1. Third Edition By : Merrill I. Skolnik
INTRODUCTION TO RADAR SYSTEMS
Third Edition By : Merrill I. Skolnik
Chapter 2 :
The Radar Equation

2. The Simple form of Radar Equation
is effective aperture of antenna
is radar cross section
is peak power
is gain of antenna
Minimum of detectable signal by receiver
Target parameter
Under control of Radar designer

3. The failure of Simple Form
Statistical nature of Smin (determined by reciever noise).
Fluctuation of radar cross section.
Losses.
Propagation effects (earth‘s surface, weather and atmosphere)
Therefore:
The probability of detection : Pd
and
The probability of false alarm : Pfa
must be considered.
This mean:

4. Detection of Signal in Noise
Threshold Detection :
A-scope presentation
(amplitude versus time or range)

5. Receiver Noise
Thermal Noise Power:

6. Probability Density Functions (PDF)

7. Probability of False Alarm
Envelope Detector:
Probability of Noise Voltage in input of IF stage is Gaussian PDF :
Mr. Rice has shown that the noise in output of IF is Rayleigh :
Probability of False Alarm :

8. Probability of False Alarm

9. Probability of False Alarm

10. Probability of Detection
Rice Probability density function
Zero-order Modified
Bessel Function

11. Integration of Radar Pulses
is Rotate Per Minute (rpm) of Antenna
is Pulse Repetition frequency (PRF) of Radar
is Half Power Beam Width (HPBW) of Antenna
is number of pulse per scan ( hit per scan )
sec
x is time on target

12. Integration of Radar Pulses
Types of Integration:
Pre-detection integration (Coherent integration ).
Post-detection integration (Non-coherent integration ).
Pre-detection integration needs to phase of pulses.
Post-detection integration don’t need to phase of pulses
Integration Efficiency :
Integration Improvement Factor :
Integration Loss:
J. I. Marcum, 1954, Rand Corporation report

13. Integration of Radar Pulses

14. The Radar Cross Section
Types of Targets:
Simple targets such as: Sphere, Cylinder, Flat plate, Rod, Ogive and cone
Complex targets such as: Aircraft, Ship, Building, …

15. The Radar Cross Section
Sphere :

16. The Radar Cross Section
Aircraft :

17. The Radar Cross Section

18. The Radar Cross Section

19. The Radar Cross Section
Ships:
f frequency (MHz)
D ship displacement (kiloton)

20. The Radar Cross Section
Ships:

21. The Radar Cross Section
Missiles:

22. The Radar Cross Section

23. Radar Cross-Section Fluctuations

24. Radar Cross-Section Fluctuations
target

25. Radar Cross-Section Fluctuations
Swerling Target Models:
Case 0:
No-Fluctuation in radar cross section occurs.
Case 1:
Scan to Scan Fluctuation (Rayleigh scattering ) or slow Fluctuation with PDF:
Case 2:
Pulse to Pulse Fluctuation or Fast Fluctuation with same PDF of case 1:
Scan to Scan Fluctuation with PDF:
Case 3:
Swerling assume that target is very big and contain many small targets
Case 4:
Pulse to Pulse Fluctuation or Fast Fluctuation with same PDF of case 3:

26. Radar Cross-Section Fluctuations

27. Radar Cross-Section Fluctuations
Fluctuations loss :
Radar Cross-Section Loss in radar equation:

28. Radar Cross-Section Fluctuations
Decorrelation by frequency Diversity & Agility :
Frequency Diversity:
Multiple TX/RX in different frequency is used. Example is air traffic control radar for reliability of detection.
Frequency Agility:
Pulse to Pulse change in radar frequency by a wide band TX.
It don’t used for MTI radars.

29. PRF (Pulse Repetition Frequency)

30. Antenna Parameters Gain : or is vertical beam width
is horizontal beam width
D is directivity of antenna

31. Antenna Parameters Beam Shape : Pencil Beam : Fan Beam :
Typical values
Typical values

32. Antenna Parameters Cosecant Squared Beam: Height Antenna Pattern TX/RX
Range
Height
TX/RX

33. Antenna Parameters
Cosecant Squared Beam:

34. Antenna Parameters Revisit Time : Rotate Per Minute (RPM)
Scan rime of antenna
Rotate Per Minute (RPM)
Number of pulse for suitable signal to noise.
Target speed.
is depending to :
Practical value for is :
5-6 rpm for long range air traffic control radars.
10-15 rpm for long range military radars.
30-60 rpm for high speed targets.