Spatial Array Digital Beamforming and Filtering

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Spatial Array Digital Beamforming and Filtering
Tim D. Reichard, M.S.
L-3 Communications Integrated Systems Garland,
Texas 972.205.8411 Timothy.D.Reichard_at_L-3Com.com
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Spatial Array Digital Beamforming and Filtering
OUTLINE

• Propagating Plane Waves Overview
• Processing Domains
• Types of Arrays and the Co-Array Function
• Delay and Sum Beamforming
• Narrowband
• Broadband
• Spatial Sampling
• Minimum Variance Beamforming
• Adaptive Beamforming and Interference Nulling
• Some System Applications and General Design
  Considerations
• Summary

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Propagating Plane Waves
Notation Lowercase Underline indicates 1-D
matrix (k) Uppercase Underline
indicates 2-D matrix (R) or
H indicates matrix conjugate-transpose
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Processing Domains
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Some Array Types and the Co-Array Function
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Delay and Sum Beamformer (Narrowband)
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Delay and Sum Beamformer (Broadband)
. . .
z(n)
S
. . .
. . .
J number of sensor channels L number of FIR
filter tap weights
J
L-1
z(n) S S wm,p ym(n - p) wHy(n)
m1
p0
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Spatial Sampling

• Motivation Reduce aberrations introduced by
  delay quantization
• Postbeamforming interpolation is illustrated
  with polyphase filter

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Minimum Variance (MV) Beamformer

• MVBF weights adjust as the steering vector
  changes
• Beampattern varies according to SNR of incoming
  signals
• Sidelobe structure can produce nulls where other
  signal(s) may be present
• MVBF provides excellent signal resolution wrt
  steered beam over the
• Conventional Delay Sum beamformer
• MVBF direction estimation accuracy for a given
  signal increases as SNR increases

R spatial correlation matrix YY
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ULA Beamformer Comparison
w wo
PCONV(z) e(z) R e(z)
PMV(z) e(z) R-1 e(z)-1
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Adaptive Beamformer Example 1 - Frost GSC
Architecture

• For Minimum Variance let C e, c 1
• e Array Steering Vector cued to SOI
• R is Spatial Correlation Matrix y(l)y(l)
• Rideal ss Is2 Signal Est. Noise Est.
• Determine Step Size (m) using Rideal
• m 0.1(3tracePRidealP)-1
• P I - C(CC)-1C
• wc C(CC)-1c
• w(l0) wc

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Example Scenario for a Digital Minimum Variance
Beamformer
PMV(z) e(z) R-1e(z)-1
M-1
W(k) S wmej(k.x)
m0
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Example of Frost GSC Adaptive Beamformer
Performance Results
- via Matlab simulation
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Adaptive Beamformer Example 2 - Robust GSC
Architecture
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Example of Robust GSC Adaptive Beamformer
Performance Results
- via Matlab simulation
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Adaptive Beamformer Relative Performance
Comparisons

• SOI Pulsewidth retained for both Robust has
  better response
• Robust methods blocking matrix isolates
  adaptive weighting to nonsteered response
• Good phase error response for the filtered
  beamformer results
• Amplitude reductions due to contributions from
  array pattern and adaptive portions
• The larger the step size (m), the faster the
  adaptation
• Additional constraints can be used with these
  algorithms
• min lPRP is proportional to noise variance gt
  adaptation rate is roughly proportional to SNR

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Applications to Passive Digital Receiver Systems

• Sparse Array useful for reducing FE hardware
  while attempting to retain aperture size -gt
  spatial resolution
• Aperture Size (D) 17d in case with d l/2 and
  sensor spacings of 0, d, 3d, 6d, 2d, 5d
• Co-array computation used to verify no spatial
  aliasing for chosen sensor spacings
• Tradeoff less HW for slightly lower array gain
• Further reductions possible with subarray
  averaging at expense of beam-steering response
  and resolution performance

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Summary

• Digital beamforming provides additional
  flexibility for spatial filtering and suppression
  of unwanted signals, including coherent
  interferers
• Various types of arrays can be used to suit
  specific applications
• Minimum Variance beamforming provides excellent
  spatial resolution performance over conventional
  BF and adjusts according to SNR of incoming
  signals
• Adaptive algorithms, implemented iteratively can
  provide moderate to fast monopulse convergence
  and provide additional reduction of unwanted
  signals relative to user defined optimum
  constraints imposed on the design
• Adaptive, dynamic beamforming aids in retention
  of desired signal characteristics for accurate
  signal parameter measurements using both
  amplitude and complex phase information
• Linear Arrays can be utilized in many ways
  depending on application and performance
  priorities

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References
D. Johnson and D. Dudgeon, Array Signal
Processing Concepts and Techniques, Prentice
Hall, Upper Saddle River, NJ, 1993. V. Madisetti
and D. Williams, The Digital Signal Processing
Handbook, CRC Press, Boca Raton, FL, 1998. H.L.
Van Trees, Optimum Array Processing - Part IV of
Detection, Estimation and Modulation Theory,
John Wiley Sons Inc., New York, 2002. J. Tsui,
Digital Techniques for Wideband Receivers -
Second Edition, Artech House, Norwood, MA, 2001.