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.

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.

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 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.