Radar Detection - MATLAB Simulations for Radar Systems Design - page 94

2.6.1. Detection of Swerling V Targets

For Swerling V (Swerling 0) target fluctuations, the probability of detection
is calculated using Eq. (2.69). In this case, the Gram-Charlier series coeffi-
cients are

SNR + 13 ⁄

C 3 = – --------------------------------------------

(2.71)

) 1.5 n p ( 2 SNR + 1

SNR + 14 ⁄

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

(2.72)

) 2

n p ( 2 SNR + 1

C 2

C 6 = ⁄ 2

(2.73)

ϖ = n p ( 2 SNR + 1 )

(2.74)

MATLAB Function Ðpd_swerling5.mÑ

The function Ðpd_swerling5.mÑ calculates the probability of detection for
Swerling V targets. It is given in Listing 2.14. The syntax is as follows:

[pd] = pd_swerling5 (input1, indicator, np, snr)

where

Symbol Description Units Status

input1 P fa , or n fa none input

indicator 1 when input1 = P fa

2 when input1 = n fa

none input

np number of integrated pulses none input

snr dB input

SNR

pd probability of detection none output

Fig. 2.9 shows a plot for the probability of detection versus SNR for cases
. This figure can be reproduced using the MATLAB program
Ðfig2_9.mÑ. It is given in Listing 2.15 in Section 2.11.

n p = 110 ,

Note that it requires less SNR, with ten pulses integrated non-coherently, to
achieve the same probability of detection as in the case of a single pulse.
Hence, for any given the SNR improvement can be read from the plot.
Equivalently, using the function Ðimprov_fac.mÑ leads to about the same
result. For example, when

P D

P D =

I 1()8.55 dB

0.8 the function Ðimprov_fac.mÑ gives an

SNR improvement factor of ≈ . Fig. 2.9 shows that the ten pulse

SNR is about 6.03 dB . Therefore, the single pulse SNR is about (from Eq.

(2.49)) 14.5 dB , which can be read from the figure.