Lecture 9
Analog and Digital I/Q
Modulation
Analog I/Q Modulation
• Time Domain View
• Polar View
• Frequency Domain View
Digital I/Q Modulation
• Phase Shift Keying
• Constellations
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Coherent Detection
Transmitter Output
0
x(t)
y(t)
2cos(2πfot)
Receiver Output
y(t)
z(t)
Lowpass
r(t)
2cos(2πfot)
• Requires receiver local oscillator to be accurately aligned in
phase and frequency to carrier sine wave
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Impact of Phase Misalignment in Receiver
Local Oscillator
Transmitter Output
0
x(t)
y(t)
2cos(2πfot)
Receiver Output
y(t)
z(t)
Lowpass
Output is zero
r(t)
2sin(2πfot)
•
Worst case is when receiver LO and carrier frequency are phase
shifted 90 degrees with respect to each other
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Analog I/Q Modulation
Baseband Input
iti(t)
(t)
it (t)
t
cos (2π f0 t ) 1t)
2cos(2πf
2sin(2πf
sin (2π f0t ) 1t)
yt (t)
qq(t)
t(t)
qt (t)
t
• Analog signals take on a continuous range of values (as viewed
in the time domain)
• I/Q signals are orthogonal and therefore can be transmitted
simultaneously and fully recovered
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Polar View of Analog I/Q Modulation
it (t) = i(t)cos (2π fot + 0° )
qt (t) = q(t)cos (2π fot + 90° ) = q(t)sin (2π fot )
i(t)
it(t)
it (t)
t
cos (2π f0 t ) t)
2cos(2πf
1
sin (2π f0t ) 1t)
2sin(2πf
yt (t) = i 2 (t) + q 2 (t) cos (2π fot + θ (t))
yt (t)
q(t)
qt(t)
where θ (t) = tan −1 q(t) / i(t)
t
qt (t)
−180° < θ < 180°
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Polar View of Analog I/Q Modulation (Con’t)
•
Polar View shows amplitude and phase of it(t), qt(t) and yt(t)
combined signal for transmission at a given frequency f.
•
Magnitude of i(t) and q(t) vary with time, representing information in
the analog domain.
Q
Q
y(t)
i 2 (t) + q2 (t)
q(t)
θ (t)
i(t)
i(t)
I
q(t)
I
θ (t)
y(t)
i 2 (t) + q2 (t)
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Frequency Domain View of Analog I/Q Modulation
1
II(f)
t(f)
1
-fo
i(t)
it(t)
f
0
Q(f)
Q
t(f)
1
fo
0
2 cos
2cos(2πf
(2π f02tt))
Transmitter Output
f
y(t)
2sin
(2π f02tt))
2sin(2πf
qq(t)
t(t)
1
1
fo
0
-fo
ffo1
0
f
Y
Qqt(f)
(f)
fo
j
-f
-fo1
-fo
j
f
0
(f)
YIit(f)
1
0
f
-j
f
-j
• Takes advantage of coherent receiver’s sensitivity to
phase alignment with transmitter local oscillator
– We have two orthogonal transmission channels (I and Q)
available to us
– Transmit two independent baseband signals (I and Q) with two
sine waves in quadrature at transmitter
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Analog I/Q Modulation-Transceiver
Baseband Input
Receiver Output
Lowpass
it(t)
ir(t)
t
t
2 cos
(2π f0t ) 1t)
2cos(2πf
2 cos (2π f0t t)
)
2cos(2πf
1
2sin(2πf
2 sin (2π f01tt)
)
Lowpass
2sin(2πf
2 sin
(2π f0t ) 1t)
qt(t)
qr(t)
t
t
• I/Q signals take on a continuous range of values (as
viewed in the time domain)
• Used for AM/FM radios, television (non-HDTV), and the
first cell phones
• Newer systems typically employ digital modulation
instead
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I/Q Transceiver Frequency Domain View
1
-fo
It(f)
1
1
1
fo
0
1
Transmitter Output
f
Yi(f)
1
-fo
1
fo
0
Lowpass
it(t)
f
0
22cos(2πf
cos (2π f02tt)
)
y(t)
22sin(2πf
sin (2π f0tt)
)
2
qt(t)
Qt(f)
1
j
ff1o
o
0
0
f
0
qr(t)
Qr(f)
2
f
f
ffo1
-j
-f1
-fo
-j
ir(t)
Ir(f)
2
2cos(2πf
2 cos (2π 1f0t)t )
y(t)
j
f
Receiver Output
f
2 sin (2π 1f0t)t )
2sin(2πf
Lowpass
fo
-fo
-f1
-f
fo
0
Yq(f)
j
f
0
-fo
f
0
0
f
-j
• Demodulate using two sine waves in quadrature at
receiver
– Must align receiver LO signals in frequency and phase to
transmitter LO signals
• Proper alignment allows I and Q signals to be recovered as shown
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Impact of 90 Degree Phase Misalignment
1
-fo
It(f)
1
j
1
fo
0
f1
Transmitter Output
f
Yi(f)
1
-f1
1
0
-j
it(t)
f
0
Qt(f)
1
2cos(2πf2t)
y(t)
2sin(2πf2t)
qt(t)
j
f1
0
Receiver Output
ir(t)
Ir(f)
2
f
f
y(t)
0
2sin(2πf1t)
Qr(f)
-2cos(2πf1t)
Yq(f)
-fo
j
-f1
fo
0
qr(t)
fo
f
0
-fo
f
0
f
f
0
-j
f
fo
-fo
0
-j
-1
f
-2
-1
• I and Q channels are swapped at receiver if its LO signal
is 90 degrees out of phase with transmitter
– However, no information is lost!
– Can use baseband signal processing to extract I/Q signals
despite phase offset between transmitter and receiver
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Digital I/Q Modulation
Baseband Input
+io
it(t)
i(t)
−io
+qo
t
t
it (t)
2cos(2πfot) t)
2cos(2πf
1
2sin(2
πf
t)
2sin(2πf
o 1t)
yt (t)
qq(t)
t(t)
−qo
qt (t)
t
t
•
I/Q signals take on discrete values at discrete time instants
corresponding to digital data
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Polar View of Digital I/Q Modulation
Polar View shows amplitude and phase of it(t), qt(t) and yt(t) combined signal for
transmission at a given frequency f.
i(t) and q(t) have discrete values. In this case, binary values. ±io ±qo
it (t) = ±io cos (2π fot )
it(t)
qt (t) = ±qo sin (2π fot )
Q
qt(t)
Q
× +qo
−io
×
+io
×
I
I
× −qo
yt (t) = io 2 + qo 2 cos (2π fot + θ (t))
where θ (t) = tan −1
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±qo
±io
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Polar View of Digital I/Q Modulation (cont’d)
it(t)
i(t
)
t
Q
it (t )
2cos(2πf
2cos(2πfot)1t)
2sin(2πf
2sin(2πfot)1t)
yt (t )
×
×
io 2 + qo 2
q
q(t
)
t(t)
45°
I
q t (t )
t
Given io = qo = 1
yt (t) = 2
×
4 QAM
Quadrature
Amplitude
Modulation
×
θ (t) can have 4 values
45°, 135°, − 45°, − 135°
Transmission signal is sine wave at frequency f0 with information
encoded in discrete values of amplitude and phase.
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Digital Modulation: 16-QAM
Baseband Input
it(t)
t
2cos(2πf1t)
2sin(2πf1t)
qt(t)
t
• I/Q signals take on discrete values at discrete time
instants corresponding to digital data
• I/Q signals may be binary or multi-bit
– Multi-bit shown above (4 levels each)
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Constellation Diagram:16-QAM
Q
00
01
11
10
00
01
Decision
Boundaries
I
11
10
Decision
Boundaries
•
•
•
We can view I/Q values at sample instants on a two-dimensional
coordinate system
Decision boundaries mark up regions corresponding to different data
values
Gray coding used to minimize number of bit errors that occur if
wrong decisions made due to noise
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Advantages of Digital Modulation
•
Allows information to be “packetized”
– Can compress information in time and efficiently send as packets
through network
– In contrast, analog modulation requires “circuit-switched” connections
that are continuously available
• Inefficient use of radio channel if there is “dead time” in information flow
•
Allows error correction to be achieved
– Less sensitivity to radio channel imperfections
•
Enables compression of information
– More efficient use of channel
•
Supports a wide variety of information content
– Voice, text and email messages, video can all be represented as digital
bit streams
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