1. Modulation and Demodulation

2. Radio telescopes used in radio astronomy
Arecibo Observatory, Puerto Rico
Very Large Array, New Mexico

3. As in movies Contact Goldeneyes
Goldeneyes

4. Why Do We Need A Large Radio Telescope like This?
Difficulties in low frequency communications
Many astronomical objects emit radiation at radio frequency (RF)
RF is much small than the frequency of visible lights
Antenna size: the same magnitude of the wavelength of a signal
Low frequency signals require large antennas.
f *l = c (speed of light)
We need a way to transmit and receive low frequency signals easily!

5. Modulation and Demodulation
Modulation: use a high frequency signal to carry information about a low-frequency signal (e.g., sound waves).
Demodulation: recreate the low-frequency signal from the high frequency signal.

6. More Motivation for Modulation
Interference
Signals occupy similar frequency bands
TV, radio stations
Modulation: allow different signals to be transmitted simultaneously with a single device
Radio and TV channels: with different frequencies.

7. Methods for Modulation
In essence, a sender must change one of the characteristics of the carrier
Amplitude modulation
Frequency modulation
Phase shift modulation
y = A sin(2p f t + f)

8. Amplitude Modulation (AM)
The amplitude of a carrier is modified in proportion to the information signal.
The frequency of the carrier is fixed.
carrier
information

9. Example The original signal: sin(x) The carrier: sin(35x)
Multiplication
sin(x) * sin(35x)

10. Problems of Amplitude Modulation
Power level to zero
Practical systems do not allow for a modulated signal to approach zero
In practice, modulation only changes the amplitude of a carrier slightly
Keeping the carrier wave near maximum

11. Example The carrier: sin(35x) The signal: sin(x)
AM with a modulation index a
[ a * sin(x) + mi ] * sin (35x)
a = 0.3, mi =1

12. Frequency Modulation (FM)
Signal amplitude can be easily affected by the environment.
Signal frequency, however, is quite stable.
In FM, frequency changes according to the signal.

13. Frequency Modulation (FM)
The carrier: sin(5t)
The signal: sin(t) FM
sin ( (sin(t) + 2) * 5 t)
Q: Is the constant “2" necessary here? 13 13

14. Modulation of Digital Signals
A different term: shift keying
Instead of a continuum of possible values, digital shift keying has a fixed set
Mapping to the power levels of a digital signal

15. a carrier wave
a digital input signal
amplitude shift keying
frequency shift keying

16. Exercise: ASK
Consider the input signal with 3 levels shown above. Assume we want to use the following sine wave as the carrier.
10 sin(2p 2 t)
And we want to use the following ASK scheme
15V  level ‘1’
10V  level ‘0’
5V  level ‘-1’
Please draw the resulting waveform after modulation.

17. Exercise: FSK
Consider the input signal with 3 levels shown above. Assume we want to use the following sine wave as the carrier.
10 sin(2p 2 t)
And we want to use the following FSK scheme
3Hz  level ‘1’
2Hz  level ‘0’
1Hz  level ‘-1’
Please draw the resulting waveform after modulation.

18. Efficiency Issues of ASK and FSK
Must capture the amplitude or frequency information of the carrier
Require at least one cycle of a carrier wave to send a single bit
Transmission capacity is limited by the carrier frequency!
A single sine wave circle
One amplitude
One frequency
Can be shifted with multiple phases!

19. Phase Shift Keying (PSK)
Almost every real world modem use PSK to send more bits.
PSK changes the phase of the carrier wave abruptly.
Each such change is called a phase shift
On a sine wave, each point correspond to a phase (angle)
90°
180°
360° 0°
270°

20. Calculating the Phase Shift
Example:
The first change:
Point A’s phase: 90°
Point B’s phase: 270°
Phase change: 270° - 90° = 180°
The second change:
360° - 180° = 180°
The third change? A A B A B B

21. Calculating the Phase Shift
Step 1: Identify the two points A & B involved in this phase shift
Step 2: Find the phase of A & B
Step 3: phase shift = B’s phase – A’s phase

22. Phase Shift and a Constellation Diagram
How to encode data into phase shifts?
A sender and receiver can agree on the number of bits per second
Use different phase shifts to denote the data bits.
A constellation diagram is used to express the exact assignment of data bits to specific phase changes

23. Constellation Diagram
Example: Assume 4 bits / cycle:
1 bit / shift
2-PSK

24. Exercise: PSK
Assume we want to use the following sine wave as the carrier.
sin(2p t)
And we want to use the 2-PSK to send four bits “0101” in one second. Please draw the resulting waveform after modulation.

25. Phase Shift and Constellation Diagram
2 bit / shift
4-PSK
Phase Shift
45°
135°
215°
305°
Bit Value 00 01 10 11

26. Phase Shift and a Constellation Diagram
In theory, it is possible to increase the data rate by decreasing the angular difference between phases
4-PSK  8-PSK
90°  45°
16-PSK: 22.5°
Noise and distortion limit the ability of practical systems to distinguish among arbitrarily small differences in phase changes.

27. Quadrature Amplitude Modulation (QAM)
ASK + PSK
In a constellation diagram, we use distance from the origin as a measure of amplitude
16QAM

28. 67. 5 ° shifted away from the original signal, but only 22
67.5 ° shifted away from the original signal, but only 22.5 ° from the previous signal
45 ° shifted away from the original signal

29. MODEM: MOdulator + DEModulator
Usually within the same device
Each location needs both a modulator to send data and a demodulator to receive data.
Most communication systems are full duplex.

30. After Class Reading
Sections – 10.16: Dial-up models and QAM