Adaptive Separation of PCMA Signals Based on Maximum Correntropy Algorithm

Nonlinear system identification in noisy environments presents a significant challenge in adaptive filtering, particularly when dealing with impulsive noise, non-Gaussian distributions, and complex system dynamics. Traditional filtering approaches, including Least Mean Squares (LMS) and Recursive Least Squares (RLS), often exhibit performance degradation due to their reliance on second-order statistical assumptions. The Maximum Correntropy Criterion (MCC) has shown promise in improving robustness; however, it suffers from limitations in capturing highly nonlinear system behaviors. This study proposes a Generalized Maximum Correntropy Criterion (GMCC) with Spline Adaptive Filtering, leveraging B-spline basis functions to enhance function approximation and noise resilience. The GMCC framework was evaluated against LMS, RLS, and conventional MCC-based adaptive filtering methods across Gaussian, Laplacian, and impulsive noise environments. Experimental results demonstrate that GMCC consistently achieves lower Mean Squared Error (MSE) values across all noise scenarios, outperforming conventional approaches in both accuracy and convergence stability. Statistical analysis using ANOVA confirmed performance consistency, though differences were not statistically significant at the 95% confidence level. Practical applications include biomedical signal processing, financial modeling, radar tracking, and autonomous systems, where robust nonlinear filtering is essential. Future research should focus on optimizing computational efficiency, incorporating deep learning enhancements, and extending real-time implementations for IoT and edge computing applications.

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 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.

In this paper, we investigate the ultimate performance limits, in terms of achievable information rate (IR), of communication systems impaired by impulse noise. We compare single carrier (SC) and multi-carrier (MC) transmission systems employing quadrature amplitude modulation (QAM) formats. More precisely, we consider SC schemes with coded modulations and MC systems based on orthogonal frequency division modulation (OFDM). For the MC schemes, we introduce a theoretically equivalent channel model which makes the computation of the IR feasible. This simple channel model will be referred to as interleaved MC. We show that, in the presence of impulse noise and except for systems operating at very high spectral efficiency, the IR of MC schemes is lower than that of SC schemes. More precisely, use of MC schemes may lead to an unavoidable fundamental loss with respect to SC schemes at typical coding rates, whereas MC schemes are to be preferred for very high coding rates or in uncoded systems. These results hold for additive white Gaussian noise (AWGN) and dispersive channels, either considering plain OFDM or MC schemes employing water-filling and bit-loading algorithms. In order to validate our theoretical results, we also obtain the bit error rate (BER) performance of SC and MC schemes through Monte Carlo simulations. A few trellis-coded modulation (TCM) and low-density parity-check (LDPC)-coded schemes are considered. The obtained SNR loss in the BER curves between the AWGN and impulse noise channels matches well with the corresponding IR gap.

A major complaint of individuals with normal hearing and hearing impairments is a reduced ability to understand speech in a noisy environment. This paper is proposed to remove the noise from the speech signal in various real time environments and to make the hearing impaired to understand the information by transforming speech in to text format. The quality of audio signal can be improved by filtering the degraded speech signal through adaptive filters. For Noise cancellation widrow & hoff’s Least Mean Square (LMS) algorithms are being used for simplicity in implementation. The LMS algorithm was simple in it's derivation and robust in a number of applications but it also have limitation in selection of a certain values such as step size and results in computational complexity. Hence to overcome all the limitations and to present an enhanced speech signal, a novel approach named VSSNDLMS algorithm is proposed. The performance of algorithms like Variable Step Size Normalised LMS , Normalised Differential LMS with proposed VSSNDLMS with different input signals are analysed in this paper . Finally, through simulation results the proposed VSSNDLMS algorithm converges fastly with minimum mean square error and it is useful in predicting the adaptive filter performance of various algorithms and the implementation indicate the improvement in quality of the speech signal and it appears to be favourable for hearing impaired. Keywords: VSSNDLMS, LMS Algorithm, Noise Cancellation, Speech Processing, Adaptive Filter

Least Mean Square (LMS) algorithm is the most popular adaptive algorithm (AA) for realization of a digital adaptive filter (AF). In digital implementation of AF, finite word length hardware is unavoidable. This finite precision (FP) effect on the performance of the AF is crucial in the sense that, if proper word length is not used the performance in terms of the mean square error (MSE) of the filter degrades substantially. In this paper, a new approach based on the probability theory is used to analyze the FP effect of the LMS based finite impulse response (FIR) AF. An expression of the adaptation failure in terms of word length and the step size is derived. Simulation study of a FP LMS adaptive equalizer is carried out to demonstrate and verify this effect. This study provides an important guide-line to the designers for selecting the optimum word length for a specific application for a given MSE criterion.

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.

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.

Orthogonal frequency division multiplexing (OFDM) is adopted in most wireless communication systems, and the performance of OFDM is affected by impulse noise (IN). Better channel estimation (CE) performance is required to detect the channel information on the receiving side. The OFDM system is considered with the number of subcarriers carrying the data and pilot symbols. In the OFDM modulator, the symbols of the frequency domain are transformed into the signals of the time domain using inverse discrete Fourier transformation (IDFT). Effective impulsive noise mitigation is crucial for improving the effectiveness of OFDM communication systems, and it improves the signal-to-noise ratio (SNR) at the receiver. A cyclic prefix is then appended before transmission through the channel. In the receiver noise, the effect of IN is mitigated jointly with CE using the Bayesian matching pursuit (BMP) and Moth-flame algorithm (MFA). In this approach, the IN and channel information is considered as a sparse vector. Here, the data symbols used are considered an unknown parameter. The approach incorporating all subcarriers has a lower mean square error (MSE) of IN estimate for impulsive noise reduction. The MFA algorithm is used to optimize the sensor matrix in BMP. The sparsity of the channel and the impulse response are observed in the time domain to represent the channel and IN together. It exactly recovers the sparse signal for finding the convex objectives of the sparse minimizer, and the sparse solution is obtained with fixed point updates. The proposed BMP algorithm improves the CE by explicitly considering the existence of IN. The BMP is a greedy algorithm that selects the most correlated residuals at each column. Under mutual incoherence, it recovers the signal with a higher probability. The simulated outcomes proved that the proposed CE and noise mitigation model achieved better performance based on the bit error rate (BER), throughput and MSE.

Adaptive beamforming for binary phase shift keying communication systems

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.

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.

An adaptive filter is the utmost essential filter castoff in statistical signal dealing. The fine-tuning of the filter factor in relation to the response signal is the adaptive filter's key feature due to fewer calculations, Least Mean Square (LMS) adaptive filters are widely used to remove noise from Electrocardiograms (ECG). The adaptive filters are realized as signal processing algorithms in Digital Signal Processors (DSPs) or in VLSI Signal Processors (VSPs). The technique provides a way to create a folded adaptive lattice LMS filter, which requires less hardware than an adaptive lattice filter. Folding is an algorithm that uses a time scheduling technique that combines arithmetic operations into one operation which reduces Register and silicon chip areas. The design and implementation of a folded lattice adaptive filter remove Power Line Interference (PLI) noise from ECG signals. The MATLAB Xilinx System Generator tool is used to design the Adaptive Lattice LMS Filter and Folded Adaptive Lattice LMS Filter with Folding Order K = 2 and K = 4 and realized in the Virtex 5 FPGA KIT. The results of the folded architecture show that the area is reduced for K = 2 and K = 4 by 82.60% and 91.05%, respectively compared with a normal adaptive lattice filter.

This paper proposes Adaptive Step-Size Least Mean Modulus (ASS-LMM) algorithm for fast convergent and robust adaptive filtering in the presence of impulse noise. The ASS-LMM algorithm for use in adaptive filters defined in the complex-number domain is basically the LMM algorithm combined with a new adaptive step-size control algorithm to improve the convergence speed of the LMM algorithm while preserving its robustness against additive impulsive observation noise. Through analysis and experiment, we demonstrate effectiveness of the proposed ASS-LMM algorithm in making adaptive filters fast convergent and highly robust in the presence of impulse noise. Good agreement between simulated and theoretical convergence behavior in the transient phase and in the steady state proves the validity of the analysis.

This paper presents an adaptive filter with adaptive window size that is effective in filtering images corrupted with impulse noise and mixed noise (Gaussian, ..., impulse) with limited blurring effects. The filter is based on an adaptive window technique, the image data order statistics, and the LMS adaptive filter. It can be viewed as a three stages filter, the first stage is to identify impulses and passible edges, then use adaptive size calculation to isolate impulses and the third stage is adaptive filtering the remaining data using the adaptive LMS filter. This process of adaptive windowing reduces the filter size and causes reduction in computations which compensates for the excessive amount of comparisons made in sorting the image data. The proposed filter simultaneously removes both positive and negative impulses as compared to other techniques which deal with only one type of impulses at a time. Comparisons with other filtering illustrate its superiority in removing the mixed noise from images.