Powerline Communications for Smart Grid

Report
Semiconductor Research Corporation Presentation
Texas Analog Center of Excellence, The University of Texas at Dallas
Smart Grid Communications
Prof. Brian L. Evans
Dept. of Electrical & Computer Engineering
Wireless Networking & Communications Group
The University of Texas at Austin
14 December 2012
In collaboration with UT Austin PhD students Ms. Jing Lin, Mr. Yousof Mortazavi,
Mr. Marcel Nassar and Mr. Karl Nieman; Freescale engineers Mr. Mike Dow and
Dr. Khurram Waheed; and TI engineers Dr. Anand Dabak and Dr. Il Han Kim
http://users.ece.utexas.edu/~bevans/projects/plc/index.html
ISTOCKPHOTO.COM/© SIGAL SUHLER MORAN
Outline
• Research group
• Smart power grids
• Powerline noise
Cyclostationary
Gaussian mixture
• Testbeds
• Conclusion
IEEE Signal Processing Magazine
Special Issue on Signal Processing Techniques
for the Smart Grid, September 2012.
1
Embedded Signal Processing Laboratory
• Present: 9 PhD, 0 MS, 5 BS
• Alumni: 20 PhD, 9 MS, 140 BS
• Communication systems
Hugo
Powerline communication systems (design tradeoffs)
Wi-Fi (interference modeling & mitigation for ISM bands)
Cloud Radio Access Networks (LTE basestation coordination)
Mixed-signal IC design (mostly digital ADCs and synthesizers)
Marcus
Jing
Chao
Debarati
Yousof
Marcel
Karl
Kyle
• Video processing (rolling shutter artifact reduction)
• Electronic design automation (EDA) tools/methods
• Part of Wireless Networking & Communications Group
160 grad students, 20 faculty members, 13 affiliate companies
2
Research Group – Completed Projects
20 PhD and 9 MS alumni
System
SW release
Prototype
Companies
Matlab
DSP/C
Freescale, TI
MIMO testbed
LabVIEW
LabVIEW/PXI
Oil&Gas
resource allocation
LabVIEW
DSP/C
Freescale, TI
Underwater space-time proc.;
comm.
MIMO testbed
Matlab
Lake Travis
testbed
Navy
Camera
image acquisition
Matlab
DSP/C
Intel, Ricoh
Display
image halftoning
Matlab
C
HP, Xerox
video halftoning
Matlab
fixed point conv.
Matlab
FPGA
Intel, NI
distributed comp.
Linux/C++
Navy sonar
Navy, NI
ADSL
Wimax/LTE
EDA tools
Contribution
equalization
DSP Digital Signal Processor
MIMO Multi-Input Multi-Output
LTE
PXI
Qualcomm
Long-Term Evolution (cellular)
PCI Extensions for Instrumentation
3
Research Group – Current Projects
9 PhD students
System
Contributions
Powerline
comm.
noise reduction;
MIMO testbed
Wi-Fi
interference
reduction
SW release
Prototype
Companies
LabVIEW
LabVIEW /
PXI chassis
Freescale,
IBM, TI
Matlab
FPGA
Intel, NI
time-based ADC
Cellular
cloud radio access
network architecture
Handheld
camera
reducing rolling
shutter artifacts
EDA tools
reliability patterns
MIMO Multi-Input Multi-Output
IBM 45nm
Huawei
Matlab
Android
TI
NI
PXI
PCI Extensions for Instrumentation
4
ISTOCKPHOTO.COM/© SIGAL SUHLER MORAN
Outline
• Research group
• Smart power grids
• Powerline noise
Cyclostationary
Gaussian mixture
• Testbeds
• Conclusion
IEEE Signal Processing Magazine
Special Issue on Signal Processing Techniques
for the Smart Grid, September 2012.
5
Today’s Power Grids in USA
• 7 large-scale power grids each managed by a regional utility company
700 GW generation capacity in total for long-haul high-voltage power transmission
Synchronized independently, and exchange power via DC transfer
• 130+ medium-scale power grids each managed by a local utility
Local power distribution to residential, commercial and industrial customers
• Heavy penalties in US for blackouts (2003 legislation)
Utilities generate expected energy demand plus 12%
Energy demand correlated with time of day
Effect of plug-in electric vehicles (EVs) on energy demand uncertain
Generation cost 30x higher during peak times vs. normal load
• Traditional ways to increase capacity to meet peak demand increase
Build new large-scale power generation plant at cost of $1-10B if permit issued
Build new transmission line at $0.6M/km which will take 5-10 years to complete
Source: Jerry Melcher, IEEE Smart Grid Short Course, 22 Oct. 2011, Austin TX USA
6
Smart Grid Goals
• Accommodate all generation types
Renewable energy sources
Energy storage options
• Improve asset utilization and operating efficiencies
Scale voltage with energy demand
Reduce peak demand
Analyze customer load profiles and system load snapshots
• Improve system reliability
Power quality monitoring
Remote disconnect/reconnect
Outage/restoration event notification
Enabled by
smart meter
communications
• Enable informed customer participation
Source: Jerry Melcher, IEEE Smart Grid Short Course, 22 Oct. 2011, Austin TX USA
7
Smart Grid
Wind farm
HV-MV Transformer
Central power plant
Grid status monitoring
Utility control center
Smart meters
Integrating distributed
energy resources
Houses
Offices
Device-specific billing
Automated control for
smart appliances
Medium Voltage (MV)
1 kV – 33 kV
Industrial plant
High Voltage (HV)
33 kV – 765 kV
8
Smart Grid Communications
Local utility
Communication backhaul
carries traffic between
concentrator and utility
on wired or wireless links
Data concentrator
MV-LV transformer
Smart meter communications
between smart meters
and data concentrator via
powerline or wireless links
Smart meters
Home area data networks
connect appliances, EV charger and smart
meter via powerline or wireless links
Low voltage (LV)
under 1 kV
9
Powerline Communications (PLC)
Categories
Band
Bit Rates
Coverage
Narrowband
3-500
kHz
~500 kbps
• (ITU) PRIME, G3
MultiSmart meter
• ITU-T G.hnem
kilometer communication
• IEEE P1901.2
Broadband
1.8-250
MHz
~200
Mbps
<1500 m
Enables
Standards
• HomePlug
Home area
• ITU-T G.hn
data networks
• IEEE P1901
• Use orthogonal frequency division multiplexing (OFDM)
• Communication challenges
o Channel distortion
o Non-Gaussian noise
10
Comparison Between Wireless and PLC Systems
Wireless Communications
Narrowband PLC (3-500 kHz)
Time-selective fading and
Doppler shift (cellular)
Periodic with period of half AC main freq.
plus lognormal time-selective fading
Power loss vs.
distance d
d –n/2 where n is
propagation constant
e – a(f) d plus additional attenuation when
passing through transformers
Propagation
Dynamically changing
Determinism from fixed grid topology
Synchronization
Varies
AC main power frequency
Additive noise/
interference
Assumed stationary
and Gaussian
Gaussian plus non-Gaussian noise
dominated by cyclostationary component
Time selectivity
Asynchronous
interference
MIMO
Uncoordinated users in
Due to power electronics and
Wi-Fi bands;
uncoordinated users using other standards
Frequency reuse in cellular
Standardized for
Wi-Fi and cellular
Number of wires minus 1;
G.9964 standard for broadband PLC
11
ISTOCKPHOTO.COM/© SIGAL SUHLER MORAN
Outline
• Research group
• Smart power grids
• Powerline noise
Cyclostationary
Gaussian mixture
• Testbeds
• Conclusion
IEEE Signal Processing Magazine
Special Issue on Signal Processing Techniques
for the Smart Grid, September 2012.
12
Types of Powerline Noise
Background Noise
Cyclostationary Noise
Impulsive Noise
-50
-100
-150
0
100
200
300
Frequency (kHz)
400
time
500
Spectrally shaped noise
with 1/f spectral decay
Period is synchronous
to half of the AC cycle
Random impulsive bursts
Superposition of low
intensity noise sources
Switching power supplies
and rectifiers
Circuit transient noise and
uncoordinated interference
Present in all PLC
Dominant in
Narrowband PLC
Dominant in
Broadband PLC
13
Cyclostationary Noise in Narrowband PLC
Medium Voltage Site
Low Voltage Site
Field measurements collected jointly with Aclara and
Texas Instruments near St. Louis, MO USA
14
Cyclostationary Noise Modeling
• Linear periodically time-varying system model
H1
v R
H2
N
n R
N
…
HM
Hi - Linear time invariant filter
N - Period in samples
o Period (half of the AC cycle) is partitioned into M segments
o Noise within each segment is stationary, i.e. modeled by an LTI system
Segment: 1
23
15
Cyclostationary Noise Model Fitting
• M = 3 segments captures temporal-spectral cyclostationarity
Measurement data
Noise synthesized from model
Proposed TI-Aclara-UT model adopted in IEEE P1901.2 narrowband PLC standard
16
Asynchronous Noise Modeling
Wireless
Emissions
Uncoordinated
Meters
(coexistence)
Total interference at receiver:
Interference
from source i
17
Asynchronous Noise Modeling
• Aggregate interference from multiple sources
Dominant interference source
Impulse rate l
Impulse duration m
Ex. Rural areas,
industrial areas with
heavy machinery
Middleton
class A
Ex. Semi-urban
areas, apartment
complexes
Middleton
class A
Ex. Dense urban
and commercial
settings
Gaussian
mixture
model
Homogeneous network
li = l, mi = m, g(di) = g
General (heterogeneous) network
li, mi, g(di) = gi
18
Asynchronous Noise Model Fitting
Homogeneous PLC Network
General PLC Network
Tail probabilities (which direct relate to communication performance)
Middleton Class A is special case of Gaussian mixture model (GMM)
19
ISTOCKPHOTO.COM/© SIGAL SUHLER MORAN
Outline
• Research group
• Smart power grids
• Powerline noise
Cyclostationary
Gaussian mixture
• Testbeds
• Conclusion
IEEE Signal Processing Magazine
Special Issue on Signal Processing Techniques
for the Smart Grid, September 2012.
20
Our PLC Testbeds
• Quantify application performance vs. complexity tradeoffs
Provide suite of user-configurable algorithms and system settings
Display statistics of communication performance
• 1x1 PLC testbeds (completed)
TI PRIME modems (testbed #1) and Freescale G3 modems (testbed #2)
Adaptive signal processing algorithms for bit loading and interference mitigation
Goal: Improve communication performance 2-3x on indoor power lines
• 2x2 PLC testbed (on-going)
Use one phase, neutral and ground for 2 x 2 differential signaling
Extend our 2 x 2 real-time DSL testbed (deployed in field by oil & gas company)
Adaptive signal processing algorithms for crosstalk cancellation
Goal: Improve communication performance by another 2x on indoor power lines
21
1 x1 PLC Testbed #1
Hardware
Software
• National Instruments (NI) controllers stream • NI LabVIEW Real-Time system runs
data
transceiver algorithms
• NI cards generates/receives analog signals
• Desktop PC running LabVIEW is used
• Texas Instruments (TI) analog front end
as an input and visualization tool to
couples to power line
display important system parameters.
1x1 Testbed
22
OFDM Systems in Impulsive Noise
• FFT spreads impulsive energy over all tones
SNR in each tone is decreased which increases symbol error rate
• Many narrowband PLC systems operate over -5 dB to 5 dB in SNR
Data subchannels/tones carry same number of bits (1-4) in current standards
3 dB SNR gain could increase one bit/subchannel for same symbol error rate
23
Parametric vs. Nonparametric Noise Mitigation
Parametric
Nonparametric
Must build a statistical
model of the noise
Yes
No
Requires training data to
compute model parameters
Yes
No
Degrades in performance
due to model mismatch
Yes
No
Has high complexity when
receiving message data
No
Yes
24
Proposed Non-Parametric Methods
• Exploit sparsity of impulsive noise in time domain
time
Build statistical model each OFDM symbol using sparse Bayesian learning (SBL)
At receiver, null tones contain only additive noise (Gaussian + impulsive)
• SNR gain vs. conventional OFDM systems at symbol error rate 10-4
Complex OFDM, 128-point FFT, QPSK, data tones 33-104, rate ½ conv. code
Gaussian mixture model w/ 3 terms; Middleton Class A with A = 0.1 and  = 0.01
6 dB SNR gain could mean +2 bits/tone
System
Uncoded
Coded
Noise
SBL w/
null tones
SBL w/
all tones
SBL w/ decision
feedback
GMM
8 dB
10 dB
-
MCA
6 dB
7 dB
-
GMM
2 dB
7 dB
9 dB
MCA
1.75 dB
6.75 dB
8.75 dB
25
Communication Performance w/o Error Correction
Gaussian mixture
model noise
Non-parametric
methods in blue
Parametric
methods in red
Proposed
NSI
CS+LS: [Caire08]
MMSE: [Haring02]
SBL: [Lin11]
26
Communication Performance w/ Error Correction
Proposed
NSI
NSI
Non-parametric methods in blue
Parametric methods in red
Gaussian mixture model noise
27
Exploiting Sparsity in Time Domain Reprise
• Time-domain block interleaved OFDM (TDI-OFDM
Bursts span consecutive OFDM symbols
Coded performance in cyclostationary noise
Interleave
Bursts spread over many OFDM symbols
Complex OFDM, 128-point FFT, QPSK,
data tones 33-104, rate ½ conv. code
28
FPGA Test System for G3 PLC Algorithms
NI PXIe-7965R
(Virtex 5)
NI PXIe-1082
Real-time host
tone map:
data
tone 0
f (kHz) 0
23
58
127
35.94
90.63
199.2
FPGA Timing/Resource Utilization
Parametric Approximate Message Passing (AMP) mitigation method
Base logic clock = 40 MHz, most data streams 16 bits wide
Execution time: 5 iterations × 4776 cycles/iteration = 23880 cycles
without AMP
with AMP
Supports streaming operation at
400 kS/s (G3 sample rate)
• Can recover up to 8 dB SNR in
impulsive noise environments
• 100x reduction in average bit
error rate using QPSK and 40 dB
impulses with 3% probability
• Preliminary resource utilization:
•
•
•
•
Possible to exploit
more parallelism for
higher throughput
(steps 1-4 of AMP)
Conclusion
• PLC systems are interference limited
• Statistical models for interference
Cyclostationary models synchronous with zero crossings of AC cycle
Gaussian mixture model for asynchronous noise
• Interference mitigation
Non-parametric sparse Bayesian learning algorithms do not map well to FPGAs
Parametric distributed approximate message algorithms map well to FPGAs
• Testbeds
• Project Web site:
http://users.ece.utexas.edu/~bevans/projects/plc/index.html
31
References
•
•
•
•
•
•
•
•
•
[Caire08] G. Caire, T.Y. Al-Naffouri, and A.K. Narayanan. Impulse noise cancellation in OFDM: an
application of compressed sensing. Proc. IEEE Int. Symp. Information Theory, pages 1293–1297, 2008.
[Cho04] J. H. Cho. Joint transmitter and receiver optimization in additive cyclostationary noise. IEEE
Trans. on Information Theory, 50(12), 2004.
[Garcia07] R. Garcia, L. Diez, J.A. Cortes, and F.J. Canete. Mitigation of cyclic short-time noise in indoor
power-line channels. Proc. IEEE Int. Symp. Power Line Comm. and Its Applications, pp. 396–400, 2007.
[Haring02] J. Haring. Error Tolerant Communication over the Compound Channel. Aachen, 2002.
[Haring03] J. Haring and A. J. H. Vinck. Iterative decoding of codes over complex numbers for impulsive
noise channels. IEEE Trans. on Information Theory, 49(5):1251–1260, 2003.
[Lampe11] L. Lampe. Bursty impulse noise detection by compressed sensing. Proc. IEEE Int. Symp.
Power Line Commun. and Appl., pages 29–34, 2011
[Liano11] A. Liano, A. Sendin, A. Arzuaga, and S. Santos. Quasi-synchronous noise interference cancellation techniques applied in low voltage PLC. Proc. IEEE Int. Symp. Power Line Comm. and Its
Applications, 2011.
[Lin11] J. Lin, M. Nassar, and B. L. Evans, “Non-Parametric Impulsive Noise Mitigation in OFDM
Systems Using Sparse Bayesian Learning”, Proc. IEEE Int. Global Comm. Conf., 2011.
[Lin12] J. Lin and B. L. Evans, “Cyclostationary Noise Mitigation in Narrowband Powerline
Communications”, Proc. APSIPA Annual Summit and Conf., 2012.
32
References
•
•
•
•
•
•
•
•
•
[Nassar09] M. Nassar, K. Gulati, M. DeYoung, B.L. Evans, and K. Tinsley. Mitigating near-field interference in
laptop embedded wireless transceivers. Journal of Signal Proc. Systems, pages 1–12, 2009.
[Nassar11] M. Nassar and B.L. Evans. Low Complexity EM-based Decoding for OFDM Systems with Impulsive
Noise. In Proc. Asilomar Conf. on Sig., Systems, and Computers, 2011. .
[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 Sig. Proc., pages 3089–3092, 2012.
[Nassar12mag] M.Nassar, J.Lin, Y. Mortazavi, A.Dabak, I.H.Kim and B.L.Evans, “Local Utility Powerline
Communications in the 3-500 kHz Band: Channel Impairments, Noise, and Standards”, IEEE Signal
Processing Magazine, vol. 29, no. 5, pp. 116-127, Sep. 2012.
[Nieman13] K. Nieman, J. Lin, M. Nassar, K. Waheed and B. L. Evans, “Cyclic Spectral Analysis of Power Line
Noise in the 3-200 kHz Band”, Proc. IEEE Int. Sym. on Power Line Communications and Its Applications, Mar.
24-27, 2012, submitted.
[Pauli06] V. Pauli, L. Lampe, and R. Schober. ”turbo dpsk” using soft multiple-symbol differential sphere
decoding. IEEE Trans. on Information Theory, 52(4):1385–1398, 2006.
[Raphaeli96] D. Raphaeli. Noncoherent coded modulation. IEEE Trans. on Comm., 44(2):172–183, 1996.
[Tipping01] M.E. Tipping. Sparse Bayesian learning and the relevance vector machine. Journal of Machine
Learning Research, 1:211–244, 2001.
[Umehara01] D. Umehara, M. Kawai, and Y. Morihiro. Performance analysis of noncoherent coded modulation
for power line communications. Proc. Int. Symp. Power Line Commun. and Its Appl., pages 291–298, 2001.
33
Backup Slides
34
Simulated Performance
• Symbol error rate in different noise scenarios
~10dB
~6dB
~6dB
~8dB
~4dB
Gaussian mixture model
Middleton class A model
• MMSE w/ (w/o) CSI: Parametric estimator assuming known (unknown) statistical parameters of noise
• CS+LS: A compressed sensing and least squares based algorithm
35
A Smart Grid
Communication to
isolated area
Power generation
optimization
Integrating
alternative energy
sources
Load balancing
Disturbance
monitoring
Smart metering
Electric car charging &
smart billing
Source: ETSI
36
Power Lines
• Built for unidirectional energy flow
• Bidirectional information flow
throughout smart grid will occur
Low Voltage (LV)
under 1 kV
High Voltage (HV)
33 kV – 765 kV
Medium Voltage (MV)
1 kV – 33 kV
Transformer
Source: ERDF
37
Local Utility Powerline Communications (PLC)
• PLC modems (PRIME, etc.) use carrier sensed multiple access
to determine when the medium is available for transmission
• MV router plays similar role as a Wi-Fi access point
38
Sources of Powerline Noise
Uncoordinated
transmission
Power line
disturbance
Electronic devices
Taken from
a local utility
point of view
39
PLC In Different Frequency Bands
Category
Band
Ultra
Narrowband
Narrowband
Broadband
Bit Rate
Applications
Standards
0.3 – 3
kHz
~100 bps
• Automatic meter reading
• Outage detection
• Load control
N/A
3 – 500
kHz
• Smart metering
~500 kbps • Real-time energy
management
1.8 – 250
~200 Mbps • Home area networks
MHz
• PRIME, G3
• ITU-T G.hnem
• IEEE P1901.2
• HomePlug
• ITU-T G.hn
• IEEE P1901
All of the above standards are based on multicarrier communications using orthogonal
frequency division multiplexing (OFDM).
40
Physical Layer Parameters for
OFDM Narrowband PLC Standards
CENELEC A band is from 3 to 95 kHz. FCC band is from 34.375 to 487.5 kHz.
PRIME and G3 use real-valued baseband OFDM. Others are complex-valued.
41
Smart Power Meters at Customer Site
• Enable local utilities to improve
Operating efficiency
System reliability
Customer participation
• Automatic metering infrastructure functions
Interval reads (every 1/15/30/60 minutes) and on-demand reads and pings
Transmit customer load profiles and system load snapshots
Power quality monitoring
Remote disconnect/reconnect and outage/restoration event notification
• Need low-delay highly-reliable communication link to local utility
• 75M smart meters sold in 2011 (20% increase vs. 2010)
Source: Jerry Melcher, IEEE Smart Grid Short Course, 22 Oct. 2011, Austin TX USA
42
Non-Gaussian Noise: Challenge to PLC
• Performance of conventional communication system degrades in
non-AWGN environment
• Statistical modeling of powerline noise
• Noise mitigation exploiting the noise model or structure
Listen to the environment
Estimate noise model
Use model or structure to mitigate noise
43
Cyclostationary Noise Modeling
in Narrowband PLC (3-500 kHz)
1. 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.,
Mar. 25-30, 2012, Kyoto, Japan.
2. M. Nassar, J. Lin, Y. Mortazavi, A. Dabak, I. H. Kim and B. L. Evans, “Local
Utility Powerline Communications in the 3-500 kHz Band: Channel
Impairments, Noise, and Standards”, IEEE Signal Processing Magazine,
Special Issue on Signal Processing Techniques for the Smart Grid, Sep.
2012, 14 pages.
44
Impulsive Noise in Broadband PLC:
Modeling and Mitigation
3. M. Nassar, K. Gulati, Y. Mortazavi, and B. L. Evans, “Statistical Modeling of
Asynchronous Impulsive Noise in Powerline Communication Networks”, Proc.
IEEE Int. Global Communications Conf., Dec. 5-9, 2011, Houston, TX USA.
4. J. Lin, M. Nassar and B. L. Evans, “Non-Parametric Impulsive Noise
Mitigation in OFDM Systems Using Sparse Bayesian Learning”, Proc. IEEE
Int. Global Communications Conf., Dec. 5-9, 2011, Houston, TX USA.
45
Statistical-Physical Modeling
• Interference from a single source
Noise envelope
k pulses in a window of duration T
(k)
(j)
Tk
Pulse emission duration
(1)
(2)
τj
Pulse arrival time
t=0
Emission duration: geometrically distributed with mean μ
Pulse arrivals: homogeneous Poisson point process with rate λ
Assuming channel between interference source and receiver has flat fading
46
Impulsive Noise Mitigation in OFDM Systems
• A linear system with Gaussian disturbance
v
y = Fe  FHF x  Fn = Fe  v ,
*

v ~ C N (x, I )
2
g
Estimate the impulsive noise and remove it from the received signal
yˆ = y  F eˆ   x  g
Apply standard OFDM decoder as if only AWGN were present
47
Parametric Vs. Non-Parametric Methods
• Noise in different PLC networks has different statistical models
• Mitigation algorithms need to be robust in different noise scenarios
Parametric Methods
Non-Parametric Methods
Assume parameterized
noise statistics
Yes
No
Performance degradation
due to model mismatch
Yes
No
Training needed
Yes
No
48
Non-Parametric Mitigation Using Null Tones
J : Index set of null tones
FJ : DFT sub-matrix
e: Impulsive noise in time domain
g: AWGN with unknown variance
• A compressed sensing problem
Exploiting the sparse structure of the time-domain impulsive noise
• Sparse Bayesian learning (SBL)
Proposed initially by M. L. Tipping
A Bayesian inference framework with sparsity promoting prior
49
Sparse Bayesian Learning
• Bayesian inference
Sparsity promoting prior:
Likelihood:
Posterior probability:
e | g ~ C N (0,  ),  = diag ( g )
yJ | g ,
2
~ C N (0, F  F   I )
*
2
e | yJ ; g , ~ CN (m ,  e )
2
• Iterative algorithm
Step 1: Maximum likelihood estimation of hyper-parameters (γ, σ2)
Solved by expectation maximization (EM) algorithm (e is latent variable)
Step 2: Estimate e from the mean of the posterior probability, go to Step 1
50
Non-Parametric Mitigation Using All Tones
• Joint estimation of data and noise
: Index set of data tones
z : Received signal in frequency domain
J
Treat the received signal in data tones as additional hyper-parameters
Estimate of z J is sent to standard OFDM equalizer and symbol detector
51

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