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

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

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:

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

Receiver Noise Thermal Noise Power:

Probability Density Functions (PDF)

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 :

Probability of False Alarm

Probability of False Alarm

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

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

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

Integration of Radar Pulses

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, …

The Radar Cross Section Sphere :

The Radar Cross Section Aircraft :

The Radar Cross Section

The Radar Cross Section

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

The Radar Cross Section Ships:

The Radar Cross Section Missiles:

The Radar Cross Section

Radar Cross-Section Fluctuations

Radar Cross-Section Fluctuations target

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:

Radar Cross-Section Fluctuations

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

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.

PRF (Pulse Repetition Frequency)

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

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

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

Antenna Parameters Cosecant Squared Beam:

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.