RADIO FREQUENCY INTERFERENCE DETECTION AND MITIGATION IN

MICROWAVE RADIOMETERS

Priscilla N. Mohammed(1, 2)

(1) NASA’s Goddard Space Flight Center

(2) Morgan State University

SMAP RFI

• SMAP (Soil Moisture Active Passive) was launched by NASA January 31, 2015 to measure soil moisture of the Earth’s land surface

• The SMAP radiometer operates in the L-band protected spectrum (1400-1427 MHz) that is known to be vulnerable to radio frequency interference (RFI)

– SMOS and Aquarius provided a good indication of the RFI environment at L-band

• On orbit results show that RFI is indeed a problem

– RFI increases brightness temperatures – Can lead to dry biases in soil moisture retrievals if undetected

• SMAP radiometer includes a digital backend enabling multiple RFI

detection and mitigation capabilities; detection and mitigation processing performed on ground

1

Channel #

Tim

e(x1

.2 m

s)

H-pol Ta(K)

5 10 15

2

4

6

8 180

190

200

210

220

Channel #

Tim

e(x1

.2 m

s)

H-pol Kurtosis

5 10 15

2

4

6

8 2.9

3

3.1

3.2

3.3

0 10 20 30180

190

200

210

220H-pol Ta(K)

Ta(K

)

Time(x350us)

0 10 20 302.8

2.9

3

3.1

3.2H-pol Kurtosis

Kur

tosi

s

Time(x350us)

MAXPD

Subband detection algorithms detect and flag RFI; also flag adjacent channels: Kurtosis, T3/T4, Cross frequency

Drop all flagged data and average remaining clean pixels of subband data to get RFI free footprint, TA

Time domain detectors detect and flag RFI; MPD flags corresponding time slice in subband data: Pulse detector, kurtosis, T3/T4

H-pol MPD Flag

Channel #

Tim

e(x1

.2 m

s)

2 4 6 8 10 12 14 16

1

2

3

4

5

6

7

8

2

RFI Probability Map

3 % of time SMAP detects RFI of 5 K or more in H-pol. April 2015 to March 2016

Weekly Peak Hold RFI Maps: H-pol

4

• 0.25° grid • December

2016 to May 2017

• V-pol show similar results

-150 -100 -50 0 50 100 150

-80

-60

-40

-20

0

20

40

60

80

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Fullband Kurtosis H-pol

• 0.25° grid • October

1-7, 2016 • V-pol

show similar results

Kurtosis – 3 Max and Min kurtosis for a week 5

-150 -100 -50 0 50 100 150

-80

-60

-40

-20

0

20

40

60

80

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Subband Kurtosis H-pol

• 0.25° grid • October

1-7, 2016 • V-pol

show similar results

Kurtosis – 3 Max and Min kurtosis for a week

70 80 90 100 110 120 130 140 150 160

0

10

20

30

40

50

60

180 200 220 240 260 280 300

70 80 90 100 110 120 130 140 150 160

0

10

20

30

40

50

60

180 200 220 240 260 280 300

TA H-pol Asia: October 1-7 2016

7

TA unfiltered TA filtered

TA filtered

Discarding measurements flagged by TB quality flag; residual RFI could still be in product

• 0.25° grid • Peak hold,

October 1-7, 2016

• TA < 100 K omitted

70 80 90 100 110 120 130 140 150 160

0

10

20

30

40

50

60

180 200 220 240 260 280 300

RFI Sources Localized by SMAP over China

8

Spectra measured by SMAP over the main Japanese cities

Osaka Tokyo

Every data point is the average of the sub-band Ta measured within a circle of 50 km radius, centered approximately at the center of the city. Similar spectra seen over Nagoya and Hiroshima.

Channels 19 and 21 of the BSAT system

Additional interferer

9

Spectra over Japan

• 0.25° grid • Middle channels

less corrupted by RFI

• TA < 125 K omitted

TA (Kelvin)

11

For detailed information on the SMAP RFI algorithm and results from the first year on orbit.

Objective

Key Milestones Approach

InVEST-15-0020

CubeRRT: CubeSat Radiometer Radio Frequency Interference Technology Validation

PI: Joel T. Johnson, Ohio State University

Co-Is/Partners:

• Demonstrate wideband radio frequency interference (RFI) mitigating backend technology for future spaceborne microwave radiometers operating 6 to 40 GHz

• Crucial to maintain US national capability for spaceborne radiometry and associated science goals

• Demonstrate successful real-time on-board RFI detection and mitigation in 1 GHz instantaneous bandwidth

• Demonstrate reliable cubesat mission operations, include tuning to Earth Exploration Satellite Service (EESS) allocated bands in the 6 to 40 GHz region

• Requirements definition and system design 03/16 • Instrument engineering model subsystem tests 4/17 • Instrument engineering model integration and test 6/17 • Instrument flight model subsystem tests 8/17 • Instrument flight model integration and test 9/17 • Spacecraft integration and test 12/17 • CubeRRT launch readiness 02/18 • On-orbit operations completion L+12 months

TRLin = 5 TRLout = 7 C. Chen, M. Andrews, OSU; S. Misra, S. Brown, J. Kocz, R. Jarnot, JPL; D. Bradley, P. Mohammed, J. Lucey, J. Piepmeier, GSFC

• Build upon heritage of airborne and spaceborne (SMAP) digital backends for RFI mitigation in microwave radiometry

• Apply existing RFI mitigation strategies onboard spacecraft; downlink additional RFI data for assessment of onboard algorithm performance

• Integrate radiometer front end, digital backend, and wideband antenna systems into 6U CubeSat

• CSLI launch from ISS into 400 km orbit; ~ 120-300 km Earth footprint for RFI mitigation validation

• Operate for one year at 25% duty cycle to acquire adequate RFI data

12/16

RFI sources in Europe at 10.7 GHz observed by GPM Microwave Imager

6U CubeSat layout of CubeRRT components

GMI

• The GMI earth-view data is contaminated by RFI in the 10 and 18 GHz channels, at both polarizations – 10 GHz RFI is mostly due to fixed earth emitters – 18 GHz low-level RFI is observed from fixed earth emitters – 18 GHz high-level RFI is observed from reflections off ocean and land

surfaces from Geosynchronous satellites around the continental United States and Hawaii.

13

10.7 GHz 18.7 GHz Picture courtesy David Draper and David Newell

Motion Detector Units

14

• Modules similar to these operate at 10.687 GHz designated for indoor use in the UK

• Likely offenders of GMI RFI

Wideband RFI Mitigation Subsystem for Microwave Radiometers

• Technical objectives – Develop a wideband (> 200 MHz) digital detector subsystem – Demonstrate innovative RFI detection and removal techniques for

microwave radiometers • The proposed techniques are the complex values kurtosis detector and blind

source separation methods. Both have the potential to improve the radio frequency interference (RFI) detection rate in high frequency bandwidth.

• 800 MHz sample-rate (200 MHz bandwidth) polarimetric radiometer test-bed was developed using the Reconfigurable Open Architecture Computing Hardware (ROACH2) system from the Collaboration for Astronomy Signal Processing and Electronics Research (CASPER) group at the University of California Berkeley

• Both the real and complex signal kurtosis algorithms were implemented in hardware and the outputs were compared to that of simulations developed in python

15

Wideband RFI Telemetry

16

3

4

IHIV+QHQV

IVQH-IHQV

H

I

Q

𝐼𝐼 , 𝐼𝐼2 , 𝐼𝐼3 , 𝐼𝐼4

𝑄𝑄 ,𝑄𝑄2 ,𝑄𝑄3 ,𝑄𝑄4

𝑰𝑰𝑰𝑰 , 𝑰𝑰𝟐𝟐𝑰𝑰 , 𝑰𝑰𝑰𝑰𝟐𝟐 , 𝑰𝑰𝟐𝟐𝑰𝑰𝟐𝟐

V

I

Q

𝐼𝐼 , 𝐼𝐼2 , 𝐼𝐼3 , 𝐼𝐼4

𝑄𝑄 ,𝑄𝑄2 ,𝑄𝑄3 ,𝑄𝑄4

𝑰𝑰𝑰𝑰 , 𝑰𝑰𝟐𝟐𝑰𝑰 , 𝑰𝑰𝑰𝑰𝟐𝟐 , 𝑰𝑰𝟐𝟐𝑰𝑰𝟐𝟐

Additional Moments for Complex Signal Kurtosis

Moments m1-m4 used to compute Real Kurtosis

Used to produce 3rd and 4th Stokes parameters

• +4 moments per Polarization • Extension on moments for real

kurtosis

H and V Cross-Correlation

Complex Kurtosis Hardware Results

17

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Probability False Alarm

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pro

babi

lity

Det

ect

Hardware ROC, Wideband RFI, N = 20000

Full Band - RSK , INR = -7 AUC = 0.917

Full Band - CSK , INR = -7 AUC = 0.951

Sub Band - RSK , INR = -7 AUC = 0.686

Sub Band - CSK , INR = -7 AUC = 0.713

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Probability False Alarm

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pro

babi

lity

Det

ect

Hardware ROC, Narrowband RFI, N = 20000

Full Band - RSK , INR = -10 AUC = 0.658

Full Band - CSK , INR = -10 AUC = 0.695

Sub Band - RSK , INR = -10 AUC = 0.942

Sub Band - CSK , INR = -10 AUC = 0.983

Narrowband CW RFI QPSK signal

CSK (Complex Signal Kurtosis) provides a better detection performance than real signal kurtosis. Interference becomes detectable at an INR (Interference to Noise Ratio) of 2 dB lower than what can be detected using RSK (Real Signal Kurtosis).

Blind Source Separation

• Objective – Extract 𝑁𝑁 unknown sources from 𝑃𝑃 observations with weak assumption about

sources

• Applications – Audio source separation, communications, …

• Mixture Models – Linear instantaneous mixture

• Questions – Can 𝑨𝑨 be identified from 𝒙𝒙(𝑡𝑡) alone up to scaling of columns? (identifiability) – Can 𝒔𝒔 𝑡𝑡 be separated? (separability) – What algorithm can be used to perform these tasks?

• Ambiguity – Scaling – Permutation

• Methods – Independent Component Analysis: 𝑃𝑃 ≥ 𝑁𝑁, sources are independent – Sparse Component Analysis: 𝑃𝑃 < 𝑁𝑁, sources have disjoint supports 18

mixing matrix (unknown)

sources (unknown)

observations (known)

𝒙𝒙 𝑡𝑡 = 𝑨𝑨𝒔𝒔 𝑡𝑡 , 𝑡𝑡 = 1, … ,𝑇𝑇

Independent Component Analysis

• Can RFI be separated from noise using blind source separation; this work focuses on independent component analysis (ICA)

• Assume noise and RFI are statistically independent sources, mixing model is linear, sources are non Gaussian.

• Model: x = As, Observe x. Sources s and mixing matrix A are unknown.

• 𝒔𝒔� = Wx, 𝒔𝒔� is the estimated independent components (source estimates).

19

Observation vector x

Linear Mixing Matrix

A

Linear Un-mixing

Matrix W

Source vector s

Original sources/signals

𝑠𝑠�1(𝑛𝑛)

𝑠𝑠�2(𝑛𝑛)

𝑠𝑠�3(𝑛𝑛)

𝑠𝑠�4(𝑛𝑛)

𝑠𝑠1(𝑛𝑛)

𝑠𝑠2(𝑛𝑛)

𝑠𝑠3(𝑛𝑛)

𝑠𝑠4(𝑛𝑛)

𝑥𝑥3(𝑛𝑛)

𝑥𝑥4(𝑛𝑛)

𝑥𝑥2(𝑛𝑛)

𝑥𝑥1(𝑛𝑛)

Estimated vector 𝒔𝒔�

Estimated sources/signals

ICA Algorithm

20

𝑥𝑥HI 0 𝑥𝑥HI 1 … 𝑥𝑥HI 𝑁𝑁 − 1𝑥𝑥HQ 0 𝑥𝑥HQ 1 … 𝑥𝑥HQ 𝑁𝑁 − 1𝑥𝑥VI 0 𝑥𝑥VI 1 … 𝑥𝑥VI 𝑁𝑁 − 1𝑥𝑥VQ 0 𝑥𝑥VQ 1 … 𝑥𝑥VQ 𝑁𝑁 − 1

=

𝑎𝑎00 𝑎𝑎01 𝑎𝑎02 𝑎𝑎03𝑎𝑎10 𝑎𝑎11 𝑎𝑎12 𝑎𝑎13𝑎𝑎20 𝑎𝑎21 𝑎𝑎22 𝑎𝑎23𝑎𝑎30 𝑎𝑎31 𝑎𝑎32 𝑎𝑎33

𝑠𝑠0,0 𝑠𝑠0,1 𝑠𝑠0,2 𝑠𝑠0,3 … 𝑠𝑠0,𝑁𝑁−1 𝑠𝑠1,0 𝑠𝑠1,1 𝑠𝑠1,2 𝑠𝑠1,3 … 𝑠𝑠1,𝑁𝑁−1 𝑠𝑠2,0 𝑠𝑠2,1 𝑠𝑠2,2 𝑠𝑠2,3 … 𝑠𝑠2,𝑁𝑁−1 𝑠𝑠3,0 𝑠𝑠3,1 𝑠𝑠2,2 𝑠𝑠3,3 … 𝑠𝑠3,𝑁𝑁−1

Independent Components

Observations Mixing Matrix

Are components 𝒔𝒔𝒊𝒊� in 𝐒𝐒� independent?

𝐒𝐒� = 𝐖𝐖�𝒙𝒙

Update 𝐖𝐖� No

Yes

Use 𝐒𝐒�

Measured 𝒙𝒙

𝒙𝒙 =As 𝑾𝑾 = 𝑨𝑨−𝟏𝟏 𝐬𝐬 = 𝐖𝐖𝐖𝐖

• Actual Signals, S , are mixed by mixing matrix, A, and observed as X

• We pick a matrix , 𝐖𝐖� , that gives us back our estimated signals, 𝐒𝐒�

ICA Input

ICA Output

Find A matrix to transform X into S

RFI Detection

21

𝑠𝑠0 0 𝑠𝑠0 1 … 𝑠𝑠0 N − 1

𝑠𝑠1 0 𝑠𝑠1 1 … 𝑠𝑠1 N − 1

𝑠𝑠2 0 𝑠𝑠2 1 … 𝑠𝑠2 N − 1

𝑠𝑠3 0 𝑠𝑠3 1 … 𝑠𝑠3 N − 1

max𝑘𝑘

{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

AUC Results – ICA Performance – Wide Band

22

+2dB INR Gain, Complex Signal Kurtosis with Complex ICA Algorithms Performs Best on DVB-S2

-12-10-8-6-4-2

INR

0.5

0.6

0.7

0.8

0.9

1

AUC

ICA Performance, DVBS2 , d = 100%, N = 9000

smap | RSK

smap | CSK

fastica | RSK

fastica | CSK

robustica | RSK

robustica | CSK

nccfastica | RSK

nccfastica | CSK

erbm | RSK

erbm | CSK

cqamsym | RSK

cqamsym | CSKcerbm | 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 smap

RSK erbm

RSK smap

RSK robustica

RSK fastica

CSK fastica

ICA Performance, DVBS2 , d = 100%, N = 9000

RSK = Real Signal Kurtosis CSK = Complex Signal Kurtosis

ICA

• CSK provides better detection over RSK • ICA assumes a critically or over determined system of

independent components • Using existing V/H polarimetric instrument architecture

we are limited to two observations but there are a minimum of three independent components in the event that RFI is present

• Hence 3 or more observations are needed; current problem is therefore an under determined case for which ICA does not work well

23

Sparse Component Analysis

• Application – BSS for 𝑃𝑃 < 𝑁𝑁 (under-determined)

• Assumption – Sources have disjoint

supports • Model

– 𝒙𝒙 𝑡𝑡 = 𝑨𝑨𝒔𝒔 𝑡𝑡 = 𝑨𝑨1, … ,𝑨𝑨𝑁𝑁𝑠𝑠1 𝑡𝑡⋮

𝑠𝑠𝑁𝑁 𝑡𝑡, 𝑡𝑡 ∈ {1, …𝑇𝑇}

• Least squares: �̂�𝑠𝑛𝑛 𝑡𝑡 = �

𝑨𝑨�𝑛𝑛2 𝑡𝑡 ∈ Λ�𝑛𝑛

0 𝑜𝑜𝑡𝑡𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑠𝑠𝑜𝑜

24

0 1 2 3 4 5 6 7 8

t 10 4

-1

0

1

s1

(t)

Sources

0 1 2 3 4 5 6 7 8

t 10 4

-1

0

1

s2

(t)

0 1 2 3 4 5 6 7 8

t 10 4

-1

0

1

s3

(t)

0 1 2 3 4 5 6 7 8

t 10 4

-0.5

0

0.5

x1

(t)

Sources Mixture

0 1 2 3 4 5 6 7 8

t 10 4

-1

-0.5

0

0.5

1

x2

(t)

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

x1

(t)

-4

-3

-2

-1

0

1

2

3

4

x2

(t)

Scatter Plot

A = [0.1, 0.2, 0.5;

0.8, 0.4, 0.3]

SCA In Practice

25

• In practice sources are not disjoint in time! • Method: change the representation of the observations so that in

the new representation, the sources are disjoint

Algorithms I • Dictionary

• Dictionary learning • Structured dictionary

• Joint sparse representation • Global optimization • Greedy algorithm

• Mixing matrix estimation • Global clustering • Local scatter plots

• Separation • Binary masking

Algorithms II • Dictionary

• Structured dictionary- different set of dictionaries

• Joint sparse representation • Global optimization- exact

sparse coding • Mixing matrix estimation

• Global clustering – Weighted histogram

• Separation • Local separation

Sparse Signal Representation

• Satisfying the SCA Assumption – Represent each source by a linear combination of a few

elementary signals (atoms): 𝑠𝑠 𝑡𝑡 = ∑ 𝑐𝑐𝑠𝑠 𝑘𝑘 𝜑𝜑𝑘𝑘 𝑡𝑡𝐾𝐾𝑘𝑘=1 • Measure of sparsity

– 𝒄𝒄𝑠𝑠 𝜏𝜏 = � ∑ |𝑐𝑐𝑠𝑠 𝑘𝑘 |𝜏𝜏𝐾𝐾

𝑘𝑘=11/𝜏𝜏 𝜏𝜏 > 0

num of nonzero coefficients 𝜏𝜏 = 0 quantifies the sparsity

of 𝒄𝒄𝑠𝑠 – Ideal 𝜏𝜏 for sparsity is 0

• Dictionary – Dictionary: set of atoms – Consider dictionaries that span 𝐶𝐶𝑇𝑇

• 𝐾𝐾 > 𝑇𝑇: redundant dictionary, infinite representation • Synthesis

– 𝒔𝒔 = 𝒄𝒄𝒔𝒔𝚽𝚽 • Effective Dictionary: enables a sparse representation

26

SCA Example: Sources with non disjoint supports

27

sources

0 100 200 300 400 500 600 700 800 900 1000

t

-5

0

5

s1

(t)

0 100 200 300 400 500 600 700 800 900 1000

t

-5

0

5

s2

(t)

0 100 200 300 400 500 600 700 800 900 1000

t

-2

0

2

s3

(t)observations

0 100 200 300 400 500 600 700 800 900 1000

t

-4

-2

0

2

4

x1

(t)

0 100 200 300 400 500 600 700 800 900 1000

t

-4

-2

0

2

4

x2

(t)

-4 -3 -2 -1 0 1 2 3

x1

(t)

-3

-2

-1

0

1

2

3

x2

(t)

scatter plot

x2

(t) vs. x1

(t) for each t

columns of A

Sparse Representation and Estimating Mixing Matrix

28

0 2000 4000 6000 8000 10000 12000

k

-5

0

5

10

cx

1

(k)

coefficients of observations

0 2000 4000 6000 8000 10000 12000

k

-5

0

5

cx

2

(k)

-5 0 5 10

coefficient cx

1

(k)

-5

0

5

coef

ficie

nt c

x2

(k)

scatter plot in Cartesian coordinates

0 1 2 3 4

angle (k)

-5

0

5

10

radi

us

(k)

scatter plot in Polar coordinates

0 0.5 1 1.5

angle (k)

0

500

1000raw histogram [naive approach]

0 0.5 1 1.5

angle l

0

100

200

300histogram weighted by | |

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9columns of A

columns of Aest

Sparse Representation

Estimating Mixing Matrix

A – red Aest – blue

Separation and Reconstruction

29

0 2000 4000 6000 8000 10000 12000

k

-5

0

5

cs

1

(k)

coefficients of sources (binary masking)

0 2000 4000 6000 8000 10000 12000

k

-5

0

5

cs

2

(k)

0 2000 4000 6000 8000 10000 12000

k

-10

0

10c

s3

(k)

0 100 200 300 400 500 600 700 800 900 1000-4

-2

0

2

4

angl

e er

ror=

0.0

(deg

)

s1

, kurtosis= 3.16

0 100 200 300 400 500 600 700 800 900 1000

ym4L5,dct,sin,wpdb1L5,wpdb2L5,wpdb4L5,wpdb6L5,wpdb12L5,wpsym24L5,dmeyL5,RnIdent

-4

-2

0

2

4

corr

elat

ion=

0.9

8

s1

reconstructed, kurtosis= 3.06

0 100 200 300 400 500 600 700 800 900 1000-4

-2

0

2

4

angl

e er

ror=

0.0

(deg

)

s2

, kurtosis= 2.83

0 100 200 300 400 500 600 700 800 900 1000

ym4L5,dct,sin,wpdb1L5,wpdb2L5,wpdb4L5,wpdb6L5,wpdb12L5,wpsym24L5,dmeyL5,RnIdent

-4

-2

0

2

4

corr

elat

ion=

0.9

8

s2

reconstructed, kurtosis= 2.83

Separation

Reconstruction

Simulation Results – Estimating Noise

30

Greedy Algorithm

INR (dB) no RFI -25 -20 -15 -10

duty-cycle

100% 0.985, 0.979

0.982, 0.977

0.978, 0.975

0.972, 0.970

0.965, 0.958

1% 0.983, 0.978

0.978, 0.975

0.970, 0.966

0.953, 0.946

Global Optimization

INR (dB)

no RFI -25 -20 -15 -10

duty-cycle

100% 0.988, 0.986

0.987, 0.987

0.984, 0.981

0.981, 0.974

0.977, 0.973

1% 0.987, 0.981

0.984, 0.980

0.976, 0.970

0.961, 0.949

Measure of performance: correlation between original noise and reconstructed noise

E[|corr. coeff. btw 𝑛𝑛𝐻𝐻 and 𝑛𝑛𝐻𝐻� | ] E[|corr. coeff. btw 𝑛𝑛𝑉𝑉 and 𝑛𝑛𝑉𝑉� |]

Simulation Results – Estimating Noise Power

• Requires scale estimation • Scale = median(reconstructed noise / original noise) • In practice, scale can be estimated by exploiting neighbors scale

• Measure of performance: relative error between power of reconstructed noise and power of original noise

31

Greedy Algorithm

INR (dB) no RFI -25 -20 -15 -10

duty-cycle

100% 1.9, 2.5

4.7, 4.5 3.2, 4.0 5.9, 5.7 6.1, 6.5

1% 2.3, 3.5 3.1, 3.9 4.8, 5.5 8.2, 10.0

Global Optimization

INR (dB) no RFI -25 -20 -15 -10

duty-cycle

100% 0.6, 2.6

1.1, 1.7 1.9, 4.1 3.5, 7.8 4.9, 6.7

1% 0.9, 5.2 1.6, 4.2 2.8, 5.9 6.0, 8.8

𝐸𝐸𝑣𝑣𝑎𝑎𝑜𝑜 𝑠𝑠𝑐𝑐𝑙𝑙𝐻𝐻 ∗ 𝑛𝑛𝐻𝐻)� − 𝑣𝑣𝑎𝑎𝑜𝑜(𝑛𝑛𝐻𝐻

𝑣𝑣𝑎𝑎𝑜𝑜 𝑛𝑛𝐻𝐻× 100% 𝐸𝐸[

𝑣𝑣𝑎𝑎𝑜𝑜 𝑠𝑠𝑐𝑐𝑙𝑙𝑉𝑉 ∗ 𝑛𝑛𝑉𝑉)� − 𝑣𝑣𝑎𝑎𝑜𝑜(𝑛𝑛𝑉𝑉𝑣𝑣𝑎𝑎𝑜𝑜 𝑛𝑛𝑉𝑉

] × 100%

RFI Detection

32

SCA Classifier (median, kurtosis)

Correlation to solve scaling

ambiguity

Inputs, x

Outputs: separated signals, �̂�𝑠

Detector

RFI signal:

𝑠𝑠� j

ROC curves

• SCA scaling ambiguity is evident from previous simulations • Use correlation after classification to minimize scaling

ambiguity

• Use statistical measures as classifiers • Use statistical measures such as median, kurtosis, etc. as

detectors • Pass only predicted RFI signal through detector

RFI Detection Using SCA • Detection criteria: median(abs(reconstructed sources) ) • SCA is capable of detecting RFI with high INR and high duty-cycle

33

• Detector: – Prob. Detection:

• Median of absolute value of reconstructed sources H1 > threshold

– Prob. False Alarm: • Median of absolute value of • reconstructed sources H0 > threshold

• ROC thresholds: 0:0.01:1

SCA Inputs, x Outputs:

separated signals, �̂�𝑠

Detector (Median)

ROC curves

RFI Detection By Median

34

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

probability of false alarm

prob

abili

ty o

f det

ectio

n

INR= 0dBINR = -10dBINR = -15dB

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

probability of false alarm

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

prob

abili

ty o

f det

ectio

n

duty-cycle = 100%

INR=-15

INR=-12.5

INR=-10

INR=-7.5

INR=-5

INR=-2.5

INR=0

INR=2.5

Algorithms I • Dictionary

• Structured dictionary • Joint sparse representation

• Greedy algorithm - OMP • Mixing matrix estimation

• Global clustering – Weighted histogram

• Separation • Binary masking

Algorithms II • Dictionary

• Structured dictionary- different set of dictionaries

• Joint sparse representation • Global optimization- exact

sparse coding • Mixing matrix estimation

• Global clustering – Weighted histogram

• Separation • Local separation

Conclusions

• SMAP’s current algorithms for RFI detection and mitigation are performing well

• Sources that are wideband and occupy much of the bandwidth cannot be corrected by any of SMAP’s RFI filtering algorithms

• Blind source separation results indicate that these type of algorithms are not sensitive enough for the RFI detection problem and they are also quite computationally intensive

• These results indicate the need for continued protection of spectrum

35

ICA Algorithms

• Fast ICA (FASTICA) – 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) – 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) – 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) – 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) – 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) – 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.

36

Radio frequency interference detection and mitigation in microwave radiometers�SMAP RFI MAXPDRFI Probability MapWeekly Peak Hold RFI Maps: H-polFullband Kurtosis H-pol Subband Kurtosis H-pol TA H-pol Asia: October 1-7 2016RFI Sources Localized by SMAP over ChinaSpectra measured by SMAP over the main Japanese citiesSpectra over JapanSlide Number 12Slide Number 13GMIMotion Detector UnitsWideband RFI Mitigation Subsystem for Microwave RadiometersWideband RFI TelemetryComplex Kurtosis Hardware ResultsBlind Source SeparationIndependent Component AnalysisICA AlgorithmRFI DetectionAUC Results – ICA Performance – Wide BandICASparse Component AnalysisSCA In PracticeSparse Signal RepresentationSCA Example: Sources with non disjoint supportsSparse Representation and �Estimating Mixing Matrix Separation and ReconstructionSimulation Results – Estimating NoiseSimulation Results – Estimating Noise PowerRFI DetectionRFI Detection Using SCARFI Detection By MedianConclusionsICA Algorithms