Modulation Evan Everett and Michael Wu ELEC 433 - Spring 2013

• Goal: overlay data onto carrier signal sinusoid • Sinusoids have two very accessible parameters • Modulate amplitude and phase Data Modulation 10100 Why not?. Digital Modulation• Maps

Evan Everett and Michael Wu

ELEC 433 - Spring 2013

Questions from Lab 1?

• Goal: overlay data onto carrier signal (sinusoid)

• Sinusoids have two very accessible parameters

• Modulate amplitude and phase

x(t) = A sin(ωt + φ)

Data

Modulation

Carrier

10100

• Goal: overlay data onto carrier signal (sinusoid)

• Sinusoids have two very accessible parameters

• Modulate amplitude and phase

Data

Modulation

10100

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

Signal Representation: Phasor

• Polar: Amplitude & Phase

• Rectangular: “In-phase” (I) & “Quadrature” (Q)

Phase Am

plitu de

0

π/2

π

-π/2

I Re[x]

Q Im[x]

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

I = A sin(φ) Q = A cos(φ)

Signal Representation

• Rectangular (I,Q) form suggests a practical implementation

cos(ωt)

sin(ωt) I

Q

90˚

I cos(ωt) + Q sin(ωt)

I Re[x]

Q Im[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

[10]

[01]

[11]

[00]

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

[10]

[01]

[11]

[00]

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

[1]

[0]

[01]

[00]

[11]

[10]

[000]

[001]

• Encodes information in both amplitude and phase

• (I,Q) grid

Quadrature Amplitude Modulation (QAM)

∈ √M × √M

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!)

[10]

[01]

[11]

[00]

[11] [01]

[10] [00]

Natural-coded

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-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

BPSK QPSK 8-PSK 16-QAM 64-QAM

E b /N 0 (dB)

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