Modulation and Demodulation

Radio telescopes used in radio astronomy

Arecibo Observatory, Puerto Rico Very Large Array, New Mexico

As in movies

• Contact– https://www.youtube.com/watch?v=C9DuMK0uo

1c• Goldeneyes

– https://www.youtube.com/watch?v=MH2qnn4D0kY

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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!

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.

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.

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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(2 p f t + f)

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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

Example

• The original signal: sin(x)• The carrier: sin(35x)

• Multiplication – sin(x) * sin(35x)

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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

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

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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.

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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?

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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

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a carrier wave

a digital input signal

amplitude shift keying

frequency shift keying

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(2 p 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.

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(2 p 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.

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!

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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)

0°

90°

180°

270°

360°

Calculating the Phase Shift

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• 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

B

A BA B

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

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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

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Constellation Diagram

Example: Assume 4 bits / cycle:

1 1 0 0

1 bit / shift

2-PSK

Exercise: PSK

Assume we want to use the following sine wave as the carrier.

sin(2 p t)

And we want to use the 2-PSK to send four bits “0101” in one second. Please draw the resulting waveform after modulation.

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Phase Shift and Constellation Diagram

Phase Shift 45° 135° 215° 305°

Bit Value 00 01 10 11

2 bit / shift

4-PSK

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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.

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Quadrature Amplitude Modulation (QAM)

• ASK + PSK• In a constellation diagram, we use distance from

the origin as a measure of amplitude

16QAM

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45 ° shifted away from the original signal

67.5 ° shifted away from the original signal, but only 22.5 ° from the previous signal

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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.

After Class Reading

• Sections 10.14 – 10.16: Dial-up models and QAM