A Norm Constraint Lorentzian Algorithm Under Alpha-stable Measurement Noise

A robust direction-of-arrival estimation method for impulsive noise environments

In this paper, we propose a modified time-domain channel estimation algorithm for OFDM systems working under impulsive noise conditions. The proposed method employs two time-domain windows to reduce additive white Gaussian noise and impulsive noise components included in the estimated channel impulse response (CIR). Meanwhile, the impulse noise equalizer further eliminates the impulse noise. As a result, the modified algorithm can overcome the mean-square error (MSE) floor caused by the conventional method in impulsive noise environment. Simulation results demonstrate that the proposed algorithm can significantly improve the MSE performance compared with the conventional estimation method, and provides about 3dB improvement in SNR for the same BER values in DVB system.

The newly proposed l 1 norm constraint zero-point attraction least mean square algorithm (ZA-LMS) demonstrates excellent performance on exact sparse system identification. However, ZA-LMS has less advantage against standard LMS when the system is near sparse. Thus, in this study, firstly the near sparse system (NSS) modelling by generalised Gaussian distribution is recommended, where the sparsity is defined accordingly. Second, two modifications to the ZA-LMS algorithm have been made. The l 1 norm penalty is replaced by a partial l 1 norm in the cost function, enhancing robustness without increasing the computational complexity. Moreover, the ZA item is weighted by the magnitude of estimation error which adjusts the ZA force dynamically. By combining the two improvements, Dynamic Windowing ZA-LMS (DWZA-LMS) algorithm is further proposed, which shows better performance on NSS identification. In addition, the mean-square performance of DWZA-LMS algorithm is analysed. Finally, computer simulations demonstrate the effectiveness of the proposed algorithm and verify the result of theoretical analysis.

Improved proportionate-type sparse adaptive filtering under maximum correntropy criterion in impulsive noise environments

In order to realize the high-resolution multipath Time Difference Of Arrival (TDOA) estimation which is not limited by the resolution limit of correlation method under impulsive noise environment, a Correntropy Expectation-Maximum (CEM) high resolution multipath TDOA estimation algorithm is proposed based on the Maximum Correntropy Criterion (MCC). The multipath TDOA is estimated by transforming multi-dimensional optimization problems into multiple one-dimensional optimization problems. The simulation results show that the CEM algorithm has good estimation performance under strong impulsive noise and low SNR environment, and the selection of kernel size in CEM algorithm is not depend on the prior information of the impulsive noise.

The least mean p-power (LMP) is one of the most popular adaptive filtering algorithms. With a proper p value, the LMP can outperform the traditional least mean square \((p=2)\), especially under the impulsive noise environments. In sparse channel estimation, the unknown channel may have a sparse impulsive (or frequency) response. In this paper, our goal is to develop new LMP algorithms that can adapt to the underlying sparsity and achieve better performance in impulsive noise environments. Particularly, the correntropy induced metric (CIM) as an excellent approximator of the \(l_0\)-norm can be used as a sparsity penalty term. The proposed sparsity-aware LMP algorithms include the \(l_1\)-norm, reweighted \(l_1\)-norm and CIM penalized LMP algorithms, which are denoted as ZALMP, RZALMP and CIMLMP respectively. The mean and mean square convergence of these algorithms are analysed. Simulation results show that the proposed new algorithms perform well in sparse channel estimation under impulsive noise environments. In particular, the CIMLMP with suitable kernel width will outperform other algorithms significantly due to the superiority of the CIM approximator for the \(l_0\)-norm.

충격성 잡음 환경에서 최대 영확률 (MZEP) 알고리듬은 최소자승오차 (MSE) 기반의 알고리듬 보다 우수한 성능을 지닌다. 그리고 알고리듬 자체에 내재한 크기 조절 입력 (MCI)가 MZEP 알고리듬을 충격성 잡음으로부터 알고리듬을 안정되게 유지하는 역할을 하는 것으로 알려져 있다. 이 논문에서는 MCI 입력의 평균전력으로 MZEP 알고리듬의 스텝 사이즈를 정규화하는 방식을 제안하였다. 충격파 발생률이 0.03인 충격성 잡음하의 시뮬레이션에서 정상상태 MSE 성능 비교에서 기존 MZEP에 비해 제안한 방식이 약 2dB 정도 향상된 특성을 보인다. The maximum zero error probability (MZEP) algorithm outperforms MSE (mean squared error)-based algorithms in impulsive noise environment. The magnitude controlled input (MCI) which is inherent in that algorithm is known to plays the role in keeping the algorithm undisturbed from impulsive noise. In this paper, a new approach to normalize the step size of the MZEP with average power of the MCI is proposed. In the simulation under impulsive noise with the impulse incident rate of 0.03, the performance enhancement in steady state MSE of the proposed algorithm, compared to the MZEP, is shown to be by about 2 dB.

A new class of nonlinear filters called FIR-weighted myriad hybrid (FIR-WMyH) filters was introduced. These filters have a combination structure of linear FIR filters and weighted myriad filter, and can efficiently utilize the special strongpoint of two filters. Through the backpropagation algorithm used in the neural networks, we derive a stochastic gradient-based adaptive algorithm for determining optimal FIR-WMyH filters under the mean square error (MSE) criterion. In two impulsive noise models, the robust performance of this adaptive algorithm is demonstrated through the computer simulation results. © 2006 IEEE.

This paper reports a solution to a linear blind equalizer used in communication systems under the effect of two factors: i) An unknown linear inter symbol interference and ii) the impulsive noise satisfying the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> -stable distribution. First, a constellation matching error-based cost function associated with the linear equalizer is designed to effectively compensate for the inter symbol interference and suppress the influence of the impulsive noise. Second, an improved form of the proposed cost function is derived through the finite alphabet property of information symbols. The theoretical analysis shows that the improved cost function significantly reduces the local minima and converges more stably in high-order modulation systems. Furthermore, based on the special structure of the designed cost function, a modified Newton scheme is constructed to quickly minimize it, and then the corresponding optimal blind equalizer can be obtained. Finally, computer simulations are presented to demonstrate the robust equalization performance and fast convergence of the novel algorithm under both impulsive and Gaussian noise environments.

Channel estimation in Underwater Acoustic Communication (UAC) faces significant challenges due to the non-Gaussian, impulsive noise in ocean environments and the inherent high dimensionality of the estimation task. This paper introduces a robust channel estimation algorithm by solving an l1−l1 optimization problem via the Alternating Direction Method of Multipliers (ADMM), effectively exploiting channel sparsity and addressing impulsive noise outliers. A non-monotone backtracking line search strategy is also developed to improve the convergence behavior. The proposed algorithm is low in complexity and has robust performance. Simulation results show that it exhibits a small performance deterioration of less than 1 dB for Channel Impulse Response (CIR) estimation in impulsive noise environments, nearly matching its performance under Additive White Gaussian Noise (AWGN) conditions. For Delay-Doppler (DD) doubly spread channel estimation, it maintains Bit Error Rate (BER) performance comparable to using ground truth channel information in both AWGN and impulsive noise environments. At-sea experimental validations for channel estimation in Orthogonal Frequency Division Multiplexing (OFDM) systems further underscore the fast convergence speed and high estimation accuracy of the proposed method.

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.

In the context of two-dimensional (2-D) direction of arrival (DOA) estimation in impulsive noise environments, this paper extends the coprime array to a crossed V-shaped distributed structure and proposes a novel exponential weighted adaptive generalized covariance (EWAGC) based on the study of impulsive noise characteristics. Building on this, a redundant averaging dual-scale EWAGC-ESPRIT algorithm is introduced, which can adaptively adjust the suppression level of impulsive noise with varying intensities, enhancing the robustness of the estimation. Simulation results validate the superior performance of the proposed method in solving the 2-D DOA estimation problem in impulsive noise environments.

This paper proposes a formulation of estimating a sparse image signal where the sparsity only occurs on the high frequency components. The formulation is for compressed sensing reconstruction when a compressed measurement signal is contaminated by impulsive noise. The approach is based on two prior well-known assumptions. First, adding an L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm penalty on a compressible signal to the cost objective of the estimation problem will promote a sparsity in the signal. Secondly, an image signal should be sparse in high frequency domain, while it is dense in low frequency domain where most of its important information lies. Our approach is therefore to impose an L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm penalty only on the signal components that need to be sparse while we allow the important low frequency part to be dense. The obtained formulation is a convex optimization which can be effectively solved by many available algorithms. The experiment demonstrated a superior impulsive noise tolerance of the proposed penalty function to a conventional scheme where all signal components are penalized by L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm. At the noise probability of less than 0.1, the reconstruction was better both quantitatively and qualitatively.

The reweighted zero-attracting least mean square (RZA-LMS) algorithm has good performance in sparse system identification. However, the convergence performance of the RZA-LMS algorithm degrades in the impulsive noise environment. In this brief, a reweighted zero-attracting least mean M-estimate (RZA-LMM) algorithm is proposed to address the issue. The RZA-LMM algorithm employs the M-estimate cost function with a sparsity-aware penalty term and is derived by using the unconstrained minimization method. In order to further enhance the convergence speed and reduce the steady-state error of the RZA-LMM algorithm, a variable step-size reweighted zero-attracting least mean M-estimate (VSSRZA-LMM) algorithm is proposed. The variable step-size scheme, which adopts the M-estimate cost function with a sparsity-aware penalty term and a constrained term of the step-size, is obtained by using the constrained minimization method. Besides, the mean-square stability is analyzed to obtain the range of the step-size, which guarantees the stabilization of the proposed algorithms. The computer simulation results show that the proposed RZA-LMM algorithm achieves better convergence performance than the RZA-LMS algorithm, and the proposed VSSRZA-LMM algorithm exhibits better convergence performance in terms of convergence speed and steady-state normalized mean square deviation (NMSD) than the RZA-LMM algorithm for sparse system identification in the impulsive noise environment.

Multitask diffusion affine projection sign algorithm and its sparse variant for distributed estimation