms are derived from QR-decomposition based RLS algorithms that are well known for their numerical stability in finite precision. Hence, these algorithms are often assumed numerically stable, although there is no rigorous analysis addressing the stability of such algorithms in finite precision. In this paper, we derive the conditions that guarantee stability of the FQRD-RLS algorithms, and also derive mathematical expressions for the mean-squared quantization error (MSQE) of internal variables of the FQRD-RLS algorithms at steady state. The objective is to quantify the propagation error due to quantization effects. The derived MSQE expressions have been verified by comparisons with fixed-point computer simulations.

An inverse QRD-RLS algorithm for linearly constrained minimum variance adaptive filtering

In this paper an inverse QR decomposition based recursive least-squares algorithm for linearly constrained minimum variance filtering is proposed. The proposed algorithm is numerically stable in finite precision environments and is suitable for implementation in systolic arrays or DSP vector architectures. Its performance is illustrated by simulations of a blind receiver for a multicarrier CDMA communication system and compared with previously proposed inverse QR decomposition recursive least-squares algorithms.

Multichannel Fast QR-Decomposition Algorithms: Weight Extraction Method and Its Applications

Multichannel fast QR decomposition RLS (MC-FQRD-RLS) algorithms are well known for their good numerical properties and low computational complexity. The main limitation is that they lack an explicit weight vector term, limiting themselves to problems seeking an estimate of the output error signal. This paper presents techniques which allow us to use MC-FQRD-RLS algorithms with applications that previously have required explicit knowledge of the adaptive filter weights. We first consider a multichannel system identification setup and present how to obtain, at any time, the filter weights associated with the MC-FQRD-RLS algorithm. Thereafter, we turn to problems where the filter weights are periodically updated using training data, and then used for fixed filtering of a useful data sequence, e.g., burst-trained equalizers. Finally, we consider a particular control structure, indirect learning, where a copy of the coefficient vector is filtering a different input sequence than that of the adaptive filter. Simulations are carried out for Volterra system identification, decision feedback equalization, and adaptive predistortion of high-power amplifiers. The results verify our claims that the proposed techniques achieve the same performance as the inverse QRD-RLS algorithm at a much lower computational cost.

Multichannel fast QRD-RLS adaptive filtering: Block-channel and sequential-channel algorithms based on updating backward prediction errors

Fast QR decomposition recursive least-squares (FQRD-RLS) algorithms are well known for their fast convergence and reduced computational complexity. A considerable research effort has been devoted to the investigation of single-channel versions of the FQRD-RLS algorithms, while the multichannel counterparts have not received the same attention. The goal of this paper is to broaden the study of the efficient and low complexity family of multichannel RLS adaptive filters, and to offer new algorithm options. We present a generalized approach for block-type multichannel FQRD-RLS (MC-FQRD-RLS) algorithms that includes both cases of equal and multiple order. We also introduce new versions for block-channel and sequential-channel processing, details of their derivations, and a comparison in terms of computational complexity. The proposed algorithms are based on the updating of backward a priori and a posteriori error vectors, which are known to be numerically robust.

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.

Acoustical echo canceller with sub-band filtering

The echo canceller is designed to be placed between a hands-free acoustical interface and a communications network. It comprises a plurality of processing paths connected in parallel and each allocated to one of a plurality of adjacent sub-bands taken from the spectrum band of the output signal. Each path comprises an analysis filter receiving the echo-containing signal for transmission after correction, a second analysis filter receiving the incoming signal coming from the network, and feeding an adaptive filter that supplies an estimated echo in the respective sub-band to the subtractive input of the subtracter and a synthesis filter. The adaptive filters in at least some of the sub-bands implement a QR decomposition RLS algorithm on the incoming signal, using the fast version thereof, with or without recursive order.

Disposable audio processor for use with implanted hearing devices

The echo canceller is designed to be placed between a hands-free acoustical interface and a communications network. It comprises a plurality of processing paths connected in parallel and each allocated to one of a plurality of adjacent sub-bands taken from the spectrum band of the output signal. Each path comprises an analysis filter receiving the echo-containing signal for transmission after correction, a second analysis filter receiving the incoming signal coming from the network, and feeding an adaptive filter that supplies an estimated echo in the respective sub-band to the subtractive input of the subtracter and a synthesis filter. The adaptive filters in at least some of the sub-bands implement a QR decomposition RLS algorithm on the incoming signal, using the fast version thereof, with or without recursive order.

Split Recursive Least-Squares: algorithms, architectures, and applications

In this paper, a new computationally efficient algorithm for adaptive filtering is presented. The proposed Split Recursive Least-Squares (Split RLS) algorithm can perform the approximated RLS with O(N) complexity for signals having no special data structure to be exploited (e.g., the signals in multichannel adaptive filtering applications, which are not shifts of a single-channel signal data), while avoiding the high computational complexity (O(N/sup 2/)) required in the conventional RLS algorithms. Our performance analysis shows that the estimation bias will be small when the input data are less correlated. We also show that for highly correlated data, the orthogonal preprocessing scheme can be used to improve the performance of the Split RLS. Furthermore, the systolic implementation of our algorithm based on the QR-decomposition RLS (QRD-RLS) array as well as its application to multidimensional adaptive filtering is also discussed. The hardware complexity for the resulting array is only O(N) and the system latency can be reduced to O(log/sub 2/ N). The simulation results show that the Split RLS outperforms the conventional RLS in the application of image restoration. A major advantage of the Split RLS is its superior tracking capability over the conventional RLS under nonstationary environments.

Dynamic range, stability, and fault-tolerant capability of finite-precision RLS systolic array based on Givens rotations

The QR decomposition recursive least-squares (QRD RLS) algorithm for mapping onto a systolic array for signal processing and communication applications is considered. Detailed analysis is presented to show that the rotation parameters of the RLS algorithm based on the Givens rotation method will eventually reach the quasi-steady-state if the forgetting factor lambda is very close to 1. With this model, the dynamic range of each processing cell can be derived, and from this a proper wordlength can be chosen to ensure correct operation of the algorithm. The proposed solutions are simple and effective. Simulations have demonstrated that the wordlengths chosen by the proposed dynamic range work well. The stability of the QRD RLS algorithm is demonstrated under a finite-precision implementation with this observation. Finally, the missing error detection and false alarm problems are considered based on the results obtained from the model. The wordlength is overflow-free without missing error detection and false alarm problems. The results in this study are of practical importance. Not only can a finite-precision QRD RLS systolic array be designed with a minimum wordlength that ensures correct operations, but also a fault-tolerant system that can detect a given error size and is false-alarm-free under the quantization effect can be provided.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>