IEEE Adaptive Antennas+ 20070418ieeenj/archived_slides/2007-04-18_MTT.pdf20070418RJL-2 Summary Slide...
Transcript of IEEE Adaptive Antennas+ 20070418ieeenj/archived_slides/2007-04-18_MTT.pdf20070418RJL-2 Summary Slide...
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20070418RJL-1
NJ IEEE
Adaptive Antennas+
April 18, 2007
Presenter: Ray Lackey
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Summary Slide
• Antennas• Application Specific Design for System Application• Architectures and Algorithms• Antenna Array Basics • Nulling Constraints• Processor Implementation• Beam Steering in Small Array• Directions in Adaptive Signal Processing• Acronyms & Abbreviations
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Antennas
• Basic Function — Interface or translate between
electronics and space.Receive - detect RF energy and provide signals to further processingTransmit – inject RF energy into space
• Additional Functions:— Provide Gain for desired signal— Block undesired signal— Spatial Separation of signals
• Antenna Design Features— Frequency band of operation— Instantaneous Bandwidth— Coverage— Directionality— Gain— Steering
BeamNull
• Physical Limitations— Not Following Moore’s Law
The antenna serves the functional equivalent of our ears in audio communication.
The antenna serves the functional equivalent of our ears in audio communication.
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Application Specific Design for System Application
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Antenna Complexity Levels• Omni – uniform sensitivity in all
directions; Signal can come from anywhere – Example- Car radio antenna.
• Directional – focused on a fixed direction; Signal is only coming from standard direction; Example – Dish TV.
• Scanning – focused but mechanically scanning a fixed volume; Need both omni coverage and gain; Radar or IFF interrogation.
• Electronic Scanning – electronic focusing and scanning; Need both zonal coverage and gain; Examples – phased array radar or IFF interrogation
• Adaptive – electronic adjustment to enhance the desired and/or reduce the interference; Either no idea where the signal or interference will come from-Examples – SNAP and EJS, omni moving desired and jammers; or known direction for desired – examples – radars, dish communications, etc.
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Signal Discrimination
NullsteeringCode (Sample Orthogonal To Epoch)Notch FilteringUndesired
BeamsteeringCode (Sample During Epoch)Passband FilteringDesired
SpaceTimeFrequencyDimension
• Can be Fixed or Changing• Adaptive Arrays are used for spatial discrimination of signals
— Nullsteering – null high powered jamming sources to reduce them below power of effectiveness
— Beamsteering – form a beam on the desired signal to enhance its signal to noise ratio
— Simultaneous Beamsteering/Nullsteering – form the best beam possible on the desired signal while forming nulls on any interfering signals to yield the best possible signal to interference plus noise ratio
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Problems with Beam Steering
• Array size determines beamwidth
• Array illumination determines sidelobe levels
• Array size determines position of sidelobes
• Discrimination is poor for small arrays
Scan= 0 deg
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Magic of Adaptive Array
• Apparently reduced sidelobes
• Apparently sharper Beamsteering
• Without increasing array size
• Need to be careful!
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Auxiliaries Designed for Coverage
Adapted Pattern
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Main BeamDifference BeamNear-Horn AuxFar-Horn AuxOmni Aux
Auxiliary Coverage
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Main BeamDifference BeamNear-Horn AuxFar-Horn AuxOmni Aux
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Adapted Beam
This kind of design constraint is insufficient for GPS Reference Antenna since, in reality, sidelobes are pushed up and allow multipath reception.
This kind of design constraint is insufficient for GPS Reference Antenna since, in reality, sidelobes are pushed up and allow multipath reception.
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Early Radar ProgramsStressed the sidelobe canceller problem in dense clutter
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AREAS OF APPLICATION of ADAPTIVE PROCESSING
• Space - Adaptive Arrays
• Frequency - Adaptive Filters
• Time - Adaptive Filters and Multipath Cancellers
• Polarization - Adaptive Polarization Cancellation
• Cosite - Adaptive Cosite Cancellation
• Co-Channel - Adaptive Co-Channel Signal Separation
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Adaptive Arrays – Spatial Separation
• Adaptive Spatial Filter— Cancels wideband signals in
space— Requires additional elements— Programmable weights— Adaptive Controller
• Advantages— Preserves Desired Signal— Very large rejection ratios possible
• Disadvantages— Additional antennas required— Platform exterior modification
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Adaptive Temporal Filtering Frequency Separation
• Adaptive FIR filters— Cancel narrowband interferers— Programmable Weights— Adaptive Controller
• Advantages— No additional antennas required— No platform exterior modification
• Disadvantages— Excises portion of code correlation— Frequency onl
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Cosite Interference Canceller
• Cancel interference from collocated transmitter— Requires sample of transmitter
• Advantages— Does not take out any spatial
coverage— Does not take out any signal
spectrum
• Disadvantages— Costly
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Architectures and Algorithms
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Adaptive Array Building Blocks
• Array of antennas— Number of antennas <(N-1)
Degrees of freedom— A degree of freedom is used for
each independent null— Output Y = Sum over all i from 1
to N of wi*xi
• Processor to control the weights
[ ] PRW 1−=
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BACKGROUND CORRELATION MATRIX CALCULATION
• ASSUME JAMMERS ARE MUTUALLY UNCORRELATED• ASSUME FREQUENCY COMPONENTS WITHIN A JAMMER ARE
INCOHERENT• ASSUME POLARIZATION COMPONENTS FOR A GIVEN JAMMER AND
FREQUENCY ARE COHERENT• FORM A CORRELATION MATRIX FOR EACH JAMMER AND
FREQUENCY USING THE JAMMER ARRIVAL ANGLES, POWER, POLARIZATION; THE ELEMENT PATTERNS AT THE JAMMER ARRIVAL ANGLES; AND THE PROPAGATION DELAYS TO THE ELEMENT PHASE CENTERS
• SUM THESE MATRICES OVER ALL JAMMERS AND FREQUENCIES• ADD NOISE LEVEL TO MATRIX DIAGONAL
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SOLVE FOR STEADY STATE ADAPTED WEIGHTS
— SPECIFY PILOT/STEERING VECTOR
— CALCULATE MATRIX INVERSE WEIGHT SOLUTION
MODIFY FOR PROCESSOR IMPOSED WEIGHT CONSTRAINTS
[ ] PRW 1−=
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Jammer Nulling
• Auxiliary Jammer Vector— Amplitude adjusted equal to
Reference Jammer Vector— Phase adjusted 180° out from
Reference Jammer Vector
• Sum goes to zero
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Desired Signal
• Auxiliary Desired Vector— Amplitude adjusted same as
Auxiliary Jammer Vector— Phase adjusted same as Auxiliary
Jammer Vector
• Sum goes to new value— Often, no control— Can be nulled
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Least Mean Square (LMS) Algorithm
• Output is correlated with Auxiliary• Correlation value is filtered to
smooth weight• Loop Gain (G) limits nulling depth• Other limits
— Integration Time Constant— Other signals— Thermal Noise— Time Match
A→C=B → CA → C → E=B → D
• Reverse the sign in the correlator and get adaptive beamsteering
A B
D
C
E
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Gram Schmidt Preprocessing
• Spread of Covariance Matrix eigenvalues yield slow adaptation
• Preprocessing orthogonalizes the matrix at each level
• Adaptation time is accelerated
• Much more complex
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Digital Control of Weights
• Output power is measured
• Weight is changed
• Output Power is Measured
• Was it a good change?
• If Yes, do it again.
• If No, try something different.
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All Digital Antenna Electronics
• Advantages— Increased functionality
BeamsteeringNullsteeringFiltering
— Parallel output channels
• Disadvantages— Front end dynamic range— A/D converter cost— A/D Converter power
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Structure Of Perturbational Adaptive Algorithm
• Use Of Odd Symmetry Sequences Provides An Unbiased Estimates Of The Weight Gradients
• Need Two Odd Symmetry Sequences Per Input Element/mode To Deal With Real And Imaginary Parts Of Each Weight
• Any Subset Of Odd Symmetry Sequences Can Be Selected
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Perturbational Adaptive Weight Controller
• Correlation Of The Instantaneous Output Power Of The Adapting Array With The Perturbational Code Set Provides Estimates Of The Components Of The Gradient For Weight Vector Updates
• Gradient Estimates Are Unbiased
• Gradient Estimates Are Averaged To Reduce Mis-adjustment Noise
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Antenna Array Basics
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Array Aperture• Array Beamwidth is inversely
proportional to perpendicular aperture in wavelengths.— As the scan angle increases from
perpendicular, the beam grows wider.
— As the array aperture is reduced, the beam grows wider.
— As the frequency goes down, the beam grows wider.
• Beamwidth (radians)— BW3dB = (λ/A)*cosθ— = (1/Aλ) cosθ— BWnull = (2/Aλ) cosθ
• Beamwidth (degrees)— BW3dB = (180/п)*(λ/A)*cosθ— = (180/пAλ) cosθ— BWnull = (360/пAλ) cosθ
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Array Aperture• Array Beamwidth is inversely
proportional to perpendicular aperture in wavelengths.— As the scan angle increases from
perpendicular, the beam grows wider.
— As the array aperture is reduced, the beam grows wider.
— As the frequency goes down, the beam grows wider.
• Beamwidth (radians)— BW3dB = (1/Aλ) cosθ
• Examples:— A: 300 MHz, # elements (N) = 9,
aperture in λ (A)=4, Steer Angle (θ) = 0°(broadside), Element Spacing in λ (D) = 0.5.
— B: 300 MHz, N=9, A=4, θ=30°, D=0.5.— C: 300 MHz, N=9, A=4, θ=60°, D=0.5.— D: 300 MHz, N=9, A=4, θ=90°, D=0.5.
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Array Aperture• Array Beamwidth is inversely
proportional to perpendicular aperture in wavelengths.— As the scan angle increases from
perpendicular, the beam grows wider.— As the array aperture is reduced, the
beam grows wider.— As the frequency goes down, the beam
grows wider.• Beamwidth
— BW3dB = (1/Aλ) cosθ• Examples:
— A: 300 MHz, # elements (N) = 9, aperture in λ (A)=4, Steer Angle (θ) = 0°(broadside), Element Spacing in λ (D) = 0.5.
— B: 300 MHz, N=8, A=3.5, θ=0°, D=0.5.— C: 300 MHz, N=7, A=3, θ=0°, D=0.5.— D: 300 MHz, N=5, A=2, θ=0°, D=0.5.
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Array Aperture• Array Beamwidth is inversely
proportional to perpendicular aperture in wavelengths.— As the scan angle increases from
perpendicular, the beam grows wider.— As the array aperture is reduced, the
beam grows wider.— As the frequency (f) goes down, the
beam grows wider.• Beamwidth
— BW3dB = (λ/A)*cosθ— BW3dB = (L/fA)*cosθ
• Examples:— A: 300 MHz, # elements (N) = 9,
aperture in λ (A)=4, Steer Angle (θ) = 0°(broadside), Element Spacing in λ (D) = 0.5.
— B: 200 MHz, N=9, A=8/3, θ=0°, D=0.33.— C: 150 MHz, N=9, A=2, θ=0°, D=0.25.— D: 100 MHz, N=9, A=4/3, θ=0°,
D=0.167.
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Element Spacing• Array Response is cyclical in cosine
space• Beamwidth
— BW3dB = cosθ/2Aλ
— BWnull = cosθ/Aλ
• Examples:— A: 300 MHz, # elements (N) = 9,
aperture in λ (A)=4, Steer Angle (θ) = 0° (broadside), Element Spacing in λ (D) = 0.5.
— B: 300 MHz, N=9, A=6, θ=0°, D=0.66.
— C: 300 MHz, N=9, A=8, θ=0°, D=1.— D: 300 MHz, N=9, A=16, θ=0°,
D=2.
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Array Characteristics
• Patterns are really 3-D and have characteristics dependent upon element and array factors.
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Nulling Constraints
• Very sensitive to variations
• Total null considers RMS across band of interest
• 40 dB Null requires— ±0.06 RMS Phase Control— ±0.1 dB Amplitude Control
NULL DEPTH LIMIT
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Array Aperture
• Array Nullwidth is inversely proportional to perpendicular aperture in wavelengths.— As the scan angle increases from
perpendicular, the null grows wider.
— As the array aperture is reduced, the null grows wider.
— As the frequency goes down, the null grows wider.
• Null moves with frequency when weights are implemented with phase control
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SYSTEM APPROACH TO DESIGN - ADAPTIVE ANTENNA SYSTEM• Reception Requirements
— Spatial Coverage - Non-Adapted— Polarization— Gain— Bandwidth
• Nulling Requirements— Auxiliary Coverage— Broadband Matching
PhaseAmplitudeGroup Delay (Time)
— Spatial Variation— Null Recovery
• Production DTUPC
NULL DEPTH LIMIT
BAE SYSTEMS Has Had Over 80 Contracts in Adaptive Signal Processing So We Understand the System Requirements, Limitations, and Tradeoffs.
BAE SYSTEMS Has Had Over 80 Contracts in Adaptive Signal Processing So We Understand the System Requirements, Limitations, and Tradeoffs.
Triple JammerDense - 25 Jammers
Single Jammer
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VS-CRPA PHASE PLOTS IN POLAR COORDINATES
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Problem Solvers - Design to Fit
• GPS AJ Capability in Small Area— Maintain Reference Element Gain— >Twice the Spatial Nulling
Capability — Keeping to the Confined Space
• Lower Installation Cost— No Platform External Modification
Fitting in Allocated Space— <Half the Fielding Cost of System
Requiring Platform Requalification
VS-CRPA-88-element, <4”
Small CRPA 8-element 7” Array
Installation Cost Can More Than Double the Unit Production Cost of a System So Array Must Be Designed to Fit the Platform’s Limited Space. Installation Cost Can More Than Double the Unit Production Cost of a
System So Array Must Be Designed to Fit the Platform’s Limited Space.
Standard CRPA7-element 14” Array
Very Small CRPA8-element 3.5” Array
Very Small CRPA4-element <3” Array
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ELEMENT PHASE RECEPTIONS VARY WITH SPATIAL ARRIVAL ANGLE AND SPACING
-400
-300
-200
-100
0
100
200
300
400
Arrival Angle
Deg
rees
PPORD=1 lamdaD=.5 lamdaD=.33 lamdaD=.25 lamdaD=.125 lamda
Typical arrays with identical elements depend upon aperture for phase variation
from center reference element.
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RELATIVE PHASE SLOPE LIMITS NULLING SHARPNESS
020406080
100120140160180200
Arrival Angle
Rel
ativ
e Ph
ase DEL D=1 lamda
DEL D=.5 lamdaDEL D=.33 lamdaDEL D=.25 lamdaDEL D=.125 lamda
Typical arrays with identical elements have a relative phase dependency on
arrival angle and spacing.
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NULLING SHARPNESS DUE TO RELATIVE PHASE SLOPE CAN BE ENHANCED BY SPATIAL ARRAY SIZE.
0
1
2
3
4
5
6
7
Arrival Angle
Rel
ativ
e Ph
ase
Slop
e
DPDA D=1 lamdaDPDA D=.5 lamdaDPDA D=.33 lamdaDPDA D=.25 lamdaDPDA D=.125 lamda
Relative phase of typical arrays with identical elements is limited
to spatial separation.
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-200
-150
-100
-50
0
50
100
150
200
Arrival Angle
Deg
rees
PPORD=.5 lamdaUPOPPOLPPORX2PPOLX2PPORX3PPOLX3
VARIATIONS IN ELEMENT PHASE RECEPTION WITH SPATIAL ANGLE PROVIDE “EFFECTIVE” APERTURE
Typical arrays with identical elements depend upon maximum aperture for phase variation from
center reference element.
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020406080
100120140160180200
Arrival Angle
Rel
ativ
e Ph
ase
DEL D=.5 lamdaDEL UPODEL PPOLDEL PPORX2DEL PPOLX2DEL PPORX3DEL PPOLX3
RELATIVE PHASE SLOPE LIMITS NULLING SHARPNESS
Relative phase is adjusted to zero to form null in a region but breaking out of the null depends
on relative phase slope.
Typical arrays with identical elements have a relative phase dependency on arrival angle.
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00.5
11.5
22.5
33.5
44.5
Arrival Angle
Rel
ativ
e Ph
ase
Slop
e DPDA D=.5 lamdaDPDA UPODPDA PPOLDPDA PPORX2DPDA PPOLX2DPDA PPORX3DPDA PPOLX3
NULLING SHARPNESS DUE TO RELATIVE PHASE SLOPE CAN BE ENHANCED BY SPATIAL ARRAY SIZE OR BY ELEMENT FACTORS.
Relative phase of typical arrays with identical elements is limited
to spatial separation.
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VS-CRPA PHASE PLOTS IN POLAR COORDINATES
Used Output Mode
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Processor Implementation
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Weight Implementation
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Correlator Implementation
• Vector Modulator is favored• Yields direct I/Q control signals• Sensitive to Mixer Characteristics
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The Adaptive LMS Loop
• Correlates Auxiliary with Feedback• Integrates to smooth weights• Null depth function of Loop Gain
and Integration Filter Time Constant• Adaptation time function of Loop
Gain and Integration Filter Time Constant
• Many modifications due to:— Application— Scenario variation— Component Limitations— Discriminants to protect the
desired signal
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Beam Steering in Small Array
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Multiple Channel Beam Steering/Adaptive Nulling
• Steers Beam In Unjammed Environment
• Maximizes S/(J+N) Along the LOS to the Satellite Being Tracked
• Parallel Processing For Each Satellite In Each Band To Individual Receivers
• IMU Provides Real-time Corrections
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Adapted Pattern with Reference Mode as Pilot Vector
Pilot vector through the LMS algorithm is with respect to the Reference mode
Under the constraint of minimizing the power delivered to
the GPS Rx.
Borderline Performance
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Adapted Pattern with Pilot Vector Steered To AZ=270,EL=72
Pilot vector through the LMS algorithm is with respect to a vector along a LOS to the satellite
Improvement over Reference Pilot = 4.70 dB even with just S-CRPA
Maximizes S/N in direction of satellite
w.r.t background
The best solution to that problem has broader
nulls in the location of the jammers
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Directions in Adaptive Signal ProcessingFuture and Past
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Directions in Adaptive Arrays for Nulling/Beamsteering• Applications
— Future requirement for GPS AJ on all platforms – huge market— Communication systems have increased need for LPI, LPD, AJ
Null steering and beam steering• Arrays
— Smaller, more dense arrays— Customized to application— LO requirements for many platforms
• Processors— Major cost driver for fielding— Diverging directions of requirements
Huge market for low cost platformsEnhanced performance requirement for valuable platforms
— Direction of arrival information desired for additional action
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ADAPTIVE ARRAY / CO-SITE INTERFERENCE CANCELLATION BACKGROUND
• Over 90 Adaptive Signal Processing Programs• Over 20 Patents in Adaptive Signal Processing• Over 10 CRPA Antenna Programs• Broad Technology Base
— VLF through EHF beginning in late 1960s— Early Radar Programs— SNAP* - Family of Processors— Avionics Adaptive Arrays— Microwave Adaptive Processors— Tactical Communications (TACOM) Mission Model— All-Digital Architectures— Microcircuit Devices— Algorithm Development
* Steerable Null Antenna Processor
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SIGNAL PROCESSING LEGACY
• Approx. 1000 SNAP (Steerable Null Antenna Processor) Units Delivered
• Pioneers in Adaptive Processing— Spatial and Temporal Processing demo’d in the 1960s— Channelized Frequency Processing demo’d in the 1970s— Digital Space and Frequency Processing demo’d in the Early 1990s— Built Processors implementing conventional LMS, Perturbational, Digital
Search and Vector Processing Algorithms— Demonstrated Multi-level Processing to reduce multiple low-level
interferers in presence of high-level dominant source— Demonstrated DF & Copy early 1990s with Digital Direction Finding,
Independent Beamsteering, Interference Nulling, and Copy— First Demonstration of Switched Beam Adaptive Arrays for Cellular Base
Stations
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SIGNAL PROCESSING LEGACY YIELDS ANTENNAREQUIREMENTS INSIGHT
• Antenna Developments for Adaptive Arrays— HF-SNAP – Ferrite-Loaded Loop Auxiliaries allowed receive nulling on
jeep— ACPA – VHF DF and Interference Nulling on P3 for Sonobuoy Link— IFF Diversity Array with Space-Time Processing— DCS – Adaptive Polarization— S-CRPA – 7-element array in 7-inch square – Four Contracts awarded –
Ours only successfully delivery and demonstration— VS-CRPA-4 – Spin-off from S-CRPA with potential for small platforms
(PGM and unattended sensors)— VS-CRPA-8 – Extension of S-CRPA concept for Submarine Mast— CRPS-3 – Packing VS-CRPA-8 into a FRPA-3 footprint— Low Observable CRPAs with and without S-CRPA techniques
• Several Patents in the area of Algorithm Design for improved performance
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CO-SITE EXPERIENCE
ICS-approach can have problems on large platforms because of the long lengths of cables involved and location of ICS in central radio room. Techniques were developed that allowed wideband ICS operation and compensation of distortions introduced by devices and long multipath loops.
WICS
A band-switched antenna was developed to reduce cosite interference for multi-radio installations. The antenna tunes for transmission or reception within its transceiver channel, rejecting out-of-channel signal reception or reducing out-of-channel emissions.
VHF SINCGARS Band-Switched Antenna for Army
Shipboard Single Channel Ground and Airborne Radio Systems study of antenna isolation, frequency hopped filters, and ICS concluded antenna isolation was the cost effective solution.
VHF SINCGARS radio
MSNAP at UHF 225 – 400 MHz included a design for an embedded ICS with a bank of four channels.
MSNAP UHF ICS
Several programs have investigated this problem on several different platforms. Solutions have included antenna isolation and/or increased filtering (notched or pass band) modifications to the individual systems.
JTIDS(MIDS) - IFF
An HFICS system was developed for the Army.HFICS
Interference Canceller Systems (ICS) developed / demonstrated on IRAD for a VHF FAA radio. Modulation was AM. Sixty to 70 dB nulling demonstrated for operation several 10s of kHz away from desired channel
FAA VHF Radio
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ADAPTIVE PROCESSING
Design/Qualify 15 Units to EDM MIL SpecsLABCOMVHFSNAP-I EDM
Advanced Microcircuit Implementation of LMS AlgorithmRADCIF @
VHFLow Cost LMS Processor
R/T SNAP with Diode SwitchesLABCOMVHFDiode SNAP
Spatial ECCM for SINCGARSLABCOMVHFSINCGARS SNAP-II Study
SAW Tapped Delay Line to Compensate for DispersionRADCIF @
VHFAdaptive Time Delay Module
SNAP-I-Program for HelicoptersLABCOMVHFAirborne SNAP
Two-Element Receive Adaptive Array for VRC-12LABCOMVHFSNAP-1 ADM
Six-Element Adaptive Array for Band III GRC-103LABCOMUHFMicrowave Steerable Null
Antenna Processor (MSNAP)
High-Power Switched Delay Lines Used in Two-Element Array for VRC-12LABCOMVHFReceive/Transmit (R/T) SNAP*
CommentsAgencyFreq.Program
* (SNAP) = Steerable Null Antenna Processor
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ADAPTIVE PROCESSING / CO-SITE INTERFERENCE
Integrated Low Cost Antenna/FH Filter and Adaptive Processor for Band I GRC-226
Company FundedUHFMSNAP
Spatial Processor Integrated with FH Filter for Testing on F-16 and C-130RADCUHFHAVE QUICK Adaptive Processor
Achieve Compatibility with GRC-226 RadioLABCOMUHFProduction Concept for MSNAP
Add Interference Cancellation System and Other Improvements to MSNAPLABCOMUHFMultichannel SNAP Refurbishment
Produce 900 Units for Army and MarinesCECOMVHFSNAP-I Production
Phased Array Adaptive Processor for Band I GRC-103LABCOMUHFMultichannel SNAP (MSNAP)
Extend HF SNAP-I to work with FH HF-STAJLABCOMHFHF SNAP-II
Jeep-Mounted Adaptive Processor for Non-Hopped CommunicationsLABCOMHFHF SNAP-I
ADM Spatial Processor for SINCGARSLABCOMVHFSNAP-II
CommentsAgencyFreq.Program
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Adaptive Control Phased Array (ACPA)
• 4-element array
• 3 degrees of freedom
• Beamport mode
• Progressive phaseomni mode
• Selectable bandwidth
• Adaptive notch filter
Sonobuoy UplinksNADC / NAVAIR-sponsored
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MARK XII Adaptive Array
• Full-diversity upper and lower arrays
• Conformal 3-element patch array
• Applique
• 3 degrees of freedom (U/L)
• Tapped delay lines
• Cross-coupledAUX ANT mode
Alternative to MARK XV/Mode 5ASD / WRDC-sponsored
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Post-processing The Correlation Matrix For DOA• Spatial Correlation Matrix Is Basis For Most DOA Processing (“Music”
As An Example)— Extract Eigenvalues And Corresponding Eigenvectors— Divide Eigenvalues Into “Signal” And Noise Subspaces— Search Noise Subspace Over The Array Manifold For Potential Signal
Directions— Select Search Nulls As “Signal” Directions— Sample Results Shown From Keystroke Program Showing Very Good
Match Of Actual And Estimated Locations.
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ACRONYMS & ABBREVIATIONS
Acronym/Abbreviation Description
AE Antenna Electronics CRPA Controlled Reception
Pattern Antenna LMS Least Mean Square SNAP Steerable Null Antenna
Processor