A variable step size total least squares affine-projection-like algorithm: Formula derivation and performance analysis

This paper presents a novel approach to Lyapunov stability theory-based adaptive filter (LAF) design. The proposed design is based on the minimization of the Euclidean norm of the difference weight vector under negative definiteness constraint defined over a novel linear Lyapunov function. The proposed fixed step size LAF (FSS-LAF) algorithm is first obtained by using the method of Lagrangian multipliers. The FSS-LAF satisfying asymptotic stability in the sense of Lyapunov provides a significant performance gain in the presence of a measurement noise. The stability of the FSS-LAF algorithm is also statistically analyzed in this study. Moreover, gradient variable step size (VSS) algorithms are adapted to the FSS-LAF algorithm to further enhance the performance for the first time in this paper. These VSS algorithms are Benveniste (BVSS), Mathews and Farhang–Ang (FVSS) algorithms. Simulation results on system identification problems show that the bounds of step size for the FSS-LAF algorithm are verified, and especially, the BVSS-LAF and FVSS-LAF algorithms provide a better trade-off between steady-state mean square deviation error and convergence rate than other proposed algorithms.

A family of generalised constant modulus algorithms (GCMAs) based on the norm of complex variables was recently proposed. However, the optimal norm and step size of GCMAs have not been derived owing to the complexity of the proposed cost function. The steady-state mean square error (MSE) of a class of GCMAs under non-stationary environments is now given in a closed form. The optimal norm and step size can be derived to minimise the steady-state MSE with this closed form. Numerical simulations confirm the superior performance of the optimal norm and step size.

This paper aims to perform the performance analysis of the Modified Variable Step Size Fractional Least Mean Square (MVSS-FLMS) algorithm in the design of Direct Adaptive Inverse Control (DAIC) nonlinear based on Volterra model. The motivation for formulating the DAIC based on Volterra model, is so that the controller can track the inverse dynamics of plants with nonlinearity of polynomial type. Since the MVSS-FLMS algorithm proposes the use of variable step size, then its application in nonlinear DAIC design allows to obtain nonconservative results for a performance analysis, with respect to convergence speed and steady-state Mean Square Error (MSE). As an increment of the complexity scenario, the present work was evaluated in the presence of a sinusoidal disturbance signal added to the control signal.

Delta Sigma Analog to Digital Converters (ADCs) are superior to their counterparts in achieving high resolution for low to medium bandwidth applications. This paper discusses an improved digital calibration technique for enhancing Signal to Noise ratio (SNR) of Delta Sigma ADC which is directly related to Effective Number of Bits (ENOB). The proposed method uses the Adaptive Line Enhancer (ALE) for improving the SNR of the modulator. Adaptive Line Enhancer filters out the estimate of signal of interest from noisy input signal by updating filter coefficients using Least Mean Square (LMS) Algorithm. Variable step size (VSS) LMS is used for updating filter coefficients in Adaptive Line Enhancer instead of Fixed step size (FSS) LMS to reduce the required number of iterations. The simulation results for second order single loop Delta Sigma modulator show approximately 20dB improvement in SNR after calibration and substitution of VSS LMS with FSS LMS has reduced approximately 4000 iterations.

Step size and tap length play critical roles in balancing the complexity and steady-state performance of an adaptive filter. For an impulse response with an exponential power decay profile, which models a wide range of practical systems, such as an acoustic echo path, this paper proposes a new variable step-size and tap-length least mean square (LMS) algorithm. In each iteration, the optimal step-size and tap-length are derived by minimizing the mean square deviation (MSD) between the true and the estimated filter coefficients. The proposed algorithm performs better in terms of both convergence rate and steady-state performance than the existing ones. Effectiveness of the proposed algorithm is demonstrated through computer simulations.

Performance analysis of the deficient length augmented CLMS algorithm for second order noncircular complex signals

This paper proposes a new application of fuzzy logic to variable step size least mean square (VS-LMS) adaptive beamforming algorithm in CDMA systems. The proposed algorithm adjusts the step size of the least mean square (LMS) by using the application of fuzzy logic in which the increase or decrease of step size depends on the fuzzy inference results of the mean square error (MSE). Computer simulation results show that the proposed algorithm has a better capacity of tracking compared with the conventional LMS algorithms and other variable step size LMS algorithms.

The paper is concerned with analyzing the roundoff error effect on the tracking performance of the block least mean square (BLMS) algorithm when used in the adaptive identification of a time-varying plant. Rounding quantization is assumed. Expressions are derived for the steady state mean square error, steady state mean square weight deviation, and the corresponding optimum step sizes. It is found that the mean square error and the mean square weight deviation are decreasing functions of both the filter coefficients wordlength and the algorithm block size. Expressions for minimum and maximum block lengths are derived. The performance of the BLMS is compared to that of the conventional LMS algorithm. It is found that the BLMS possesses a higher resistance to roundoff errors than the LMS algorithm. The theoretical results of the paper are validated by computer simulations.

In this paper, we have proposed a new steering direction determination mechanism and step-size update algorithm for piloted adaptive notch filter architecture. A timedomain averaging based gradient analysis of the piloted notch cost function has been utilized to determine the direction of the main notch with respect to the input sinusoid frequency. The steering direction will indicate the distance between the frequency of the input sinusoid and the zero of the main notch. This frequency domain information has been interleaved with time domain information to develop a novel algorithm for determination of variable step-sizes for improved speed of convergence with comparatively huge reduction in steady-state mean square error (MSE). The simulation results verifies the excellent performance exhibited by our proposed steering mechanism and the step-size update algorithm over original piloted adaptive notch filter with respect to the speed of convergence and MSE.

A new super-exponential decision feedback blind equalization algorithm is proposed in this paper. In comparison with the conventional SEI-DFE equalization algorithm, the proposed algorithm presents a new fast convergence weight update error function. Therefore, phase compensation ability and steady-state Mean Square Error (MSE) performance have been increased, but they don't significantly increase the computational complexity. At the same time, a second order digital phase-locked loop is introduced in order to track and compensate phase rotation. The MSE and carrier recovery performance of the proposed algorithm are better than that of the SEI-DFE algorithm, which is verified by computer simulation. In addition, the MULAN Lake experiment shows that the performance of the proposed algorithm is better than that of the SEI-DFE algorithm in terms of Bit Error Rate (BER) by comparing the influences causing filter weight vector length, step size and Q matrix size.

Maximum correntropy criterion (MCC) based adaptive filters are found to be robust against impulsive interference. This paper proposes a novel MCC based adaptive filter with variable step size in order to obtain improved performance in terms of both convergence rate and steady state error with robustness against impulsive interference. The optimal variable step size is obtained by minimizing the Mean Square Deviation (MSD) error from one iteration to the other. Simulation results in the context of a highly impulsive system identification scenario show that the proposed algorithm has faster convergence and lesser steady state error than the conventional MCC based adaptive filters.

Summary form only given. This paper presents a Variable Step Size (VSS) technique that is integrated with a Stop-And-Go (SAG) approach for blind adaptive equalization of Quadrature Amplitude Modulation (QAM) signals. The proposed technique is applied to the Constant-Modulus Algorithm (CMA) and the Multi-Modulus Algorithm (MMA). The SAG approach allows the VSS technique to either vary the step size or to hold the previous one depending on a specific error criterion. This leads to the reduction of the amount of computations involved Simulation results show that algorithms with the VSS technique result in less steady-state Mean-Squared Errors (MSEs) than those obtained for algorithms without the VSS technique for the same speed of convergence.

An adaptive system is a well-known method for removing noise from noise-corrupted speech. The problem arises in many situations such as airplane cockpits and automobiles. The variable step size normalized least mean squares (VSS-NLMS) algorithm incorporating a variable step size parameter whose values are based on the ratio of signal-to-noise power has very good convergence speed and low steady-state misadjustment. This paper investigates the rate of convergence by the wavelet based LMS (WLMS) algorithm to the noise speech problem. Simulation results are presented to compare the performance of the variable step size NLMS algorithm, the wavelet based LMS Algorithm, and other commonly used fixed step size LMS algorithms.

In this paper, we investigate the convergence performance of a sparsified kernel least mean square (KLMS) algorithm in which the input is added into the dictionary only when the prediction error in amplitude is larger than a preset threshold. Under certain conditions, we derive an approximate value of the steady-state excess mean square error (EMSE). Simulation results confirm the theoretical predictions and provide some interesting findings, showing that the sparsification can not only be used to constrain the network size (hence reduce the computational burden) but also be used to improve the steady-state performance in some cases.

The adaptive kernel algorithms usually achieve a good convergence performance and a tracking performance due to the universal approximator, offering an excellent solution to many problems with nonlinearities. However, as is well known, the convergence rate and steady-state error of adaptive filtering algorithm are a pair of inherent contradictions, and the kernel method is not exceptional. For this problem, a robust kernel adaptive filtering algorithm, called the variable-scaling factor kernel fractional lower power adaptive filtering algorithm based on the Sigmoid function, is developed by creating a new framework of cost function which combines the kernel fractional low power error criterion with the Sigmoid function for system identification of different noise environments. This new cost framework incorporates a scaling factor into the cost function of the Sigmoid kernel fractional lower power adaptive filtering algorithm (VS-SKFLP) in this paper. One of the main features in the new framework is its scaling factor. This scaling factor is used to control the steepness of the Sigmoid function, and the steepness can affect the convergence speed of filtering algorithm. The scaling factor provides a tradeoff between the convergence rate and the steady-state mean square error (MSE), which improves the convergence rate under the same steady-state mean square error. However, it is also an important problem to choose an appropriate scale factor. Therefore, a variable-scale factor SKFLP algorithm is also proposed to improve the convergence rate and steady-state MSE, simultaneously. The proposed variable-scale factor structure consists of a function of error, featuring the adaptive updates of their parameter estimated by making discerning use of the error. In this paper, the nonlinear saturation characteristic of the Sigmoid function and low order norm criterion are used to overcome the performance degradation of training data destroyed by non-Gaussian impulse noise and colored noise. Through the convergence analysis, the parameter estimation sequence of our proposed algorithm proves convergent. Simulation results show that the proposed algorithm (VS-SKFLP) outperforms other kernel adaptive filtering algorithms in system recognition with different noise environments.