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Transcript
Short Course:
Wireless Communications
Professor Andrea Goldsmith
UCSD
March 22-23
La Jolla, CA
Course Outline












Overview of Wireless Communications
Path Loss, Shadowing, and WB/NB Fading
Capacity of Wireless Channels
Digital Modulation and its Performance
Adaptive Modulation
Diversity
MIMO Systems
Multicarrier Modulation
Spread Spectrum
Multiuser Communications
Wireless Networks
Future Wireless Systems
Lecture 1
Lecture 2
Lecture 3
Wireless History




Ancient Systems: Smoke Signals, Carrier Pigeons, …
Radio invented in the 1880s by Marconi
Many sophisticated military radio systems were
developed during and after WW2
Cellular has enjoyed exponential growth since the
mid 1980s, with billions of users worldwide today




Ignited the wireless revolution
Voice, data, and multimedia becoming ubiquitous
Use in third world countries growing rapidly
Wifi also enjoying tremendous success and growth

Wide area networks (e.g. Wimax) and short-range
systems other than Bluetooth (e.g. UWB) less successful
Future Wireless Networks
Ubiquitous Communication Among People and Devices
Next-generation Cellular
Wireless Internet Access
Wireless Multimedia
Sensor Networks
Smart Homes/Spaces
Automated Highways
In-Body Networks
All this and more …
Future Cell Phones
Burden for this
performance
is oninthe
Everything
wireless
onebackbone
device network
San Francisco
BS
BS
Internet
Nth-Gen
Cellular
Phone
System
Nth-Gen
Cellular
New York
BS
Much better performance and reliability than today
- Gbps rates, low latency, 99%
coverage indoors and out
Future Wifi:
Multimedia Everywhere, Without Wires
Performance burden also on the (mesh) network
802.11n++
• Streaming video
• Gbps data rates
• High reliability
• Coverage in every room
Wireless HDTV
and Gaming
Challenges

Network Challenges







Scarce difficult spectrum
Interference
Demanding applications
Reliability
Ubiquitous coverage
Indoor to outdoor operation
Device Challenges




Size, Power, Cost
Multiple Antennas in Silicon
Multiradio Integration
Coexistance
BT
Cellular
FM/XM
GPS
DVB-H
Apps
Processor
WLAN
Media
Processor
Wimax
Software-Defined (SD) Radio:
Is this the solution to the device challenges?
BT
Cellular
FM/XM
GPS
DVB-H


A/D
Apps
Processor
WLAN
Media
Processor
Wimax
A/D
A/D
DSP
A/D
Wideband antennas and A/Ds span BW of desired signals
DSP programmed to process desired signal: no specialized HW
Today, this is not cost, size, or power efficient
Compressed sensing may be a solution for sparse signals
Compressed Sensing

Basic premise is that signals with some sparse
structure can be sampled below their Nyquist rate

Signal can be perfectly reconstructed from these
samples by exploiting signal sparsity

This significantly reduces the burden on the front-end
A/D converter, as well as the DSP and storage

Might be key enabler for SD and low-energy radios

Only for incoming signals “sparse” in time, freq., space, …
Evolution of Current Systems

Wireless systems today



Next Generation is in the works



3G Cellular: ~200-300 Kbps.
WLANs: 802.11n; 600 Mbps (and growing).
4G Cellular: LTE ; R>100Mbps
4G WLANs: 802.11ac, 802.11ad; R>1Gbps
Technology Enhancements




Hardware: Better circuits/processors.
Link: More bandwidth, more antennas, better modulation
and coding, adaptivity, cognition.
Network: MU MIMO, cooperation, relaying, femtocells.
Application: Soft and adaptive QoS.
Evolution of Tradeoffs
Other Tradeoffs:
Rate vs. Coverage
Rate vs. Delay
Rate vs. Cost
Rate vs. Energy
802.11ac,ad
Rate
802.11n
802.11b WLAN
2G
4G
3G
LTE
Wimax/3G
2G Cellular
Mobility
Other tradeoffs becoming more important
Multimedia Requirements
Voice
Data
Video
Delay
<100ms
-
<100ms
Packet Loss
BER
<1%
10-3
0
10-6
<1%
10-6
Data Rate
8-32 Kbps
Continuous
1-100 Mbps
Bursty
Traffic
1-20 Mbps
Continuous
One-size-fits-all protocols and design do not work well
Wired networks use this approach, with poor results
Quality-of-Service (QoS)

QoS refers to the requirements associated with a
given application, typically rate and delay
requirements.

It is hard to make a one-size-fits all network that
supports requirements of different applications.

Wired networks often use this approach with
poor results, and they have much higher data
rates and better reliability than wireless.

QoS for all applications requires a cross-layer
design approach.
Crosslayer Design

Application

Network

Access

Link

Hardware
Delay Constraints
Rate Constraints
Energy Constraints
Adapt across design layers
Reduce uncertainty through scheduling
Provide robustness via diversity
Current Wireless Systems

Cellular Systems

Wireless LANs

Wimax

Satellite Systems

Paging Systems

Bluetooth

Zigbee radios
Cellular Phones
Everything Wireless in One Device
Burden for this performance is on the backbone network
San Francisco
BS
BS
Internet
Nth-Gen
Cellular
Phone
System
Nth-Gen
Cellular
New York
BS
Much better performance and reliability than today
- Gbps rates, low latency, 99%
coverage indoors and out
3G Cellular Design:
Voice and Data

Data is bursty, whereas voice is continuous


3G “widens the data pipe”:





Typically require different access and routing strategies
384 Kbps (802.11n has 100s of Mbps).
Standard based on wideband CDMA
Packet-based switching for both voice and data
3G cellular popular in Asia and Europe
Evolution of existing systems in US (2.5G++)
GSM+EDGE, IS-95(CDMA)+HDR
 100 Kbps
 Dual phone (2/3G+Wifi) use (iPhone, Android)


3G insufficient for smart phone requirements
4G/LTE/IMT Advanced

Much higher peak data rates (50-100 Mbps)

Greater spectral efficiency (bits/s/Hz)

Flexible use of up to 100 MHz of spectrum

Low packet latency (<5ms).

Increased system capacity

Reduced cost-per-bit

Support for multimedia
Wifi Networks
Multimedia Everywhere, Without Wires
802.11n++
• Streaming video
• Gbps data rates
• High reliability
• Coverage in every room
Wireless HDTV
and Gaming
Wireless Local Area
Networks (WLANs)
01011011
0101
1011
Internet
Access
Point




WLANs connect “local” computers (100m range)
Breaks data into packets
Channel access is shared (random access)
Backbone Internet provides best-effort service
 Poor performance in some apps (e.g. video)
Wireless LAN Standards

802.11b (Old – 1990s)




802.11a/g (Middle Age– mid-late 1990s)




Standard for 2.4GHz ISM band (80 MHz)
Direct sequence spread spectrum (DSSS)
Speeds of 11 Mbps, approx. 500 ft range
Standard for 5GHz band (300 MHz)/also 2.4GHz
OFDM in 20 MHz with adaptive rate/codes
Speeds of 54 Mbps, approx. 100-200 ft range
802.11n (New – since Fall’09)




What’s next?
Many
WLAN
cards
have
all 4
(a/b/g/n)
802.11ac/ad
Standard in 2.4 GHz and 5 GHz band
Adaptive OFDM /MIMO in 20/40 MHz (2-4 antennas)
Speeds up to 600Mbps, approx. 200 ft range
Other advances in packetization, antenna use, etc.
Wimax (802.16)

Wide area wireless network standard
 System architecture similar to cellular
 Called “3.xG” (e.g. Sprint EVO), evolving
into 4G
OFDM/MIMO is core link technology
 Operates in 2.5 and 3.5 GHz bands

 Different for different countries,
 Bandwidth is 3.5-10 MHz

5.8 also used.
Fixed (802.16d) vs. Mobile (802.16e) Wimax
 Fixed: 75 Mbps max, up to 50 mile cell radius
 Mobile: 15 Mbps max, up to 1-2 mile cell radius
WiGig and Wireless HD

New standards operating in 60 GHz band

Data rates of 7-25 Gbps

Bandwidth of around 10 GHz (unregulated)

Range of around 10m (can be extended)

Uses/extends 802.11 MAC Layer

Applications include PC peripherals and
displays for HDTVs, monitors & projectors
Satellite Systems

Cover very large areas

Different orbit heights


GEOs (39000 Km) versus LEOs (2000 Km)
Optimized for one-way transmission
Radio (XM, Sirius) and movie (SatTV, DVB/S) broadcasts
 Most two-way systems struggling or bankrupt


Global Positioning System (GPS) use growing

Satellite signals used to pinpoint location

Popular in cell phones, PDAs, and navigation devices
Paging Systems

Broad coverage for short messaging

Message broadcast from all base stations

Simple terminals

Optimized for 1-way transmission

Answer-back hard

Overtaken by cellular
Bluetooth

Cable replacement RF technology (low cost)

Short range (10m, extendable to 100m)

2.4 GHz band (crowded)

1 Data (700 Kbps) and 3 voice channels, up
to 3 Mbps

Widely supported by telecommunications,
PC, and consumer electronics companies

Few applications beyond cable replacement
8C32810.61-Cimini-7/98
IEEE 802.15.4/ZigBee Radios

Low-Rate WPAN

Data rates of 20, 40, 250 Kbps

Support for large mesh networking or star clusters

Support for low latency devices

CSMA-CA channel access

Very low power consumption

Frequency of operation in ISM bands
Focus is primarily on low power sensor networks
Tradeoffs
802.11n
3G
Rate
802.11g/a
Power
802.11b
UWB
Bluetooth
ZigBee
Range
Scarce Wireless Spectrum
$$$
and Expensive
Spectrum Regulation

Spectrum a scarce public resource, hence allocated

Spectral allocation in US controlled by FCC
(commercial) or OSM (defense)

FCC auctions spectral blocks for set applications.

Some spectrum set aside for universal use

Worldwide spectrum controlled by ITU-R

Regulation is a necessary evil.
Innovations in regulation being considered worldwide,
including underlays, overlays, and cognitive radios
Spectral Reuse
Due to its scarcity, spectrum is reused
In licensed bands
and unlicensed bands
BS
Cellular, Wimax
Wifi, BT, UWB,…
Reuse introduces interference
Need Better Coexistence
Many devices use the same radio band

Technical Solutions:
 Interference Cancellation
 Smart/Cognitive Radios
Standards

Interacting systems require standardization

Companies want their systems adopted as standard
 Alternatively try for de-facto standards

Standards determined by TIA/CTIA in US
 IEEE standards often adopted
 Process fraught with inefficiencies and conflicts

Worldwide standards determined by ITU-T
 In Europe, ETSI is equivalent of IEEE
Emerging Systems

4th generation cellular (LTE)
 OFDMA
is the PHY layer
 Other new features
Ad hoc/mesh wireless networks
 Cognitive radios
 Sensor networks
 Distributed control networks
 Biomedical networks

Ad-Hoc/Mesh Networks
Outdoor Mesh
ce
Indoor Mesh
Design Issues

Ad-hoc networks provide a flexible network
infrastructure for many emerging applications.

The capacity of such networks is generally
unknown.

Transmission, access, and routing strategies for
ad-hoc networks are generally ad-hoc.

Crosslayer design critical and very challenging.

Energy constraints impose interesting design
tradeoffs for communication and networking.
Cognitive Radios

Cognitive radios can support new wireless users in
existing crowded spectrum


Utilize advanced communication and signal
processing techniques


Without degrading performance of existing users
Coupled with novel spectrum allocation policies
Technology could


Revolutionize the way spectrum is allocated worldwide
Provide sufficient bandwidth to support higher quality
and higher data rate products and services
Cognitive Radio Paradigms

Underlay
 Cognitive
radios constrained to cause minimal
interference to noncognitive radios

Interweave
 Cognitive
radios find and exploit spectral holes
to avoid interfering with noncognitive radios

Overlay
 Cognitive
radios overhear and enhance
noncognitive radio transmissions
Knowledge
and
Complexity
Wireless Sensor Networks
Data Collection and Distributed Control
•
•
•
•
•
•




Smart homes/buildings
Smart structures
Search and rescue
Homeland security
Event detection
Battlefield surveillance
Energy (transmit and processing) is the driving constraint
Data flows to centralized location (joint compression)
Low per-node rates but tens to thousands of nodes
Intelligence is in the network rather than in the devices
Energy-Constrained Nodes

Each node can only send a finite number of bits.




Short-range networks must consider transmit,
circuit, and processing energy.



Transmit energy minimized by maximizing bit time
Circuit energy consumption increases with bit time
Introduces a delay versus energy tradeoff for each bit
Sophisticated techniques not necessarily energy-efficient.
Sleep modes save energy but complicate networking.
Changes everything about the network design:



Bit allocation must be optimized across all protocols.
Delay vs. throughput vs. node/network lifetime tradeoffs.
Optimization of node cooperation.
Distributed Control over Wireless
Automated Vehicles
- Cars
- Airplanes/UAVs
- Insect flyers
Interdisciplinary design approach
•
•
•
•
Control requires fast, accurate, and reliable feedback.
Wireless networks introduce delay and loss
Need reliable networks and robust controllers
Mostly open problems : Many design challenges
Wireless and Health,
Biomedicine and Neuroscience
Body-Area
Networks
Doctor-on-a-chip
-Cell phone info repository
-Monitoring, remote
intervention and services
The brain as a wireless network
- EKG signal reception/modeling
- Signal encoding and decoding
- Nerve network (re)configuration
Cloud
Main Points

The wireless vision encompasses many exciting systems
and applications

Technical challenges transcend across all layers of the
system design.

Cross-layer design emerging as a key theme in wireless.

Existing and emerging systems provide excellent quality
for certain applications but poor interoperability.

Standards and spectral allocation heavily impact the
evolution of wireless technology
Course Outline











Overview of Wireless Communications
Path Loss, Shadowing, and Fading Models
Capacity of Wireless Channels
Digital Modulation and its Performance
Adaptive Modulation
Diversity
MIMO Systems
Multicarrier Modulation
Spread Spectrum
Multiuser Communications & Wireless Networks
Future Wireless Systems
Propagation Characteristics

Path Loss (includes average shadowing)

Shadowing (due to obstructions)

Multipath Fading
Slow
Pt
Pr
Pr/Pt
v
Fast
Very slow
d=vt
d=vt
Path Loss Modeling

Maxwell’s equations
 Complex

Free space path loss model
 Too

simple
Ray tracing models
 Requires

site-specific information
Empirical Models
 Don’t

and impractical
always generalize to other environments
Simplified power falloff models
 Main
characteristics: good for high-level analysis
Free Space (LOS) Model
d=vt

Path loss for unobstructed LOS path

Power falls off :
to 1/d2
 Proportional to l2 (inversely proportional to f2)
 Proportional
Ray Tracing Approximation
Represent wavefronts as simple particles
 Geometry determines received signal from
each signal component
 Typically includes reflected rays, can also
include scattered and defracted rays.
 Requires site parameters

 Geometry
 Dielectric
properties
Two Path Model



Path loss for one LOS path and 1 ground (or
reflected) bounce
Ground bounce approximately cancels LOS
path above critical distance
Power falls off



Proportional to d2 (small d)
Proportional to d4 (d>dc)
Independent of l (f)
General Ray Tracing

Models all signal components
 Reflections
 Scattering
 Diffraction

Requires detailed geometry and dielectric
properties of site
 Similar

to Maxwell, but easier math.
Computer packages often used
Simplified Path Loss Model
Used when path loss dominated by
reflections.
 Most important parameter is the path loss
exponent , determined empirically.


 d0 
Pr  Pt K   ,
d 
2 8
Empirical Models

Okumura model



Hata model


Analytical approximation to Okumura model
Cost 231 Model:


Empirically based (site/freq specific)
Awkward (uses graphs)
Extends Hata model to higher frequency (2 GHz)
Walfish/Bertoni:
 Cost 231 extension to include diffraction from rooftops
Commonly used in cellular system simulations
Main Points

Path loss models simplify Maxwell’s equations

Models vary in complexity and accuracy

Power falloff with distance is proportional to d2
in free space, d4 in two path model

Empirical models used in 2G simulations

Main characteristics of path loss captured in
simple model Pr=PtK[d0/d]
Shadowing
Xc



Models attenuation from obstructions
Random due to random # and type of obstructions
Typically follows a log-normal distribution




dB value of power is normally distributed
m=0 (mean captured in path loss), 4<s<12 (empirical)
LLN used to explain this model
Decorrelated over decorrelation distance Xc
Combined Path Loss
and Shadowing

Linear Model: y lognormal

Pr
 d0 
 K  y
Pt
d 

10logK
Pr/Pt
(dB)
Slow
Very slow
-10
dB Model
 d 
Pr
(dB)  10 log 10 K  10 log 10   y dB ,
Pt
 d0 
2
y dB ~ N (0, sy )
log d
Outage Probability
and Cell Coverage Area

Path loss: circular cells

Path loss+shadowing: amoeba cells
 Tradeoff

between coverage and interference
Outage probability
 Probability

Pr
received power below given minimum
Cell coverage area
 % of cell locations at desired power
 Increases as shadowing variance decreases
 Large % indicates interference to other cells
Model Parameters from
Empirical Measurements
K (dB)


Fit model to data
Pr(dB)
Path loss (K,), d0 known:
sy2
10
log(d0)
 “Best fit” line through dB data
 K obtained from measurements at d0.
 Exponent is MMSE estimate based on
 Captures mean due to shadowing

log(d)
data
Shadowing variance
 Variance
of data relative to path loss model
(straight line) with MMSE estimate for 
Main Points

Random attenuation due to shadowing modeled as
log-normal (empirical parameters)

Shadowing decorrelates over decorrelation distance

Combined path loss and shadowing leads to outage
and amoeba-like cell shapes

Cellular coverage area dictates the percentage of
locations within a cell that are not in outage

Path loss and shadowing parameters are obtained
from empirical measurements
Statistical Multipath Model

Random # of multipath components, each with




Random amplitude
Random phase
Random Doppler shift
Random delay

Random components change with time

Leads to time-varying channel impulse response
Time Varying Impulse Response

Response of channel at t to impulse at t-t:
N
c (t , t )    n (t )e
n 1
 j n ( t )
 (t  t n (t ))
 t is time when impulse response is observed
 t-t is time when impulse put into the channel
t
is how long ago impulse was put into the
channel for the current observation


path delay for MP component currently observed
Received Signal
r (t )  s(t ) * c(t , t )  u(t )e
j 2f c t
* c(t , t )
Received Signal Characteristics
N (t )

jn ( t ) j 2f c t
r (t )  {s(t ) * c(t , t )}    n (t )e
e
[u (t  t n (t ))]
 n 0


Received signal consists of many multipath
components

Amplitudes change slowly

Phases change rapidly
 Constructive
and destructive addition of signal
components
 Amplitude fading of received signal (both
wideband and narrowband signals)
Narrowband Model

Assume delay spread maxm,n|tn(t)-tm(t)|<<1/B

Then u(t)u(t-t).

Received signal given by
N (t )


j 2f c t
j n ( t )  
r (t )  u (t )e
   n (t )e

 n 0



No signal distortion (spreading in time)

Multipath affects complex scale factor in brackets.

Characterize scale factor by setting u(t)=(t)
In-Phase and Quadrature
under CLT Approximation

In phase and quadrature signal components:
N (t )
rI (t )   n (t )e jn (t ) cos( 2f ct ),
n 0
N (t )
rQ (t )   n (t )e
n 0
jn ( t )
sin( 2f ct )

For N(t) large, rI(t) and rQ(t) jointly Gaussian (sum
of large # of random vars).

Received signal characterized by its mean,
autocorrelation, and cross correlation.

If n(t) uniform, the in-phase/quad components are
mean zero, indep., and stationary.
Auto and Cross Correlation
Assume n~U[0,2]
 Recall that qn is the multipath arrival angle
 Autocorrelation of inphase/quad signal is

ArI (t )  ArQ (t )  PEq n [cos 2f Dnt ],

Cross Correlation of inphase/quad signal is
Ar ,r (t )  PEq [sin 2f D t ]   Ar ,r (t )
I

f Dn  v cos q n / l
Q
n
n
I
Q
Autocorrelation of received signal is
Ar (t )  ArI (t ) cos(2f ct )  ArI ,rQ (t ) sin( 2f ct )
Uniform AOAs

Under uniform scattering, in phase and quad comps
have no cross correlation and autocorrelation is
ArI (t )  ArQ (t )  PJ 0 (2f Dt )
Decorrelates over roughly half a wavelength

The PSD of received signal is
S r ( f )  .25[ S rI ( f  f c )  S rI ( f  f c )]
Sr(f)
S rI ( f )  F [ PJ 0 (2f Dt )]
Used to generate simulation values
fc-fD
fc
fc+fD
Signal Envelope Distribution

CLT approx. leads to Rayleigh distribution (power
is exponential)

When LOS component present, Ricean
distribution is used

Measurements support Nakagami distribution in
some environments


Similar to Ricean, but models “worse than Rayleigh”
Lends itself better to closed form BER expressions
Level crossing rate and
Average Fade Duration

LCR: rate at which the signal crosses a fade value

AFD: How long a signal stays below target R/SNR

Derived from LCR
R

t1
t2
t3
For Rayleigh fading
r2
t R  (e 1) /( rf D 2 )


Depends on ratio of target to average level (r)
Inversely proportional to Doppler frequency
Markov Models for Fading

Model for fading dynamics


Simplifies performance analysis
A2
A1
A0
Divides range of fading power into
discrete regions Rj={: Aj   < Aj+1}
 Aj

R2
s and # of regions are functions of model
Transition probabilities (Lj is LCR at Aj):
p j , j 1 
L j 1T
j
, p j , j 1 
L jT
j
, p j , j  1  p j , j 1  p j , j 1
R1
R0
Main Points

Narrowband model has in-phase and quad. comps
that are zero-mean stationary Gaussian processes


Uniform scattering makes autocorrelation of inphase
and quad follow Bessel function



Auto and cross correlation depends on AOAs of multipath
Signal components decorrelate over half wavelength
Cross correlation is zero (in-phase/quadrature indep.)
The power spectral density of the received signal has
a bowl shape centered at carrier frequency

PSD useful in simulating fading channels
Main Points

Narrowband fading distribution depends on
environment

Rayleigh, Ricean, and Nakagami all common

Average fade duration determines how long a user is
in continuous outage (e.g. for coding design)

Markov model approximates fading dynamics.
Wideband Channels
Individual multipath components resolvable
 True when time difference between
components exceeds signal bandwidth

t  1 / Bu
t  1 / Bu
t 1
t
Narrowband
t 2
Wideband
t
Scattering Function

Fourier transform of c(t,t) relative to t
Typically characterize its statistics, since
c(t,t) is different in different environments
 Underlying process WSS and Gaussian, so
only characterize mean (0) and correlation
 Autocorrelation is Ac(t1,t2,t)=Ac(t,t)
 Statistical scattering function:

s(t,r)=Ft[Ac(t,t)]
r
t
Multipath Intensity Profile
Ac(t)

Defined as Ac(t,t=0)= Ac(t)
TM
Determines average (TM ) and rms (st) delay spread
 Approximate max delay of significant m.p.


Coherence bandwidth Bc=1/TM


Maximum frequency over which Ac(f)=F[Ac(t)]>0
Ac(f)=0 implies signals separated in frequency by f
will be uncorrelated after passing through channel
Bu  Bc
Tm  1 / Bu
t 1
t 2
t
Ac(f)
Bc
f
t
Doppler Power Spectrum
Sc(r)

Sc(r)=F[Ac(t0,t)]= F[Ac(t)]

Doppler spread Bd is maximum doppler for
which Sc (r)=>0.

Coherence time Tc=1/Bd


Bd
Maximum time over which Ac(t)>0
Ac(t)=0 implies signals separated in time by t will
be uncorrelated after passing through channel
r
Summary of Wideband
Channel Models

Scattering Function: s(t,r)=Ft[Ac(t,t)]


t
Multipath Intensity Profile


Determines average (TM ) and rms (st) delay spread
Coherence bandwidth Bc=1/TM
Bu  Bc
Tm  1 / Bu
t 1

r
Used to characterize c(t,t) statistically
t 2
t
Ac(f)
0 Bc
Doppler Power Spectrum: Sc(r)= F[Ac(t)]
 Power
of multipath at given Doppler
f
Main Points

Scattering function characterizes rms delay and
Doppler spread. Key parameters for system design.

Delay spread defines maximum delay of significant
multipath components. Inverse is coherence
bandwidth of channel

Doppler spread defines maximum nonzero doppler,
its inverse is coherence time
Course Outline











Overview of Wireless Communications
Path Loss, Shadowing, and Fading Models
Capacity of Wireless Channels
Digital Modulation and its Performance
Adaptive Modulation
Diversity
MIMO Systems
Multicarrier Modulation
Spread Spectrum
Multiuser Communications & Wireless Networks
Future Wireless Systems
Shannon Capacity

Defined as the maximum MI of channel

Maximum error-free data rate a channel
can support.

Theoretical limit (not achievable)

Channel characteristic
 Not
dependent on design techniques
Capacity of Flat-Fading Channels

Capacity defines theoretical rate limit
 Maximum
error free rate a channel can support

Depends on what is known about channel

Fading Statistics Known


Hard to find capacity
Fading Known at Receiver Only

C   B log 2 1    p( )d  B log 2 (1   )
0
Fading Known at
Transmitter and Receiver

For fixed transmit power, same as with
only receiver knowledge of fading

Transmit power S() can also be adapted

Leads to optimization problem

 S ( ) 
C
B log 2 1 
 p( )d

S ( ) : E[ S ( )]  S 0
S 

max
Optimal Adaptive Scheme

S ( )  

S  0
1
0

Waterfilling
Power Adaptation
1

1

 0
else
Capacity

 
R
  log 2   p( )d .
B 0
0 
0
1

0

Channel Inversion

Fading inverted to maintain constant SNR

Simplifies design (fixed rate)

Greatly reduces capacity
 Capacity

is zero in Rayleigh fading
Truncated inversion
 Invert channel above cutoff fade depth
 Constant SNR (fixed rate) above cutoff
 Cutoff greatly increases capacity

Close to optimal
Capacity in Flat-Fading
Rayleigh
Log-Normal
Frequency Selective
Fading Channels
For TI channels, capacity achieved by
water-filling in frequency
 Capacity of time-varying channel unknown
 Approximate by dividing into subbands

 Each
subband has width Bc (like MCM).
 Independent fading in each subband
 Capacity is the sum of subband capacities
1/|H(f)|2
P
Bc
f
Main Points

Fundamental capacity of flat-fading channels
depends on what is known at TX and RX.
Capacity when only RX knows fading same as when TX
and RX know fading but power fixed.
 Capacity with TX/RX knowledge: variable-rate variablepower transmission (water filling) optimal
 Almost same capacity as with RX knowledge only
 Channel inversion practical, but should truncate


Capacity of wideband channel obtained by
breaking up channel into subbands
 Similar
to multicarrier modulation
Course Outline











Overview of Wireless Communications
Path Loss, Shadowing, and Fading Models
Capacity of Wireless Channels
Digital Modulation and its Performance
Adaptive Modulation
Diversity
MIMO Systems
Multicarrier Modulation
Spread Spectrum
Multiuser Communications & Wireless Networks
Future Wireless Systems
Passband Modulation Tradeoffs

Want high rates, high spectral efficiency, high power
Our focus
efficiency, robust to channel, cheap.

Amplitude/Phase Modulation (MPSK,MQAM)




Information encoded in amplitude/phase
More spectrally efficient than frequency modulation
Issues: differential encoding, pulse shaping, bit mapping.
Frequency Modulation (FSK)




Information encoded in frequency
Continuous phase (CPFSK) special case of FM
Bandwidth determined by Carson’s rule (pulse shaping)
More robust to channel and amplifier nonlinearities
Amplitude/Phase Modulation
Signal over ith symbol period:
s(t )  si1 g (t ) cos(2f ct  0 )  si 2 g (t ) sin( 2f ct  0 )

si 2
s i1




Pulse shape g(t) typically Nyquist
Signal constellation defined by (si1,si2) pairs
Can be differentially encoded
M values for (si1,si2)log2 M bits per symbol
Linear Modulation in AWGN

ML detection induces decision regions
 Example:
8PSK
dmin

Ps depends on
 # of nearest neighbors M
 Minimum distance dmin (depends
 Approximate expression

Ps   M Q  M  s

on s)
Alternate Q Function
Representation
Traditional Q function representation

1  x2 / 2
Q ( z )  p( x  z )  
e
dx, x ~ N (0,1)
z
2

 Infinite integrand
 Argument in integral

limits
New representation (Craig’93)
1  / 2  z 2 /(sin2  )
Q( z)  
e
d
 0
 Leads to closed form solution for Ps in PSK
 Very useful in fading and diversity analysis
Linear Modulation in Fading

In fading s and therefore Ps random

Performance metrics:
 Outage probability:
 Average Ps , Ps:
p(Ps>Ptarget)=p(<target)

Ps   Ps ( ) p( )d
0
 Combined
outage and average Ps
Outage Probability
Ps
Outage
Ts
Ps(target)
t or d

Probability that Ps is above target

Equivalently, probability s below target

Used when Tc>>Ts
Average Ps
Ts
Ps   Ps ( s ) p( s )d s
Ps
Ps
t or d

Expected value of random variable Ps

Used when Tc~Ts

Error probability much higher than in AWGN alone

Alternate Q function approach: Q ( z ) 

1
 /2

0
Simplifies calculations (Get a Laplace Xfm)
e
 z 2 /(sin2  )
d
Combined outage and average Ps
Ps(s)
Ps(s)
Outage
Pstarget
Ps(s)



Used in combined shadowing and flat-fading
Ps varies slowly, locally determined by flat fading
Declare outage when Ps above target value
Doppler Effects

High doppler causes channel phase to
decorrelate between symbols

Leads to an irreducible error floor for
differential modulation
 Increasing

power does not reduce error
Error floor depends on BdTs
ISI Effects


Delay spread exceeding a symbol time
causes ISI (self interference).
2
0
Ts
3
4
5
Tm
ISI leads to irreducible error floor


1
Increasing signal power increases ISI power
ISI requires that Ts>>Tm (Rs<<Bc)
Main Points

In fading Ps is a random variable, characterized by
average value, outage, or combined outage/average



Outage probability based on target SNR in AWGN.
Fading greatly increases average Ps .
Alternate Q function approach simplifies Ps calculation,
especially its average value in fading (Laplace Xfm).

Doppler spread only impacts differential modulation
causing an irreducible error floor at low data rates

Delay spread causes irreducible error floor or
imposes rate limits

Need to combat flat and frequency-selective fading

Main focus of the remainder of the short course
Main Points


Linear modulation more spectrally efficient but less
robust than nonlinear modulation
Ps approximation in AWGN: Ps   M Q



M s

Alternate Q function representation simplifies calculations
In fading Ps is a random variable, characterized by
average value, outage, or combined outage/average



Fading greatly increases average Ps .
Doppler spread only impacts differential modulation
causing an irreducible error floor at low data rates
Delay spread causes irreducible error floor or
imposes rate limits
Main Takeaway

Need to combat flat and frequencyselective fading

Focus of the next section of the short
course
Lecture 1 Summary
Future Wireless Networks
Ubiquitous Communication Among People and Devices
Wireless Internet access
Nth generation Cellular
Wireless Ad Hoc Networks
Sensor Networks
Wireless Entertainment
Smart Homes/Spaces
Automated Highways
All this and more…
•Hard Delay/Energy Constraints
•Hard Rate Requirements
Signal Propagation

Path Loss

Shadowing

Multipath
d
Pr/Pt
d=vt
Statistical Multipath Model

Random # of multipath components, each with
varying amplitude, phase, doppler, and delay

Narrowband channel



Signal amplitude varies randomly (complex Gaussian).
2nd order statistics (Bessel function), Fade duration, etc.
Wideband channel

Characterized by channel scattering function (Bc,Bd)
Capacity of Flat Fading Channels

Three cases
 Fading statistics known
 Fade value known at receiver
 Fade value known at receiver

and transmitter
Optimal Adaptation
 Vary rate and power relative to channel
 Optimal power adaptation is water-filling
 Exceeds AWGN channel capacity at low SNRs
 Suboptimal techniques come close to capacity
Modulation Considerations

Want high rates, high spectral efficiency, high power
efficiency, robust to channel, cheap.

Linear Modulation (MPAM,MPSK,MQAM)





Information encoded in amplitude/phase
More spectrally efficient than nonlinear
Easier to adapt.
Issues: differential encoding, pulse shaping, bit mapping.
Nonlinear modulation (FSK)


Information encoded in frequency
More robust to channel and amplifier nonlinearities
Linear Modulation in AWGN

ML detection induces decision regions
 Example:
8PSK
dmin

Ps depends on
 # of nearest neighbors
 Minimum distance dmin (depends
 Approximate expression

Ps   M Q  M  s

on s)
Linear Modulation in Fading
In fading s and therefore Ps random
 Metrics: outage, average Ps , combined
outage and average.

Ts
Outage
Ps
Ps(target)
Ps
Ts
Ps   Ps ( s ) p( s )d s
ISI Effects


Delay spread exceeding a symbol time causes
ISI (self interference).
2
0
Ts
3
4
5
Tm
ISI leads to irreducible error floor


1
Increasing signal power increases ISI power
Without compensation, requires Ts>>Tm
 Severe constraint on data rate (Rs<<Bc)