1. Non-Parametric Mitigation of Periodic Impulsive Noise in Narrowband Powerline Communications
Jing Lin and Brian L. Evans
Department of Electrical and Computer Engineering
The University of Texas at Austin
Dec. 11, 2013

2. PLC for Local Utility Smart Grid Applications
Transformer
Smart meters
Data concentrator
Communication backhaul
MV (1kV – 72.5kV))
Narrowband (NB) PLC:
3 – 500 kHz band
~500 kbps using OFDM
Communication between smart meters and data concentrators
LV (<1kV)
Powerline comm has played an important role in local utility smart grid applications. For example, broadband PLC operating in the 1.8 – 250 MHz band has been used in smart homes to interconnect various smart appliances with smart meters for controlling and monitoring. On the other hand, narrowband PLC is used to provide communication between the data concentrators on the utility side and the smart meters. It delivers hundreds of kbps in the 3 – 500 kHz band using OFDM.
Broadband PLC:
1.8 – 250 MHz
200 Mbps
Home area networks

3. Periodic Impulsive Noise in NB PLC
Dominant noise component in 3 – 500 kHz band
Noise power spectral density raised by 30 – 50 dB during bursts
One of the primary challenges for NB PLC is to overcome additive powerline noise. Recent field measurements on both indoor and outdoor power lines have identified that the dominant noise component in NB PLC is periodic impulsive noise synchronous to the main powerline frequency. This type of noise is periodically varying in both time domain and frequency domain. The noise bursts occur periodically near the zero crossings of the AC cycle. During the bursts, the noise power spectral density could reach 30–50 dB higher than in the rest of the period.
Noise bursts arriving periodically – twice per AC cycle
Noise measurements collected at an outdoor LV site [Nassar12]

4. Periodic Impulsive Noise in NB PLC
Noise sources
Switching mode power supplies generate harmonic contents that cannot be perfectly removed by analog filtering
Examples: inverters, DC-DC converters
Causes severe performance degradation
Commercial PLC modems feature low power transmission
Average SNR at receiver is between -5 and 5 dB
Conventional receiver designs assuming AWGN become sub-optimal
Such noise is typically due to switching mode power supplies, such as the unipolar pulse-width-modulation (PWM) inverters. These circuits contain high speed MOSFET switches and output harmonic contents at frequencies above 20 kHz and up to several hundred kHz, which cannot be perfectly removed by analog filtering. The presence of the noise may cause severe deterioration in communication performance in NB PLC systems. Since commercial PLC modems feature low power transmission, average SNR at a NB PLC receiver is typically between -5 and 5 dB. Apart from the low SNR values, the time and frequency-selective nature of the noise deviates significantly from the AWGN, and therefore conventional communication systems designed under the assumption of AWGN could be highly sub-optimal.

5. Performance Improvement Performance Improvement
Prior Work
Transmitter methods
Receiver methods
Methods
Data Rate Reduction
RX-TX Feedback
Performance Improvement
Concatenated coding [G3]
Yes No
Moderate
Time-domain interleaving [Dweik10]
Low
Cyclic waterfilling [Nieman13]
High
Prior work on combating periodic impulsive noise in NB PLC involves efforts from both transmitter’s and receiver’s perspectives. On the transmitter side, multiple types of FEC codes can be concatenated for enhanced error correction capability. Heavy FEC coding not only decreases data rates, but also increases implementation complexity at the receiver. It was proposed to use time-domain sample-level block interleaving to lower the bit error rate by averaging the impact of impulsive noise over a large number of OFDM symbols. However, such approach itself could only achieve marginal BER improvement at higher SNRs. In a very recent paper, the author suggested using non-uniform constellation mapping across time and frequency to maximize the throughput while maintaining a low BER level. It requires feedback from the receiver to the transmitter regarding subchannel SNRs.
On the receiver side, pre-processing methods have been proposed to mitigate the effect of impulsive noise prior to decoding. Some of the methods exploit the cyclostationarity of the noise, which can be captured by the second order statistics (e.g. correlation matrix and filter coefficients [9], [10], [11]). Based on these parameters, which can be estimated by training and/or adaptive tracking, frequency-domain and time-domain filters were derived to equalize [8], [11] or predict [9], [10] the periodic impulsive noise at the receivers. Unfortunately, these algorithms entail heavy training overhead for accurate estimation of model parameters.
Methods
Training Overhead
RX Complexity
Performance Improvement
MMSE equalizer [Yoo08]
High
Moderate
Whitening filter [Lin12]
Low

6. Our Approach
Non-parametric methods to mitigate periodic impulsive noise
No assumption on statistical noise models & No training overhead
Impulsive noise estimation exploiting its sparsity in the time domain
Consider a time-domain block interleaving (TDI) OFDM system
In this paper, we aim to develop non-parametric receiver methods to mitigate the effect of periodic impulsive noise. Non-parametric means no assumptions on statistical noise models and no training overhead because there is no need for parameter estimation. We exploit the sparsity of the noise in the time domain to estimate it from its projection on the unused tones. Towards that end, we consider a time-domain block interleaving OFDM system.

7. Time-Domain Block Interleaving
After the de-interleaver at the receiver
An OFDM symbol observes a sparse noise vector in time domain
Interleaver size and burst duration determine the sparsity
Typical burst duration: 10% - 30% of a period
Interleaver size: one or more periods
spread into short impulses
Interleave
A noise burst spans multiple OFDM symbols
The purpose of adopting time-domain interleaving is to spread the noise bursts, which originally spans multiple OFDM symbols, into short impulses, so that each OFDM symbol observes a sparse noise vector in the time domain. The sparsity of the noise after the deinterleaver is determined by the interleaver size and the burst duration. In NB PLC, the noise bursts typically take 10%-30% of a period. We suggest using the interleaver size that equal to one or multiple periods of the noise to result in a sparsity level between 10%-30%.

8. Impulsive Noise Estimation
A compressed sensing problem [Caire08, Lin11]
Observe noise in null tones of received signal
Estimate time-domain noise exploiting its sparsity
- Sub-DFT matrix
- Indices of null tones
- Impulsive noise after de-interleaving
- AWGN
We can now estimate the deinterleaved noise by observing its projection on the null tones of the received signal. Basically, the null tones of the received signal is a linear transformation of the impulsive noise plus some AWGN disturbance. The transformation matrix is the sub-DFT matrix. Exploiting the sparsity structure of e, we can possibly solve a compressed sensing problem to recover e. Such approach was proposed initially by Caire, where the compressed sensing problem was solved using deterministic algorithms such as basis pursuit.

9. Sparse Bayesian Learning (SBL)
A Bayesian learning approach for compressed sensing [Tipping01]
Prior on promotes sparsity
ML estimation by expectation maximization (EM)
- Latent variables
- Hyper-parameters
MAP estimate of
Shape
Scale
In our previous work, we use sparse Bayesian learning developed by Tipping to solve the problem, since it generally has the best recovery performance. The SBL imposes a prior on e that promotes its sparsity. The prior basically says that each element of e is Gaussian distributed with an individual variance parameter, which is drawn from a Gamma hyper-prior with two parameters. To see why this prior promotes sparsity, we marginalize the prior over the hyperparameter lambda, the resulting distribution is a product of independent student t distributions. As shown in the 2-d example, the probability density concentrates at the origin, as well as along the two axis, which means with high probability, either one or two elements of e is zero. With that prior, SBL first does a maximum likelihood estimation of the hyper-parameters lambda and sigma2. Since close-form solution doesn’t exist, it uses expectation maximization by treating e as latent variables. Then we can obtain the MAP estimate of e given the observation y I and the estimated hyperparameters.

10. Exploiting More Information
SBL performance is limited by the number of measurements
Null tones occupy 40 – 50% of the transmission band in PLC standards
A heuristic exploiting information on all tones
Iteratively estimate impulsive noise and transmitted data
Disadvantage: sensitive to initial value of
IN estimator + -
Zero out null tones
Like other CS techniques, given the number of parameters to be estimated, performance of SBL is limited by the number of measurements, and in this case the number of null tones. In standardized PLC systems, null tones generally occupy 40-50% of the transmission band, which in most cases can give us satisfactory recovery performance. To further improve the performance, we need to exploit more information. This can be done in two ways. First, we can increase the number of measurements by using data tones. However, these tones not only contain noise, but also contain unknown data. A heuristic approach is therefore to iteratively estimate noise and data. Assuming that one is known when estimating the other. A disadvantage of such heuristic, as shown in the experiments, is that it is sensitive to the initial guess of the data. This can be addressed by starting from different initializations and averaging the estimates, which however introduces further complexities.

11. Exploiting More Information (cont.)
Decision feedback estimation
Use to update hyperparameters
In this paper, we extend our prior work to a third algorithm that uses decision feedback from the decoder output to improve the quality of noise estimation. Using the decoder output, we can generate an estimate of the data symbol. Subtracting it from the received signal, we can obtain a second estimate of the noise. If you could recall, in the prior that we impose on e, there are two hyper-parameters, namely a and b, that are used to incorporate any prior knowledge on the noise. Given the an estimate of e, the distribution of lambda, or more specifically a and b, can be updated accordingly. Before the first iteration, we set a and b to be 0, which gives a non-informative prior. Then we update a and b during the iterations. By incorporating the side information via the decision feedback, we can significantly speed up the convergence and get a more accurate estimate of the noise,

12. Forward Error Correction Code
Simulation Settings
Baseband complex OFDM system
Periodic impulsive noise synthesized using a linear periodically time varying model in the IEEE P standard [Nassar12]
Parameters
Values
FFT Size
128
Modulation
QPSK
# of tones
Data tones
# 33 - # 104
Interleaver size
~ 2 periods of noise
Forward Error Correction Code
Rate-1/2 Convolutional

13. Coded Bit Error Rate (BER) Performance
Burst duration = 10%
Burst duration = 30%

14. Conclusion
Non-parametric receiver methods to mitigate periodic impulsive noise in NB PLC
Do not assume statistical noise models, and do not need training
Work in time-domain block interleaving OFDM systems
Exploit the sparsity of the noise in the time domain
Estimate the noise samples from various subcarriers of the received signal and from decision feedback
Future work
Complexity reduction
Joint transmitter and receiver optimization

15. Reference
[Nassar12] M. Nassar, A. Dabak, I. H. Kim, T. Pande, and B. L. Evans, “Cyclostationary Noise Modeling In Narrowband Powerline Communication For Smart Grid Applications,” Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Proc, 2012.
[Dweik10] A. Al-Dweik, A. Hazmi, B. Sharif, and C. Tsimenidis, “Efficient interleaving technique for OFDM system over impulsive noise channels,” in Proc. IEEE Int. Symp. Pers. Indoor and Mobile Radio Comm., 2010.
[Nieman13] K. F. Nieman, J. Lin, M. Nassar, K. Waheed, and B. L. Evans, “Cyclic spectral analysis of power line noise in the khz band,” in Proc. IEEE Int. Symp. Power Line Commun. and Appl., 2013.
[Yoo08] Y. Yoo and J. Cho, “Asymptotic analysis of CP-SC-FDE and UW-SC-FDE in additive cyclostationary noise,” Proc. IEEE Int. Conf. Commun., pp. 1410–1414, 2008.
[Lin12] J. Lin and B. Evans, “Cyclostationary noise mitigation in narrowband powerline communications,” Proc. APSIPA Annual Summit Conf., 2012.
[Caire08] G.Caire, T. Al-Naffouri, and A. Narayanan, “Impulse noise cancellation in OFDM: an application of compressed sensing,” in Proc. IEEE Int. Symp. Inf. Theory, 2008, pp. 1293–1297.
[Lin11] J. Lin, M. Nassar, and B. L. Evans, “Non-parametric impulsive noise mitigation in OFDM systems using sparse Bayesian learning,” Proc. IEEE Global Comm. Conf., 2011.
[Tipping01] M. Tipping, “Sparse Bayesian learning and the relevance vector machine,” J. Mach. Learn. Res., vol. 1, pp. 211–244, 2001.

16. Thank you

17. Local Utility Powerline Communications
Category
Band
Bit Rate (bps)
Coverage
Applications
Standards
Ultra Narrowband (UNB)
0.3-3 kHz
~100
>150 km
Last mile comm.
TWACS
Narrowband (NB)
3-500 kHz
~500k
Multi-kilometer
PRIME, G3
ITU-T G.hnem
IEEE P1901.2
Broadband (BB)
MHz
~200M
<1500 m
Home area networks
HomePlug
ITU-T G.hn
IEEE P1901

18. Sparse Bayesian Learning (SBL)
A Bayesian learning approach for compressed sensing [Tipping01]
Prior on promotes sparsity
ML estimation by expectation maximization (EM)
- Latent variables
- Hyper-parameters
MAP estimate of
Degrees of freedom
Scale
Shape
Scale
We use sparse Bayesian learning algorithm developed by Tipping to solve the compressed sensing problem, since it generally has the best recovery performance. The SBL imposes a prior on e that promotes its sparsity. The prior basically says that each element of e is Gaussian distributed with an individual variance parameter, which is drawn from a Gamma hyper-prior with two parameters. To see why this prior promotes sparsity, we marginalize the prior over the hyperparameter lambda, the resulting distribution is a product of independent student t distributions. As shown in the 2-d example, the probability density concentrates at the origin, as well as along the two axis, which means with high probability, either one or two elements of e is zero. With that prior, SBL first does a maximum likelihood estimation of the hyper-parameters lambda and sigma2. Since close-form solution doesn’t exist, it uses expectation maximization by treating e as latent variables. Then we can obtain the MAP estimate of e given the observation y I and the estimated hyperparameters.