Adaptive noise cancellation using adaptive filters is a known method for removing noise that interferes with signal measurements. The adaptive noise canceller performs filtering based on the current situation through a windowing process. The shape of the window function determines the tracking performance of the adaptive noise canceller with respect to the fluctuation of the property of the unknown system that noise (reference signal) passes. However, the shape of the window function in the field of adaptive filtering has not yet been considered in detail. This study mathematically treats the effect of the window function on the adaptive noise canceller and proposes an optimization method for the window function in situations where offline processing can be performed, such as biomedical signal measurements. We also demonstrate the validity of the optimized window function through numerical experiments.

Periodic interference frequently affects the measurement of small signals and causes problems in clinical diagnostics. Adaptive filters can be used as potential tools for cancelling such interference. However, when the interference has a frequency fluctuation, the ideal adaptive-filter coefficients for cancelling the interference also fluctuate. When the adaptation property of the algorithm is slow compared with the frequency fluctuation, the interference-cancelling performance is degraded. However, if the adaptation is too quick, the performance is degraded owing to the target signal. To overcome this problem, we propose an adaptive filter that suppresses the fluctuation of the ideal coefficients by utilizing a $rac{pi}{2}$ phase-delay device. This method assumes a frequency response that characterizes the transmission path from the interference source to the main input signal to be sufficiently smooth. In the numerical examples, the proposed method exhibits good performance in the presence of a frequency fluctuation when the forgetting factor is large. Moreover, we show that the proposed method reduces the calculation cost.

A new adaptive algorithm is proposed by introducing some modifications to the recursive least squares (RLS) algorithm. Except for the noise variance, the proposed algorithm does not require any statistics or knowledge of the desired signal, thus, it is suitable for adaptive filtering for channel estimation in code division multiple access (CDMA) systems in cases where the standard RLS approach cannot be used. A theoretical analysis demonstrates the convergence of the proposed algorithm, and simulation results for CDMA channel estimation show that the proposed algorithm outperforms existing channel estimation schemes.

Frequency-domain equalization (FDE) based on the minimum mean square error (MMSE) criterion can increase the downlink bit error rate (BER) performance of DS-CDMA beyond that possible with conventional rake combining in a frequency-selective fading channel. FDE requires accurate channel estimation. Recently, we proposed a pilot-assisted channel estimation (CE) based on the MMSE criterion. Using MMSE-CE, the channel estimation accuracy is almost insensitive to the pilot chip sequence, and a good BER performance is achieved. In this paper, we propose a channel estimation scheme using one-tap recursive least square (RLS) algorithm, where the forgetting factor is adapted to the changing channel condition by the least mean square (LMS) algorithm, for DS-CDMA with FDE. We evaluate the BER performance using RLS-CE with adaptive forgetting factor in a frequency-selective fast Rayleigh fading channel by computer simulation.

The performance of the blind multiuser detector for a DS-CDMA system with linearly constrained constant modulus (LCCM) criterion is known to highly depend on the exact knowledge of the desired user amplitude; it is usually not available at receiver end. In this paper, we propose a novel LC adaptive CM RLS (LC-ACM-RLS) algorithm to adaptively implement the optimal solution of the LCCM receiver, and to track the desired user's amplitude, simultaneously. From computer simulations, we verify the superiority of the new proposed algorithm over the conventional LCCM-RLS algorithm for multiple access interference (MAI) suppression. Also, for time-varying channel during the adaptation processes, if the amplitude of desired user is not available and varies with time, such as hand-off and Rayleigh fading environments, we show that the proposed LC-ACM-RLS algorithm has better tracking capability compared with the conventional approaches.

An adaptive filtering algorithm based on the sliding window criterion is known to be very attractive for violent changing environments. In this paper, a new sliding window linearly constrained recursive least squares (SW-LC-RLS) algorithm based on the modified minimum mean squared error (MMSE) structure is devised for the RAKE receiver in direct sequence spread spectrum code-division multiple access (DS-SS CDMA) system over multipath fading channels, where the channel estimation scheme is accomplished at the output of adaptive filter. The proposed SW-LC-RLS algorithm has the advantage of having faster convergence property and tracking ability, and can be applied to the environments, where the narrowband interference is joined suddenly to the system, to achieve desired performance. Via computer simulation, we show that the performance, in terms of mean square errors (MSE), signal to interference plus noise ratio (SINR) and bit error rate (BER), is superior to the conventional LC-RLS and orthogonal decomposition-based LMS algorithms based on the MMSE structure.

In this paper we propose a new blind adaptive compensator associated with the inverse QRD-RLS (IQRD-RLS) algorithm to adaptively estimate the parameters, related to the effects of gain/phase imbalance and DC offsets occur in the Quadrature demodulator, for compensation. In this new approach the power measurement of the received signal is employed to develop the blind adaptation algorithm for compensator, it does not require any reference signal transmitted from the transmitter and possess the fast convergence rate and better numerical stability. To verify the great improvement, in terms of reducing the effects of the imbalance and offset, over existing techniques computer simulation is carried out for the coherent 16 PSK-communication system. We show that the proposed blind scheme has rapidly convergence rate and the smaller mean square error in steady state.

Recursive least absolute(RLA) error algorithm is derived which is basically the sign algorithm (SA) combined with recursive estimation of the inverse covariance matrix of the reference input. The name RLA comes from the absolute error criterion. Analysis of the transient behavior and steady-state performance of the RLA algorithm is fully developed. Results of experiment show that the RLA algorithm considerably improves the convergence rate of the SA while preserving the robustness against impulse noise. Good agreement between the simulation and the theoretically calculated convergence validates the analysis.

This paper proposes a non-linear adaptive algorithm, the amplitude banded RLS (ABRLS) algorithm, as an adaptation procedure for time variant channel equalizers. In the ABRLS algorithm, a coefficient matrix is updated based on the amplitude level of the received sequence. To enhance the capability of tracking for the ABRLS algorithm, a parallel adaptation scheme is utilized which involves the structures of decision feedback equalizer (DFE). Computer simulations demonstrate that the novel ABRLS based equalizer provides a significant improvement relative to the conventional RLS DFE on a rapidly time variant communication channel.

The sub-recursive least squares (sub-RLS) algorithm estimates the coefficients of adaptive filter under the least squares (LS) criterion, however, does not require the calculation of inverse matrix. The sub-RLS algorithm, based on the different principle from the RLS algorithm, still provides a convergence property similar to that of the RLS algorithm. This paper first rewrites the convergence condition of the sub-RLS algorithm, and then proves that the convergence property of the sub-RLS algorithm successively approximates that of the RLS algorithm on the convergence condition.

This paper presents the outline of the systolic array recursive least-squares (RLS) processor prototyped primarily with the aim of broadband mobile communication applications. To execute the RLS algorithm effectively, this processor uses an orthogonal triangularization technique known in matrix algebra as QR decomposition for parallel pipelined processing. The processor board comprises 19 application-specific integrated circuit chips, each with approximately one million gates. Thirty-two bit fixed-point signal processing takes place in the processor, with which one cycle of internal cell signal processing requires approximately 500 nsec, and boundary cell signal processing requires approximately 80 nsec. The processor board can estimate up to 10 parameters. It takes approximately 35 µs to estimate 10 parameters using 41 known symbols. To evaluate signal processing performance of the prototyped systolic array processor board, processing time required to estimate a certain number of parameters using the prototyped board was comapred with using a digital signal processing (DSP) board. The DSP board performed a standard form of the RLS algorithm. Additionally, we conducted minimum mean-squared error adaptive array in-lab experiments using a complex baseband fading/array response simulator. In terms of parameter estimation accuracy, the processor is found to produce virtually the same results as a conventional software engine using floating-point operations.

It is well known that based on the structure of a transversal filter, the RLS equaliser provides the fastest convergence in stationary environments. This paper addresses an adaptive transversal equaliser which has the potential to provide more faster convergence than the RLS equaliser. A comparison is made with respect to computational complexity required for each update of equaliser coefficients, and computer simulations are demonstrated to show the superiority of the proposed equaliser.

Adaptive estimation of nonstationary sinusoidal signals or quasi-periodic signals in additive noise is of essential importance in many diverse engineering fields, such as communications, biomedical engineering, power systems, pitch detection in transcription and so forth. So far, Kalman filtering based techniques, recursive least square (RLS), simplified RLS (SRLS) and LMS algorithms, for examples, have been developed for this purpose. This work presents in detail a performance analysis for the SRLS algorithm proposed recently in the literature, which is used to estimate an enhanced sinusoid. Its dynamic and tracking properties, noise and lag misadjustments are developed and discussed. It is found that the SRLS estimator is biased, and its misadjustments are functions of not only the noise variance but also, unpleasantly, of the signal parameters. Simulations demonstrate the validity of the analysis. Application of the SRLS to a real-life piano sound is also given to peek at its effectiveness.

The numerical property of the recursive least squares (RLS) algorithm has been extensively, studied. However, very few investigations are reported concerning the numerical behavior of the predictor-based least squares (PLS) algorithms which provide the same least squares solutions as the RLS algorithm. In Ref. [9], we gave a comparative study on the numerical performances of the RLS and the backward PLS (BPLS) algorithms. It was shown that the numerical property of the BPLS algorithm is much superior to that of the RLS algorithm under a finite-precision arithmetic because several main instability sources encountered in the RLS algorithm do not appear in the BPLS algorithm. This paper theoretically shows the stability of the BPLS algorithm by error propagation analysis. Since the time-variant nature of the BPLS algorithm, we prove the stability of the BPLS algorithm by using the method as shown in Ref. [6]. The expectation of the transition matrix in the BPLS algorithm is analyzed and its eigenvalues are shown to have values within the unit circle. Therefore we can say that the BPLS algorithm is numerically stable.

In the last few years analog adaptive filters have been a subject of active research because they have the ability to handle in real time much higher frequencies, with a smaller size and lower power consumption that their digital counterparts. During this time several analog adaptive filter algorithms have been reported in the literature, almost all of them use the continuous time version of the least mean square (LMS) algorithm. However the continuous time LMS algorithm presents the same limitations than its digital counterpart, when operates in noisy environments, although their convergence rate may be faster than the digital versions. This fact suggests the necessity of develop analog versions of recursive least square (RLS) algorithm, which in known to have a very low sensitivity to additive noise. However a direct implementation of the RLS in analog way would require a considerable effort. To overcome this problem, we propose an analog RLS algorithm in which the adaptive filter coefficients vector is estimated by using a fully connected network that resembles a Hopfield network. Theoretical and simulations results are given which show that the proposed and conventional RLS algorithms have quite similar convergence properties when they operate with the same sampling rate and signal-to-noise ratio.

The numerical properties of the recursive least squares (RLS) algorithm and its fast versions have been extensively studied. However, very few investigations are reported concerning the numerical behavior of the predictor based least squares (PLS) algorithms that provide the same least squares solutions as the RLS algorithm. This paper presents a comparative study on the numerical performances of the RLS and the backward PLS (BPLS) algorithms. Theoretical analysis of three main instability sources reported in the literature, including the overrange of the conversion factor, the loss of symmetry and the loss of positive definiteness of the inverse correlation matrix, has been done under a finite-precision arithmetic. Simulation results have confirmed the validity of our analysis. The results show that three main instability sources encountered in the RLS algorithm do not exist in the BPLS algorithm. Consequently, the BPLS algorithm provides a much more stable and robust numerical performance compared with the RLS algorithm.

The convergence characteristics of the adaptive beamformer with the RLS algorithm are analyzed in this paper. In case of the RLS adaptive beamformer, the convergence characteristics are significantly affected by the spatial characteristics of the signals/noises in the environment. The purpose of this paper is to show how these physical parameters affect the convergence characteristics. In this paper, a typical environment where a few directional noises are accompanied by background noise is assumed, and the influence of each component of the environment is analyzed separately using rank analysis of the correlation matrix. For directional components, the convergence speed is faster for a smaller number of noise sources since the effective rank of the input correlation matrix is reduced. In the presence of background noise, the convergence speed is slowed down due to the increase of the effective rank. However, the convergence speed can be improved by controlling the initial matrix of the RLS algorithm. The latter section of this paper focuses on the physical interpretation of this initial matrix, in an attempt to elucidate the mechanism of the convergence characterisitics.

In this letter, we introduce a predictor based least square (PLS) algorithm. By involving both order- and time-update recursions, the PLS algorithm is found to have a more stable performance compared with the stable version (Version II) of the RLS algorithm shown in Ref.[1]. Nevertheless, the computational requirement is about 50% of that of the RLS algorithm. As an application, the PLS algorithm can be applied to the fast Newton transversal filters (FNTF). The FNTF algorithms suffer from the numerical instability problem if the quantities used for extending the gain vector are computed by using the fast RLS algorithms. By combing the PLS and the FNTF algorithms, we obtain a much more stable performance and a simple algorithm formulation.

This paper presents a new structure for noise and echo cancelers based on a combined fast abaptive algorithm. The main purpose of the new structure is to detect both the double-talk and the unknown path change. This goal is accomplished by using two adaptive filters. A main adaptive filter Fn, adjusted only in the non-double-talk period by the normalized LMS algorithm, is used for providing the canceler output. An auxiliary adaptive filter Ff, adjusted by the fast RLS algorithm, is used for detecting the double-talk and obtaining a near optimum tap-weight vector for Fn in the initialization period and whenever the unknown path has a sudden or fast change. The proposed structure is examined through computer simulation on a noise cancellation problem. Good cancellation performance and stable operation are obtained when signal is a speech corrupted by a white noise, a colored noise and another speech signal. Simulation results also show that the proposed structure is capable of distinguishing the near-end signal from the noise path change and quickly tracking this change.