1. Military Radar Summit
Smart Antennas
101
Frank Gross
2/25/15

2. Relevant Books

3. Examples of “Smart Antennas”
Precision Acquisition Vehicle Entry Phased Array Warning System
450MHz: 1,792 Antennas, kW
Detect and Track ICBMs
PAVE PAWS

4. Very Large Array (VLA) – New Mexico
74 MHz to 50 GHz
13 mi
82’
120o

5. HF Antennas/ HAARP Facility
High Frequency Active
Auroral Research Program
Gakona, Alaska
HF: 2.8 – 10MHz / Antennas

6. Active Electronically Steered Array (AESA)
L-Band (1-2 GHz)
X-Band (8-12 GHz)
F-16

7. Definition of “Smart Antennas”
The term “Smart Antenna” refers to any antenna or array which can adjust or adapt its beam pattern according to a desired criteria. w1  wM w2 y
Algorithm d  + -
Desired signal
Suppressed Interference w1  wM w2 y
“Dumb” Antenna
“Smart/Cognitive” Antenna

8. Smart Antennas can encompass:
Smart Switched Beam Arrays –
Butler Matrix, Rotman Lens, Plasma Array
Smart Reconfigurable Antennas –
Change electrical properties to steer beam
Smart Surfaces/Metamaterials –
Substrate change causes beam change
Smart Vector Antennas –
Direction finding with single antenna using polarization
Smart Adaptive Arrays –
Steer the beam to any direction of interest while simultaneously minimizing/nulling interfering signals

9. Switched Beam Array – Rotman Lens
True Time Delay = Large Bandwidth
Beam Direction
Feed
Rotman Lens Feeding a Vivaldi Array
32 Ports/32 Beams
Frontiers in Antennas, 2011
REMCOM Software Rotman Design

10. Applications for Smart Antennas
Beamsteering
Jammer Nulling
Adaptive Tracking
Multipath Mitigation
Active Electronically Steered Arrays (AESA)

11. Uniform Linear Antenna Array Modern Steering Vector:
Antenna Array Basics  d 2d
(N-1)d z
Antennas, d  /2
N-Element
Uniform Linear Antenna Array
Uniform Weights
Classic Array Factor:
Modern Steering Vector:

12. Uniform Array Weights
30o
Equal Gains Across Array
Simple Array: Can’t manipulate sidelobes or nulls

13. Second Level of Control
By applying varying scalar weights (gains) to the array elements, we can suppress sidelobes
Similar to windowing sampled data in the FFT world
Window functions can be
Bartlett
Hanning
Hamming
Kaiser-Bessel
Dolph-Chebyshev, etc…
MATLAB has many of these window functions  w1 w2 wM
d/2
-d/2
3d/2
-3d/2
(2M-1)d/2
-(2M-1)d/2
  

14. Scalar Weight Beamforming
Kaiser-Bessel weights
, k = 0,1,... N/2,  > 1
15dB

15. Complex Weight Beamforming
Weights can also include amplitude and phase to allow us to steer the beam to a desired angle
0o o o
d = spacing between antennas
k = wavenumber = 2/
Beamsteering + Kaiser-Bessel

16. Propagation Over Water
Low flying threats
Low grazing angle means highly correlated multipath
AOA accuracy is exacerbated by low-angle multipath
The evaporation duct can also contribute to multipath
Let’s use Maximum Likelihood detection
Find the projection of measured data onto a 2-D space of Gram-Schmidt orthonormalized steering vectors.
Model glistening rough sea surface
Various sea states (SS=0,…,5)
Model direct path, specular path, & diffuse path, vertical and horizontal polarization, rms wave height, and rms facet slope.
Include divergence factor for curved earth, specular scattering factor, and diffuse scattering factor for rough surfaces
Use a vertical sparse array to find direct signal

17. Diffuse and Specular vs. Roughness

18. Like what you see when looking out over the ocean at sunset
Glistening Surface
Like what you see when looking out over the ocean at sunset h2
Glistening Surface

19. Total received field
The signal received at the kth antenna element is composed of the direct path, specular path, and diffuse path
Direct Specular Scattering Diffuse Scattering
Where, k= Classic Fresnel reflection coefficient wrt antenna element k
D = divergence factor
s= specular scattering factor
d =.5*(1- s) diffuse scattering factor
Rk = specular path length difference to element k
Fm = Amplitude function over range of glistening surface
m = phase function over range of glistening surface
m = discrete glistening flash points

20. Multipath The direct path angle is positive relative to the horizon
Need algorithm to search simultaneously for positive angle direct paths and negative angle multipath 
direct
diffuse
specular + -
Phased Array

21. Maximum Likelihood Solution to Multipath
Helps tackle highly correlated multipath
N element array;
D arriving angles
kth time sample
a = array steering vector

22. Maximum Likelihood Solution to Multipath
Now form the NxD signal matrix.
We may now perform the Gram-Schmidt orthonormalization procedure to find D basis vectors sd where d = 1,2,…,D.
The S matrix is given as:
Where,

23. Maximum Likelihood Solution to Multipath
We define the likelihood function as:
Where,
We can form the L2-norm of the likelihood function to be

24. Example with 5 Element Array
SS = 5; Known direct angle =
Estimated direct angle = 12.50
Maximum Likelihood Surface

25. Example 2: Highly Correlated Multipath
Three frequencies of 2GHz, 8GHz, and 14GHz. 5-element vertical array. Assume direct, specular, and diffuse angles 

26. Adaptive Algorithms
Adaptive algorithms attempt to minimize a “Cost Function” J(w)
The cost function is derived based upon a specified criteria such as
Maximum signal-to-interference ratio (SIR)
Minimum variance distortionless response (MVDR)
Minimum mean-square error (MSE)
Constant modulus algorithm (CMA)
Once the cost function is defined, various methods can be used to find the minimum either in closed form or by using a recursion relationship

27. Maximum Signal-to-Interference Ratio (SIR)
 0 1
x1(k)
x2(k)
xM(k)
w1*
s(k) 
y(k)
w2*
wM* N
i1 (k)
iN (k) ?
Let us define the signal-to-interference ratio
Power in desired received signal
Power in undesired received signal
Cost Function

28. Maximum Signal-to-Interference Ratio (SIR)
We can maximize the SIR by taking a derivative of the cost function with respect to the needed weights (amplitude and phase out of HPA)
This leads to an eigenvector equation
The largest eigenvalue gives the highest SIR
The eigenvector solution yields the optimum weights

29. Example of maximum SIR
M=10 elements, 0 =300, 1 =-300, 2 =-400, 3 =500
300
-400
500
-300

30. Minimum Variance Distortionless Response (MVDR)
If the array output:
We can define the variance as:
Where,
s = undistorted desired output signal
u = undesired interferers

31. Minimum Variance Distortionless Response (MVDR)
Minimizing the cost function we derive the optimum weights
Where
= covariance matrix of undesired signals +noise
= steering vector for desired signal

32. Airborne Cantor Ring Array
3-D Example of MVDR
Airborne Cantor Ring Array
Nulled Interferers

33. High Altitude Constrained Beams

34. AESA
Modern Active Electronically Steered Arrays (AESA) are filled arrays of wideband elements
Vivaldi elements
Fragmented patch elements
The arrays have GaAs T/R modules for every antenna element
The cost per element can be $40 to $500 depending on the power demands

35. Applied Radar, Inc. & UMASS
AESA
Vivaldi Array
Fragmented Patch Array
GTRI
Applied Radar, Inc. & UMASS
Fragmented Aperture
33:1 Bandwidth
Vivaldi Array
12:1
Bandwidth

36. Wideband Vivaldi Array
AESA
MMIC T/R Modules
Wideband Vivaldi Array
High-Performance Composite Radome
12-Channel Dual-Pol T/R Module 36

37. Wideband Dual-Pol AESA Antenna
Vivaldi Array Backing Plate
T/R Module Housings 3”

38. Low-Cost Phased Arrays
Applied Radar
UMASS Design
Vivaldi Elements
Slant Left/Right Polarizations 24 8
192 elements

39. Low-Cost Phased Arrays
AESA arrays are filled arrays with large numbers of elements
Wideband array elements cannot be removed because the inter-element coupling is crucial
A template can be devised to thin the array and preserve performance requirements
Thinned elements are terminated in dummy loads reducing T/R modules, power demands, heat, $$$

40. Low-Cost Phased Arrays
We can thin the number of active AESA elements?
Resolution
Uses fewer active elements
Side Lobe Levels -15 to -20 dB
Robust with 5 or 4-bit phase shifters
Use same element phase centers
Distinct “thinned” pattern
43% thinning
110 elements
not 192

41. Low-Cost Phased Arrays
-13dB
-16dB
Elevation; 9 GHz; 5-bit phase
Azimuth; 9 GHz; 5-bit phase
-22dB
Robust with 4 or 5-bit phase shifters (11o to 16o)
43% of elements eliminated
43% fewer elements means lower cost
Requires ~ 2x HPA power for same ERP

42. AESA Summary Filled Vivaldi Array Challenges
NxM elements, cost, temperature gradients, cooling, weight
Thinning is a viable option
Array Thinning
A novel new approach
Uses 43% fewer elements for a 192 element array
Reduces total # elements, weight, heat, etc…
Performance
Produces nearly the same beamwidths with lower sidelobes
Thinned array can be weighted/tapered to suppress sidelobes
Performs well with 5 bit phase and amplitude quantization

43. Questions?