While the Hammerstein expression is computationally attractive for modeling of nonlinear systems, the optimal calculation of filter coefficients is practically cumbersome. A proper solution to this problem is the use of adaptive algorithms. In this paper, the Hammerstein Normalized LMS algorithm is proposed by deriving the corresponding time varying optimal step-size parameter in a closed form. The convergence behavior of this algorithm is inspected using computer simulations. The results show that the proposed algorithm achieves a faster convergence speed compared to the Hammerstein LMS algorithm, practically at the cost of an acceptable increase in computations.

Modified Normalized Least Mean Square (MNLMS) algorithm, which is a sign form of NLMS based on set-membership (SM) theory in the class of optimal bounding ellipsoid (OBE) algorithms, requires a priori knowledge of error bounds that is unknown in most applications. In a special but popular case of measurement noise, a simple algorithm has been proposed. With some simulation examples the performance of algorithm is compared with MNLMS.

In this paper, set-membership identification is used to derive a simple algorithm which is a sign version of the normalized least mean square algorithm. Convergence analysis is carried out.With some simulation examples. the performance of the algorithm, in the cases of slow and fast variations of a parameter is compared with the modified Dasgupta-Huang optimal bounding ellipsoid algorithm. These examples show the performance of the proposed-algorithm.

Existence of a high inter-channel correlation in a stereo communication system results in a considerable performance degradation in the associated stereo acoustic echo canceller and also weight misalignment of adaptive filters even after finalizing the convergence period. In this paper an approach for improving the performance of NLMS adaptive filter is developed based on reducing the correlation of input signals employing a multi-input-multi-output décor relation network. This approach has a low-complexity neural network structure and can train in a real-time manner. Simulation results show an improvement in weight convergence rate and misalignment employing the proposed method.

Selective partial update (SPU) strategy in adaptive filter algorithms is used to reduce the computational complexity. In this paper we apply the SPU normalized least mean squares algorithm (SPU-NLMS) for distributed estimation problem in an incremental network. The distributed SPU-NLMS (dSPU-NLMS) has close convergence speed to dNLMS, low steady-state mean square error (MSE), and low computational complexity features. In addition, the mean-square performance analysis of dSPU-NLMS algorithm for each individual node is presented. The theoretical expressions for stability bounds, transient and steady-state performance analysis of dSPU-NLMS are introduced. The validity of the theoretical results and the good performance of dSPU-NLMS are demonstrated by several computer simulations.

In this paper we show how the classical and modern adaptive filter algorithms can be introduced in a unified way. The Max normalized least mean squares (MAX-NLMS), N-Max NLMS, the family of SPU-NLMS, SPU transform domain adaptive filter (SPU-TDAF), and SPU subband adaptive filter (SPU-SAF) are particular algorithms are established in a unified way. Following this, the concept of set-membership (SM) adaptive filtering is extended to this framework, and a unified approach to derivation of SM and SM-SPU adaptive filters is presented. The SM-NLMS, SM-TDAF, SM-SAF, SM-SPU-NLMS, and SM-SPUSAF are presented based on this approach. Also, this concept is extended to the SPU affine projection (SPU-AP) and SPUTDAF algorithms and two new algorithms which are called SM-SPU-AP and SM-SPU-TDAF algorithms, are established. These novel algorithms are computationally efficient. The good performance of the presented algorithms is demonstrated in system identification application.

As a fundamental device in acoustic echo cancellation (AEC) systems, the echo canceller based on adaptive filters relies on the adaptive approximation of the echo-path. However, the adaptive filter must face the risk of divergence during the double-talk periods when the near-end is present. To solve this problem, the double-talk-detector (DTD) is often used to detect the double-talk periods and prevent the echo canceller from being disturbed by the other end of the speaker’s signal. In this paper, we propose a DTD based on a new method that can detect quickly and track accurately double-talk periods. It is based on the sum of energies of the estimated echo and the microphone signals which is continuously compared to the error energy. A window that moves with time and tracks energy variations of the different input signals of the DTD represents a fundamental feature of the proposed method compared to several other methods based on correlation. The goal is to outperform conventional normalized cross-correlation (NCC) methods which are well-known in terms of small steady-state misalignment and stability of decision variable. In this work, the normalized least mean squares (NLMS) algorithm is used to update the filter coefficients along speech signals which are taken from the NOIZEUS database. Efficiency of the proposed method is particularly compared to the conventional Geigel algorithm and normalized cross-correlation method (NCC) that depends on the cross-correlation between the microphone signal and the error signal of AEC. Performance evaluation is confirmed by computer simulation

In order to demolition of performance in radar systems, intentional jamming is used. One of the best methods to delete the effect of jammer is to use the adaptive filters. In the radar systems, it is commonly used the linear adaptive algorithms to prevent the saturation of receiver. Linear algorithms don't have any feedback and are resistant against saturation. In this paper, a linear adaptive algorithm based on NLMS algorithm is introduced which is named as improved NLMS algorithm. Improved NLMS algorithm is simulated for input signal of pulse radar affected by jamming and is compared with existing algorithms in terms of efficiency. Output SJR versus input SJR for each algorithm is plotted. Simulation results show that, for input SJR equal to 5 dB, the output SJR improves approximately equal to 6db for RLS algorithm and 8db for NLMS algorithm, respectively. For such input SJR, the proposed algorithm shows 11 dB improvement in output SJR versus to input SJR. This means that the proposed algorithm creates 3dB improvement compared to the best existing adaptive filter. This improvement is obtained by increasing the computational complexity compared to the NLMS algorithm.

Two-dimensional (2D) adaptive filtering is a technique that can be applied to many image and signal processing applications. This paper extends the one-dimensional adaptive filter algorithms to 2D structure and the novel 2D adaptive filters are established. Based on this extension, the 2D variable step-size normalized least mean squares (2D-VSSNLMS), the 2D-VSS affine projection algorithms (2D-VSS-APA), the 2D set-membership NLMS (2D-SM-NLMS), the 2D-SM-APA, the 2D selective partial update NLMS (2DSPU- NLMS), and the 2D-SPU-APA are presented. In 2D-VSS adaptive filters, the stepsize changes during the adaptation which leads to improve the performance of the algorithms. In 2D-SM adaptive filter algorithms, the filter coefficients are not updated at each iteration. Therefore, the computational complexity is reduced. In 2D-SPU adaptive algorithms, the filter coefficients are partially updated which reduce the computational complexity. We demonstrate the good performance of the proposed algorithms thorough several simulation results in 2D adaptive noise cancellation (2D-ANC) for image denoising. The results are compared with the classical 2D adaptive filters such as 2D-LMS, 2D-NLMS, and 2D-APA.