Radar Detection - MATLAB Simulations for Radar Systems Design - page 103

2.10. Kanter 1 developed an exact analysis for calculating the fluctuation loss.
In this text the authors will take advantage of the computational power of
MATLAB and the MATLAB functions developed for this text to numerically
calculate the amount of fluctuation loss with an accuracy of or better.
For this purpose the MATLAB function Ðfluct_loss.mÑ was developed. It is
given in Listing 2.25 in Section 2.11. Its syntax is as follows:

0.005 dB

[Lf, Pd_Sw5] = fluct_loss(pd, pfa, np, sw_case)

where

Symbol Description Units Status

pd desired probability of detection none input

pfa probability of false alarm none input

np number of pulses none input

sw_case 1, 2, 3, or 4 depending on the

desired Swerling case

none input

Lf fluctuation loss dB output

Pd_Sw5 Probability of detection correspond-

ing to a Swerling V case

none output

For example, using the syntax

[Lf,Pd_Sw5]=fluct_loss(0.65, 1e-9, 10,1)

will calculate the corresponding to both Swerling V and Swerling I fluc-
tuation when the desired probability of detection and probability
of false alarm and 10 pulses of non-coherent integration. The fol-
lowing is a reprint of the output:

SNR

P D = 0.65

– 9

P fa = 10

PD_SW5 = 0.65096989459928
SNR_SW5 = 5.52499999999990
PD_SW1 = 0.65019653294095
SNR_SW1 = 8.32999999999990
Lf = 2.80500000000000

Note that a negative value for indicates a fluctuation SNR gain instead of
loss. Finally, it must be noted that the function Ðfluct_loss.mÑ always assumes
non-coherent integration. Fig. 2.15 shows a plot for the additional SNR (or
fluctuation loss) required to achieve a certain probability of detection. This fig-
ure can be reproduced using MATLAB program Ðfig2_16.mÑ given in Listing
2.26 in Section 2.11.

L f

1. Kanter, I., Exact Detection Probability for Partially Correlated Rayleigh Targets,
IEEE Trans, AES-22, pp. 184-196, March 1986.