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### Transcript of 2 Modulation

• Modulation

Evan Everett and Michael WuELEC 433 - Spring 2013

• Questions from Lab 1?

• Modulation

Goal: overlay data onto carrier signal (sinusoid)

Sinusoids have two very accessible parameters

Modulate amplitude and phase

x(t) = A sin(t + )

DataModulation

Carrier

10100

• Modulation

Goal: overlay data onto carrier signal (sinusoid)

Sinusoids have two very accessible parameters

Modulate amplitude and phase

DataModulation

10100

Why not? 1) Interference avoidance2) High freq small antennas

• Signal Representation: Phasor

Polar : Amplitude & Phase

Rectangular : In-phase (I) & Quadrature (Q)

Phase

Amplitude

0

/2

-/2

I Re[x]

QIm[x]

x(t) = A sin(t + ) x(t) = I cos(t) +Q sin(t)

I = A sin() Q = A cos()

• Signal Representation

Rectangular (I,Q) form suggests a practical implementation

cos(t)

sin(t)

I

Q

90

I cos(t) +Q sin(t)

I Re[x]

QIm[x]

Modulation = mapping data bits to (I,Q) values

10100

• Digital Modulation

Maps bits to complex values (I/Q) (focus of the Lab 3)

Complex modulated values are called symbols

Set of symbols is called constellation or alphabet

# of symbols in constellation is modulation order, M

M-order constellation can encode ______ bits per symbol





• Digital Modulation

Maps bits to complex values (I/Q) (focus of the Lab 2)

Complex modulated values are called symbols

Set of symbols is called constellation or alphabet

# of symbols in constellation is modulation order, M

M-order constellation can encode log2(M) bits per symbol





• Phase Shift Keying (PSK)

Encodes information only in phase

Constant power envelope

Pros: no need to recover amplitude, no need for linear amplifier

Con: wastes amplitude dimension

BPSK (M =2) QPSK (M =4) 8-PSK (M =8)









• Encodes information in both amplitude and phase

(I,Q) grid

Quadrature Amplitude Modulation (QAM)

M

M

4-QAM 16-QAM 64-QAM

802.11b 802.11g/n 802.11ac

16-QAM 64-QAM 256-QAM

Common in wideband systems:

• Bit-to-Symbol Mapping Confusing with neighbor is most likely error

Best to minimize bit-difference between neighbors

Gray Coding

Neighboring symbols differ by only one bit

Extra performance at zero cost (this is rare!)









Natural-codedQPSK

Gray-codedQPSK

• Tradeoff: Rate vs. Error Probability

By increasing modulation order, M, we get:

More data in same bandwidth :)

Lower noise tolerance (i.e. higher error probability) :(

Therefore, SNR dictates feasible constellation size

• QPSK: 2 bits/symbol

I

Q

• QPSK: 2 bits/symbol

I

Q

• 16-QAM: 4 bits/symbol

I

Q

• 64-QAM: 6 bits/symbol

I

Q

• 1E-09

1E-08

1E-07

1E-06

1E-05

1E-04

1E-03

1E-02

1E-01

1E+00

0 2 4 6 8 10 12 14 16 18

BER

BPSKQPSK8-PSK16-QAM64-QAM

Eb/N0 (dB)

Bit error rate (BER) vs. SNR per bit (Eb/N0)