Radar Detection - MATLAB Simulations for Radar Systems Design - page 98

2.6.3. Detection of Swerling II Targets

In the case of Swerling II targets, the probability of detection is given by

V T

 

P D = 1 Γ I – ------------------------- , n p ; n P ≤ 50 (2.77)

 

( 1 + SNR )

For the case when n P > 50 Eq. (2.69) is used to compute the probability of

detection. In this case,

C 2
2

1

C 3 = – ------------ , C 6 = ------

(2.78)

3 n p

1
4 n P

C 4 = ---------

(2.79)

ϖ = n P ( 1 + SNR )

(2.80)

MATLAB Function Ðpd_swerling2.mÑ

The function Ðpd_swerling2.mÑ calculates for Swerling II type targets.
It is given in Listing 2.19 in Section 2.11. The syntax is as follows:

P D

[pd] = pd_swerling2 (nfa, np, snr)

where

Symbol Description Units Status

nfa MarcumÓs false alarm number none input

np number of integrated pulses none input

snr dB input

SNR

pd probability of detection none output

Fig. 2.12 shows a plot of the probability of detection as a function of SNR
for , where . This figure can be reproduced
using MATLAB program Ðfig2_12.mÑ given in Listing 2.20.

– 10

n P = 11050100 , , , P fa = 10

2.6.4. Detection of Swerling III Targets

The exact formulas, developed by Marcum, for the probability of detection
for Swerling III type targets when n P = 12 , is

– V T

 n P

– 2

2
n P SNR

  

P D = exp --------------------------------- 1 + ----------------- × K 0

   

1 + n P SNR ⁄ 2

(2.81)

V T

2
n P SNR

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

K 0 = 1 + --------------------------------- – ( n P – 2 )

1 + n P SNR ⁄ 2