Radar Detection - MATLAB Simulations for Radar Systems Design - page 112

Instead, resort to accomplishing the desired probability of detection by using
cumulative probabilities. The single frame increment for the missile and air-
craft cases are

R Missile = scan rate × v m = 2 × 150 = 300 m (2.111)

R Aircraft = scan rate × v a = 2 0 × = 800 m

(2.112)

2.10.2.1 Single Pulse (Per Frame) Design Option

As a first design option, consider the case where during each frame only a
single pulse is used for detection (i.e., no integration). Consequently, if the sin-
gle pulse detection does not achieve the desired probability of detection at 90
Km for the aircraft or at 55 Km for the missile, then non-coherent integration
of a few pulses per frame can then be utilized. Keep in mind that only non-
coherent integration can be used in the cases of Swerling type I and III fluctua-
tions (see Section 2.4).

Assume that the first frame corresponding to detecting the aircraft is 106
Km. This assumption is arbitrary and it provides the designer with 21 frames.
It follows that the first frame, when detecting the missile, is at 61 Km. Further-
more, assume that the SNR at is , for the
aircraft case. And, for the missile case assume that at the corre-
sponding SNR is . Note that these values are simply edu-
cated guesses, and the designer may be required to perform several iterations in
order to accomplish the desired cumulative probability of detection,
. In order to calculate the cumulative probability of detection at a
certain range, the MATLAB program Ðmyradar_visit2_2.mÑ was developed.
This program is given in Listing 2.28 in Section 2.11.

R = 90 Km ( SNR ) aircraft = 8.5 dB

R = 55 Km

( SNR ) missile = 9 dB

P D ≥ 0.995

Initialization of the program Ðmyradar_visit2_2.mÑ includes entering the
following inputs: The desired ; the number of pulses to be used for non-
coherent integration per frame; the range at which the desired cumulative oper-
ability of detection must be achieved; the frame size; and finally the target fluc-
tuation type. For notational purposes, denote the range at which the desired
cumulative probability of detection must be achieved as . Then for each
frame, the following list includes the outputs of this program: SNR, probability
of detection, fluctuation loss, and cumulative probability of detection.

P fa

R 0

The logic used by this program for calculating the proper probability of
detection at each frame and for computing the cumulative probability of detec-
tion is described as follows:

Initialize the program, by entering the desired input values. Assume Swer-
ling V fluctuation and use Eq. (2.98) to calculate the frame-SNR,

1.

( SNR ) i .