1. Tutorial I: Radar Introduction and basic concepts
Radar Signals
Tutorial I: Radar Introduction and basic concepts

2. Outline Introduction to radar Two important concepts Radar history
Radar principles
Radar category
Two important concepts
Doppler effect
Matched filter

3. Radar history First radar test (1904)
German high frequency engineer Christian Hulsmeyer
Traffic supervision on water: he measures the running time of electro-magnetic waves to a metal ship and back
An aircraft was first located by radar in 1930
Lawrence A. Hyland (Naval Research Lab)
Radar development underwent a strong push during World War II

4. Radar principles
A radar does nothing but measures the round-trip time delay → the range R = c t / 2
radar: radio detection and ranging

5. Radars work in high frequencies
The radar beam can be focused to a specific direction → azimuth and elevation
Radars work in high frequencies
High resolution (small wavelength → small object)
Small antenna size
Mechanical rotation / phased-array

6. Frequency ranges GHz Airborne radar
(small size, shirt range, high resolution)
Over the horizon
(high power, low resolution)

7. The radar equation received power (w) transmitted power (w)
antenna gain
effective antenna aperture (m2)
radar cross section (m2)

8. Range ambiguity
The radar time is set to zero each time a pulse is transmitted
If echo signals from the first pulse arrive after the second pulse transmission, ambiguity arises
Maximum unambiguous range

9. Range resolution Without intra-pulse modulation
is the pulse width
With intra-pulse modulation and range compression
is the bandwidth of the pulse
very small resolution
100 MHz → 1.5 m

10. Angular resolution
High directivity of radar antennas → small beam width → small resolution

11. Classification of radar systems

12. Doppler effect A
( )

13. Taylor expansion:

14. What if wideband signals?
We cannot simply inverse T
The received signal is a time-scaled and delayed version of the transmitted signal:
If bandwidth < 0.1 carrier frequency, it is reasonable to assume that the motion causes only a Doppler shift to the carrier frequency.
envelop of the signal affected

15. Complex representation of signals
Majority are narrow bandpass signals

17. Matched filter
Probability of detection is more related to SNR rather than the exact shape of the waveform
A matched filter maximizes SNR at the output of the filter

18. Equality holds if and only if
Matched filter output:
Auto-correlation function

19. The matched filter
Its impulse response is linearly related to the time-inverted complex-conjugate signal
When the input to the matched filter is the correct signal plus white noise, the peak output is linearly related to the signal's energy.
At the peak output, the SNR is the highest attainable, which is 2E / N0
The response is described by the autocorrelation function of the signal

21. MF response to Doppler-shifted signals
Ambiguity function
The AF describes the output of a matched filter when the input signal is delayed by tau and Doppler shifted by nu relative to nominal values for which the matched filter was designed.

23. To be continued... Thank you Ambiguity function Basic radar signals
Various properties
Basic radar signals
Constant frequency pulse
Linear-frequency modulated pulse
A train of pulses
Thank you
Sep. 2009