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Modulation Evan Everett and Michael Wu ELEC 433 - Spring 2013 - - PowerPoint PPT Presentation
Modulation Evan Everett and Michael Wu ELEC 433 - Spring 2013 - - PowerPoint PPT Presentation
Modulation Evan Everett and Michael Wu ELEC 433 - Spring 2013 Questions from Lab 1? Modulation Carrier x ( t ) = A sin( t + ) Data 10100 Modulation Goal: overlay data onto carrier signal (sinusoid) Sinusoids have two very
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Modulation
- 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
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Modulation
- Goal: overlay data onto carrier signal (sinusoid)
- Sinusoids have two very accessible parameters
- Modulate amplitude and phase
Data
Modulation
10100
Why not?
1) Interference avoidance 2) High freq → small antennas
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Signal Representation: Phasor
- Polar: Amplitude & Phase
- Rectangular: “In-phase” (I) & “Quadrature” (Q)
Phase A m p l i t u d e 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)
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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
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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]
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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]
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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]
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- 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:
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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 QPSK Gray-coded QPSK
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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
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QPSK: 2 bits/symbol
I Q
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QPSK: 2 bits/symbol
I Q
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16-QAM: 4 bits/symbol
I Q
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64-QAM: 6 bits/symbol
I Q
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1E-09 1E-08 1E-07 1E-06 1E-05 1E-04 1E-03 1E-02 1E-01 1E+00 2 4 6 8 10 12 14 16 18
BER
BPSK QPSK 8-PSK 16-QAM 64-QAM