Radar Detection - MATLAB Simulations for Radar Systems Design - page 87

3 0 8

c
2 R u

×

f r = --------- = ------------------------ = 12.5 KHz

2 × 12000

The pulsewidth is proportional to the inverse of the bandwidth,

1
---

1
2 0 6

τ == = ----------------- 0 . 5 µ s

×

The probability of false alarm is

1
BT fa

1
2 0 6

. 4 0 10

–

P fa = ----------- = ------------------------------------------ = ×

× × 12 × 60

It follows that by using MATLAB functionÐmarcumsq.mÑthe probability of
detection is calculated from

A 2
ψ 2

1
P fa

------  

Q ------2 , ln

with the following syntax

marcumsq(alpha, beta)

where

13.85 ⁄ 10

alpha = 2 × = 6.9665

1

 

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

beta = 2 ln = 6.494

 

– 10

6.94 × 10

A 2 ψ 2

Remember that ( ⁄ ) = 2 SNR . Thus, the detection probability is

P D = marcumsq 6.9665 6.944 ( , ) = 0.508

Using the radar equation one can calculate the radar peak power. More pre-
cisely,

4( 3 R 4 kT 0 BFL
G 2 λ 2 σ

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

P t = SNR ⇒

10 1.385 4( 3

12000 4

– 23

2 0 6

× × 1.38 × 10 × 290 × × × 6.309 × 2.511

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

P t =

5000 2 0.2 2 × × 1

= 126.61 Watts

And the minimum detectable signal is