automotive mimo radar - alp sayin · [12] j. h. holland, adaptation in natural and artificial...

1
DEPARTMENT OF ELECTRONIC, ELECTRICAL AND SYSTEMS ENGINEERING For more enquiries, please contact: Head of MISL: Professor Mike Cherniakov, +44(0)121 414 4286 [email protected] University of Birmingham, Department of EESE, Edgbaston, Birmingham B15 2TT. www.birmingham.ac.uk/misl MIMO Sensor Array for Short-Range High-Resolution Automotive Sensing Mr A Sayin, Dr. E Hoare, Dr. M Antoniou, Prof M Cherniakov Name, [email protected], +44(0) 121 xxx xxxx 5.Experimental Results 2.Phased vs. MIMO Array A phased-array-antenna radar can be used with beam-forming techniques to direct a beam to a specific location [3]. And then the radar can scan the desired area electronically. This can be achieved since, the correlated signals from transmit antennas would add up constructively or destructively in different directions in space [2]. On the other hand, a MIMO radar uses the advantage of orthogonality for various advantages [4]. These advantages can be; reduced amount of necessary array elements, increased angular resolution, faster scan time, simultaneous search & track etc. With a MIMO array; beamforming process does not have to happen in the space but in the digital space, so we can “illuminate” the whole space of interest with single transmission [ 1]. 1.Introduction The aim of the project is to investigate a novel Multiple-Input-Multiple-Output (MIMO) sensor system for automotive applications. Compared to traditional phased arrays, a MIMO array can achieve the same fine angular resolution, but with a drastically reduced amount of sensor elements. A MIMO array of 8 elements can deliver the same resolution as a phased array of 16 elements [1]. The other highlight of this technology is that it can operate at short ranges, which is physically impossible with a phased array as the beam requires significant distance from the antenna aperture to form [2]. Therefore a MIMO system can potentially provide very high angular resolution at short ranges. These properties make such a system attractive for a number of automotive applications, including parking aids, short-range cruise control, speed-over-ground estimation, pedestrian and object detection and collision detection. 4. Nonlinear MIMO 3. Nearfield MIMO To further optimize the MIMO arrays, we looked into thinned arrays. Since MIMO array patterns are obtained from their equivalent virtual arrays, optimizing MIMO array patterns is not a straightforward job. To achieve this task, we utilized various optimization algorithms to find solutions; namely random descent[7][8], simulated annealing[9][10] and genetic algorithm[11][12]. Our specialized implementations of these algorithms have successfully yielded us practical solutions. Below is a comparison of a conventional MIMO array and one of our Nonlinear MIMO arrays. (Scanning 0 degrees) # of Elements Beamwidth Sidelobe Level Equivalent PA Elements Conventional MIMO (sim) 8 (4+4) 6.30 -13.1 dB 16 Conventional MIMO (exp) 8 (4+4) 6.48 -12.9 dB 16 Nonlinear MIMO (sim) 8 (4+4) 4.20 (~65%) -10.5 dB 24 Nonlinear MIMO (exp) 8 (4+4) 4.25 (~65%) -7.3 dB 24 14.9 19.8 21 4.1 4.5 43.3 mm [1] D. Bliss, K. Forsythe, and G. Fawcett, ‘MIMO Radar: Resolution, Performance, and Waveforms’, in Proc. 14th Annual Adaptive Sensor Array Processing Workshop, MIT, 2006, pp. 67. [2] C. A. Balanis, Antenna theory: analysis and design, 3rd ed. Hoboken, NJ: John Wiley, 2005, ISBN: 047166782X. [3] P. Z. Peebles, Radar principles. New York: Wiley, 1998, ISBN: 0471252050. [4] M. Lesturgie, ‘Tutorial on MIMO Radar’, Glasgow, UK, 21- September-2012. [5] R. A. Kennedy, T. Abhayapala, D. B. Ward, and R. C. Williamson, ‘Nearfield broadband frequency invariant beamforming’, in Acoustics, Speech, and Signal Processing, 1996. ICASSP-96. Conference Proceedings., 1996 IEEE International Conference on, 1996, vol. 2, pp. 905908, [6] R. A. Kennedy, D. B. Ward, and P. T. D. Abhayapala, ‘Nearfield beamforming using nearfield/farfield reciprocity’, in Acoustics, Speech, and Signal Processing, 1997. ICASSP-97., 1997 IEEE International Conference on, 1997, vol. 5, pp. 37413744, Available at http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=604683. [7] N. Mladenović and P. Hansen, “Variable neighborhood search,” Comput. Oper. Res., vol. 24, no. 11, pp. 1097 1100, 1997 [Online]. Available: http://www.sciencedirect.com/science/article/pii/S030505489 7000312 [8] P. Hansen, N. Mladenović, and J. A. Moreno Pérez, “Variable neighbourhood search: methods and applications,” Ann. Oper. Res., vol. 175, no. 1, pp. 367407, Mar. 2010 [Online]. Available: http://link.springer.com/10.1007/s10479- 009-0657-6. [Accessed: 16-Apr-2015] [9] S. Kirkpatrick, M. P. Vecchi, and others, “Optimization by simmulated annealing,” science, vol. 220, no. 4598, pp. 671– 680, 1983 [Online]. Available: http://leonidzhukov.net/hse/2013/stochmod/papers/Kirkpatric kGelattVecchi83.pdf. [Accessed: 20-Apr-2015] [10] V. Černỳ, “Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm,” J. Optim. Theory Appl., vol. 45, no. 1, pp. 4151, 1985 [Online]. Available: http://link.springer.com/article/10.1007/BF00940812. [Accessed: 20-Apr-2015] [11] A. M. Turing, “A quarterly review of psychology and philosophy,” Pattern Recognit. Introd. -Dowden Hutchinson Ross Inc, 1973. [12] J. H. Holland, Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence, 1st MIT Press ed. Cambridge, Mass: MIT Press, 1992. [13]J. A. Högbom, “Aperture Synthesis with a Non-Regular Distribution of Interferometer Baselines,” \aaps, vol. 15, p. 417, Jun. 1974. 8.References Less reflective targets can be disguised as range/angular sidelobes. Or the reverse can happen; angular/range sidelobes can constructively add up to create fake targets. To overcome these problems CLEAN algorithm was modified for our purposes, which is mainly used in radio astronomy[13]. MIMO concept applied to automotive context Obtained further performance improvements Produced acoustic technology demonstrator, tested and verified Technology is not limited to sonar, can be moved into RF domain (e.g. for higher maximum range) 6. Conclusions Practical MIMO Applications Taking an image of a practical object with conventional MIMO Taking an image of a practical object with Non-Linear MIMO (e.g. bicycle, baby cart) Replacing receivers with miniature SMD components To have a fully functional “plug and play” prototype 7. Future Work Tx/Rx Virtual Array Tx Rx Tx Rx MIMO Matched filtered signals can be interpreted as the signals out of the virtual array elements. Virtual Array Concept: M+N MIMO elements give the same angular resolution of MxN phased array Drastic reduction in antenna elements Example: 4+4 MIMO = 4x4 Phased Array Cheaper and more diverse system Matched Filter #M Matched Filter #m Rx #1 Rx #2 Rx #n Rx #N Matched Filter #2 Matched Filter #1 Matched Filter #M Matched Filter #m Matched Filter #2 Matched Filter #1 Matched Filter #M Matched Filter #m Matched Filter #2 Matched Filter #1 Matched Filter #M Matched Filter #m Matched Filter #2 Matched Filter #1 Virtual Array Element #1 Virtual Array Element #2 Virtual Array Element #3 Virtual Array Element #4 Virtual Array Element #mxn Virtual Array Element #MxN Nearfield MIMO techniques can be used for scanning areas without losing focus in close ranges with a tradeoff with more computation. The solution uses an actual geometric model rather than a far-field approximated model to derive the array factor[5][6]. Below are our experimental results from our nearfield algorithms at close ranges with an array with the size of 40cm looking at about 1.1 metres. -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 -0.5 0 0.5 1 1.5 x (meters) Slant Range: 1.14m Az-Angle: 0.51D RCS: 0.07 y (meters) Transmit Array Receive Array Targets Single Target at 0 degrees -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -0.5 0 0.5 1 1.5 Slant Range: 1.30m Az-Angle: 31.23D RCS: 0.07 x (meters) y (meters) Transmit Array Receive Array Targets Single Target at 30 degrees -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Slant Range: 1.08m Az-Angle: 24.29D RCS: 0.07 x (meters) y (meters) Transmit Array Receive Array Targets Single Target at 25 degrees -80 -60 -40 -20 0 20 40 60 80 -30 -20 -10 0 Azimuth (Degrees) Return (dB) Azimuth Cut at 1.15 meters [ball0far-background2] Beamwidth: 6.8312 Sidelobe Level: -11.6715 dB -80 -60 -40 -20 0 20 40 60 80 -30 -20 -10 0 Azimuth (Degrees) Return (dB) Azimuth Cut at 1.15 meters [ball25far-background2] Beamwidth: 7.9496 Sidelobe Level: -11.5429 dB -80 -60 -40 -20 0 20 40 60 80 -30 -20 -10 0 Azimuth (Degrees) Return (dB) Azimuth Cut at 1.34 meters [ball30far-background2] Beamwidth: 7.7805 Sidelobe Level: -7.0442 dB -100 -50 0 50 100 0.5 1 1.5 2 Azimuth (Degrees) Range (meters) -20 -15 -10 -5 0 Range-Azimuth Map -100 -50 0 50 100 0.5 1 1.5 2 Azimuth (Degrees) Range (meters) -20 -15 -10 -5 0 Range-Azimuth Map -100 -50 0 50 100 0.5 1 1.5 2 Azimuth (Degrees) Range (meters) -20 -15 -10 -5 0 Range-Azimuth Map

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Page 1: Automotive MIMO Radar - Alp Sayin · [12] J. H. Holland, Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial

DEPARTMENT OF ELECTRONIC, ELECTRICAL

AND SYSTEMS ENGINEERING

For more enquiries, please contact:

Head

of

MIS

L:

Pro

fessor

Mik

e C

hern

iakov,

+4

4(0

)12

1 4

14 4

28

6

m.c

hern

iakov@

bha

m.a

c.u

k U

niv

ers

ity o

f B

irm

ingh

am

, D

epa

rtm

ent

of E

ES

E, E

dg

ba

sto

n,

Birm

ingh

am

B15 2

TT.

www.birmingham.ac.uk/misl

MIMO Sensor Array for Short-Range

High-Resolution Automotive Sensing

Mr A Sayin, Dr. E Hoare, Dr. M Antoniou, Prof M Cherniakov

Name, [email protected], +44(0) 121 xxx xxxx

5.Experimental Results

2.Phased vs. MIMO ArrayA phased-array-antenna radar can be used with beam-forming techniques to direct a beam to a specific

location [3]. And then the radar can scan the desired area electronically. This can be achieved since,

the correlated signals from transmit antennas would add up constructively or destructively in different

directions in space [2]. On the other hand, a MIMO radar uses the advantage of orthogonality for

various advantages [4]. These advantages can be; reduced amount of necessary array elements,

increased angular resolution, faster scan time, simultaneous search & track etc. With a MIMO array;

beamforming process does not have to happen in the space but in the digital space, so we can

“illuminate” the whole space of interest with single transmission [1].

1.IntroductionThe aim of the project is to investigate a novel Multiple-Input-Multiple-Output (MIMO) sensor system

for automotive applications. Compared to traditional phased arrays, a MIMO array can achieve the

same fine angular resolution, but with a drastically reduced amount of sensor elements. A MIMO

array of 8 elements can deliver the same resolution as a phased array of 16 elements [1]. The other

highlight of this technology is that it can operate at short ranges, which is physically impossible with a

phased array as the beam requires significant distance from the antenna aperture to form [2].

Therefore a MIMO system can potentially provide very high angular resolution at short ranges. These

properties make such a system attractive for a number of automotive applications, including parking

aids, short-range cruise control, speed-over-ground estimation, pedestrian and object detection

and collision detection.

4. Nonlinear MIMO

3. Nearfield MIMO

To further optimize the MIMO arrays, we looked into thinned arrays. Since MIMO array patterns are

obtained from their equivalent virtual arrays, optimizing MIMO array patterns is not a straightforward

job. To achieve this task, we utilized various optimization algorithms to find solutions; namely

random descent[7][8], simulated annealing[9][10] and genetic algorithm[11][12]. Our specialized

implementations of these algorithms have successfully yielded us practical solutions. Below is a

comparison of a conventional MIMO array and one of our Nonlinear MIMO arrays.

(Scanning 0

degrees)

# of

Elements

Beamwidth Sidelobe

Level

Equivalent

PA Elements

Conventional

MIMO (sim)

8 (4+4) 6.30 -13.1 dB 16

Conventional

MIMO (exp)

8 (4+4) 6.48 -12.9 dB 16

Nonlinear

MIMO (sim)

8 (4+4) 4.20 (~65%) -10.5 dB 24

Nonlinear

MIMO (exp)

8 (4+4) 4.25 (~65%) -7.3 dB 24

14.9 19.8 21

4.1 4.543.3

mm

[1] D. Bliss, K. Forsythe, and G. Fawcett, ‘MIMO Radar:

Resolution, Performance, and Waveforms’, in Proc. 14th

Annual Adaptive Sensor Array Processing Workshop, MIT,

2006, pp. 6–7.

[2] C. A. Balanis, Antenna theory: analysis and design, 3rd

ed. Hoboken, NJ: John Wiley, 2005, ISBN: 047166782X.

[3] P. Z. Peebles, Radar principles. New York: Wiley, 1998,

ISBN: 0471252050.

[4] M. Lesturgie, ‘Tutorial on MIMO Radar’, Glasgow, UK, 21-

September-2012.

[5] R. A. Kennedy, T. Abhayapala, D. B. Ward, and R. C.

Williamson, ‘Nearfield broadband frequency invariant

beamforming’, in Acoustics, Speech, and Signal Processing,

1996. ICASSP-96.

Conference Proceedings., 1996 IEEE International

Conference on, 1996, vol. 2, pp. 905–908,

[6] R. A. Kennedy, D. B. Ward, and P. T. D. Abhayapala,

‘Nearfield beamforming using

nearfield/farfield reciprocity’, in Acoustics, Speech, and

Signal Processing, 1997. ICASSP-97.,

1997 IEEE International Conference on, 1997, vol. 5, pp.

3741–3744, Available at

http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=604683.

[7] N. Mladenović and P. Hansen, “Variable neighborhood

search,” Comput. Oper. Res., vol. 24, no. 11, pp. 1097 –

1100, 1997 [Online]. Available:

http://www.sciencedirect.com/science/article/pii/S030505489

7000312

[8] P. Hansen, N. Mladenović, and J. A. Moreno Pérez,

“Variable neighbourhood search: methods and applications,”

Ann. Oper. Res., vol. 175, no. 1, pp. 367–407, Mar. 2010

[Online]. Available: http://link.springer.com/10.1007/s10479-

009-0657-6. [Accessed: 16-Apr-2015]

[9] S. Kirkpatrick, M. P. Vecchi, and others, “Optimization by

simmulated annealing,” science, vol. 220, no. 4598, pp. 671–

680, 1983 [Online]. Available:

http://leonidzhukov.net/hse/2013/stochmod/papers/Kirkpatric

kGelattVecchi83.pdf. [Accessed: 20-Apr-2015]

[10] V. Černỳ, “Thermodynamical approach to the traveling

salesman problem: An efficient simulation algorithm,” J.

Optim. Theory Appl., vol. 45, no. 1, pp. 41–51, 1985 [Online].

Available:

http://link.springer.com/article/10.1007/BF00940812.

[Accessed: 20-Apr-2015]

[11] A. M. Turing, “A quarterly review of psychology and

philosophy,” Pattern Recognit. Introd. -Dowden Hutchinson

Ross Inc, 1973.

[12] J. H. Holland, Adaptation in natural and artificial

systems: an introductory analysis with applications to biology,

control, and artificial intelligence, 1st MIT Press ed.

Cambridge, Mass: MIT Press, 1992.

[13]J. A. Högbom, “Aperture Synthesis with a Non-Regular

Distribution of Interferometer Baselines,” \aaps, vol. 15, p.

417, Jun. 1974.

8.References

Less reflective targets can be disguised as range/angular sidelobes. Or the reverse can happen;

angular/range sidelobes can constructively add up to create fake targets. To overcome these problems

CLEAN algorithm was modified for our purposes, which is mainly used in radio astronomy[13].

• MIMO concept applied to automotive context

• Obtained further performance improvements

• Produced acoustic technology demonstrator, tested and verified

• Technology is not limited to sonar, can be moved into RF domain (e.g. for higher maximum range)

6. Conclusions

• Practical MIMO Applications

• Taking an image of a practical object with conventional MIMO

• Taking an image of a practical object with Non-Linear MIMO (e.g. bicycle, baby cart)

• Replacing receivers with miniature SMD components

• To have a fully functional “plug and play” prototype

7. Future Work

Tx/Rx

Virtual Array

Tx

Rx

Tx

Rx

MIMO

• Matched filtered signals can be interpreted as the signals out of the virtual array elements.

• Virtual Array Concept: M+N MIMO elements give the same angular resolution of MxN phased array

• Drastic reduction in antenna elements

• Example: 4+4 MIMO = 4x4 Phased Array

• Cheaper and more diverse system

Matched Filter #M

Matched Filter #mRx #1

Rx #2

Rx #n

Rx #N

Matched Filter #2

Matched Filter #1

Matched Filter #M

Matched Filter #m

Matched Filter #2

Matched Filter #1

Matched Filter #M

Matched Filter #m

Matched Filter #2

Matched Filter #1

Matched Filter #M

Matched Filter #m

Matched Filter #2

Matched Filter #1

Virtual Array Element #1

Virtual Array Element #2

Virtual Array Element #3

Virtual Array Element #4

Virtual Array Element #mxn

Virtual Array Element #MxN

Nearfield MIMO techniques can be used for scanning areas without losing focus in close ranges with a

tradeoff with more computation. The solution uses an actual geometric model rather than a far-field

approximated model to derive the array factor[5][6]. Below are our experimental results from our

nearfield algorithms at close ranges with an array with the size of 40cm looking at about 1.1 metres.

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8-0.5

0

0.5

1

1.5

Scenario Sketch [3 x 5]

x (meters)

Slant Range: 1.14m Az-Angle: 0.51D

RCS: 0.07

y (

mete

rs)

Transmit Array

Receive Array

Targets

Single Target at 0 degrees

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-0.5

0

0.5

1

1.5

Slant Range: 1.30m Az-Angle: 31.23D

RCS: 0.07

Scenario Sketch [3 x 5]

x (meters)

y (

mete

rs)

Transmit Array

Receive Array

Targets

Single Target at 30 degrees

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Slant Range: 1.08m Az-Angle: 24.29D

RCS: 0.07

Scenario Sketch [3 x 5]

x (meters)

y (

mete

rs)

Transmit Array

Receive Array

Targets

Single Target at 25 degrees

-100 -50 0 50 1000.5

1

1.5

2

background2

Azimuth (Degrees)

Ra

ng

e (

mete

rs)

-100 -50 0 50 1000.5

1

1.5

2

ball0far

Azimuth (Degrees)

Ra

ng

e (

me

ters

)

-100 -50 0 50 1000.5

1

1.5

2

abs(ball0far)-abs(background2)

Azimuth (Degrees)

Ra

ng

e (

me

ters

)

-80 -60 -40 -20 0 20 40 60 80-30

-20

-10

0

Azimuth (Degrees)

Re

turn

(d

B)

Azimuth Cut at 1.15 meters [ball0far-background2]

Beamwidth: 6.8312

Sidelobe Level: -11.6715 dB

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

-40

-30

-20

-10

0

Range (meters)

Re

turn

(d

B)

Range Cut at 0.50 degrees [ball0far-background2]

-80 -60 -40 -20 0 20 40 60 80-30

-20

-10

0

Azimuth (Degrees)

Re

turn

(d

B)

Azimuth Cut at 1.15 meters [ball0far]

Beamwidth: 6.7705

Sidelobe Level: -9.5346 dB

-20

-15

-10

-5

0

-20

-15

-10

-5

0

-20

-15

-10

-5

0

-100 -50 0 50 1000.5

1

1.5

2

background2

Azimuth (Degrees)

Ra

ng

e (

me

ters

)

-100 -50 0 50 1000.5

1

1.5

2

ball25far

Azimuth (Degrees)

Ra

ng

e (

me

ters

)

-100 -50 0 50 1000.5

1

1.5

2

abs(ball25far)-abs(background2)

Azimuth (Degrees)

Ra

ng

e (

me

ters

)

-80 -60 -40 -20 0 20 40 60 80-30

-20

-10

0

Azimuth (Degrees)

Re

turn

(d

B)

Azimuth Cut at 1.15 meters [ball25far-background2]

Beamwidth: 7.9496

Sidelobe Level: -11.5429 dB

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

-40

-30

-20

-10

0

Range (meters)

Re

turn

(d

B)

Range Cut at 23.50 degrees [ball25far-background2]

Range Resolution: 0.19548

-80 -60 -40 -20 0 20 40 60 80-30

-20

-10

0

Azimuth (Degrees)

Re

turn

(d

B)

Azimuth Cut at 1.15 meters [ball25far]

Beamwidth: 8.8729

Sidelobe Level: -9.9224 dB

-20

-15

-10

-5

0

-20

-15

-10

-5

0

-20

-15

-10

-5

0

-100 -50 0 50 1000.5

1

1.5

2

background2

Azimuth (Degrees)

Ra

ng

e (

me

ters

)

-100 -50 0 50 1000.5

1

1.5

2

ball30far

Azimuth (Degrees)

Ra

ng

e (

me

ters

)

-100 -50 0 50 1000.5

1

1.5

2

abs(ball30far)-abs(background2)

Azimuth (Degrees)

Ra

ng

e (

me

ters

)

-80 -60 -40 -20 0 20 40 60 80-30

-20

-10

0

Azimuth (Degrees)

Re

turn

(d

B)

Azimuth Cut at 1.34 meters [ball30far-background2]

Beamwidth: 7.7805

Sidelobe Level: -7.0442 dB

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

-40

-30

-20

-10

0

Range (meters)

Re

turn

(d

B)

Range Cut at 31.00 degrees [ball30far-background2]

Range Resolution: 0.25331

-80 -60 -40 -20 0 20 40 60 80-30

-20

-10

0

Azimuth (Degrees)

Re

turn

(d

B)

Azimuth Cut at 1.34 meters [ball30far]

Beamwidth: 9.034

Sidelobe Level: -8.7073 dB

-20

-15

-10

-5

0

-20

-15

-10

-5

0

-20

-15

-10

-5

0

-100 -50 0 50 1000.5

1

1.5

2

background2

Azimuth (Degrees)

Ran

ge (

mete

rs)

-100 -50 0 50 1000.5

1

1.5

2

ball0far

Azimuth (Degrees)

Ran

ge (

mete

rs)

-100 -50 0 50 1000.5

1

1.5

2

abs(ball0far)-abs(background2)

Azimuth (Degrees)

Ran

ge (

mete

rs)

-80 -60 -40 -20 0 20 40 60 80-30

-20

-10

0

Azimuth (Degrees)

Retu

rn (

dB

)

Azimuth Cut at 1.15 meters [ball0far-background2]

Beamwidth: 6.8312

Sidelobe Level: -11.6715 dB

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

-40

-30

-20

-10

0

Range (meters)

Retu

rn (

dB

)

Range Cut at 0.50 degrees [ball0far-background2]

-80 -60 -40 -20 0 20 40 60 80-30

-20

-10

0

Azimuth (Degrees)

Retu

rn (

dB

)

Azimuth Cut at 1.15 meters [ball0far]

Beamwidth: 6.7705

Sidelobe Level: -9.5346 dB

-20

-15

-10

-5

0

-20

-15

-10

-5

0

-20

-15

-10

-5

0

Range-Azimuth Map

-100 -50 0 50 1000.5

1

1.5

2

background2

Azimuth (Degrees)

Ran

ge (

mete

rs)

-100 -50 0 50 1000.5

1

1.5

2

ball25far

Azimuth (Degrees)

Ran

ge (

mete

rs)

-100 -50 0 50 1000.5

1

1.5

2

abs(ball25far)-abs(background2)

Azimuth (Degrees)

Ran

ge (

mete

rs)

-80 -60 -40 -20 0 20 40 60 80-30

-20

-10

0

Azimuth (Degrees)

Retu

rn (

dB

)

Azimuth Cut at 1.15 meters [ball25far-background2]

Beamwidth: 7.9496

Sidelobe Level: -11.5429 dB

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

-40

-30

-20

-10

0

Range (meters)

Retu

rn (

dB

)

Range Cut at 23.50 degrees [ball25far-background2]

Range Resolution: 0.19548

-80 -60 -40 -20 0 20 40 60 80-30

-20

-10

0

Azimuth (Degrees)

Retu

rn (

dB

)

Azimuth Cut at 1.15 meters [ball25far]

Beamwidth: 8.8729

Sidelobe Level: -9.9224 dB

-20

-15

-10

-5

0

-20

-15

-10

-5

0

-20

-15

-10

-5

0

Range-Azimuth Map

-100 -50 0 50 1000.5

1

1.5

2

background2

Azimuth (Degrees)

Ran

ge (

mete

rs)

-100 -50 0 50 1000.5

1

1.5

2

ball30far

Azimuth (Degrees)

Ran

ge (

mete

rs)

-100 -50 0 50 1000.5

1

1.5

2

abs(ball30far)-abs(background2)

Azimuth (Degrees)

Ran

ge (

mete

rs)

-80 -60 -40 -20 0 20 40 60 80-30

-20

-10

0

Azimuth (Degrees)

Retu

rn

(d

B)

Azimuth Cut at 1.34 meters [ball30far-background2]

Beamwidth: 7.7805

Sidelobe Level: -7.0442 dB

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

-40

-30

-20

-10

0

Range (meters)

Retu

rn

(d

B)

Range Cut at 31.00 degrees [ball30far-background2]

Range Resolution: 0.25331

-80 -60 -40 -20 0 20 40 60 80-30

-20

-10

0

Azimuth (Degrees)

Retu

rn

(d

B)

Azimuth Cut at 1.34 meters [ball30far]

Beamwidth: 9.034

Sidelobe Level: -8.7073 dB

-20

-15

-10

-5

0

-20

-15

-10

-5

0

-20

-15

-10

-5

0

Range-Azimuth Map