Constrained least lncosh adaptive filtering algorithm

Spectrum sensing is important for a cognitive radio (CR) system to protect primary users (PUs) from harmful interference. At present, most of the existing sensing schemes are proposed in Gaussian noise environments. Nevertheless, a CR system actually also suffers from non-Gaussian noise, such as man-made impulsive noise, ultrawideband interference and co-channel interference. In this article, to handle the degradation of detection performance in non-Gaussian impulsive noise environments, a robust spectrum sensing scheme named hyperbolic tangent-based energy detector (HT-ED) is proposed. The hyperbolic tangent function is applied to suppress the impulsive noise by the nonlinear behavior, but without restraining the normal noise by the linear behavior. This property enables the new method to achieve the good detection performance in both Gaussian and non-Gaussian noise environments. In addition, it is similar to an energy detector, the new detector does not need to know the characteristics of the PU's signal. The performance analysis of the proposed HT-ED scheme is also presented. The simulation results show the HT-ED is robust against impulsive noise, which is modeled as Laplace or α-stable noise. Moreover, the HT-ED provides a superior detection performance compared with the other existing relative methods in a wide range of non-Gaussian noise.

Robust adaptive sparse channel estimation problem has been attracted highly attention in the next-generation wireless communications systems. Re-weighted L1-norm penalized sign least mean square error (RL1-SLMS) algorithm is considered as one of attractive methods to estimate unknown sparse system as well as to mitigate impulsive noises. However, the convergence performance of RL1-SLMS is very ambiguous comparing with its preliminary version. This paper provides comprehensive convergence analysis for the RL1-SLMS algorithm under non-Gaussian impulsive noise environment. Numerical simulations are given to show the fast convergence and robustness with respect to system sparsity as well as non-Gaussian noise.

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 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.

A robust method for detecting the communication signals impinging on an antenna with interference and non-Gaussian impulsive noise is introduced in this paper. Degradation of the conventional cyclic detector which based on max-output-SNR criterion in impulsive noise is shown both theoretically and experimentally. By fusing second-order cyclostationarity and fractional lower-order statistics, a type of cyclic fractional lower-order statistics is developed which is defined for exploiting cyclostationarity property. Then, a new robust type of detection algorithm is developed using the theory of optimal filtering based on max-output-SNR criterion and alpha-stable distribution, including the fractional lower-order cyclic matched filter, which is formulated for detecting the communication signals in the presence of interference and non-Gaussian alpha-stable distribution impulsive noise. It is shown that the new method is robust to Gaussian and non-Gaussian impulsive noises, and is immune to the interfering signals which occupy the same spectral band as that of the received signal. Simulation results show the robustness and effectiveness of the proposed algorithm.

Time-difference-of-arrival estimation algorithms for cyclostationary signals in impulsive noise

The Gaussian noise profile has been demonstrated to be an inaccurate model in several antenna beamforming problems. Many available beamformers are based on second-order statistics and their efficiency degrades significantly due to impulsive noise existed in the received signal. Therefore, a demand exists for attention to address beamforming problems under nonGaussian noise environments. According to the robust performance of information theoretic learning (ITL) criteria in nonGaussian environments, we propose a linearly constrained version of maximum correntropy learning algorithm in order to solve beamforming problem in presence of nonGaussian and impulsive noises. Simulation results of the proposed adaptive beamformer are provided to illustrate its accurate and resistant performance in comparison with conventional second-order-moment-based beamformers.

This paper takes an Alpha-stable distribution as the noise model to solve the parameter estimation problem of bistatic multiple-input multiple-output (MIMO) radar system in the impulsive noise environment. For a moving target, its echo often contains a time-varying Doppler frequency. Furthermore, the echo signal may be corrupted by a non-Gaussian noise. It causes the conventional algorithms and signal models degenerating severely in this case. Thus, this paper proposes a new signal model and a novel method for parameter estimation in bistatic MIMO radar system in the impulsive noise environment. It combines the fractional lower-order statistics (FLOS) and fractional power spectrum density (FPSD), for suppressing the impulse noise and estimating parameters of the target in fractional Fourier transform domain. Firstly, a new signal array model is constructed based on the $$\alpha $$ź-stable distribution model. Secondly, Doppler parameters are jointly estimated by peak searching of the FLOS---FPSD. Furthermore, two modified algorithms are proposed for the estimation of direction-of-departure and direction-of-arrival (DOA), including the fractional power spectrum density based on MUSIC algorithm (FLOS---FPSD---MUSIC) and the fractional lower-order ambiguity function based on ESPRIT algorithm (FLOS---FPSD---ESPRIT). Simulation results are presented to verity the effectiveness of the proposed method.

A robust direction-of-arrival estimation method for impulsive 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.

A class of spread-spectrum signals, referred to as ‘continuous phase chirp modulation’ (CPCM), is examined for error rate performance in an impulsive noise environment. Optimum and locally optimum multiple-bit observation algorithms are derived and the latter is analysed for close-form error performance. Optimum weak coherent CPCM signalling systems are determined as a function of sample size and decision observation length of the receiver. It is shown that the optimized CPCM offers a performance equal to that of PSK/MSK. Suboptimum receivers that are easy-to-implement are also analysed and their performance compared with that of the locally optimum receiver.

Automatic modulation classification plays an essential role in cognitive communication systems. Traditional automatic modulation classification approaches are primarily developed under Gaussian noise assumptions. Nevertheless, recent empirical studies show that the impulsive noise has emerged in numerous wireless communication systems. The bursty nature of impulsive noise fundamentally challenges the applicability of traditional automatic modulation classification approaches. In order to accurately identify the modulation schemes in impulsive noise environment, in this paper, we propose a novel modulation classification approach through using hyperbolic-tangent cyclic spectrum and multi-branch attention shuffle neural networks. First, based on the designed hyperbolic-tangent autocorrelation function, hyperbolic-tangent cyclic spectrum is proposed to effectively suppress impulsive noise and extract the discriminating features. Then, based on the hyperbolic-tangent cyclic spectrum, a novel deep shuffle neural network is proposed as a classifier to perform the modulation classification through multi-branch attention mechanism to reweight all features. Both numerical and real-data experimental results demonstrate that the proposed algorithm can correctly classify modulation schemes with high accuracy and robustness in impulsive noise.

In many practical communication systems, the channel is corrupted by non-Gaussian impulsive noise (IN). It introduces decoding metric mismatch for the traditional Euclidean metric decoders and limits system performance. The situation is worsen by the practical difficulty in accurately estimating the IN statistics. Recently, some metric clipping based decoders with a properly chosen clipping threshold has been shown to be very effective in mitigating the effect of IN, even without a precise knowledge of its statistics. However, we observe that such a clipping threshold is derived based on some assumptions which lead to an error floor in the bit error probability curve at high signal-to-noise ratio (SNR). In this work, a clipping threshold is derived by an optimization approach without exploiting the IN statistics. It is demonstrated by experiment that with our proposed clipping threshold, the optimized metric clipping decoder is able to perform close to the maximum likelihood decoding performance at high SNR under the Bernoulli Gaussian noise model with various parameters.

Underwater acoustic azimuth and elevation angle estimation using spatial invariance of two identically oriented vector hydrophones at unknown locations in impulsive noise

The use of sensors configured into various geometrical shapes called arrays are of fundamental importance in extracting temporal, spatial, frequency, and probability distribution information in underwater acoustic and other applications. This paper explores the effectiveness of a two-dimensional or planar array in extracting spatial and frequency information. The method utilizes a receiver which converts digitized data at the output of each element, which may be nonlinear, into its frequency components using a discrete-Fourier transform. The frequency components are then weighted and summed over all spatial elements. The objective of the optimum receiver is to choose the weights so that a performance measure is maximized. To combat non-Gaussian interference an ideal nonlinearity is introduced. Several examples are given comparing the performance of a receiver with and without an ideal nonlinearity in an impulsive or non-Gaussian noise environment.