Radar Detection - MATLAB Simulations for Radar Systems Design - page 88

P t G 2 λ 2 σ
4( 3 R 4 L

5000 2 0.2 2

126.61 × × × 1

– 12

S min = ----------------------- = -------------------------------------------------------------- = 1 . 2 2 5 4 × 1 0 Volts

4( 3 12000 4 × × 2.511

When 10 pulses are integrated non-coherently, the corresponding improvement
factor is calculated from the MATLAB function Ðimprov_fac.mÑ using the fol-
lowing syntax

improv_fac (10,1e-11,0.5)

which yields . Consequently, by keeping the probability
of detection the same (with and without integration) the SNR can be reduced by
a factor of almost 6 dB (13.85 - 7.78). The integration loss associated with a
10-pulse non-coherent integration is calculated from Eq. (2.50) as

I 1()6 = ⇒ 7.78 dB

n P
I 1()

10
6

L NCI = ------------- = ------ = . 7 . dB ⇒

Thus the net single pulse SNR with 10-pulse non-coherent integration is

( SNR ) NCI = 13.85 – 7.78 + 2.2 = 8.27 dB .

Finally, the improvement in the SNR due to decreasing the detection range to 9
Km is

4

12000
9000

 

---------------

( SNR ) 9 Km = 10 log + 13.85 = 18.85 dB .

 

2.5. Detection of Fluctuating Targets
So far the probability of detection calculations assumed a constant target
cross section (non-fluctuating target). This work was first analyzed by Mar-
cum. 1 Swerling 2 extended MarcumÓs work to four distinct cases that account
for variations in the target cross section. These cases have come to be known as
Swerling models. They are: Swerling I, Swerling II, Swerling III, and Swerling
IV. The constant RCS case analyzed by Marcum is widely known as Swerling
0 or equivalently Swerling V. Target fluctuation lowers the probability of
detection, or equivalently reduces the SNR.

1. Marcum, J. I., A Statistical Theory of Target Detection by Pulsed Radar , IRE Trans-
actions on Information Theory. Vol IT-6, pp 59-267. April 1960.
2. Swerling, P., Probability of Detection for Fluctuating Targets , IRE Transactions on
Information Theory. Vol IT-6, pp 269-308. April 1960.