11/4/2006

Analog I/Q Modulation• Time Domain View• Polar View• Frequency Domain ViewDigital I/Q Modulation• Phase Shift Keying• Constellations

Lecture 9Analog and Digital I/Q

Modulation

L11/4/2006 2Lecture 9 Fall 2006

Coherent Detection

• Requires receiver local oscillator to be accurately aligned in phase and frequency to carrier sine wave

2cos(2πfot)

y(t)

2cos(2πfot)

z(t)Lowpass

r(t)

Transmitter Output

Receiver Output

x(t)

y(t)

0

L11/4/2006 3Lecture 9 Fall 2006

Impact of Phase Misalignment in Receiver Local Oscillator

2cos(2πfot)

y(t)

z(t)Lowpass

r(t)

Transmitter Output

Receiver Output

x(t)

y(t)

0

2sin(2πfot)

Output is zero

• Worst case is when receiver LO and carrier frequency are phase shifted 90 degrees with respect to each other

L11/4/2006 4Lecture 9 Fall 2006

Analog I/Q Modulation

• 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

it(t)

qt(t)

2cos(2πf1t)2sin(2πf1t)

t

t

Baseband Input

i(t) it (t)

cos 2π f0t( )sin 2π f0t( )

q(t)qt (t)

yt (t)

L11/4/2006 5Lecture 9 Fall 2006

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( )

yt (t) = i2 (t) + q2 (t) cos 2π fot +θ(t)( )

where θ(t) = tan−1 q(t) / i(t)

−180° < θ < 180°

it(t)

qt(t)

2cos(2πf1t)2sin(2πf1t)

t

t

i(t) it (t)

q(t)

qt (t)

yt (t)cos 2π f0t( )sin 2π f0t( )

L11/4/2006 6Lecture 9 Fall 2006

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.

θ(t)q(t)

i(t)

i2(t)+ q2(t)

Q

I

Q

Ii(t)

i2(t)+ q2(t)

q(t) θ(t)

y(t)

y(t)

L11/4/2006 7Lecture 9 Fall 2006

Frequency Domain View of Analog I/Q Modulation

• 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

Transmitter Outputf

-fo fo0

1 1

f0

f-f1

f10

j

-j

2cos(2πf2t)

2sin(2πf2t)

y(t)

it(t)

qt(t)

It(f)

Qt(f)

f0

f-fo fo0

1 11

1

f-fo

fo0

j

-j

Yi(f)

Yq(f)

2cos 2π f0t( )2sin 2π f0t( )

-fo

fo

Q(f)

I(f) It(f)

Qt(f)

i(t)

q(t)

L11/4/2006 8Lecture 9 Fall 2006

Analog I/Q Modulation-Transceiver

• 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

Receiver Output

2cos(2πf1t)2sin(2πf1t)

Lowpassir(t)

Lowpassqr(t)

it(t)

qt(t)

2cos(2πf1t)2sin(2πf1t)

t

t

t

t

Baseband Input

2cos 2π f0t( )2sin 2π f0t( )

2cos 2π f0t( )2sin 2π f0t( )

L11/4/2006 9Lecture 9 Fall 2006

I/Q Transceiver Frequency Domain View

• 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

Transmitter Outputf

-fo fo0

1 1

f0

Receiver Output

f-f1

f10

j

-j

2cos(2πf1t)

2sin(2πf1t)

y(t)

Lowpassir(t)

Lowpassqr(t)

2cos(2πf2t)

2sin(2πf2t)

y(t)

it(t)

qt(t)

It(f)

Qt(f)

f0

f-fo fo0

1 11

1

f-fo

fo0

j

-j

Yi(f)

Yq(f)

f-fo fo0

1 1

f-f1

f10

j

-j

f0

Ir(f)

Qr(f)

f0

2

2

2 cos 2π f0t( )2sin 2π f0t( )

2 cos 2π f0t( )2sin 2π f0t( )

fofo

-fo-fo

L11/4/2006 10Lecture 9 Fall 2006

Impact of 90 Degree Phase Misalignment

• 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

Transmitter Outputf

-fo fo0

1 1

f0

Receiver Output

f-f1

f10

j

-j

-2cos(2πf1t)

2sin(2πf1t)y(t)

ir(t)

qr(t)

2cos(2πf2t)

2sin(2πf2t)

y(t)

it(t)

qt(t)

It(f)

Qt(f)

f0

f-fo fo0

1 11

1

f-fo

fo0

j

-j

Yi(f)

Yq(f)

f-fo fo

0-1 -1

f-f1

f10

j

-j

f0

Ir(f)

Qr(f)

f0

-2

2

L11/4/2006 11Lecture 9 Fall 2006

Digital I/Q Modulation

• I/Q signals take on discrete values at discrete time instants corresponding to digital data

+io

−io

t+qo

−qo

t

Baseband Input

it(t)

qt(t)

2cos(2πf1t)2sin(2πf1t)

t

t

it (t)

qt (t)

yt (t)2cos(2πfot)2sin(2 πfot)

i(t)

q(t)

L11/4/2006 12Lecture 9 Fall 2006

Polar View of Digital I/Q Modulation

i(t) and q(t) have discrete values. In this case, binary values. ±io ±qo

it (t) = ±io cos 2π fot( )qt (t) = ±qo sin 2π fot( )

yt (t) = io2 + qo

2 cos 2π fot +θ(t)( )

where θ(t) = tan−1 ±qo

±io

× ×

Q

−io +ioI

×

×

Q

+qo

−qo

I

Polar View shows amplitude and phase of it(t), qt(t) and yt(t) combined signal for transmission at a given frequency f.

it(t) qt(t)

L11/4/2006 13Lecture 9 Fall 2006

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

Transmission signal is sine wave at frequency f0 with information encoded in discrete values of amplitude and phase.

×

×

×

×

45°

io2 + qo

2

Q

I

4 QAMQuadrature

Amplitude Modulation

Given io = qo = 1

yt (t) = 2θ(t) can have 4 values45°, 135°, − 45°, −135°

it(t)

qt(t)

2cos(2πf1t)2sin(2πf1t)

t

t

it (t )

qt (t )

yt (t )2cos(2πfot)2sin(2πfot)

i(t )

q(t )

L11/4/2006 14Lecture 9 Fall 2006

Digital Modulation: 16-QAM

• 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)

it(t)

qt(t)

2cos(2πf1t)2sin(2πf1t)

t

t

Baseband Input

L11/4/2006 15Lecture 9 Fall 2006

Constellation Diagram:16-QAM

• 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

DecisionBoundaries I

Q

DecisionBoundaries

00 01 11 10

00

01

11

10

L11/4/2006 16Lecture 9 Fall 2006

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