A state-space approach for adaptive second-order IIR notch digital filters is explored. A simplified iterative algorithm is derived from the gradient-descent method to minimize the mean-squared output of an adaptive notch digital filter. The stability and parameter-estimation bias are then analyzed by employing a first-order linear dynamical system. As a consequence, it is clarified that the resulting parameter estimate is unbiased. Finally, a numerical example is presented to demonstrate the validity and effectiveness of the adaptive state-space notch digital filter and bias analysis of parameter estimation.

This paper deals with a state-space approach for adaptive second-order IIR notch digital filters with constrained poles and zeros. A simplified iterative algorithm is derived from the gradient-descent method to minimize the mean-squared output of an adaptive notch digital filter. Then, stability and parameter-estimation bias are analyzed for the simplified iterative algorithm. A numerical example is presented to demonstrate the validity and effectiveness of the proposed adaptive state-space notch digital filter and parameter-estimation bias analysis.

Multibeam massive multiple-input multiple-output (MIMO) configuration has been proposed that selects high-power beams in an analog part and uses a blind algorithm, such as the constant-modulus algorithm (CMA), in the digital part. The CMA does not require channel state information. However, when least-squares CMA (LS-CMA) is applied to a quadrature amplitude modulation signal whose amplitude changes, the interference cancellation effect decreases as the modulation order increases. In this paper, a variable-step-size-based CMA (VS-CMA), which modifies the step size of the steepest-descent CMA, is proposed as a blind adaptive algorithm to replace LS-CMA. The basic performance of VS-CMA, its success in cancelling interference, and its effectiveness in multibeam massive MIMO transmission are verified via simulation and compared with other blind algorithms such as independent component analysis, particularly when the data smoothing size is small.

This paper investigates an adaptive notch digital filter that employs normal state-space realization of a single-frequency second-order IIR notch digital filter. An adaptive algorithm is developed to minimize the mean-squared output error of the filter iteratively. This algorithm is based on a simplified form of the gradient-decent method. Stability and frequency estimation bias are analyzed for the adaptive iterative algorithm. Finally, a numerical example is presented to demonstrate the validity and effectiveness of the proposed adaptive notch digital filter and the frequency-estimation bias analyzed for the adaptive iterative algorithm.

The step size is a parameter of fundamental importance in learning algorithms, particularly for the natural policy gradient (NPG) methods. We derive an upper bound for the step size in an incremental NPG estimation, and propose an adaptive step size to implement the derived upper bound. The proposed adaptive step size guarantees that an updated parameter does not overshoot the target, which is achieved by weighting the learning samples according to their relative importances. We also provide tight upper and lower bounds for the step size, though they are not suitable for the incremental learning. We confirm the usefulness of the proposed step size using the classical benchmarks. To the best of our knowledge, this is the first adaptive step size method for NPG estimation.

In this letter, an effective acoustic feedback cancellation algorithm is proposed based on the normalized sub-band adaptive filter (NSAF). To improve the confliction between fast convergence rate and low misalignment in the NSAF algorithm, a variable step size is designed to automatically vary according to the update state of the filter. The update state of the filter is adaptively detected via the normalized distance between the long term average and the short term average of the tap-weight vector. Simulation results demonstrate that the proposed algorithm has superior performance in terms of convergence rate and misalignment.

In this paper, we propose a step size control method capable of quickly canceling acoustic echo even when double talk continues from the echo path change. This method controls the step size by substituting the norm of the difference vector between the coefficient vectors of a main adaptive filter (Main-ADF) and a sub-adaptive filter (Sub-ADF) for the estimation error provided by the former. Actually, the number of taps of Sub-ADF is limited to a quarter of that of Main-ADF, and the larger step size than that applied to Main-ADF is given to Sub-ADF; accordingly the norm of the difference vector quickly approximates to the estimation error. The estimation speed can be improved by utilizing the norm of the difference vector for the step size control in Main-ADF. We show using speech signals that in single talk the proposed method can provide almost the same estimation speed as the method whose step size is fixed at the optimum one and verify that even in double talk the estimation error, quickly decreases.

To attain good performance in an acoustic echo cancellation system, it is important to have a variable step size (VSS) algorithm as part of an adaptive filter. In this paper, we are concerned with the development of a VSS algorithm for a recently proposed subband affine projection (SAP) adaptive filter. Two popular VSS algorithms in the literature are the methods of delayed coefficients (DC) and variable regularization (VR). However, the merits and demerits of them are mutually exclusive. We propose a VSS algorithm that is a hybrid of both methods and combines their advantages. An extensive study of the new algorithm in different scenarios like the presence double-talk (DT) during the transient phase of the adaptive filter, DT during steady state, and varying DT power is conducted and reasoning is given to support the observed behavior. The importance of the method of VR as part of a VSS algorithm is emphasized.

We have proposed a noise reduction method based on a noise reconstruction system (NRS). The NRS uses a linear prediction error filter (LPEF) and a noise reconstruction filter (NRF) which estimates background noise by system identification. In case a fixed step size for updating tap coefficients of the NRF is used, it is difficult to reduce background noise while maintaining the high quality of enhanced speech. In order to solve the problem, a variable step size is proposed. It makes use of cross-correlation between an input signal and an enhanced speech signal. In a speech section, a variable step size becomes small so as not to estimate speech, on the other hand, large to track the background noise in a non-speech section.

In the acoustic echo canceller (AEC), the step-size parameter of the adaptive filter must be varied according to the situation if double talk occurs and/or the echo path changes. We propose an AEC that uses a sub-adaptive filter. The proposed AEC can control the step-size parameter according to the situation. Moreover, it offers superior convergence compared to the conventional AEC even when the double talk and the echo path change occur simultaneously. Simulations demonstrate that the proposed AEC can achieve higher ERLE and faster convergence than the conventional AEC. The computational complexity of the proposed AEC can be reduced by reducing the number of taps of the sub-adaptive filter.

We propose a new closed-loop power control scheme for wireless mobile communication systems using an adaptive step size. The proposed scheme selects the basic power control step size by considering the speed of the mobile station and a variable step size by using instantaneous companding logic based on power control command bit patterns. We show its improved performance in view of the standard deviation of received power at the base station in consideration of channel BER.

We propose two novel blind LMS algorithms, called exponential step size LMS algorithms (ES-LMS), for adaptive array antennas with fast convergence speeds. Both of the proposed algorithms are much better at tracking signal sources than the conventional LMS algorithms. In addition, they require neither spatial knowledge nor reference signals since they use the finite symbol property of digital signal. Computer simulations verify performances of the two proposed algorithms.

We propose a blind source separation algorithm for the mixture of finite alphabet sources where sensors are less than sources. The algorithm consists of an update equation of an estimated mixing matrix and enumeration of the inferred sources. We present the bound of a step size for the stability of the algorithm and two methods of assignment of the initial point of the estimated mixing matrix. Simulation results verify the proposed algorithm.

As the nonlinear adaptive filter, the neural filter is utilized to process the nonlinear signal and/or system. However, the neural filter requires large number of iterations for convergence. This letter presents a new structure of the multi-layer neural filter where the orthonormal transform is introduced into all inter-layers to accelerate the convergence speed. The proposed structure is called the transform domain neural filter (TDNF) for convenience. The weights are basically updated by the Back-Propagation (BP) algorithm but it must be modified since the error back-propagates through the orthogonal transform. Moreover, the variable step size which is normalized by the transformed signal power is introduced into the BP algorithm to realize the orthonormal transform. Through the computer simulation, it is confirmed that the introduction of the orthonormal transform is effective for speedup of convergence in the neural filter.

In this paper, we propose a new structure of the frequency domain adaptive filter (FDAF). The proposed structure is based on the modified DFT pair which consists of the FIR filters, so that un-delayed output signal can be obtained with stable convergence and without accumulated error which are problems for the conventional FDAFs. The convergence performance of the proposed FDAF is examined through the computer simulations in the adaptive line enhancer (ALE) comparing with the conventional FDAF and the DCT domain adaptive filter. Furthermore, in order to improve the error performance of the FDAF, we propose a composite algorithm which consists of the normalized step size algorithm for fast convergence and the variable step size one for small estimation error. The advantage of the proposed algorithm is also confirmed through simulations in the ALE. Finally, we propose a reduction method of the computational complexity of the proposed FDAF. The proposed method is to utilize a part of the FFT flow-graph, so that the computational complexity is reduced to O(N log N).

This paper first presents the performance analysis of the NACF algorithm. The results show the possibility of the degradation in the convergence speed. To improve the convergence speed, the bias term is introduced into the NACF algorithm and its efficiency is investigated through the computer simulations.

A new variable step size Least Mean Square (LMS) FIR adaptive filter algorithm (VSS-CC) is proposed. In the VSS-CC algorithm the step size adjustment (α) is controlled by using the correlation between the output error (e(n)) and the adaptive filter output ((n)). At small times, e(n) and (n) are correlated which will cause a large α providing faster tracking. When the algorithm converges, the correlation will result in a small size α to yield smaller misadjustments. Computer simulations show that the proposed VSS-CC algori thm achieves a better Echo Return Loss Enhancemen (ERLE) than a conventional NLMS Algorithm. The VSS-CC algorithm was also compared with another variable step algorithm, achieving the VSS-CC a better ERLE when the additive noise is incremented.

This paper proposes new algorithms for adaptive FIR filters. The proposed algorithms provide both fast convergence and small final misadjustment with an adaptive step size even under an interference to the error. The basic algorithm pays special attention to the interference which contaminates the error. To enhance robustness to the interference, it imposes a special limit on the increment/decrement of the step-size. The limit itself is also varied according to the step-size. The basic algorithm is extended for application to nonstationary signals. Simulation results with white signals show that the final misadjustment is reduced by up to 22 dB under severe observation noise at a negligible expense of the convergence speed. An echo canceler simulation with a real speech signal exhibits its potential for a nonstationary signal.