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(ωt + φ)

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

π/2

π

-π/2

I Re[x]

QIm[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]

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

[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

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

[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

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

[1][0]

[01][00]

[11][10]

[000][001]

• 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!)

[10][01]

[11][00]

[11][01]

[10][00]

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)