Factors affecting radar range resolution

EECS 725 Introduction to Radar

Presented by

Susobhan Das

Outline……• Introduction

• Range Resolution

• Factors related to Range Resolution

• Theory of Range Resolution Development

• Dependency on relative RCS factor

• Dependency on Location Deviation

• Conclusion

• Reference

Introduction

Range Resolution

c : Speed of light in air /vacuum medium τ : Pulse width B : Bandwidth of the pulse = 1/τ

B

ccRd 22

Factors related to Range Resolution

Probability of resolving two targets

• Difference in RCS of the targets• SNR of the system• Separation between targets

Range resolution depends on

• Bandwidth of pulse• SNR of the system• RCS of the targets• Apparent target location ( deviation from the actual location)

2)( kRrk erf

2ln4

cB

2

1

)()(k

k rfrF

)(2

121 RRRm

)())()((2

121 mRFRFRF

σk RCS of the kth target (k=1,2)Rk Range location of the respective targetr range variable

Half Power bandwidth = c/2B

Gaussian profile of the pulse-compressed return signal from a single point target

Assuming random phase difference between two targets and distributed on [-π, +π]The envelop of the over all signal

Local minimum at

Deviation of peaks from the local minimum

Theory of Range Resolution Development

Continue…

)()()()(

11

12

12mm RFRFRR

RR

RFRF

kR

mR

: exact location of peaks

: exact location of minimum1.0

25.0

0)( drrdF 0)( 22 drrFd

0)()(22

1

k

kk rfRr

0)()2)(4(2

1

22 k

kk rfRr

12

For local minimum

Without loss of generality, assume Where α<1

)(2 LMdR

1

1

2

3

2

33)(LM

2ln

)(

4

LMd B

cR

Dependency on relative RCS factor

0)()2)(4()()()(2)( 2

1

222

1

k

kkk

kk RfRRRRRfRRRd

RdF

2

1

2

2

1

)(]1)(2[

)()(

kkk

kkk

RfRR

RfRRRR

kkk RR

dR

k

),(2 MDdR

11

2

1

1 2

11

2

1),( eWMD

k : deviation from the true location

: maximum allowable deviation relative to the target range

W-n nth branch Lambert W function

2ln

),(),(max

4

MDLMd B

cR

Dependency on Location Deviation

2ln

),(

4

MDd B

cR

Conclusion

• Common definition of Range Resolution modified with unequal strength of targets

• Existence of local minimum between two peaks and limiting deviation of peaks from true target location

Reference

1. Hasan S. Mir, and Blair D. Carlson, “On the Definition of Radar Range Resolution for Targets of Greatly Differing RCS” ieee transactions on instrumentation and measurement, vol. 61, no. 3, March 2012

2. P.-R. Wu, “A criterion for radar resolution enhancement with Burg algorithm,” IEEE Trans. Aerosp. Electron. Syst., vol. 31, no. 3, pp. 897–915,Jul. 1995.

3. H. S. Mir and J. D. Wilkinson, “Radar target resolution probability in a noise-limited environment,” IEEE Trans. Aerosp. Electron. Syst., vol. 44, no. 3, pp. 1234–1239, Jul. 2008.