Transient and steady-state analysis of Adaptive Step-Size Least Mean Modulus algorithm

The paper presents an adaptive algorithm named adaptive threshold nonlinear algorithm for use in adaptive filters in the complex-number domain (c-ATNA) in applications to digital QAM systems. Although the c-ATNA is very simple to implement, it makes adaptive filters highly robust against impulse noise and at the same time it ensures filter convergence as fast as that of the well-known LMS algorithm. Analysis is developed to derive a set of difference equations for calculating transient behavior as well as steady-state performance. Experiment with simulations and theoretical calculations for some examples of filter convergence in the presence of Contaminated Gaussian Noise demonstrates that the c-ATNA is effective in combating impulse noise. Good agreement between simulated and theoretical convergence proves the validity of the analysis.

In this letter, a novel robust two-dimensional nearfield millimeter-wave (MMW) image reconstruction algorithm is developed based on compressed sensing (CS) in the presence of impulsive measurement noise. To enable the sparse MMW image recovery, the CS algorithm usually employs the popular l 2 -norm as the data fidelity term and a combination of multiple sparsityinduced functions as the penalty term. The l 2 -norm is non-robust against impulsive noise since the Gaussian noise distribution assumption is not valid, and the presence of impulsive noise will severely degrade the robustness of the compressive MMW image recovery. To gain more robustness performance, a complex correntropy based data-fitting term, namely complex correntropic loss (CC-loss), is used to replace the l2-norm for the near-field MMW measurement contaminated by impulsive noise. In order to solve the corresponding minimization problem, an additive half quadratic method is used to transform the CC-loss term to its convex form, and then a parallel primal-dual process is used to guarantee the convergence of the proposed algorithm. In total, 150-GHz MMW experimental results show that the proposed algorithm can achieve accurate image reconstruction from compressive measurements under different impulsive noise levels.

One of the challenges of modulation techniques used in Fifth-Generation (5G) is their robustness in noisy environment. Conventional Orthogonal Frequency Division Multiplexing (OFDM) cannot be considered as a 5G waveform in its original form because of its certain limitations, such as performance degradation by impulsive noise (IN) and high peak to average power ratio (PAPR). Numerous modulation schemes proposed for 5G communications are able to overcome these drawbacks. Generalised Frequency Division Multiplexing (GFDM) is one of them. This paper analyses the performance of GFDM in presence of Additive White Gaussian Noise (AWGN), IN and Narrow Band Interference (NBI). It is found that GFDM is able to perform better than OFDM and Vector Orthogonal Frequency Division Multiplexing (VOFDM) in presence of noises, which can potentially be present in 5G applications. Simulation results show that GFDM achieve lower PAPR and Symbol Error Rate (SER) and an average of 10.73 dB and 4.73 dB gain in Signal to Noise Ratio (SNR) in presence of IN and combined IN and NBI respectively, as compared to OFDM and VOFDM.

The direct sequence-code division multiple accesses (DS-CDMA) signals are transmitted over multipath channels that introduce fading and shadowing. Combined effect of multipath fading and shadowing along with multiple access interference (MAI) and inter-symbol interference (ISI) worsens the system performance. Further, experimental results have confirmed the presence of impulsive noise in wireless mobile communication channels. Hence, this paper presents a comprehensive learning particle swarm optimization (CLPSO) based multiuser detection technique for DS-CDMA systems over generalized-K (GK) fading channels in presence of impulsive noise. Maximal ratio combining (MRC) receive diversity is also incorporated to mitigate the effects of fading and shadowing. Performance of proposed M-decorrelator is studied by evaluating average error rate. Simulation results show that the proposed M-decorrelator performs better in the presence of fading, shadowing and heavy-tailed impulsive noise when compared to least squares, Huber and Hampel M-estimator based detectors.

We address the distributed estimation of a scalar Gaussian source in wireless sensor networks. The sensor nodes transmit their noisy observations, using the amplify-and-forward relaying strategy through coherent multiple access channel to the fusion center (FC) that reconstructs the source parameter. In this letter, we assume that the received signal at the FC is corrupted by impulsive noise and channel fading, as encountered for instance within power substations. Over Rayleigh fading channel and in presence of Middleton class-A impulsive noise, we derive the minimum mean square error (MMSE) optimal Bayesian estimator along with its mean square error performance bounds. From the obtained results, we conclude that the proposed optimal MMSE estimator outperforms the linear MMSE estimator developed for Gaussian noise scenario.

In this paper, a new robust adaptive FIR filter algorithm with variable forgetting factor for time-varying parameters estimation in the presence of impulsive noise is discussed. The proposed algorithm is based on the robust recursive least square and extended prediction error variable forgetting factor adaptation algorithms. The feasibility of the approach is demonstrated in a system identification simulation using a FIR filter application.

A robust adaptive filter is usually unaffected by spurious disturbances at the error sensor. In an endeavour to improve robustness of the adaptive filter, a novel modified Champernowne function (MCF) is proposed as a robust norm and the corresponding robust Champernowne adaptive filter (CMAF) is derived. To improve modelling accuracy and convergence performance for sparse systems along with being robust, a reweighted zero attraction (RZA) norm is incorporated in the cost function along with MCF and the corresponding RZA-CMAF algorithm is proposed. To further improve filter performance, the CMAF- l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> algorithm is proposed where the l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -norm is approximated using the multivariate Geman-McClure function (GMF). Bound on learning rate for the proposed algorithms is also derived. Extensive simulation study shows the improved robustness achieved by the CMAF algorithm, especially when impulsive noises are present for a longer duration. On the other hand, RZA-CMAF and CMAF- l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> can provide improved convergence performance under sparse and impulsive noise conditions, with CMAF- l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> providing the best performance.

This paper first reviews Correlation Phase Algorithm (CPhiA) for adaptive filters in the complex-number domain with colored Gaussian reference inputs. Stochastic models are presented for two types of impulse noise intruding adaptive filters: one in observation noise and another at filter input. To improve the filter convergence speed for a strongly correlated filter reference input, we combine the CPhiA with simple recurrent calculation of the inverse covariance matrix of the filter input using the Newton's method (CPhi-Newton algorithm). We further propose a new adaptive step-size (ASS) control algorithm to be combined with the CPhi-Newton algorithm. We develop performance analysis of the ASS-CPhi-Newton algorithm to derive difference equations for theoretically calculating transient and steady-state convergence behavior. Through experiment with some examples, it is demonstrated that faster convergence and high robustness are realized with the proposed ASS-CPhi-Newton algorithm in impulsive noise environments. Good agreement between simulated and theoretical convergence validates the analysis.

Underwater communications systems are being increasingly used in defence, security service, oil exploration, ocean science and in many other applications. The underwater acoustic channel is characterised by the large delay spread, Doppler shifts, limited bandwidths and time variability. The channel is also affected by additive impulsive noise, which makes the underwater communication even more challenging. Since the channel and noise characteristics vary immensely, an adaptive equaliser at the communications receiver forms a viable solution for increasing the bit error rate of the communication link. The adaptive multistage clustering based equaliser is one such solution which provides high throughput. However, the performance of the multistage clustering equaliser degrades in the presence of impulsive noise. To improve the throughput and robustness, we propose an adaptive normalised multistage clustering based blind equaliser for underwater acoustic channel. From simulation results, it is observed that the proposed algorithm has better convergence and symbol error rate performance. Convergence analysis of the proposed algorithm is also presented in the paper.

A novel direction finding algorithm for distributed sources under impulsive noise environments

An improved method for direction-of-arrival (DOA) estimation algorithm based on Multistage Wiener Filters (MSWF) in the presence of impulsive noise is proposed in this paper. There are many DOA estimation algorithms based on Multistage Wiener Filters, but all of them must satisfy the requirement of the noise is Gaussian white noise, which can not the accurately in the presence of impulsive noise. The improved method has good performance at DOA estimate when the noise is impulsive noise, and some computer simulations show it.

ABSTRACTPaired carrier multiple access (PCMA) is a critical technique in satellite communication systems for frequency reuse and optimizing spectrum utilization. While separation of PCMA signals in Gaussian noise environments is well‐established, designing algorithms for impulsive noise remains a challenge. This paper proposes a novel correntropy‐based adaptive filter with an equalizer to separate PCMA signals in the presence of impulsive noise. It is important to note that our approach is currently limited to single‐beam applications and specifically for constant QPSK modulations. We compare the performance of our method with the well‐known least mean square (LMS) adaptive filter using bit error rate (BER) and mean square deviation (MSD) simulations, demonstrating the superiority of our approach.

Rolling element bearings are widely used in various industrial machines. Fault diagnosis of rolling element bearings is a necessary tool to prevent any unexpected accidents and improve industrial efficiency. Although proved to be a powerful method in detecting the resonance band excited by faults, the spectral kurtosis (SK) exposes an obvious weakness in the case of impulsive background noise. To well process the bearing fault signal in the presence of impulsive noise, this paper proposes a fault diagnosis method based on the cyclic correntropy (CCE) function and its spectrum. Furthermore, an important parameter of CCE function, namely kernel size, is analyzed to emphasize its critical influence on the fault diagnosis performance. Finally, comparisons with the SK-based Fast Kurtogram are conducted to highlight the superiority of the proposed method. The experimental results show that the proposed method not only largely suppresses the impulsive noise, but also has a robust self-adaptation ability. The application of the proposed method is validated on a simulated signal and real data, including rolling element bearing data of a train axle.

Predictions of bit error rate caused by a combination of impulsive and Gaussian noise are made for data communication systems using PSK, DPSK and FSK, with direct carrier modulation. The technique uses the amplitude probability distribution (APD) to characterise the noise at the input of the receiver demodulator. A direct numerical approach (with numerical integration, where appropriate) is used to produce predictions for the case where decisions are made by sampling the demodulated signal at times nominally at the centre of the received data symbols, there being a minimum amount of postdetector filtering. Error rates in mobile data communication systems have been measured at roadside locations and in the laboratory. In the latter case, an impulsive noise simulator capable of producing noise with specified statistical characteristics was used. Laboratory measurements have also been made with fading signals, and the prediction techniques have been extended to cover this case. Generally, agreement between theory and experiment is good, and it is concluded that the techniques ar applicable in any system where channel separations are well defined and, consequently, where IF filters are adequately standardised.

Additive asynchronous and cyclostationary impulsive noise limits\ncommunication performance in OFDM powerline communication (PLC) systems.\nConventional OFDM receivers assume additive white Gaussian noise and hence\nexperience degradation in communication performance in impulsive noise.\nAlternate designs assume a parametric statistical model of impulsive noise and\nuse the model parameters in mitigating impulsive noise. These receivers require\noverhead in training and parameter estimation, and degrade due to model and\nparameter mismatch, especially in highly dynamic environments. In this paper,\nwe model impulsive noise as a sparse vector in the time domain without any\nother assumptions, and apply sparse Bayesian learning methods for estimation\nand mitigation without training. We propose three iterative algorithms with\ndifferent complexity vs. performance trade-offs: (1) we utilize the noise\nprojection onto null and pilot tones to estimate and subtract the noise\nimpulses; (2) we add the information in the data tones to perform joint noise\nestimation and OFDM detection; (3) we embed our algorithm into a decision\nfeedback structure to further enhance the performance of coded systems. When\ncompared to conventional OFDM PLC receivers, the proposed receivers achieve SNR\ngains of up to 9 dB in coded and 10 dB in uncoded systems in the presence of\nimpulsive noise.\n