PaperlayerView exact revision on arXiv

Source-linked AI summary

Impulsive Noise Mitigation in Powerline Communications Using Sparse Bayesian Learning

Jing Lin, Marcel Nassar, Brian L. Evans

arXiv:1303.1217v1stat.MLcs.IT

TL;DR

Additive non-Gaussian impulsive noise impairs OFDM PLC systems, motivating denoising methods that avoid noise-model assumptions and extra training. The paper applies sparse Bayesian learning and reports substantial SNR gains over conventional OFDM receivers.

  • Problem

    Additive non-Gaussian noise is a major impairment in PLC systems, including asynchronous and cyclostationary impulsive noise in OFDM PLC.

  • Method

    The paper proposes three OFDM PLC denoising algorithms based on sparse Bayesian learning that are non-parametric and do not require extra training or prior statistical noise-model knowledge.

  • Results

    Up to 10 dB SNR gain over conventional OFDM receivers is achieved in coded systems under asynchronous impulsive noise, with an extra 2 dB from convolutional decoding.

  • Takeaways & Limitations

    The proposed methods improve OFDM PLC communication performance under asynchronous and cyclostationary impulsive noise without requiring prior statistical noise-model parameters.

Abstract

from arXiv · show

Additive asynchronous and cyclostationary impulsive noise limits communication performance in OFDM powerline communication (PLC) systems. Conventional OFDM receivers assume additive white Gaussian noise and hence experience degradation in communication performance in impulsive noise. Alternate designs assume a parametric statistical model of impulsive noise and use the model parameters in mitigating impulsive noise. These receivers require overhead in training and parameter estimation, and degrade due to model and parameter mismatch, especially in highly dynamic environments. In this paper, we model impulsive noise as a sparse vector in the time domain without any other assumptions, and apply sparse Bayesian learning methods for estimation and mitigation without training. We propose three iterative algorithms with different complexity vs. performance trade-offs: (1) we utilize the noise projection onto null and pilot tones to estimate and subtract the noise impulses; (2) we add the information in the data tones to perform joint noise estimation and OFDM detection; (3) we embed our algorithm into a decision feedback structure to further enhance the performance of coded systems. When compared to conventional OFDM PLC receivers, the proposed receivers achieve SNR gains of up to 9 dB in coded and 10 dB in uncoded systems in the presence of impulsive noise.

I. INTRODUCTION

OFDM PLC systems are impaired by asynchronous and cyclostationary impulsive noise, while model-based mitigation can be inflexible. The paper proposes three non-parametric SBL denoising algorithms that estimate sparse time-domain noise without extra training.

  • Motivation: Impulsive powerline noise includes short, high-power bursts that may occur periodically or randomly.These correspond to cyclostationary and asynchronous impulsive noise, respectively.
  • Motivation: 50 dB-above-background noise bursts reduce SNR across frequency bands and time durations, limiting overall channel capacity.
  • Prior approaches: Statistical noise models can improve reliability and throughput but are inflexible and require significant design effort in specific noise scenarios.
  • Proposed approach: The paper targets both asynchronous and cyclostationary impulsive noise with three denoising algorithms based on sparse Bayesian learning.
  • Proposed approach: The algorithms estimate sparse time-domain noise from nulls and pilots or jointly decode across all tones without noise-model assumptions or extra training.For bursts spanning multiple OFDM symbols, time-domain interleaving and deinterleaving spread them into shorter sparse bursts.
  • Proposed approach: A decision-feedback structure and a low-complexity implementation are included among the proposed receiver designs and analyses.

II. STATISTICAL MODELING OF IMPULSIVE NOISE IN PLC

PLC noise deviates from Gaussian behavior because power-electronic devices inject random or periodic emissions into power lines. The paper distinguishes asynchronous and cyclostationary impulsive noise and reviews statistical models used to represent them.

  • Noise characteristics: Power-electronic switching devices inject emissions that produce impulsive noise deviating from the Gaussian model.
  • Noise types: PLC impulsive noise is classified as asynchronous or cyclostationary according to its operating-frequency behavior.
  • Asynchronous noise: Asynchronous impulsive noise arises from random emission events at residential and industrial sites, including appliance switching and uncoordinated PLC transmissions.
  • Asynchronous noise: Asynchronous impulsive noise is dominant from several hundred kHz to 20 MHz and has been fitted using Gaussian mixture, Middleton Class A, and SαS models.
  • Asynchronous noise: Statistical-physical asynchronous-noise models have also been derived from PLC network topologies and temporal Poisson point processes.

1) Gaussian Mixture Model:

Impulsive-noise mitigation in PLC has used parametric and non-parametric approaches, with sparse Bayesian learning proposed to improve recovery without assuming a particular noise model. The section contrasts model-based limitations with a sparse time-domain formulation applicable across impulsive-noise scenarios.

  • Gaussian Mixture Model: Gaussian mixture models represent impulsive-noise probability densities as weighted sums of zero-mean Gaussian components.Each component is characterized by variance γk and mixing probability πk.
  • Parametric methods: Parametric receivers exploit noise-model information but require training and can degrade under model or parameter mismatch.The mismatch concern is especially relevant when impulsive-noise statistics vary over time.
  • Non-parametric methods: Non-parametric methods avoid additional training and parameter estimation by not assuming a particular noise model.This design is described as more robust to changing environments and model mismatch.
  • Prior sparse recovery: Compressed-sensing recovery from null tones is constrained by a threshold determined by DFT size and the number of null tones.For common OFDM settings, the threshold can be too restrictive when symbols contain multiple impulses.
  • Proposed approach: The proposed work extends compressed sensing to sparse Bayesian learning for non-parametric asynchronous-noise mitigation applicable to all impulsive-noise scenarios.The approach targets improved performance while exploiting time-domain sparsity.

B. Cyclostationary Impulsive Noise Mitigation

Cyclostationary PLC noise has periodically varying statistics and can include long, high-power bursts, motivating mitigation across multiple OFDM symbols. Non-parametric asynchronous-noise techniques are presented as applicable to cyclostationary noise as well.

  • Noise characteristics: Cyclostationary noise has periodically varying statistics, with harmonic peaks that can support detection and extraction.The period is stated to equal half the AC mains cycle.
  • Model-based methods: Accurate cyclic-spectrum estimation generally requires substantial data, potentially limiting real-time communications applications.This constrains approaches that rely on estimated cyclic statistics.
  • Filter-based mitigation: Filter-based cyclostationary-noise algorithms can suffer over-fitting when asynchronous impulsive noise is also present.Improving robustness against such outliers generally requires longer training sequences.
  • Multi-symbol mitigation: Mitigation spanning multiple OFDM symbols is desirable because uncontaminated symbols may provide information for recovering contaminated symbols.Time-domain block interleaving spreads long bursts across multiple OFDM symbols before deinterleaving.
  • Cross-scenario applicability: Non-parametric techniques developed for asynchronous impulsive noise can also mitigate cyclostationary noise.The connection follows from the presence of sparse time-domain noise vectors after the relevant transceiver processing.

IV. SYSTEM MODEL

The system models conventional and time-domain interleaved OFDM receivers, where interleaving spreads bursty impulsive noise so it appears sparse after deinterleaving. Impulsive-noise recovery is therefore posed as sparse estimation from non-data tones.

  • Conventional OFDM: A coded OFDM transmitter encodes binary data, maps the codeword to OFDM symbols, and uses N−M data subcarriers plus M non-data subcarriers.Non-data subcarriers can be null tones for spectral shaping or pilots for channel estimation and synchronization.
  • Conventional OFDM: Each OFDM symbol is converted by IDFT, protected with a cyclic prefix, then recovered by cyclic-prefix removal and frequency-domain equalization.The cyclic prefix is assumed longer than the channel delay spread to prevent inter-symbol interference.
  • Conventional OFDM: In the conventional model, the received signal contains the channel-processed OFDM symbol, impulsive noise e, and AWGN n.The channel convolution matrix is circulant because of cyclic-prefix insertion, and the DFT of AWGN remains AWGN because the DFT is unitary.
  • Time-Domain Interleaving: Time-domain block interleaving spreads long noise bursts across multiple OFDM symbols, making the deinterleaved impulsive noise e′ sparse under a sufficiently large interleaver.The equalized signal is deinterleaved before DFT, while the resulting Gaussian noise is approximated as AWGN.
  • Sparse Recovery Formulation: Estimating the length-N impulsive-noise vector from null and pilot tones forms a noisy underdetermined M×N linear system.The problem is generally ill-conditioned, but sparsity enables compressed-sensing-based recovery and subsequent subtraction from data tones.
  • Sparse Recovery Formulation: The estimated impulsive noise is subtracted from received data tones, after which conventional detection and decoding proceed assuming the estimate is accurate.This forms a new decision metric for the data tones.

V. NON-PARAMETRIC IMPULSIVE NOISE ESTIMATION

The paper formulates impulsive-noise estimation as an underdetermined sparse regression problem and selects sparse Bayesian learning to obtain non-parametric estimators. It proposes three algorithms with different complexity–performance trade-offs.

  • Problem Formulation: Impulsive-noise estimation is posed as solving an underdetermined linear regression problem under sparsity constraints.The sparse vector represents impulsive noise in the time domain.
  • Sparse Bayesian Learning: Sparse Bayesian learning is applied because it generally achieves strong sparse-recovery performance.The paper uses SBL to avoid imposing a parametric impulsive-noise model.
  • Sparse Bayesian Learning: Three non-parametric impulsive-noise estimation algorithms are proposed with different complexity versus performance trade-offs.The algorithms are developed after introducing the SBL framework.

A. Sparse Bayesian Learning

The SBL framework places a parameterized Gaussian prior on the sparse noise vector and estimates its hyperparameters iteratively. The resulting MAP estimate is used to mitigate impulsive noise, with all-tone estimation improving as non-data tones increase but reducing throughput.

  • SBL Framework: SBL models the sparse weight vector with a parameterized Gaussian prior whose diagonal variances are the hyperparameters γ.The observation likelihood is combined with maximum-likelihood estimation of γ and σ².
  • SBL Framework: The maximum-likelihood hyperparameters are computed iteratively using expectation maximization, yielding a posterior distribution for the impulsive noise.The MAP estimate is the posterior mean, and sparsity drives most components toward zero.
  • Null and Pilot Tones: SBL can estimate impulsive noise from null and pilot tones by substituting the corresponding observation, sensing matrix, sparse vector, and Gaussian-noise variables into the generic model.After EM convergence, the MAP estimate is transformed to the frequency domain and subtracted from data tones.
  • Null and Pilot Tones: Performance of the null-and-pilot-tone estimator improves as the number of non-data tones increases.More non-data tones provide more information for estimation.
  • All Tones: Fewer data tones reduce throughput, creating a trade-off between impulsive-noise estimation quality and transmission rate.When non-data tones are limited, the paper motivates exploiting information from all tones.
  • All Tones: The all-tone estimator treats the unknown transmitted data-tone signal as an additional hyperparameter and temporarily relaxes its constellation values to be continuous.Its EM updates involve γ, σ², and the data-tone signal.

D. Decision Feedback Estimation

The decision-feedback estimator incorporates prior information on the noise precision and uses decoder-derived data estimates to refine impulsive-noise estimation. Coding redundancy is transferred back to the estimator through an iterative feedback structure.

  • Prior Information: The decision-feedback approach augments the Gaussian prior on impulsive noise with a conjugate Gamma prior on the precision hyperparameters.Setting all prior parameters to zero recovers the uninformative prior used in the earlier SBL framework.
  • Prior Information: Non-zero prior parameters integrate additional information into the likelihood and affect the maximum-likelihood estimates of γ.The paper explicitly compares the resulting update with the earlier SBL update.
  • Decision Feedback: A second impulsive-noise estimate can be fused with the non-data-tone MAP estimate by updating the prior parameters before re-estimating the precision hyperparameters.The second estimate is denoted ẽ and is incorporated through the posterior distribution of p.
  • Decision Feedback: In coded OFDM, decoder decisions recover estimated data tones that are transformed through the channel and subtracted from the received signal to generate ẽ.This uses coding redundancy as side information for noise estimation.
  • Decision Feedback: The resulting decision-feedback estimator exchanges information between non-data-tone noise estimation and data-tone decoding.The structure is expected to outperform the all-tone estimator by exploiting redundant coding information on data tones.

VI. LOW-COMPLEXITY IMPLEMENTATION

The low-complexity implementation accelerates SBL by sequentially managing model bases and exploiting known background-noise power. This reduces computational cost relative to using all tones.

  • Computational bottleneck: The core SBL algorithm requires an M × M matrix inversion, where M is the number of null and pilot tones.This inversion contributes substantially to implementation cost.
  • Sequential SBL: Sequential SBL adds, removes, or updates candidate basis functions until convergence, with retained bases identifying impulse locations.The basis support represents the nonzero entries of the sparse impulsive-noise vector.
  • Performance preservation: The accelerated SBL algorithm preserves reconstruction performance while sequentially adding and deleting candidate bases.The implementation is described at a high level, with mathematical details referred to prior work.
  • Complexity reduction: Known background-noise power enables efficient calculations without matrix inversion operations.This information can simplify steps 9, 11, and 13 of the sequential algorithm.
  • Complexity comparison: Using all tones increases complexity from O(N^2M) to O(N^3) per iteration, with N denoting the DFT size.The all-tone estimator is therefore more computationally demanding than the non-data-tone estimator.
  • Sequential complexity: Sequential SBL has per-iteration matrix multiplication and inversion complexities of O(N^2K) and O(K^3), respectively.K is the number of model bases in the current iteration.

VII. SIMULATION RESULTS

Simulations evaluate the proposed estimators under asynchronous and cyclostationary impulsive-noise models in coded and uncoded OFDM PLC systems. The proposed methods generally provide substantial SNR gains over conventional and parametric baselines, with gains depending on estimator and noise setting.

  • Uncoded asynchronous noise: 6–8 dB SNR gain is achieved by the null-tone estimator over conventional OFDM receivers in uncoded asynchronous impulsive noise.Using all tones adds 1–2 dB in a relatively wide SNR region, with marginal low-SNR loss.
  • Baseline comparison: The proposed estimators outperform the MMSE estimator without noise-state information in moderate and high SNR regimes.The parametric MMSE baselines assume perfect knowledge of the Gaussian-mixture model, and one assumes perfect per-time noise variance.
  • Cyclostationary noise: Around 5 dB SNR gain is achieved by the coded null-tone estimator in cyclostationary impulsive noise.All-tone estimation adds 2–4 dB, and decision feedback adds an extra 4 dB over the all-tone estimator.
  • Baseline comparison: The compressed-sensing-plus-least-squares algorithm performs worse than the proposed estimators in both asynchronous noise scenarios.The cited explanation is that compressed sensing recovers impulsive noise only at high sparsity, typically fewer than five impulses per OFDM symbol.

VIII. CONCLUSION

The paper proposes three non-parametric SBL-based methods for mitigating asynchronous and cyclostationary impulsive noise in OFDM PLC systems. The methods use null, pilot, or all subcarriers, and apply time-domain interleaving for long cyclostationary bursts.

  • Conclusion: The paper proposes three methods to improve OFDM PLC communication performance under asynchronous and cyclostationary impulsive noise.The methods target both noise settings evaluated in the paper.
  • Asynchronous-noise mitigation: SBL estimates asynchronous impulsive noise using information from null and pilot subcarriers or from all subcarriers.These alternatives support different complexity and information-use trade-offs.
  • Cyclostationary-noise mitigation: Time-domain interleaving breaks long cyclostationary noise bursts spanning multiple OFDM symbols into shorter bursts before SBL processing.The interleaved transceiver structure is used specifically for cyclostationary noise.
  • Non-parametric design: All proposed methods are non-parametric and require neither prior statistical noise-model knowledge nor model parameters.The algorithms are validated using Gaussian-mixture and Middleton Class A impulsive-noise models.
Loading 1303.1217v1…