FPGA Implementation of a Message-Passing OFDM
Receiver for Impulsive Noise Channels
Karl F. Nieman†, Marcel Nassar‡, Jing Lin†, and Brian L. Evans†
†Wireless Communications and Networks Group, The University of Texas at Austin, Austin, TX
‡Mobile Solutions Lab, Samsung Information Systems America, San Diego, CA
IEEE Asilomar Conference on Signals, Systems, and Computers
Pacific Grove, CA
November 6, 2013
Smart Grid Communications
Communication backhaul
carries traffic between
concentrator and utility on
wired or wireless links
Local utility
Data concentrator
Medium Voltage (MV)
1 kV – 33 kV
Low voltage (LV)
< 1 kV
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
Background | Impulsive Noise Mitigation | Mapping to Hardware | Implementation
2
Impulsive Noise in 3-200 kHz PLC Band
Outdoor medium-voltage line
(St. Louis, MO)
Indoor low-voltage line
(UT Campus)
𝑓𝑠 = 1 MHz
Interleave
Cyclostationary noise becomes
asynchronous after interleaving
Impulsive noise can be 40 dB
above background noise
Background | Impulsive Noise Mitigation | Mapping to Hardware | Implementation
3
Impulsive Noise in OFDM Systems
𝐬
IFFT
Vector
of symbol
amplitudes
(complex)
Filter
Channel
+
Receiver
FFT
𝐲
Equalizer
and
detector
Gaussian (𝐛) +
Impulsive
Noise (𝐱)
FFT spreads received impulsive noise across all FFT bins
– SNR of each FFT bin is decreased
– Receiver communication performance degrades
Background | Impulsive Noise Mitigation | Mapping to Hardware | Implementation
4
Impulsive Noise Mitigation (Denoising)
𝐬
IFFT
Vector
of symbol
amplitudes
(complex)
Filter
Channel
+
Gaussian (𝐛) +
Impulsive
Noise (𝐱)
Receiver
Impulsive
noise
estimation
• 𝑁 FFT bins (tones)
– Transmitter null tones have zero power
– Received null tones contain noise
• Impulsive noise estimation
–
–
–
–
+
Exploit sparse structure of null tones
𝐅Ω is over complete dictionary
𝐱 is sparse vector
𝐠 is complex Gaussian (𝐠 = 𝐅 𝐱)
-
+
FFT
𝐲
Equalizer
and
detector
Conventional OFDM system
Added in our system
𝑦𝑖 =
𝐅𝑖
=
𝐱 + 𝐛
+
|Ω| × 𝑁
Ω is set of null tones (i.e. 𝑥Ω𝑖 = 0)
𝐅 is 𝑁 × 𝑁 DFT matrix
Background | Impulsive Noise Mitigation | Mapping to Hardware | Implementation
5
Impulsive Noise Mitigation Techniques
• Compressive sensing approaches are used for low SNR
• AMP provides best performance vs. complexity tradeoff
compressive sensing
Method
Low
SNR
High
SNR
NonParametric?
Computational
Complexity
Nulling/
Clipping[Tse12]
Low
Thresholded Least
Squares/MMSE[Cai08]
Med
Sparse Bayesian
Learning[Lin13]
l1-norm
minimization[Cai08]
Approximate Message
Passing (AMP) [Nas13]
High
(matrix inversion)
High
Med
Background | Impulsive Noise Mitigation | Mapping to Hardware | Implementation
6
Approximate Message Passing (AMP)
1. Initialization
𝑥𝑗 0 = 0
𝜏𝑗𝑥 𝑡
= 1 − 𝜋 𝛾𝑋
∀ 𝑗 ∈ {1, … , 𝑁}
𝑠𝑖 𝑡 = 0
∀ 𝑖 ∈ {1, … , 𝑀}
• M = null tones
• N = FFT size
• Iterate
– Time-frequency
projections
2. Output Linear
𝑝
𝜏𝑗𝑥 𝑡
𝜏𝑖 𝑡 =
3. Output Non-Linear
𝜏𝑖𝑠 𝑡 =
𝑗
𝑝𝑖 𝑡 = 𝐼Ω 𝐅𝐅𝐓 𝑥 𝑡
𝑝
− 𝜏𝑖 𝑡 𝑠𝑖 𝑡 − 1
𝑠𝑖 𝑡 = 𝜏𝑖𝑠 𝑡 𝑦𝑖 − 𝑝𝑖 𝑡
5. Input Non-Linear
𝑁
𝑡 =
𝑀𝜏 𝑠 𝑡
𝑟𝑗 𝑡 =
𝜏𝑗𝑟
𝑥𝑗 𝑡 + 𝜏𝑗𝑟 𝑡 𝐈𝐅𝐅𝐓 𝐼Ω𝑇 𝑥 𝑡
• Mostly scalar arithmetic and data
• Parallelizable for hardware implementation
– FFT/IFFT, exponential, vector multiplies, divisions
1
𝛾𝐵 + 𝜏 𝑝
∀ 𝑖 ∈ {1, … , 𝑀}
4. Input Linear
𝜏𝑗𝑟 𝑡
𝜋
𝜂𝑗 =
1 − 𝜋 𝛾𝐼 + 𝜏𝑗𝑟 𝑡
×
𝐞𝐱𝐩
𝜌𝑗 =
𝛾𝐼 𝑟𝑗 𝑡
2
𝜂
𝜏𝑗𝑟 𝑡𝑗 𝛾𝐼 +𝜏𝑗𝑟 𝑡
1 + 𝜂𝑗
𝑥𝑗 𝑡 + 1 =
𝛾𝐼
𝜌𝑟 𝑡
𝛾𝐼 + 𝜏𝑗𝑟 𝑡 𝑗 𝑗
Background | Impulsive Noise Mitigation | Mapping to Hardware | Implementation
7
Synchronous Dataflow (SDF) Model
• Targeted architecture for real-time streaming performance:
– Xilinx Virtex V field programmable gate arrays (FPGAs)
– Embedded x86 computers running real-time OS (Phar Lap ETS)
Task
• SDF model of OFDM receiver with
AMP noise mitigation:
• Periodic schedule is
6950𝐎 278𝐀 278𝐁 𝐂𝐃𝐄𝐅𝐇𝐈
Processing
O
Input samples from ADC
A
Resampling FIR filters
B
Time and Freq. Offset
Correction
C
FFT + Index Active and
Null Subcarriers
D
AMP Noise Estimation
E
FFT + Index Active
Subcarriers
F
Subtract Noise Estimate,
De-Interleave Reference
Symbols
H
Zero-Forcing Equalization
I
Equalize and Detect
Background | Impulsive Noise Mitigation | Mapping to Hardware | Implementation
8
Mapping AMP to Fixed-Point
• Variables sized using MATLAB Fixed-Point Toolbox
• Most variables sized within 16-bit wordlengths
sizing for 𝑟 using graphical tool
Background | Impulsive Noise Mitigation | Mapping to Hardware | Implementation
9
Graphical High-Level FPGA Synthesis
National Instruments Communication System Design Tools
– LabVIEW DSP Design Module
– LabVIEW FPGA
– LabVIEW Real-Time
2. Output Linear
Step 2
of AMP
𝑝
𝜏𝑗𝑥 𝑡
𝜏𝑖 𝑡 =
𝑗
𝑝𝑖 𝑡 = 𝐼Ω FFT 𝑥 𝑡
𝑝
− 𝜏𝑖 𝑡 𝑠𝑖 𝑡 − 1
DSP diagram
replaces
thousands of lines
of VHDL code
Background | Impulsive Noise Mitigation | Mapping to Hardware | Implementation
10
AMP-Enhanced OFDM Testbed
TX Chassis
RX Chassis
1 × PXIe-1082
1 × PXIe-8133
1 × PXIe-7965R
1 × NI-5781 FAM
1 × PXIe-1082
1 × PXIe-8133
2 × PXIe-7965R
1 × NI-5781 FAM
differential MCX pair
(quadrature component = 0)
differential MCX pair
16-bit DAC
sample
rate
conversion
256 IFFT
w/ 22 CP
insertion
zero
padding
(null tones)
generate
complex
conjugate
pair
data and
reference
symbol
interleave
Ref. symbol
LUT
LabVIEW RT
LabVIEW DSP Design Module
NI 5781
14-bit ADC
FlexRIO FPGA Module 1 (G3TX)
sample
rate
conversion
time and
frequency
offset
correction
256 FFT
w/ 22 CP
removal,
noise
injection
LabVIEW DSP Design Module
NI 5781
FlexRIO FPGA Module 2 (G3RX)
null tone
and active
tone
separation
testbench control/data visualization
data symbol
generation
LabVIEW
RT controller
AMP noise
estimate
256 FFT,
tone select
Subtract
noise
estimate
from active
tones
Host Computer
data and
reference
symbol deinterleave
channel
estimation/
ZF
equalization
LabVIEW DSP Design Module
FlexRIO FPGA Module 3 (AMPEQ)
BER/SNR
calculation w/
and w/o AMP
LabVIEW RT
RT controller
2-mode Gaussian Mixture noise injected here: 𝐺𝑀 𝜋, 𝛾𝐵 , 𝛾𝑋 ~ 𝜋𝑁 𝜋, 𝛾𝐵 + 𝛾𝑋 + (1 − 𝜋)𝑁 𝜋, 𝛾𝐵
Background | Impulsive Noise Mitigation | Mapping to Hardware | Implementation
11
Results
• System implemented using G3-PLC signaling structure 𝑓𝑠 =
0.4 MHz, 𝑁 = 256 (real-valued), 36 active tones
• Receiver w/ AMP was mapped across two FPGAs
– ‘G3RX’ – Downsampling, IFFT, time/frequency offset correction
– ‘AMPEQ’ – AMP algorithm, equalization, and detection
Received QPSK constellation at equalizer output
Resource Utilization
Utilization
FPGA
conventional receiver
with AMP
Trans.
Rec.
AMP+Eq
1
2
3
total slices
32.6% 64.0%
94.2%
slice reg.
15.8% 39.3%
59.0%
slice LUTs
17.6% 42.4%
71.4%
DSP48s
2.0%
7.3%
27.3%
blockRAMs
7.8% 18.4%
29.1%
Background | Impulsive Noise Mitigation | Mapping to Hardware | Implementation
12
Bit-Error-Rate Measurements
uncoded bit-error-rate (BER)
8 dB for 30 dB
impulsive noise
4 dB for 20 dB
impulsive noise
No loss (or gain)
in non-impulsive
(AWGN) noise
signal-to-noise ratio (SNR)
Background | Impulsive Noise Mitigation | Mapping to Hardware | Implementation
13
Conclusions
• Approximate Message Passing Framework allows
– Impulsive noise mitigation at low and high SNR
– Conversion of matrix operations to scalar and vector operations
– Parallelization and efficient mapping to hardware
• Up to 8 dB impulsive noise mitigation achieved using
– Fixed-point data and arithmetic
– Streaming G3-PLC rates
• LabVIEW project and FPGA bitfiles available here:
– http://users.ece.utexas.edu/~bevans/papers/2013/fpgaReceiver/index.html
Background | Impulsive Noise Mitigation | Mapping to Hardware | Implementation
14
References
[Cai08] – G. Caire; T. Y. Al-Naffouri; A. K. Narayanan, "Impulse noise cancellation in OFDM: an
application of compressed sensing," Information Theory, 2008. ISIT 2008. IEEE
International Symposium on , 2008.
[Tse12] – D-F. Tseng; Y. S. Han; W. H. Mow; L-C. Chang; A.J.H. Vinck, "Robust Clipping for
OFDM Transmissions over Memoryless Impulsive Noise Channels," Communications
Letters, IEEE , vol.16, no.7, 2012.
[Lin13] – J. Lin; M. Nassar; B. L. Evans, "Impulsive Noise Mitigation in Powerline
Communications Using Sparse Bayesian Learning," Selected Areas in Communications,
IEEE Journal on , vol.31, no.7, 2013.
[Nas13] – M. Nassar; P. Schniter; B. L. Evans, "A factor graph approach to joint OFDM channel
estimation and decoding in impulsive noise environments," IEEE Trans. on Signal
Processing, accepted for publication, 2013.
[Max11] – Maxim and ERDF, "Open Standard for Smart Grid Implementation," 2011.
15
Questions?
16
Backup Slides
17
Powerline Communications (PLC)
Categories
Band
Bit Rates
Coverage
Enables
Standards
Narrowband
3-500
kHz
up to
800 kbps
Multikilometer
• (ITU) PRIME, G3
Smart meter
• ITU-T G.hnem
communication
• IEEE P1901.2
Broadband
1.8-250
MHz
up to
200 Mbps
<1500 m
Home area
data networks
• HomePlug
• ITU-T G.hn
• IEEE P1901
• Uses orthogonal frequency-division multiplexing (OFDM)
• Communication challenges
– Channel distortions
– Non-Gaussian impulsive noise
Background | Impulsive Noise Mitigation | Mapping to Hardware | Implementation
18
Background | System Design and Implementation | Demo | Conclusion
AMPEQ.lvdsp
(first half)
(second half)
19
Approximate Message Passing (AMP)
• Reconstruct time-domain
noise from frequencydomain null tones
• Iterate until convergence
• Algorithm consists of:
• Mostly scalar arithmetic
• FFT/IFFTs
• Exponential
𝑀 = number of
null tones
𝑁 = FFT size
• Targeted at G3-PLC
signaling structure
Background | Impulsive Noise Mitigation | Mapping to Hardware | Implementation
20