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.

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.

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.

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.

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 SYS-PNLMS algorithm is proposed. The analysis reveals that it performs a faster convergence rate compared to that of the recently introduced SPNLMS, PNLMS algorithms. Compared with its proportionate counterparts e.g. PNLMS and SPNLMS, the proposed SYS-PNLMS algorithm not only results in a faster convergence rate for both white and colored noise inputs, but also preserves its initial fast convergence rate until it reaches to its steady state condition. It also presents a higher tracking behavior for quasi-stationary inputs such as speech signal in addition to better performance in terms of computational complexity and resulting ERLE. In addition, the proposed SYS-PNLMS algorithm is also evaluated with previously proposed algorithms in a theoretical framework which validates the computer simulation results in terms of CPU time and number of iterations needed for each algorithm to get converged. Finally, a region of convergence for the proposed algorithm is derived for different input cases including white, colored noise and speech signal. This region is also compared with the practical value usually used in echo cancellation application.

In this paper a cyclostationarya-a based wideband spectrum sensing method is proposed. The received signal passes through a rough and flexible filter with its effective band tuned to a specific part of the received signal spectrum. This part belongs to a target signal which potentially exists in the received signal. Some cyclic frequencies of the target signal are employed to derive a normalized least mean square (NLMS) adaptive algorithm that estimates the output of the filter from its frequency shifted samples. If the target is absent in the received signal, the norm of the weights of the NLMS algorithm is almost zero. On the other hand, in the case of presence of the target, the norm of the weights will be greater than a certain threshold. The procedure is repeated to cover the entire band of the received signal and therefore it detects all cyclostationary signals with known cyclic frequencies in the received signal. The overall system is very easy to implement and fast and its performance is comparable to other spectrum sensing counterparts.

One of the destructive factors in communication and radar systems is intentional interference which is created by using jammers to disrupt the enemy's systems. If the intentional interference is not reduced well, the efficiency of the communication system would be completely disrupted. Jammers purposefully interfere and affect the optimal performance of the system. The NLMS adaptive algorithm is one of effective algorithms in eliminating intentional interference. In this paper, a new algorithm for eliminating intentional interference in cognitive radio systems using wavelet transform is presented. In the simulations, a 25-user cognitive radio system is used as a victim network in the vicinity of a network of primary users with Markov channel functionality. Considering eleven different scenarios, the performance of the proposed algorithm is investigated. To evaluate the performance of the proposed algorithm, the criterion of successful transmission of information in terms of signal to jammer ratio in each of the scenarios is discussed. According to the simulation results, the proposed algorithm, compared to the adaptive algorithm (NLMS), shows a significant improvement. The results, show 13% improvement for the proposed algorithm in successful transmission at SJR=5dB compared to the NLMS adaptive algorithm.