Modulation
Modulation Evan Everett and Michael Wu ELEC 433 - Spring 2013
Questions from Lab 1?
Modulation x(t) = A sin(ωt + φ) Carrier
Data 10100 Modulation • Goal: overlay
data onto carrier signal (sinusoid)
• Sinusoids
have two very accessible parameters
• Modulate
amplitude and phase
Modulation Why not?
1) Interference avoidance 2) High freq → small antennas
Data 10100 Modulation • Goal: overlay
data onto carrier signal (sinusoid)
• Sinusoids
have two very accessible parameters
• Modulate
amplitude and phase
Signal Representation: Phasor • Polar: Amplitude
& Phase
• Rectangular: “In-phase” (I)
& “Quadrature” (Q)
Am pl
itu de
π/2
Q Im[x]
Phase 0
π
I Re[x]
-π/2
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 I
Q Im[x]
cos(ωt)
10100
I Re[x]
I cos(ωt) + Q sin(ωt)
90˚
sin(ωt)
Q • Modulation
= mapping data bits to (I,Q) values
Digital Modulation [01]
[10]
[00]
[11]
• Maps
bits to complex values (I/Q) (focus of the Lab 3)
• Complex • Set •#
modulated values are called “symbols”
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 [01]
[10]
[00]
[11]
• Maps
bits to complex values (I/Q) (focus of the Lab 2)
• Complex • Set •#
modulated values are called “symbols”
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
BPSK (M =2)
QPSK (M =4)
8-PSK (M =8) [000]
[0]
• Constant
[00]
[01]
[10]
[11]
[001]
[1]
power envelope
•
Pros: no need to recover amplitude, no need for linear amplifier
•
Con: wastes amplitude dimension
Quadrature Amplitude Modulation (QAM) • Encodes •
information in both amplitude and phase
(I,Q) ∈
√
M×
4-QAM
•
√
M grid
16-QAM
Common in wideband systems:
64-QAM
802.11b
802.11g/n
802.11ac
16-QAM
64-QAM
256-QAM
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-coded QPSK
[01]
[10]
[00]
[11]
Gray-coded QPSK
[01]
[11]
[00]
[10]
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 Q
I
QPSK: 2 bits/symbol Q
I
16-QAM: 4 bits/symbol Q
I
64-QAM: 6 bits/symbol Q
I
Bit error rate (BER) vs. SNR per bit (Eb/N0) 1E+00 BPSK QPSK 8-PSK 16-QAM 64-QAM
1E-01 1E-02
BER
1E-03 1E-04 1E-05 1E-06 1E-07 1E-08 1E-09 0
2
4
6
8
10
12
Eb/N0 (dB)
14
16
18
Questions from Lab 1?
Modulation x(t) = A sin(ωt + φ) Carrier
Data 10100 Modulation • Goal: overlay
data onto carrier signal (sinusoid)
• Sinusoids
have two very accessible parameters
• Modulate
amplitude and phase
Modulation Why not?
1) Interference avoidance 2) High freq → small antennas
Data 10100 Modulation • Goal: overlay
data onto carrier signal (sinusoid)
• Sinusoids
have two very accessible parameters
• Modulate
amplitude and phase
Signal Representation: Phasor • Polar: Amplitude
& Phase
• Rectangular: “In-phase” (I)
& “Quadrature” (Q)
Am pl
itu de
π/2
Q Im[x]
Phase 0
π
I Re[x]
-π/2
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 I
Q Im[x]
cos(ωt)
10100
I Re[x]
I cos(ωt) + Q sin(ωt)
90˚
sin(ωt)
Q • Modulation
= mapping data bits to (I,Q) values
Digital Modulation [01]
[10]
[00]
[11]
• Maps
bits to complex values (I/Q) (focus of the Lab 3)
• Complex • Set •#
modulated values are called “symbols”
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 [01]
[10]
[00]
[11]
• Maps
bits to complex values (I/Q) (focus of the Lab 2)
• Complex • Set •#
modulated values are called “symbols”
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
BPSK (M =2)
QPSK (M =4)
8-PSK (M =8) [000]
[0]
• Constant
[00]
[01]
[10]
[11]
[001]
[1]
power envelope
•
Pros: no need to recover amplitude, no need for linear amplifier
•
Con: wastes amplitude dimension
Quadrature Amplitude Modulation (QAM) • Encodes •
information in both amplitude and phase
(I,Q) ∈
√
M×
4-QAM
•
√
M grid
16-QAM
Common in wideband systems:
64-QAM
802.11b
802.11g/n
802.11ac
16-QAM
64-QAM
256-QAM
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-coded QPSK
[01]
[10]
[00]
[11]
Gray-coded QPSK
[01]
[11]
[00]
[10]
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 Q
I
QPSK: 2 bits/symbol Q
I
16-QAM: 4 bits/symbol Q
I
64-QAM: 6 bits/symbol Q
I
Bit error rate (BER) vs. SNR per bit (Eb/N0) 1E+00 BPSK QPSK 8-PSK 16-QAM 64-QAM
1E-01 1E-02
BER
1E-03 1E-04 1E-05 1E-06 1E-07 1E-08 1E-09 0
2
4
6
8
10
12
Eb/N0 (dB)
14
16
18
