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)

π 2cos(2 fot) Receiver Output

Lowpass y(t) z(t) r(t)

π 2cos(2 fot)

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

11/4/2006 L Lecture 9 Fall 2006 2 Impact of Phase Misalignment in Receiver Local Oscillator

Transmitter Output 0

x(t) y(t)

π 2cos(2 fot) Receiver Output Output is zero

Lowpass y(t) z(t) r(t)

π 2sin(2 fot)

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

11/4/2006 L Lecture 9 Fall 2006 3 Analog I/Q Modulation

Baseband Input

iti(t)(t) it (t) t

cos 2 f tπ yt (t) 2cos(2( π 0 )f1t) π 2sin(2sin() 2π f0t f1t)

qqt(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

11/4/2006 L Lecture 9 Fall 2006 4 Polar View of Analog I/Q Modulation

it (t) = i(t)cos() 2π fot + 0°

ii(t(t)t) it (t)

qt (t) = q(t)cos() 2π fot + 90° = q(t)sin() 2π fot t

cos 2π f tπ y (t) 2cos(2( 0 )f1t) t 2 2 π 2sin(2sin() 2π f0t f1t) yt (t) = i (t) + q (t) cos() 2π fot + θ(t)

qq(tt(t)) −1 where θ(t) = tan q(t)/i(t) t qt (t) −180°<θ < 180°

11/4/2006 L Lecture 9 Fall 2006 5 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

2 2 y(t) i (t) + q (t) q(t) θ(t) i(t) I I q(t) i(t) y(t) θ(t) i2 (t)+ q2 (t)

11/4/2006 L Lecture 9 Fall 2006 6 Frequency Domain View of Analog I/Q Modulation

11 Transmitter Output f II(f)(f) -f 0 fo t o YIit(f)(f) 1 11 i(t)it(t) f f -f f π o 0 o 0 2cos2cos(2( 2π ff02tt)) y(t) QQ(f)t(f) π 2sin2sin(2() 2π ff02tt) 1 j YQqt(f)(f) qq(t)t(t) fo f f 0 j -fo 0 -j fo 1 f 0 -f-fo1 -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

11/4/2006 L Lecture 9 Fall 2006 7 Analog I/Q Modulation-Transceiver

Baseband Input Receiver Output

Lowpass it(t) ir(t) t t 2cos( 2π f tπ) 2cos 2ππf t 2cos(20 f1t) 2cos(2( f01t)) 2sin(2πf t) 2sin(2πf t) 2sin() 2π f0t 1 2sin() 2π f1t 0 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

11 11 Transmitter Output Receiver Output f f I (f) -fo 0 fo -fo 0 fo I (f) t 11Yi(f) r 1 Lowpass 2 it(t) ir(t) f f -f f f π o 0 o 0 2cos2cos(2 2π ff2tt) y(t) y(t) 2cos(2πf t) 0 ( 0 ) 2cos( 2π 1f0t) Q (f) Q (f) t 2sin() 2ππf0t 2sin 2π f t r 2sin(2 f2t) 2sin(2()f10t) Lowpass 1 j Yq(f) 2 qt(t) qr(t) fo f f f 0 j -fo 0 j 0 -j fo ffo1 1 f f 0 -f 0 -f-f1 1 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

11 j

Transmitter Output f1 Receiver Output f f It(f) -fo 0 fo -f 0 I (f) 11Yi(f) 1 r 1 -j 2 it(t) ir(t) f f -f f f π o 0 o π 0 2cos(2 f2t) y(t) y(t) 2sin(2 f1t) 0

Qt(f) π π Qr(f) 2sin(2 f2t) -2cos(2 f1t) 1 j Yq(f) qt(t) qr(t) fo f f f 0 j -fo 0 0 -j f1 -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

ii(t(t)t) it (t)

−i o t 2cos(2πf πt) yt (t) t 2cos(2o f1t) 2sin(2 πfπot)f t) +qo 1

qt((t)t)

−qo qt (t) t t

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

11/4/2006 L Lecture 9 Fall 2006 11 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)

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

× +qo

−io +io I × × I

× −qo

2 2 yt (t) = io + qo cos( 2π fot + θ(t)) ±q where θ(t) = tan−1 o ±io

11/4/2006 L Lecture 9 Fall 2006 12 Polar View of Digital I/Q Modulation (cont’d)

Q ii(t(t)t) it (t)

t × × π yt (t) 2cos(22cos(2πfoft)1t) π t) 2sin(22sin(2πfot)f1 2 2 io + qo 4 QAM qt((t)t) 45° q 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.

11/4/2006 L Lecture 9 Fall 2006 13 Digital Modulation: 16-QAM

Baseband Input

it(t)

t π 2cos(2 f1t) π 2sin(2 f1t)

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)

11/4/2006 L Lecture 9 Fall 2006 14 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

11/4/2006 L Lecture 9 Fall 2006 15 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

11/4/2006 L Lecture 9 Fall 2006 16