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Complex Signal Kurtosis and Independent Component Analysis for
Wideband Radio Frequency Interference Detection
Adam Schoenwald (ASRC Federal Space and Defense)
Dr. Priscilla Mohammed, (Morgan State University)Dr. Damon Bradley (NASA, GSFC)
Dr. Jeffrey Piepmeier (NASA, GSFC) Dr. Englin Wong (NASA, GSFC)
Dr. Armen Gholian (NASA, GSFC)
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016
Acronym List
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 2
Acronym Definition Acronym Definition
ABS() Absolute Value GSFC Goddard Space Flight Center
AS&D ASRC Federal Space and Defense H Horrizontal
AUC Area Under Curve ICA Independent Component Analysis
CERBM Complex Entropy Rate Bound Minimization INR Interference to Noise Ratio
CONUS Continental United States NASA National Aeronautics and Space Administration
CQAMSYM Complex Quadrature Amplitude Modulation NCCFASTICA Non Circular Complex Fast ICA
CSK Complex Signal Kurtosis PI Principal Investigator
CW Continuous Wave QPSK Quadrature Phase Shift Keying)
dB Decibel RADAR RAdio Detection And Ranging
DDC Digital Down Converter RF Radio Frequency
DSP Digital Signal Processing RFI Radio Frequency Interference
DVB-S2 Digital Video Broadcasting - Satellite - Second Generation ROACH Reconfigurable Open Architecture Computing Hardware
ERBM Entropy Rate Bound Minimization ROC Receiver Operating Characteristic
ESTO Earth Science Technology Office RRCOS Root Raise Cosine
FB Full Band RSK Real Signal Kurtosis
FPGA Field Programmable Gate Array SB Sub Band
Gbps Billions of Bits per Second SERDES Serializer / Deserializer
GMI GPM Microwave Imager SMAP Soil Moisture Active Passive
GPM Global Precipitation Measurement V Vertical
Motivation
• Unmitigated RFI (Radio Frequency Interference) can cause errors in science measurements– L- and C-Band: soil moisture measurements over land– L-, C- and X-band: ocean salinity, sea surface
temperature, wind speed direction– K band: water vapor, liquid water
• Approach– RF front end development for 18 GHz (K band)
• These allocations are known to be corrupted by direct broadcast services
– Digital back end to allow sophisticated RFI detection and mitigation techniques
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 3
L, X band RFI
SMAP TA H-pol 1400 MHz
SMAP TA H-pol filtered-15 -10 -5 0 5 10 15 20 25
30
35
40
45
50
55
60
180 200 220 240 260 280 300 320 340 360 380 400
10 GHz GMI Tb V-pol (Vertical)
SMAP (Soil Moisture Active Passive) algorithms developed previously under ESTO (Earth Science Technology Office)
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 4
RFI from Geosynchronous Satellites Reflecting from the Surface
18 V Maximum of daily average RFI index
The 18 GHz Channel sees significant RFI from surface reflections around CONUS (Continental United States) and Hawaii
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 5
Picture from David W. Draper, [1]
GMI data
Real Signal Kurtosis (RSK)
Thermal
waveformSinusoidal
waveform
Gaussian
PDFNon-Gaussian
Sketches of noise and sinusoidal waveforms/PDFs
Figure from [2]
Based on Thermal Noise Amplitude Probability Distribution
4
1
2
12
2
2
4
12
2
1314
22
4
2
364
])[(
])[(
mmmm
mmmmmm
xxE
xxEK
BK
24
K = 3 for Gaussian signal
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 6
RSK [2] is used on SMAP [3] to help flag measurements that are contaminated with RFI
Real Signal Kurtosis (RSK)
Given a complex baseband signal 𝑧 𝑛 = 𝐼 𝑛 + 𝑗𝑄 𝑛 , the fourth
standardized moment is computed independently for both the real
and imaginary vectors, I and Q, as was used in SMAP[3].
RSKI =𝔼[ I−𝔼 I 4]
𝔼 (I−𝔼[I]) 2 − 3 , RSKQ =𝔼[ Q−𝔼 Q 4]
𝔼 (Q−𝔼[Q]) 2 − 3
The test statistic, RSK [2,3] (Real Signal Kurtosis), is then defined as
RSK =|RSKI|+|𝑅𝑆𝐾𝑄|
2
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 7
Complex Signal Kurtosis
Given a complex baseband signal 𝑧 𝑛 = 𝐼 𝑛 + 𝑗𝑄(𝑛), moments 𝛼ℓ,𝑚 of 𝑧(𝑛) are defined as
𝛼ℓ,𝑚 = 𝔼 (𝑧 − 𝔼 𝑧 )ℓ(𝑧 − 𝔼 𝑧 )∗𝑚 , ℓ ,𝑚 ∈ ℝ ≥ 0
With 𝜎2 = 𝛼1,1 , Standardized moments 𝜚ℓ,𝑚 can then be found as
𝜚ℓ,𝑚 =𝛼ℓ,𝑚𝜎ℓ+𝑚
Leading to the CSK (Complex Signal Kurtosis) RFI test statistic used [4].
𝐶𝐾 =𝜚2;2 − 2 − 𝜚2;0
2
1 +12𝜚2;0
2
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 8
Complex signal kurtosis (CSK) [4] is used to improve ability of the digital radiometer to detect RFI. It makes use of additional information in complex signals.
Algorithm Simulation and Verification
Hardware VerificationSimulation
COMPUTER
MatlabPython
Noise + RFI Test Signals
ROACH2
ADC
Algorithms
Ethernet(10 Gbps)
AWG
MatlabSimulink
Xilinx
FPGA Firmware
MatlabPython
Performance Evaluation
4x
Python
Algorithms
Noise + RFI Test Signals
Performance Evaluation
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 9
ROACH2 Implementation of RFI Detection Algorithms
• As a base line, a modified version of the Soil Moisture Active Passive Mission (SMAP) digital signal processing architecture was implemented in the Reconfigurable Open Architecture Computing Hardware (ROACH2) with a bandwidth of 24 MHz and verified using test signals generated. [5,6]
• This architecture provided outputs for the real and complex kurtosis statistical computations at 24 MHz
• The architecture was then implemented and verified at 200 MHz bandwidth in the ROACH2
• The real and complex kurtosis were also computed using outputs from the 200 MHz bandwidth architecture
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 10
ROACH2 Hardware Description Two 4x 10 Gigabit Ethernet Cards
Xilinx FPGA
DDR RAM
DAC
ADC
PowerPC
2 (1 Gigabit) Ethernet Ports to FPGA and PowerPC
Main Board
ZDOK Expansion
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 11
SMAP Modified DSP Architecture at Faster Sampling Rate
• The FPGA clock speed was increased from 96 MHz to 200 MHz (ratio of 1 : 2.08)
• The ADC sampling rate was increased from 96 MHz to 800 MHz (ratio of 1 : 8.33)– Two ADCs clocked at 800 MSPS each– Each channel has a 1 : 4 SERDES (Serializer/Deserializer)
reception• The FPGA reads four samples from each channel every clock cycle
• The DSP (Digital Signal Processing) algorithm had to be parallelized to handle the data throughput– A SERDES block natively implements the first stage of a
polyphase decomposition– The down-sampling is now performed before modulation and
filtering, but the entire system input / output is identical
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 12
Modified DSP Architecture at Faster Sampling Rate
x(n) x0(n)
xQ(n)
4 h0,h4,h8,...
Z-1
4
4
4
Z-1
Z-1
x1,x5,x9...
x0,x4,x8...
x2,x6,x10...
x3,x7,x11...
x1(n)
x2(n)
x3(n)h1,h5,h9,...
-(h2,h6,h10,…)
-(h3,h7,h11,…)
Z-1
Z-1
xI(n)
Equivalent Polyphase Decomposition for Serdes Inputs
Inherent Duality Between
Serdes and DSP Polyphase Decomposition
x(n)
Re{c(t)}=cos(2pfmn/Fs)
Im{c(t)}=-sin(2pfmn/Fs)
H(z)
H(z)
xI(n)
xQ(n)
4
4
Effective Analog of DDC From SMAP DSP Architecutre
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 13
Wideband RFI Telemetry - RSK
3
4
IHIV+QHQV
IVQH-IHQV
H
I
Q
𝐼 , 𝐼2 , 𝐼3 , 𝐼4
𝑄 ,𝑄2 , 𝑄3 , 𝑄4
V
I
Q
𝐼 , 𝐼2 , 𝐼3 , 𝐼4
𝑄 ,𝑄2 , 𝑄3 , 𝑄4
Moments m1-m4 used to compute Real Kurtosis
Used to produce 3rd
and 4th Stokes parameters
H and V Cross-Correlation
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 14
Wideband RFI Telemetry - CSK
3
4
IHIV+QHQV
IVQH-IHQV
H
I
Q
𝐼 , 𝐼2 , 𝐼3 , 𝐼4
𝑄 ,𝑄2 , 𝑄3 , 𝑄4
𝑰𝑸 , 𝑰𝟐𝑸 ,𝑰𝑸𝟐 , 𝑰𝟐𝑸𝟐
V
I
Q
𝐼 , 𝐼2 , 𝐼3 , 𝐼4
𝑄 ,𝑄2 , 𝑄3 , 𝑄4
𝑰𝑸 , 𝑰𝟐𝑸 ,𝑰𝑸𝟐 , 𝑰𝟐𝑸𝟐
Additional Moments for Complex Kurtosis
Moments m1-m4 used to compute Real Kurtosis
Used to produce 3rd
and 4th Stokes parameters
• +4 moments per Polarization [6]• Extension on moments for real
kurtosis
H and V Cross-Correlation
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 15
ROC Curves and AUC• Each point on an ROC curve can be
represented by the set {FAR, PD}– {False alarm Rate , Probability of Detection}
• ROC curves will generate from (0,0) to (1,1) by varying the threshold
• Poor detectors are close to the 1:1 line
• Better detectors show higher PD and smaller FAR
• Figure of Merit = Area Under Curve (AUC)– 0.5≤AUC ≤1
– When AUC = 0.5 detector does not work
– When AUC = 1 the detector works perfectly
ROC curve example, from [7].
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 16
Better Detection Worse Detection
AUC = 1 AUC = 0.5
Better Detection
Worse Detection
Simulation Results
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 17
Sub Band
Full Band
Smaller duty cycles are easier to detect;sub-banding improves detection [6].
0 0.05 0.1 0.15 0.2 0.25 0.3
Duty Cycle
0.4
0.5
0.6
0.7
0.8
0.9
1
Area
Under
Curve
Simulated Pulsed Narrow Band at INR = -20dB , N = 20000
Full Band RSK
Full Band CSK
Sub Band RSK
Sub Band CSK
CW ModulationCSK is outperforming RSK
Simulation Results
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 18
CSK
Sub Band PCW
Full Band PCW
Sub Band CW
Wide Band
Full Band CW
RSK
• Wide Band revers to QPSK with a RRCOS filter simulating a DVB-S2 Channel, • Band occupancy = 0.0375 Fs , Carrier = 0.175 Fs
• Using Monte Carlo Simulations, INR is swept is for different types of RFI modulations.• Algorithms are compared by looking at INR when AUC = 0.75 .• CSK shows improved detection over RSK.• PCW is easiest to detect. Wideband is hardest to detect [6].
AUC Results: Kurtosis As Detector
Kurtosis yields poor detector for CW and Wide Band RFI
Kurtosis yields good detection for PCW (Such as RADAR)
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 19
-40-35-30-25-20-15-10-50
INR
0.4
0.5
0.6
0.7
0.8
0.9
1A
UC
AUC vs INR for PCW , CW , and Wideband , N = 9000
PCW d = 1% , RSK
PCW d = 1% , CSK
CW d = 100% , RSK
CW d = 100% , CSK
Wideband d = 100% , 30 / 200 MHZ , RSK
Wideband d = 100% , 30 / 200 MHZ , CSK
Sub-banding Verification with Chirp
• 200 MHz BW
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 20
Channelized Complex Kurtosis
Visual Verification of channelization.
Deviation away from 0 means interference is detected.
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 21
Hardware Results
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 22
Sub banding decreased detection on wide band RFI
Sub banding improved detection on narrow band RFI
Independent Component Analysis• ICA [8] uses higher order statistics to perform blind source separation
• This suggests it may be useful for separating RFI from Gaussian noise in the radiometry context.
• We assume noise and RFI are statistically independent sources, mixing is linear, sources are non Gaussian
• Mixture model: x = As, observe x
• 𝒔 = Wx, 𝒔 is the estimated independent source
Observation vector x
Linear Mixing A
Linear Un-mixing
W
Source vector s
Original sources/signals
𝑠1(𝑛)
𝑠2(𝑛)
𝑠3(𝑛)
𝑠4(𝑛)
𝑠1(𝑛)
𝑠2(𝑛)
𝑠3(𝑛)
𝑠4(𝑛)
𝑥3(𝑛)
𝑥4(𝑛)
𝑥2(𝑛)
𝑥1(𝑛)
Estimated vector 𝒔
Estimated sources/signals
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 23
ICA Algorithm𝑥HI 0 𝑥HI 1 … 𝑥HI 𝑁 − 1
𝑥HQ 0 𝑥HQ 1 … 𝑥HQ 𝑁 − 1
𝑥VI 0 𝑥VI 1 … 𝑥VI 𝑁 − 1
𝑥VQ 0 𝑥VQ 1 … 𝑥VQ 𝑁 − 1
=
𝑎00 𝑎01 𝑎02 𝑎03𝑎10 𝑎11 𝑎12 𝑎13𝑎20 𝑎21 𝑎22 𝑎23𝑎30 𝑎31 𝑎32 𝑎33
𝑠0,0 𝑠0,1 𝑠0,2 𝑠0,3 … 𝑠0,𝑁−1𝑠1,0 𝑠1,1 𝑠1,2 𝑠1,3 … 𝑠1,𝑁−1𝑠2,0 𝑠2,1 𝑠2,2 𝑠2,3 … 𝑠2,𝑁−1𝑠3,0 𝑠3,1 𝑠2,2 𝑠3,3 … 𝑠3,𝑁−1
Independent ComponentsObservations Mixing Matrix
Are components 𝒔𝒊in 𝐒 independent?
𝐒 = 𝐖𝒙
Update 𝐖No
Yes
Use 𝐒
Measured 𝒙
𝒙 =As𝑾 = 𝑨−𝟏
𝐬 = 𝐖𝐱
• Actual Signals, S , are mixed by mixing matrix, A, and observed as X
• We pick a matrix , 𝐖 , that gives us back our
estimated signals, 𝐒
ICA Input
ICA Output
Find A matrix to transform X into S
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 24
Signal Model
Gaussian Noise
Interference
• Assumptions– Gaussian Noise between H and V
polarizations is Independent and Uncorrelated
– Interference is circularly polarized
𝑥H 𝑡 = rfi 𝑡 + wgn1 𝑡
𝑥V 𝑡 = rfi 𝑡 𝑒−
𝑖𝜋2 +wgn2 𝑡
CW Example:
𝑥H 𝑡 = 𝑎 sin 𝜔0𝑡 + w2 𝑡 ∗ ℎ(𝑡)
𝑥v 𝑡 = 𝑎 sin 𝜔0𝑡 − 𝜋/2 + w2 𝑡 ∗ ℎ(𝑡)
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 25
ICA RFI Detection
𝑠0 0 𝑠0 1 … 𝑠0 N − 1
𝑠1 0 𝑠1 1 … 𝑠1 N − 1
𝑠2 0 𝑠2 1 … 𝑠2 N − 1
𝑠3 0 𝑠3 1 … 𝑠3 N − 1
max𝑘
{ABS(RSKk – 3)}
ICA Detector Output
Kurtosis
Kurtosis
Kurtosis
Kurtosis
RSK0
RSK1
RSK2
RSK3
Step 1: Take Kurtosis of each estimated independent component vector Step 2: Select the kurtosis value that
deviated the furthest from 3
ICA Output
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 26
AUC Results- ICA Performance - PCW+2dB INR Gain,Real Signal Kurtosis with FastICA performs just as well as other algorithms for PCW
RSK = Real Signal KurtosisCSK = Complex Signal Kurtosis
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 27
-24-22-20-18-16-14
INR
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
AU
C
ICA Performance, PCW d = 1%, N = 9000
direct | RSK
direct | CSK
fastica | RSK
fastica | CSK
robustica | RSK
robustica | CSK
nccfastica | RSK
nccfastica | CSK
erbm | RSK
erbm | CSK
cqamsym | RSK
cqamsym | CSK
cerbm | RSK
cerbm | CSK
-20-15-10-50
INR at AUC = 0.75
RSK robustica
CSK cqamsym
CSK nccfastica
RSK fastica
CSK cerbm
RSK nccfastica
CSK robustica
RSK cqamsym
CSK erbm
RSK cerbm
CSK fastica
RSK erbm
CSK direct
RSK direct
ICA Performance, PCW d = 1%, N = 9000
Various ICA algorithms are tested [9,10,11,12,13,14,15,16,17].No ICA pre-processing is done on ‘direct’ data sets.
AUC Results- ICA Performance - CW
+2dB INR Gain,Complex Signal Kurtosis with Complex ICA Algorithms Performs Best on CW
RSK = Real Signal KurtosisCSK = Complex Signal Kurtosis
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 28
-14-12-10-8-6-4
INR
0.4
0.5
0.6
0.7
0.8
0.9
1
AU
C
ICA Performance, CW d = 100%, N = 9000
direct | RSK
direct | CSK
fastica | RSK
fastica | CSK
robustica | RSK
robustica | CSK
nccfastica | RSK
nccfastica | CSK
erbm | RSK
erbm | CSK
cqamsym | RSK
cqamsym | CSK
cerbm | RSK
cerbm | CSK
-8-6-4-20
INR at AUC = 0.75
CSK cerbm
CSK cqamsym
CSK nccfastica
CSK erbm
CSK robustica
RSK nccfastica
RSK cqamsym
RSK cerbm
CSK direct
RSK erbm
RSK direct
RSK fastica
RSK robustica
CSK fastica
ICA Performance, CW d = 100%, N = 9000
Various ICA algorithms are tested [9,10,11,12,13,14,15,16,17].No ICA pre-processing is done on ‘direct’ data sets.
AUC Results – ICA Performance – Wide Band
+2dB INR Gain,Complex Signal Kurtosis with Complex ICA Algorithms Performs Best on Wideband
RSK = Real Signal KurtosisCSK = Complex Signal Kurtosis
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 29
-12-10-8-6-4-2
INR
0.5
0.6
0.7
0.8
0.9
1
AU
C
ICA Performance, Wideband, d = 100%, N = 9000
direct | RSK
direct | CSK
fastica | RSK
fastica | CSK
robustica | RSK
robustica | CSK
nccfastica | RSK
nccfastica | CSK
erbm | RSK
erbm | CSK
cqamsym | RSK
cqamsym | CSK
cerbm | RSK
cerbm | CSK
-8-6-4-20
INR at AUC = 0.75
CSK cerbm
CSK cqamsym
CSK nccfastica
CSK robustica
CSK erbm
RSK cerbm
RSK cqamsym
RSK nccfastica
CSK direct
RSK erbm
RSK direct
RSK robustica
RSK fastica
CSK fastica
ICA Performance, Wideband, d = 100%, N = 9000
Various ICA algorithms are tested [9,10,11,12,13,14,15,16,17].No ICA pre-processing is done on ‘direct’ data sets.
Conclusions
• CSK provides better detection over RSK
• ICA allowed equivalent detection at about 2dB lower INR when used as a preprocessor for RSK and CSK normality tests
• ICA performance mainly limited due to an underdetermined observation matrix
• May be more suitable to systems with a greater number of observation channels
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 30
ICA Algorithms Used
• Fast ICA (FASTICA) [9,15]– A. Hyvärinen. “Fast and Robust Fixed-Point Algorithms for Independent Component Analysis”, IEEE
Transactions on Neural Networks 10(3):626-634, 1999.
• Robust ICA (ROBUSTICA) [10,16]– V. Zarzoso and P. Comon, "Robust Independent Component Analysis by Iterative Maximization of the
Kurtosis Contrast with Algebraic Optimal Step Size", IEEE Transactions on Neural Networks, Vol. 21, No. 2, February 2010, pp. 248-261.
• Non Circular Complex Fast ICA (NCCFASTICA) [11,17]– Mike Novey and T. Adali, "On Extending the complex FastICA algorithm to noncircular sources" IEEE Trans.
Signal Processing, vol. 56, no. 5, pp. 2148-2154, May 2008.
• Entropy Rate Bound Minimization (ERBM) [12,17]– X.-L. Li, and T. Adali, "Blind spatiotemporal separation of second and/or higher-order correlated sources by
entropy rate minimization," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing (ICASSP), Dallas, TX, March 2010.
• Complex Quadrature Amplitude Modulation (CQAMSYM) [13,17]– Mike Novey and T. Adali, "Complex Fixed-Point ICA Algorithm for Separation of QAM Sources using Gaussian Mixture
Model" in IEEE Conf. ICASSP 2007
• Complex Entropy Rate Bound Minimization (CERBM) [14,17]– G.-S. Fu, R. Phlypo, M. Anderson, and T. Adali, "Complex Independent Component Analysis Using Three Types of
Diversity: Non-Gaussianity, Nonwhiteness, and Noncircularity," IEEE Trans. Signal Processing, vol. 63, no. 3, pp. 794-805, Feb. 2015.
To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 31
References1) Draper, David W., “Report on GMI Special Study #15: Radio Frequency Interference” , Ball Aerospace and Technologies Corp., Jan 16, 2015
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International Geoscience and Remote Sensing Symposium (IGARSS), Milan, 2015, pp. 3489-3492.
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frequency interference detector," 2016 14th Specialist Meeting on Microwave Radiometry and Remote Sensing of the Environment (MicroRad), Espoo, 2016, pp. 71-75.
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To be presented by Adam Schoenwald at Coexisting with Radio Frequency Interference, Socorro NM, October 17-20, 2016 32