2 Modulation
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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)