Radar Detection - MATLAB Simulations for Radar Systems Design - page 76



) 2



1
2πψ 2

( rA –

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

f () ≈ exp – -------------------

 

(2.13)

2ψ 2

 

Fig. 2.2 shows plots for the Rayleigh and Gaussian densities. For this purpose,
use MATLAB program Ðfig2_2.mÑ given in Listing 2.1 in Section 2.11. This
program uses MATLAB functions Ðnormpdf.mÑ and Ðraylpdf.mÑ . Both func-
tions are part of the MATLAB Statistics toolbox. Their associated syntax is as
follows

normpdf(x,mu,sigma)

raylpdf(x,sigma)

ÐxÑ is the variable, ÐmuÑ is the mean, and ÐsigmaÑ is the standard deviation.

Figure 2.2. Gaussian and Rayleigh probability densities.

The density function for the random variable ϕ is obtained from

r
∫

f () fr ϕ = ( , ) d r

(2.14)

0

While the detailed derivation is left as an exercise, the result of Eq. (2.14) is

A 2 ) 2

   

1
2π

–
2ψ 2

A cos

2πψ 2

ϕ – ( A sin ϕ A cos

ψ

ϕ

 

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

f () = exp + exp F

   

(2.15)

 

2ψ 2    