digital modulation (part i) - cppsim · m.h. perrott©2007 digital modulation (part i), slide 2...
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M.H. Perrott©2007 Digital Modulation (Part I), Slide 1
DigitalModulation(Part I)
• Communication using symbols and bits• Constellation diagrams and decision boundaries • Transmit bandwidth vs.intersymbol interference• Eye Diagrams and sample time sensitivity
Copyright © 2007 by M.H. PerrottAll rights reserved.
M.H. Perrott©2007 Digital Modulation (Part I), Slide 2
Review of Analog I/Q Modulation
• Consider modulating with both a cosine and sine wave and then adding the results– This is known as I/Q modulation
• The I/Q signals occupy the same frequency band, but one is real and one is imaginary– We can recover both of these signals
I stands forin-phasecomponent
Q stands forquadraturecomponent
Transmitter Outputf
-fo fo0
1 1
f0
f-fo
fo
0
j
-j
2cos(2πfot)
2sin(2πfot)
y(t)
it(t)
qt(t)
It(f)
Qt(f)
f0
f-fo fo0
1 11
1
f-fo
fo
0
j
-j
Yi(f)
Yq(f)
M.H. Perrott©2007 Digital Modulation (Part I), Slide 3
Review of Analog I/Q Demodulation
• Demodulate with both a cosine and sine wave– Both I and Q channels are recovered!
• I/Q modulation allows twice the amount of information to be sent compared to basic AM modulation with same bandwidth
Receiver Output
2cos(2πfot)
2sin(2πfot)
y(t)
ir(t)
qr(t)
f
f
f-fo fo0
1 1
f-fo
fo
0
j
-j
f0
Ir(f)
Qr(f)
f0
2
2
Transmitter Outputf
-fo fo0
1 1
f0
f-fo
fo
0
j
-j
2cos(2πfot)
2sin(2πfot)
y(t)
it(t)
qt(t)
It(f)
Qt(f)
f0
f-fo fo0
1 11
1
f-fo
fo
0
j
-j
Yi(f)
Yq(f)
Lowpass
H(f)
Lowpass
H(f)
M.H. Perrott©2007 Digital Modulation (Part I), Slide 4
Summary of Analog I/Q Demodulation• Frequency domain view
• Time domain view
f0
Receiver Output
2cos(2πfot)2sin(2πfot)
ir(t)
qr(t)
it(t)
qt(t)
It(f)
Qt(f)
f0
1
1
f0
Ir(f)
Qr(f)
f0
2
2
2cos(2πfot)2sin(2πfot)
Baseband Input
Lowpass
H(f)
Lowpass
H(f)
t
t
t
t
Receiver Output
2cos(2πfot)2sin(2πfot)
ir(t)
qr(t)
it(t)
qt(t)
2cos(2πfot)2sin(2πfot)
Baseband Input
Lowpass
H(f)
Lowpass
H(f)
M.H. Perrott©2007 Digital Modulation (Part I), Slide 5
Digital I/Q Modulation
• Leverage analog communication channel to send discrete-valued symbols– Example: send symbol from set {-3,-1,1,3} on both
I and Q channels each symbol period• At receiver, sample I/Q waveforms every symbol
period– Associate each sampled I/Q value with symbols from
set {-3,-1,1,3} on both I and Q channels
2cos(2πfot)
2sin(2πfot)
ir(t)
qr(t)
it(t)
qt(t)
2cos(2πfot)
2sin(2πfot)
Lowpass
H(f)
Lowpass
H(f)
Receiver Output
t
t
t
Baseband Input
t
SampleTimes
31
-1-3
31
-1-3
31
-1-3
31
-1-3
I
Q
M.H. Perrott©2007 Digital Modulation (Part I), Slide 6
Advantages of going Digital• 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
M.H. Perrott©2007 Digital Modulation (Part I), Slide 7
Constellation Diagrams
• Plot I/Q samples on x-y axis– Example: sampled I/Q value of
{1,-3} forms a dot at x=1, y=-3– As more samples are plotted,
constellation diagram eventually displays all possible symbol values
• Constellation diagram provides a sense of how easy it is to distinguish between different symbols
2cos(2πfot)
2sin(2πfot)
ir(t)
qr(t)
it(t)
qt(t)
2cos(2πfot)
2sin(2πfot)
Lowpass
H(f)
Lowpass
H(f)
Receiver Output
t
t
t
Baseband Input
t
SampleTimes
31
-1-3
31
-1-3
31
-1-3
31
-1-3
-3 -1 1 3
-3
-1
1
3
I
Q
I
Q
M.H. Perrott©2007 Digital Modulation (Part I), Slide 8
Sending Digital Bits
• Assign each I/Q symbol to a set of digital bits– Example: I/Q = {1,3} translates
to bits of 1110– Gray coding minimizes bit errors
when symbol errors are made• Example: I/Q = {1,1} translates
to bits of 1010– Only one bit change from
I/Q = {1,3}
2cos(2πfot)
2sin(2πfot)
ir(t)
qr(t)
it(t)
qt(t)
2cos(2πfot)
2sin(2πfot)
Lowpass
H(f)
Lowpass
H(f)
Receiver Output
t
t
t
Baseband Input
t
SampleTimes
31
-1-3
31
-1-3
31
-1-3
31
-1-3
00 01 11 10
00
01
11
10
I
Q
I
Q
M.H. Perrott©2007 Digital Modulation (Part I), Slide 9
The Impact of Noise
• Noise perturbs sampled I/Q values– Constellation points no longer
consist of single dots for each symbol
• Issue: what is the best way to match received I/Q samples with their corresponding symbols?
00 01 11 10
00
01
11
10
I
Q
2cos(2πfot)
2sin(2πfot)
ir(t)
qr(t)
it(t)
qt(t)
2cos(2πfot)
2sin(2πfot)
Lowpass
H(f)
Lowpass
H(f)
Receiver Output
t
t
t
Baseband Input
t
SampleTimes
31
-1-3
31
-1-3
31
-1-3
31
-1-3
ReceiverNoise I
Q
M.H. Perrott©2007 Digital Modulation (Part I), Slide 10
Symbol Selection Based on Slicing
• Match I/Q samples to their corresponding symbols based on decision regions– Choose decision regions
to minimize symbol errors
– Decision boundaries are also called slicing levels
DecisionBoundaries I
Q
DecisionBoundaries
00 01 11 10
00
01
11
10
2cos(2πfot)
2sin(2πfot)
ir(t)
qr(t)
it(t)
qt(t)
2cos(2πfot)
2sin(2πfot)
Lowpass
H(f)
Lowpass
H(f)
Receiver Output
t
t
t
Baseband Input
t
SampleTimes
31
-1-3
31
-1-3
31
-1-3
31
-1-3
ReceiverNoise I
Q
M.H. Perrott©2007 Digital Modulation (Part I), Slide 11
Transitioning Between Symbols
• Transition behavior between symbols is influenced by both transmit I/Q input waveforms and receive filter– We will focus on impact of
transition behavior at transmitter today
– Ignore the impact of noise for this analysis
I
Q
00 01 11 10
00
01
11
10
2cos(2πfot)
2sin(2πfot)
ir(t)
qr(t)
it(t)
qt(t)
2cos(2πfot)
2sin(2πfot)
Lowpass
H(f)
Lowpass
H(f)
Receiver Output
t
t
t
Baseband Input
t
SampleTimes
31
-1-3
31
-1-3
31
-1-3
31
-1-3
ReceiverNoise I
Q
M.H. Perrott©2007 Digital Modulation (Part I), Slide 12
Influence of Transitions at Transmitter
• Ideal analog communication channel simply transports the transmitter I/Q signals to the receiver
• Constellation diagram can be constructed at transmitter to evaluate its performance– Bad constellation at transmitter implies
bad one at receiver
I
Q
00 01 11 10
00
01
11
10
2cos(2πfot)
2sin(2πfot)
ir(t)
qr(t)
it(t)
qt(t)
2cos(2πfot)
2sin(2πfot)
Lowpass
H(f)
Lowpass
H(f)
Receiver Output
t
t
t
Baseband Input
t
SampleTimes
31
-1-3
31
-1-3
31
-1-3
31
-1-3
ReceiverNoise I
Q
SampleTimes
M.H. Perrott©2007 Digital Modulation (Part I), Slide 13
Transitions and the Transmitted Spectrum
• Want transmitted spectrum with minimal bandwidth– Wireless communication
channels are a sharedresource
• Issue: sharply changing I/Q waveforms lead to a wide bandwidth spectrum
I
Q
00 01 11 10
00
01
11
10
it(t)
qt(t)
2cos(2πfot)
2sin(2πfot)
t
t
Baseband Input31
-1-3
31
-1-3
SampleTimes
tt
T
t
|Pzoh(f)|
f
d(t) (one trial) pzoh(t)
f00
*
f
T
it(t) (one trial)
|D(f)|
(one trial)
|It(f)|
(one trial)
-1T
1T
0-1T
1T
y(t)
f
|Y(f)|
(one trial)
0-1T
1T
M.H. Perrott©2007 Digital Modulation (Part I), Slide 14
Impact of Transmit Filter
• Transmit filter enables reduced bandwidth for transmitted spectrum
• Issue: can lead to intersymbol interference (ISI)– Constellation diagram displays
vulnerability to making bit errors
I
Q
00 01 11 10
00
01
11
10
it(t)
qt(t)
2cos(2πfot)
2sin(2πfot)
t
t
Baseband Input31
-1-3
31
-1-3
SampleTimes
y(t)
f
|Y(f)|
(one trial)
0-1T
1T
Lowpass
P(f)
Lowpass
P(f)
t
t
31
-1-3
31
-1-3
f
P(f)
f0-1
T1T
|Di(f)|
(one trial)
di(t)
M.H. Perrott©2007 Digital Modulation (Part I), Slide 15
Impact of Low Bandwidth Transmit Filter
• Lowering the transmit filter bandwidth leads to– Lower bandwidth
transmitted spectrum– Increased ISI
• Eye diagrams allow ISI to be intuitively examined
I
Q
00 01 11 10
00
01
11
10
it(t)
qt(t)
2cos(2πfot)
2sin(2πfot)
t
t
Baseband Input31
-1-3
31
-1-3
SampleTimes
y(t)
f
|Y(f)|
(one trial)
0-1T
1T
Lowpass
P(f)
Lowpass
P(f)
t
t
31
-1-3
31
-1-3
f
P(f)
f0-1
T1T
|Di(f)|
(one trial)
di(t)
M.H. Perrott©2007 Digital Modulation (Part I), Slide 16
Eye Diagrams
• Key idea: wrap signal back onto itself in periodic time intervals and retain all traces– Similar to action of oscilloscope
t
3
1
-1
-3
I(t)
t
3
1
-1
-3
Eye Diagram
of I(t)
M.H. Perrott©2007 Digital Modulation (Part I), Slide 17
t
t
3
1
-1
-3
3
1
-1
-3
I(t)
Eye Diagram
of I(t)
Looking at Many Symbols
• Increasing the number of symbols eventually reveals all possible symbol transition trajectories– Intuitively displays the impact of filtering on ISI
M.H. Perrott©2007 Digital Modulation (Part I), Slide 18
t
t
3
1
-1
-3
3
1
-1
-3
I(t)
Eye Diagram
of I(t) Decision
Boundaries
Sample Times
(also called
Slicing levels)
Assessing the Quality of an Eye Diagram
• Eye diagram allows visual inspection of the impact of sample time and decision boundary choices– Large eye opening implies less vulnerability to symbol errors
M.H. Perrott©2007 Digital Modulation (Part I), Slide 19
Relating Eye Diagrams to Constellation
• Open eye diagrams lead to tight symbol groupings in constellation– Assumes proper
sample time placement
I
Q
00 01 11 10
00
01
11
10
it(t)
qt(t)
2cos(2πfot)
2sin(2πfot)
t
t
Baseband Input31
-1-3
31
-1-3
SampleTimes
y(t)Lowpass
P(f)
Lowpass
P(f)
t
t
31
-1-3
31
-1-3
f
P(f)
di(t)
I and Q Eye Diagrams
SampleTimes
t
M.H. Perrott©2007 Digital Modulation (Part I), Slide 20
Impact of Low Transmit Bandwidth
• Eye diagrams intuitively show increased ISI– Also show
sensitivity of bit errors to sample time placement Sample
Times
t
t
Baseband Input31
-1-3
31
-1-3
f
P(f)
I
Q
00 01 11 10
00
01
11
10
it(t)
qt(t)
2cos(2πfot)
2sin(2πfot)
SampleTimes
y(t)Lowpass
P(f)
Lowpass
P(f)
t
t
31
-1-3
31
-1-3
di(t)
I and Q Eye Diagrams
t
M.H. Perrott©2007 Digital Modulation (Part I), Slide 21
Summary• Digital modulation operates by sending discrete-
valued symbols through an analog communication channel– Receiver must sample I/Q signals at the appropriate time– Receiver matches I/Q sample values to corresponding
symbols based on decision regions– Constellation diagrams are a convenient tool to see
likelihood of bit errors being made
• Choice of transmit filter is a tradeoff between achieving a minimal bandwidth transmitted spectrum and minimal intersymbol interference (ISI)– Eye diagrams are a convenient tool to see effects of ISI
and sensitivity of bit errors to sample time choice
• Next lecture: a closer look at the receiver…