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(t + )
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
/2
-/2
I Re[x]
QIm[x]
x(t) = A sin(t + ) x(t) = I cos(t) +Q sin(t)
I = A sin() Q = A cos()
Signal Representation
Rectangular (I,Q) form suggests a practical implementation
cos(t)
sin(t)
I
Q
90
I cos(t) +Q sin(t)
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)
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