6.976
High Speed Communication Circuits and Systems
Lecture 19
Basics of Wireless Communication
Michael Perrott
Massachusetts Institute of Technology
Copyright © 2003 by Michael H. Perrott
Amplitude Modulation (Transmitter)
Transmitter Output
0
x(t)
y(t)
2cos(2πfot)
ƒ
ƒ
Vary the amplitude of a sine wave at carrier frequency fo
according to a baseband modulation signal
DC component of baseband modulation signal
influences transmit signal and receiver possibilities
- DC value greater than signal amplitude shown above
ƒ Allows simple envelope detector for receiver
ƒ Creates spurious tone at carrier frequency (wasted power)
M.H. Perrott
MIT OCW
Impact of Zero DC Value
Transmitter Output
0
x(t)
y(t)
2cos(2πfot)
ƒ
ƒ
Envelope of modulated sine wave no longer
corresponds directly to the baseband signal
- Envelope instead follows the absolute value of the
baseband waveform
- Envelope detector can no longer be used for receiver
The good news: less transmit power required for same
transmitter SNR (compared to nonzero DC value)
M.H. Perrott
MIT OCW
Accompanying Receiver (Coherent Detection)
Transmitter Output
0
x(t)
y(t)
2cos(2πfot)
Receiver Output
y(t)
z(t)
Lowpass
r(t)
2cos(2πfot)
ƒ
ƒ
Works regardless of DC value of baseband signal
Requires receiver local oscillator to be accurately
aligned in phase and frequency to carrier sine wave
M.H. Perrott
MIT OCW
Impact of Phase Misalignment in Receiver Local Oscillator
Transmitter Output
0
x(t)
y(t)
2cos(2πfot)
Receiver Output
y(t)
z(t)
Lowpass
r(t)
2sin(2πfot)
ƒ
Worst case is when receiver LO and carrier frequency
are phase shifted 90 degrees with respect to each other
- Desired baseband signal is not recovered
M.H. Perrott
MIT OCW
Frequency Domain View of AM Transmitter
avg(x(t))
X(f)
Transmitter Output
Y(f)
f
0
x(t)
y(t)
-fo
0
fo
f
2cos(2πfot)
1
-fo
ƒ
1
0
fo
f
Baseband signal is assumed to have a nonzero DC
component in above diagram
- Causes impulse to appear at DC in baseband signal
- Transmitter output has an impulse at the carrier frequency
M.H. Perrott
ƒ For coherent detection, does not provide key information
about information in baseband signal, and therefore is a
waste of power
MIT OCW
Impact of Having Zero DC Value for Baseband Signal
avg(x(t))
=0
X(f)
Transmitter Output
Y(f)
f
0
x(t)
y(t)
-fo
0
fo
f
2cos(2πfot)
1
1
-fo
ƒ
0
fo
f
Impulse in DC portion of baseband signal is now gone
- Transmitter output now is now free from having an
impulse at the carrier frequency (for ideal
implementation)
M.H. Perrott
MIT OCW
Frequency Domain View of AM Receiver (Coherent)
X(f)
Transmitter Output
Y(f)
f
0
x(t)
y(t)
-fo
f
fo
0
2cos(2πfot)
1
-fo
Z(f)
1
0
Lowpass
fo
Receiver Output
f
-2fo
y(t)
z(t)
-fo
0
Lowpass
fo
2fo
f
r(t)
2cos(2πfot)
1
-fo
M.H. Perrott
1
0
fo
f
MIT OCW
Impact of 90 Degree Phase Misalignment
X(f)
Transmitter Output
Y(f)
f
0
x(t)
y(t)
-fo
f
fo
0
2cos(2πfot)
1
-fo
Z(f)
1
0
Lowpass
fo
Receiver Output
=0
f
2fo
-2fo
y(t)
z(t)
-fo
0
Lowpass
f
fo
r(t)
2sin(2πfot)
j
f1
-f1
M.H. Perrott
0
f
-j
MIT OCW
Quadrature Modulation
1
-fo
It(f)
1
1
fo
0
Transmitter Output
f
it(t)
f
0
Qt(f)
1
2cos(2πf2t)
y(t)
2sin(2πf2t)
qt(t)
j
f1
ƒ
fo
0
0
f
f
Yq(f)
-fo
j
-f1
-fo
1
fo
f
0
Yi(f)
1
0
f
-j
-j
Takes advantage of coherent receiver’s sensitivity to
phase alignment with transmitter local oscillator
- We essentially have two orthogonal transmission
channels (I and Q) available to us
- Transmit two independent baseband signals (I and Q)
onto two sine waves in quadrature at transmitter
M.H. Perrott
MIT OCW
Accompanying Receiver
1
-fo
It(f)
1
1
1
fo
0
y(t)
2cos(2πf2t)
2sin(2πf2t)
qt(t)
-fo
1
fo
0
-fo
f1
0
-j
f
fo
0
f
Lowpass
y(t)
ir(t)
Ir(f)
2
0
2cos(2πf1t)
2sin(2πf1t) Lowpass
0
Receiver Output
f
Yq(f)
fo
j
-f1
-fo
j
f
0
Yi(f)
1
f
Qt(f)
1
ƒ
Transmitter Output
f
it(t)
0
1
f
qr(t)
-j
f1
-f1
Qr(f)
2
0
j
0
f
f
f
-j
Demodulate using two sine waves in quadrature at
receiver
- Must align receiver LO signals in frequency and phase to
transmitter LO signals
ƒ Proper alignment allows I and Q signals to be recovered as
shown
M.H. Perrott
MIT OCW
Impact of 90 Degree Phase Misalignment
1
-fo
It(f)
1
j
1
fo
0
f
y(t)
2cos(2πf2t)
Qt(f)
1
2sin(2πf2t)
qt(t)
fo
0
0
-j
f
0
f
-j
Receiver Output
ir(t)
y(t)
0
2sin(2πf1t)
-j
qr(t)
f
1
-fo
2
0
1
0
fo
f
Qr(f)
2cos(2πf1t)
0
Ir(f)
2
f
Yq(f)
-fo
f1
ƒ
-f1
1
fo
j
-f1
-fo
j
f
0
Yi(f)
1
it(t)
0
f1
Transmitter Output
f
f
f
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
M.H. Perrott
MIT OCW
Simplified View
Baseband Input
It(f)
1
it(t)
0
0
Lowpass
ir(t)
f
2cos(2πf1t)
2sin(2πf1t)
Qt(f)
1
ƒ
Receiver Output
qt(t)
2cos(2πf1t)
2sin(2πf1t)
Lowpass
f
Ir(f)
2
0
qr(t)
f
Qr(f)
2
0
f
For discussion to follow, assume that
- Transmitter and receiver phases are aligned
- Lowpass filters in receiver are ideal
- Transmit and receive I/Q signals are the same except for
scale factor
ƒ
In reality
- RF channel adds distortion, causes fading
- Signal processing in baseband DSP used to correct
M.H. Perrott
problems
MIT OCW
Analog Modulation
Baseband Input
Receiver Output
it(t)
Lowpass
ir(t)
t
t
2cos(2πf1t)
2sin(2πf1t)
qt(t)
t
ƒ
ƒ
ƒ
2cos(2πf1t)
2sin(2πf1t)
Lowpass
qr(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
M.H. Perrott
MIT OCW
Digital Modulation
Receiver Output
Baseband Input
Lowpass
it(t)
t
2cos(2πf1t)
2sin(2πf1t)
qt(t)
2cos(2πf1t)
2sin(2πf1t)
Lowpass
t
ƒ
ir(t)
t
qr(t)
Decision
Boundaries
t
Sample
Times
I/Q signals take on discrete values at discrete time
instants corresponding to digital data
- Receiver samples I/Q channels
ƒ Uses decision boundaries to evaluate value of data at
each time instant
ƒ
I/Q signals may be binary or multi-bit
- Multi-bit shown above
M.H. Perrott
MIT OCW
Advantages of Digital Modulation
ƒ
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
ƒ Inefficient use of radio channel if there is “dead time” in
information flow
ƒ
Allows error correction to be achieved
ƒ
Enables compression of information
ƒ
Supports a wide variety of information content
- Less sensitivity to radio channel imperfections
- More efficient use of channel
- Voice, text and email messages, video can all be
represented as digital bit streams
M.H. Perrott
MIT OCW
Constellation Diagram
Q
00
01
11
10
00
01
Decision
Boundaries
I
11
10
Decision
Boundaries
ƒ
We can view I/Q values at sample instants on a twodimensional coordinate system
ƒ Decision boundaries mark up regions corresponding
to different data values
ƒ Gray coding used to minimize number of bit errors
that occur if wrong decision is made due to noise
M.H. Perrott
MIT OCW
Impact of Noise on Constellation Diagram
Q
00
01
11
10
00
01
Decision
Boundaries
I
11
10
Decision
Boundaries
ƒ
ƒ
ƒ
Sampled data values no longer land in exact same
location across all sample instants
Decision boundaries remain fixed
Significant noise causes bit errors to be made
M.H. Perrott
MIT OCW
Transition Behavior Between Constellation Points
Q
00
01
11
10
00
01
Decision
Boundaries
I
11
10
Decision
Boundaries
ƒ
ƒ
Constellation diagrams provide us with a snapshot of I/Q
signals at sample instants
Transition behavior between sample points depends on
modulation scheme and transmit filter
M.H. Perrott
MIT OCW
Choosing an Appropriate Transmit Filter
p(t)
data(t)
x(t)
Td
*
t
ƒ
ƒ
t
t
|P(f)|2
Sdata(f)
0
Td
f
0 1/Td
Sx(f)
f
0 1/Td
f
Transmit filter, p(t), convolved with data symbols that are
viewed as impulses
- Example so far: p(t) is a square pulse
Output spectrum of transmitter corresponds to square of
transmit filter (assuming data has white spectrum)
- Want good spectral efficiency (i.e. narrow spectrum)
M.H. Perrott
MIT OCW
Highest Spectral Efficiency with Brick-wall Lowpass
p(t)
data(t)
x(t)
Td
*
t
Sdata(f)
0
t
t
-Td 0 Td
Sx(f)
|P(f)|2
f
0 1/(2Td)
f
ƒ
Use a sinc function for transmit filter
ƒ
Issues
0 1/(2Td)
f
- Corresponds to ideal lowpass in frequency domain
- Nonrealizable in practice
- Sampling offset causes significant intersymbol interference
M.H. Perrott
MIT OCW
Requirement for Transmit Filter to Avoid ISI
data(t)
Td
Td
t
ƒ
x(t)
p(t)
*
Td
t
t
Time samples of transmit filter (spaced Td apart) must
be nonzero at only one sample time instant
- Sinc function satisfies this criterion if we have no offset
in the sample times
ƒ
ƒ
Intersymbol interference (ISI) occurs otherwise
Example: look at result of convolving p(t) with 4
impulses
- With zero sampling offset, x(kT ) correspond to
associated impulse areas
M.H. Perrott
d
MIT OCW
Derive Nyquist Condition for Avoiding ISI (Step 1)
data(t)
Td
Td
t
*
Td
t
Td
t
p(kTd)
p(t)
impulse train
Td
t
ƒ
x(t)
p(t)
Td
t
t
Consider multiplying p(t) by impulse train with period Td
- Resulting signal must be a single impulse in order to
avoid ISI (same argument as in previous slide)
M.H. Perrott
MIT OCW
Derive Nyquist Condition for Avoiding ISI (Step 2)
P(f)
impulse train
1/Td
f
F{p(kTd)}
1/Td
*
1/Td
f
f
0
Td
Td
t
ƒ
p(kTd)
p(t)
impulse train
Td
t
t
In frequency domain, the Fourier transform of sampled
p(t) must be flat to avoid ISI
- We see this in two ways for above example
M.H. Perrott
ƒ Fourier transform of an impulse is flat
ƒ Convolution of P(f) with impulse train in frequency is flat
MIT OCW
A More Practical Transmit Filter
ƒ
Raised-cosine filter is quite popular in many applications
p(t)
P(f)
1-α 1+α
2Td 2Td
t
-Td
ƒ
0
Td
-1/Td
0
1/Td
f
Transition band in frequency set by “rolloff” factor, α
M.H. Perrott
ƒ Rolloff factor = 0: P(f) becomes a brick-wall filter
ƒ Rolloff factor = 1: P(f) looks nearly like a triangle
ƒ Rolloff factor = 0.5: shown above
MIT OCW
Raised-Cosine Filter Satisfies Nyquist Condition
Nyquist Condition
Observed in Time
Nyquist Condition
Observed in Frequency
p(t)
P(f)
t
-Td
ƒ
ƒ
0
-1/Td
Td
0
f
1/Td
In time
- p(kT ) = 0 for all k not equal to 0
In frequency
- Fourier transform of p(kT ) is flat
- Alternatively: Addition of shifted P(f) centered about k/T
d
d
leads to flat Fourier transform (as shown above)
M.H. Perrott
d
MIT OCW
Spectral Efficiency With Raised-Cosine Filter
p(t)
data(t)
x(t)
Td
*
t
Sdata(f)
0
t
t
-Td 0 Td
Sx(f)
|P(f)|2
f
0 1/(2Td)
f
0 1/(2Td)
ƒ
ƒ
More efficient than when p(t) is a square pulse
Less efficient than brick-wall lowpass
ƒ
Note: Raised-cosine P(f) often “split” between
transmitter and receiver
f
- But implementation is much more practical
M.H. Perrott
MIT OCW
Receiver Filter: ISI Versus Noise Performance
Raised-Cosine
Filter
It(t)
it(t)
ir(t)
Lowpass
Ir(t)
f
Baseband
Input
2cos(2πf1t)
2sin(2πf1t)
Qt(t)
qt(t)
f
ƒ
2cos(2πf1t)
2sin(2πf1t)
qr(t)
Lowpass
Receiver
Output
Qr(t)
Conflicting requirements for receiver lowpass
- Low bandwidth desirable to remove receiver noise and
to reject high frequency components of mixer output
- High bandwidth desirable to minimize ISI at receiver
output
M.H. Perrott
MIT OCW
Split Raised-Cosine Filter Between Transmitter/Receiver
Raised-Cosine
Filter
It(t)
it(t)
Raised-Cosine
Filter
ir(t)
f
Baseband
Input
f
2cos(2πf1t)
2sin(2πf1t)
Qt(t)
qt(t)
f
ƒ
Additional
Lowpass
Filtering
Ir(t)
f
Receiver
Output
2cos(2πf1t)
2sin(2πf1t)
qr(t)
f
f
Qr(t)
We know that passing data through raised-cosine
filter does not cause additional ISI to be produced
- Implement P(f) as cascade of two filters corresponding
to square root of P(f)
ƒ Place one in transmitter, the other in receiver
ƒ
Use additional lowpass filtering in receiver to further
reduce high frequency noise and mixer products
M.H. Perrott
MIT OCW
Multiple Access Techniques
The Issue of Multiple Access
ƒ
ƒ
ƒ
Want to allow communication between many different
users
Freespace spectrum is a shared resource
- Must be partitioned between users
Can partition in either time, frequency, or through
“orthogonal coding” (or nearly orthogonal coding) of
data signals
M.H. Perrott
MIT OCW
Frequency-Division Multiple Access (FDMA)
Channel
1
Channel
2
Channel
N
f
ƒ
ƒ
Place users into different frequency channels
Two different methods of dealing with transmit/receive of
a given user
- Frequency-division duplexing
- Time-division duplexing
M.H. Perrott
MIT OCW
Frequency-Division Duplexing
Antenna
Duplexer
Transmitter
TX
TX
RX
f
Receiver
ƒ
ƒ
RX
Transmit Receive
Band
Band
Separate frequency channels into transmit and receive
bands
Allows simultaneous transmission and reception
- Isolation of receiver from transmitter achieved with duplexer
- Cannot communicate directly between users, only between
handsets and base station
ƒ
ƒ
Advantage: isolates users
Disadvantage: deplexer has high insertion loss (i.e.
attenuates signals passing through it)
M.H. Perrott
MIT OCW
Time-Division Duplexing
Switch
Transmitter
Receiver
ƒ
ƒ
ƒ
ƒ
ƒ
Antenna
TX
RX
switch
control
Use any desired frequency channel for transmitter and
receiver
Send transmit and receive signals at different times
Allows communication directly between users (not
necessarily desirable)
Advantage: switch has low insertion loss relative to
duplexer
Disadvantage: receiver more sensitive to transmitted
signals from other users
M.H. Perrott
MIT OCW
Time-Division Multiple Access (TDMA)
Time Slot Time Slot Time Slot
1
2
N
Time Slot Time Slot
N
1
t
Time Frame
ƒ
Place users into different time slots
ƒ
Often combined with FDMA
- A given time slot repeats according to time frame period
- Allows many users to occupy the same frequency
channel
M.H. Perrott
MIT OCW
Channel Partitioning Using (Nearly) “Orthogonal Coding”
Uncorrelated Signals
1
-1
1
B
-1
1
-1
x(t)
1
-A
-1
1
B
-1
1
-1
x(t)
A
ƒ
Correlated Signals
y(t)
c(t)
c(t)
y(t)
1
-1
1
B
-1
1
-1
x(t)
1
-B
-1
1
B
-1
1
-1
x(t)
B
y(t)
c(t)
y(t)
c(t)
Consider two correlation cases
- Two independent random Bernoulli sequences
ƒ Result is a random Bernoulli sequence
- Same Bernoulli sequence
ƒ Result is 1 or -1, depending on relative polarity
M.H. Perrott
MIT OCW
Code-Division Multiple Access (CDMA)
Separate
Transmitters
x1(t)
y1(t)
Td
PN1(t)
Transmit Signals
Combine
in Freespace
y(t)
x2(t)
y2(t)
PN2(t)
Tc
ƒ
ƒ
Assign a unique code sequence to each transmitter
Data values are encoded in transmitter output stream by
varying the polarity of the transmitter code sequence
- Each pulse in data sequence has period T
ƒ Individual pulses represent binary data values
- Each pulse in code sequence has period T
d
c
ƒ Individual pulses are called “chips”
M.H. Perrott
MIT OCW
Receiver Selects Desired Transmitter Through Its Code
Separate
Transmitters
x1(t)
y1(t)
Transmit Signals
Combine
in Freespace
PN1(t)
x2(t)
y2(t)
PN2(t)
PN1(t)
r(t)
Lowpass
x(t)
y(t)
Receiver
(Desired Channel = 1)
ƒ
Receiver correlates its input with desired transmitter code
- Data from desired transmitter restored
Data from other transmitter(s) remains randomized
M.H. Perrott
MIT OCW
Frequency Domain View of Chip Vs Data Sequences
1
Tc
data(t)
p(t)
1
*
t
-1
x(t)
1
t
t
Tc
data(t)
-1
p(t)
x(t)
1
1
Td
*
t
-1
1
t
t
Td
Sdata(f)
Td
-1
|P(f)|2
Td
Tc
0
ƒ
f
Sx(f)
Tc
0 1/Td
1/Tc
f
0 1/Td
1/Tc
f
Data and chip sequences operate on different time scales
- Associated spectra have different width and height
M.H. Perrott
MIT OCW
Frequency Domain View of CDMA
Td
Sx1(f)
Sy1(f)
Transmitter 1
x1(t)
0 1/Td
Td
f
y1(t)
Tc
0
PN1(t)
Sx2(f)
1/Tc
x2(t)
ƒ
ƒ
f
y2(t)
PN2(t)
Td
PN1(t)
Sy2(f)
Sx1(f)
Lowpass
y(t)
Transmitter 2
0 1/Td
Sx(f)
f
r(t)
Tc
Tc
0
1/Tc
f
0 1/Td
1/Tc
f
CDMA transmitters broaden data spectra by encoding it
onto chip sequences
CDMA receiver correlates with desired transmitter code
- Spectra of desired channel reverts to its original width
- Spectra of undesired channel remains broad
M.H. Perrott
ƒ Can be “mostly” filtered out by lowpass
MIT OCW
Constant Envelope Modulation
The Issue of Power Efficiency
Baseband
Input
ƒ
ƒ
Power Amp
Baseband to RF
Modulation
Transmitter
Output
Variable-Envelope Modulation
Constant-Envelope Modulation
Power amp dominates power consumption for many wireless
systems
- Linear power amps more power consuming than nonlinear ones
Constant-envelope modulation allows nonlinear power amp
- Lower power consumption possible
M.H. Perrott
MIT OCW
Simplified Implementation for Constant-Envelope
Baseband
Input
Baseband to RF Modulation
Transmit
Filter
Power Amp
Transmitter
Output
Constant-Envelope Modulation
ƒ
ƒ
Constant-envelope modulation limited to phase and
frequency modulation methods
Can achieve both phase and frequency modulation with
ideal VCO
- Use as model for analysis purposes
- Note: phase modulation nearly impossible with practical VCO
M.H. Perrott
MIT OCW
Example Constellation Diagram for Phase Modulation
Q
000
001
100
011
Decision 101
Boundaries
I
010
111
110
Decision
Boundaries
ƒ
I/Q signals must always combine such that amplitude
remains constant
- Limits constellation points to a circle in I/Q plane
- Draw decision boundaries about different phase regions
M.H. Perrott
MIT OCW
Transitioning Between Constellation Points
Q
000
001
100
011
Decision 101
Boundaries
I
010
111
110
Decision
Boundaries
ƒ
Constant-envelope requirement forces transitions to
allows occur along circle that constellation points sit on
- I/Q filtering cannot be done independently!
- Significantly impacts output spectrum
M.H. Perrott
MIT OCW
Modeling The Impact of VCO Phase Modulation
ƒ
Recall unmodulated VCO model
Phase
Noise
Sout(f)
Phase/Frequency
modulation Signal
Spurious
Noise
Overall
phase noise
SΦmod(f)
Φtn(t)
f
Φmod(t)
fo
Φout
2cos(2πfot+Φout(t))
f
out(t)
0
ƒ
Relationship between sine wave output and instantaneous
phase
ƒ
Impact of modulation
- Same as examined with VCO/PLL modeling, but now we
consider Φout(t) as sum of modulation and noise components
M.H. Perrott
MIT OCW
Relationship Between Sine Wave Output and its Phase
ƒ
Key relationship (note we have dropped the factor of 2)
ƒ
Using a familiar trigonometric identity
ƒ
Approximation given |Φtn(t)| << 1
M.H. Perrott
MIT OCW
Relationship Between Output and Phase Spectra
ƒ
Approximation from previous slide
ƒ
Autocorrelation (assume modulation signal
independent of noise)
ƒ
Output spectral density (Fourier transform of
autocorrelation)
- Where * represents convolution and
M.H. Perrott
MIT OCW
Impact of Phase Modulation on the Output Spectrum
Phase
Noise
Sout(f)
Phase/Frequency
modulation Signal
Spurious
Noise
Overall
phase noise
SΦmod(f)
Φtn(t)
f
fo
Φout
Φmod(t)
2cos(2πfot+Φout(t))
f
out(t)
0
Sout(f)
Phase/Frequency
modulation Signal
Overall
phase noise
SΦmod(f)
Φtn(t)
f
Φmod(t)
fo
Φout
2cos(2πfot+Φout(t))
f
out(t)
0
ƒ
ƒ
Spectrum of output is distorted compared to SΦmod(f)
Spurs converted to phase noise
M.H. Perrott
MIT OCW
I/Q Model for Phase Modulation
ƒ
Applying trigonometric identity
ƒ
Can view as I/Q modulation
- I/Q components are coupled and related nonlinearly to
Φmod(t)
cos(Φmod(t))
SΦmod(f)
Sa(f)
it(t)
0
Φmod(t)
0
sin(Φmod(t))
y(t)
sin(2πf2t)
-fo
qt(t)
0
M.H. Perrott
cos(2πf2t)
Sb(f)
f
Sy(f)
f
0
fo
f
f
MIT OCW