Impulsive Noise Mitigation in Powerline Communications Using Sparse Bayesian Learning

Accurate channel state information is the foundation of the receiver design for power line communication (PLC) system. However, the presence of impulsive noise makes the problem more complex. As traditional impulsive noise mitigation methods are based on the assumption that the channel state information is known in advance, which limits their applications. In this paper, by exploiting the parametric sparsity, we propose a joint channel and impulsive noise estimation scheme based on compressed sensing theory for narrowband PLC systems. Observing the strong coherence of measurements matrix, we adopt the sparse Bayesian learning (SBL) to solve the compressed sensing problem. Simulation results verify our proposed algorithm has smaller mean square error and bit error rate.

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.

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.

The impulsive noise and the time-varying channel are two major detrimental factors which greatly constrain the performance of underwater acoustic communications (UACs). Utilizing the joint sparsity of the impulsive noise and the channel impulse response, the paper proposes the generalized approximate message passing (GAMP)-based sparse Bayesian learning (SBL) frameworks for joint impulsive noise mitigation and channel estimation and tracking for orthogonal frequency division multiplexing (OFDM) UACs. Firstly, the SBL framework for the joint estimation is employed. To reduce the computational complexity, the GAMP is introduced into the expectation-maximization (EM) algorithm, and a low-complexity GAMP based SBL framework is formulated without performance degradation. To further estimate and track the impulsive noise and channel state information in the slow time-varying scenarios, we propose a novel GAMP-based temporal SBL framework. The factor graph and GAMP are used to achieve the approximated estimation for the posterior statistics of both the channel state information and the impulsive noise. The algorithm formulates the message passing scheduling for the EM algorithm to solve the joint multiple sparse signal recovery problem. Simulations and sea-trial results demonstrate that the proposed algorithms significantly improve the performance in terms of the mean square error of channel estimation, impulsive noise estimation, bit error rate and computational complexity compared with their corresponding SBL-based counterparts.

Robust Bayesian learning approach for massive MIMO channel estimation

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.

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.

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.

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.

We propose an empirical compressed learning approach based on generalized approximate message passing (GAMP) for deterministic sensing matrix with low spark. The spark of a matrix is defined as the minimum number of correlated columns. In contrast to previous works, GAMP with independent and non-identically distributed Gaussian prior for the sparse signal to be estimated is used to avoid the over-fitting problem in the original GAMP. Specifically, we consider the discrete Fourier transform (DFT) sub-matrix as part of the sensing matrix which is common used in communication systems. Then we consider using the proposed approach to the estimation and mitigation of impulsive noise in orthogonal frequency division multiplexing (OFDM) systems utilizing null tones. Numerical results show that the performance of the proposed method is close to sparse Bayesian learning (SBL) for low spark DFT matrices and about 1dB performance gain in symbol error rate (SER) is observed over existing GAMP based approaches for Gaussian mixture interferences and more than 5dB gain at symbol error rate (SER) of 0.01 for stable-alpha-symmetric interference. The complexity is only O(Nlog2N), where N is the size of the signal to be estimated.

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

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.

Impulse noise is a potential impairment of very-high speed digital subscriber line (VDSL) services. VDSL systems are protected from impulse noise using a combination of Reed-Solomon coding and interleaving. Since there are two competing proposals for VDSL, the first one based on the use of QAM line code and the second one using DMT modulation, it is interesting to compare their performance in terms of immunity to impulse noise. The paper presents a comparison of the behavior of QAM-VDSL and DMT-VDSL in the presence of impulse noise in real configurations. The required interleaving delay to correct all the generated errors for both systems is investigated. It is shown that when no notches are used in the radio-amateur bands, QAM and DMT systems require similar delays in order to achieve the same level of protection against impulse noise. However, when notches are implemented, DMT-VDSL achieves higher rates than QAM-VDSL. Therefore, larger error-correcting code redundancy can be used, which results in lower end-to-end delays for DMT-VDSL systems.

In this paper, an algorithm that estimates the parameters of impulse noise (IN) is proposed in power line communication. The Peak to Average Power Ratio (PAPR) of the Orthogonal Frequency Division Multiplexing (OFDM) symbol sent by the transmitter is reduced by the selective mapping (SLM) technology. In addition, the peak value of each OFDM symbol is sent with a separate control channel. At receiver, the frequency characteristics of IN is calculated using the received peak value and the OFDM symbol. The noise used for simulation comes from actual measurement. Results from simulations show that the proposed algorithm can estimate the IN well under different IN environments, and the obtained parameters are very valuable for mitigating IN in power line communication.