1. Lecture 4.1 Ambiguity Function

2. Understanding of SISO, SIMO, MISO and MIMO (note that the terms input and output refer to the radio channel carrying the signal, not to the devices having antennas)

3. Radar Ambiguity Function
t: delay
n: Doppler
u(t-t)ej2pnt
u(t)

4. Radar Ambiguity Function
t: delay
n: Doppler
u(t-t)ej2pnt
u(t)
Matched filter
output

5. Radar Ambiguity Function
t: delay
n: Doppler
u(t-t)ej2pnt
u(t)
Matched filter
output

6. Radar Ambiguity Function
t: delay
n: Doppler
u(t-t)ej2pnt
u(t)
Matched filter
output
Radar ambiguity
function

7. Radar Ambiguity Function
t: delay
n: Doppler
u(t-t)ej2pnt
u(t)
Matched filter
output
Radar ambiguity
function
Ambiguity function characterizes the Doppler and range resolution.

8. Radar Ambiguity Function
Multiple targets
(tk,nk)

9. Radar Ambiguity Function
Multiple targets
(tk,nk)

10. Radar Ambiguity Function
Multiple targets
(tk,nk)
Matched filter
output

11. Radar Ambiguity Function
Multiple targets
(tk,nk)
Matched filter
output n
target 1 (t1,n1)
target 2 (t2,n2) t

12. Radar Ambiguity Function
Multiple targets
(tk,nk)
Matched filter
output n
target 1 (t1,n1)
target 2 (t2,n2) t

13. Radar Ambiguity Function
Ambiguity function characterizes the Doppler and range resolution. n
target 1 (t1,n1)
target 2 (t2,n2) t
Ambiguity function

14. Radar Ambiguity Function
Ambiguity function characterizes the Doppler and range resolution. n
target 1 (t1,n1)
target 2 (t2,n2) t
Ambiguity function

15. Properties of Radar Ambiguity Function
Signal component n t

16. Properties of Radar Ambiguity Function
Signal component
Energy n t

17. Properties of Radar Ambiguity Function
Signal component
Energy
Symmetry n t

18. Properties of Radar Ambiguity Function
Signal component
Energy
Symmetry
Linear frequency modulation (LFM) n t

19. MIMO Radar f2(t) w2f(t) f1(t) w1f(t) f0(t) w0f(t) Advantages
The radar systems which emits orthogonal (or noncoherent) waveforms in each transmitting antennas are called MIMO radar.
MIMO radar
f2(t)
f1(t)
f0(t)
SIMO radar (Traditional)
w2f(t)
w1f(t)
w0f(t)
Advantages
Better spatial resolution
Flexible transmit beampattern design
Improved parameter identifiability

20. Properties of the MIMO ambiguity function

21. Properties of the signal component
Ambiguity function:
Signal component:

22. Linear frequency modulation (LFM)

23. Linear frequency modulation (LFM)
Cross ambiguity function

24. Linear frequency modulation (LFM)

25. Linear frequency modulation (LFM)
Shear off n t n t

26. Linear frequency modulation (LFM)
Shear off n t n t
The range resolution is improved by LFM. n n t t

27. Radar Ambiguity Diagram
The thumbtack ambiguity function is common to noiselike or pseudonoise waveforms. By increasing the bandwidth or pulse duration the width of the spike narrow along the time or the frequency axis, respectively.
Where:
B - bandwidth
T - pulse width
fd - doppler delay
td - time delay
This shows that as we increase the bandwidth B, we have better range resolution. Conversely if we increase the pulse width T, we increase the doppler resolution.

28. Radar Ambiguity Diagram
The first null occurs at
Doppler
Delay
The main peak of the ambiguity function corresponds to the resolution of the system in terms of range and Doppler.
The additional peaks correspond to potential ambiguities, resulting in confusion at choosing the correct range of the target and its velocity

29. Analog FM Ambiguity Diagram
Analog FM – Speech Ambiguity Plot

30. Digital Audio Ambiguity Diagram
Ambiguity Plot with speech content