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
11/4/2006
 Coherent Detection
Transmitter Output
0

x(t) y(t)

2cos(2πfot)

Receiver Output

Lowpass
y(t) z(t) 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 Output is zero

Lowpass
y(t) z(t) 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 yt (t)
sin (2π f0t ) 1t)
2sin(2πf

qq(t)
t(t)

t qt (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° )

i(t)
it(t) it (t)
qt (t) = q(t)cos (2π fot + 90° ) = q(t)sin (2π fot ) t
cos (2π f0 t ) t)
2cos(2πf 1
yt (t)
yt (t) = i 2 (t) + q 2 (t) cos (2π fot + θ (t)) sin (2π f0t ) 1t)
2sin(2πf
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 I
i(t) q(t)
y(t) θ (t)
i 2 (t) + q2 (t)

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Frequency Domain View of Analog I/Q Modulation
1 1
Transmitter Output
f
II(f)
t(f) -fo 0 fo YIit(f)
(f)
1 1 1
i(t)
it(t)

f f
-fo 0 fo
0 2 cos (2π f02tt))
2cos(2πf y(t)
Q(f)
Qt(f) 2sin (2π f02tt))
2sin(2πf
Y
1 j Qqt(f)
(f)
qq(t)
t(t)
fo
f f
0 j -fo 0
ffo1 -j
f
-f
-fo1 0
-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
)
(2π f0t ) 1t)
2sin(2πf
2 sin 2 sin (2π f01tt)
2sin(2πf )
Lowpass
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

11/4/2006 L Lecture 9 Fall 2006 8

 I/Q Transceiver Frequency Domain View
1 1 1 1
Transmitter Output Receiver Output
f f
It(f) -fo 0 fo Yi(f)
-fo 0 fo Ir(f)
1 1 1 Lowpass 2
it(t) ir(t)

f f f
-fo 0 fo
0 cos (2π f02tt)
22cos(2πf ) y(t) y(t) 2 cos (2π 1f0t)t )
2cos(2πf 0
Qt(f) sin (2π f0tt)
22sin(2πf ) 2 sin (2π 1f0t)t )
2sin(2πf
Qr(f)
2 Lowpass
1 j Yq(f) 2
qt(t) qr(t)
fo
f f f
0 j -fo 0 j 0
ff1o -j ffo1
f f
-f1 0 -f1 0
-f o -j
-fo -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

11/4/2006 L Lecture 9 Fall 2006 9

 Impact of 90 Degree Phase Misalignment
1 1 j
Transmitter Output f1 Receiver Output
f f
It(f) -fo 0 fo Yi(f) -f1 0 Ir(f)
1 1 1 -j 2
it(t) ir(t)

f f f
-fo 0 fo
0 2cos(2πf2t) y(t) y(t) 2sin(2πf1t) 0
Qt(f) Qr(f)
2sin(2πf2t) -2cos(2πf1t)
1 j Yq(f)
qt(t) qr(t)
fo
f f f
0 j -fo 0 0
f1 -j -fo fo -2
f f
-f1 0 0
-j -1 -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

11/4/2006 L Lecture 9 Fall 2006 10

 Digital I/Q Modulation
Baseband Input
+io
it(t)
i(t) it (t)
−io
t yt (t)
t 2cos(2πf
2cos(2πfot) t)
1
2sin(2 πf
2sin(2πf o 1t)
t)
+qo

t(t)
qq(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 ) qt(t) Q

Q
× +qo
−io +io I
× × I
× −qo

yt (t) = io 2 + qo 2 cos (2π fot + θ (t))

±qo
where θ (t) = tan −1
±io

11/4/2006 L Lecture 9 Fall 2006 12

 Polar View of Digital I/Q Modulation (cont’d)

it(t)
i(t ) it (t ) Q

t × ×
2cos(2πfot)1t)
2cos(2πf yt (t )
2sin(2πf
2sin(2πfot)1t)
io 2 + qo 2
q 4 QAM
t(t)
q(t ) 45°
I Quadrature
q t (t ) Amplitude
t Modulation
Given io = qo = 1
× ×
yt (t) = 2
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)

• 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

Decision 01
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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