2: The Wireless Channel
Fundamentals of
Wireless Communication
David Tse
University of California, Berkeley
Fundamentals of Wireless Communication, Tse&Viswanath
University of California, Berkeley
Pramod Viswanath
University of Illinois, Urbana-Champaign
2: The Wireless Channel
1. Introduction
Fundamentals of Wireless Communication, Tse&Viswanath
2: The Wireless Channel
Course Objective
• Past decade has seen a surge of research activities in the field of wireless communication.
• Emerging from this research thrust are new points of view on how to communicate effectively over wireless channels.
• The goal of this course is to study in a unified way the
Fundamentals of Wireless Communication, Tse&Viswanath 2
• The goal of this course is to study in a unified way the fundamentals as well as the new research developments.
• The concepts are illustrated using examples from several modern wireless systems (GSM, IS-95, CDMA 2000 1x EV-DO, Flarion's Flash OFDM, ArrayComm systems.)
2: The Wireless Channel
System Implementation
Capacity limits and
Fundamentals of Wireless Communication, Tse&Viswanath 3
Capacity limits and communication techniques
Channel modelling
2: The Wireless Channel
Course Outline
Part I: Basics
2. The Wireless Channel
3. Diversity
Fundamentals of Wireless Communication, Tse&Viswanath 4
3. Diversity
4. Multiple Access and Interference Management
5. Capacity of Wireless Channels
2: The Wireless Channel
Course Outline (2)
Part II: Modern Wireless Communication
6. Opportunistic Communication and Multiuser Diversity
7. MIMO I: Spatial Multiplexing and Channel Modeling
Fundamentals of Wireless Communication, Tse&Viswanath 5
7. MIMO I: Spatial Multiplexing and Channel Modeling
8. MIMO II: Capacity and Multiplexing Architectures
9. MIMO III: Diversity-Multiplexing Tradeoff
2: The Wireless Channel
Assumed background:
• Basic signals and systems, linear algebra and
proabability.
Fundamentals of Wireless Communication, Tse&Viswanath 6
• Basic digital communications.
2: The Wireless Channel
These slides only gives an overview of the
ideas.
Full details can be found in:
http://www.eecs.berkeley.edu/~dtse/book.html
Fundamentals of Wireless Communication, Tse&Viswanath 7
2: The Wireless Channel
2. The Wireless Channel
Fundamentals of Wireless Communication, Tse&Viswanath
2: The Wireless Channel
Wireless Mulipath Channel
Fundamentals of Wireless Communication, Tse&Viswanath 9
Channel varies at two spatial scales:
large scale fading
small scale fading
2: The Wireless Channel
Large-scale fading
• In free space, received power attenuates like 1/r2.
• With reflections and obstructions, can attenuate even more rapidly with distance. Detailed modelling complicated.
Fundamentals of Wireless Communication, Tse&Viswanath 10
• Time constants associated with variations are very long as the mobile moves, many seconds or minutes.
• More important for cell site planning, less for communication system design.
2: The Wireless Channel
Small-scale multipath fading
• Wireless communication typically happens at very high carrier frequency. (eg. fc = 900 MHz or 1.9 GHz for cellular)
• Multipath fading due to constructive and destructiveinterference of the transmitted waves.
• Channel varies when mobile moves a distance of the
Fundamentals of Wireless Communication, Tse&Viswanath 11
• Channel varies when mobile moves a distance of the order of the carrier wavelength. This is about 0.3 m for 900 Mhz cellular.
• For vehicular speeds, this translates to channel variation of the order of 100 Hz.
• Primary driver behind wireless communication system design.
2: The Wireless Channel
Game plan
• We wish to understand how physical parameters such as
– carrier frequency
– mobile speed
– bandwidth
– delay spread
– angular spread
Fundamentals of Wireless Communication, Tse&Viswanath 12
– angular spread
impact how a wireless channel behaves from the
communication system point of view.
• We start with deterministic physical model and progress
towards statistical models, which are more useful for
design and performance evaluation.
2: The Wireless Channel
Physical Models
• Wireless channels can be modeled as linear time-
varying systems:
where ai(t) and τi(t) are the gain and delay of path i.
Fundamentals of Wireless Communication, Tse&Viswanath 13
where ai(t) and τi(t) are the gain and delay of path i.
• The time-varying impulse response is:
• Consider first the special case when the channel is time-
invariant:
2: The Wireless Channel
Passband to Baseband Conversion
• Communication takes place at
• Processing takes place at baseband
Fundamentals of Wireless Communication, Tse&Viswanath 14
2: The Wireless Channel
Complex Baseband Equivalent Channel
• The frequency response of the system is shifted
from the passband to the baseband.
Fundamentals of Wireless Communication, Tse&Viswanath 15
• Each path is associated with a delay and a
complex gain.
2: The Wireless Channel
Modulation and Sampling
Fundamentals of Wireless Communication, Tse&Viswanath 16
2: The Wireless Channel
Multipath Resolution
Sampled baseband-equivalent channel model:
where hl is the l th complex channel tap.
Fundamentals of Wireless Communication, Tse&Viswanath 17
and the sum is over all paths that fall in the delay bin
System resolves the multipaths up to delays of 1/W .
2: The Wireless Channel
Sampling Interpretation
• hl is the l th sample of the
low-pass version of the
channel response hb(¢).
• Contribution of the i th
1
W
Main contribution l = 0
Main contribution l = 0
i = 0
i = 1
Fundamentals of Wireless Communication, Tse&Viswanath 18
• Contribution of the i th
path is the projection of
aib δ(τ-τi) onto sinc(Wτ-l). Main contribution l = 1
Main contribution l = 2
Main contribution l = 2
i = 2
i = 3
i = 4
0 1 2l
2: The Wireless Channel
Flat and Frequency-Selective Fading
• Fading occurs when there is destructive interference of
the multipaths that contribute to a tap.
Delay spread
Fundamentals of Wireless Communication, Tse&Viswanath 19
Delay spread
Coherence bandwidth
single tap, flat fading
multiple taps, frequency selective
2: The Wireless Channel
Fundamentals of Wireless Communication, Tse&Viswanath 20
Effective channel depends on both physical environment and bandwidth!
2: The Wireless Channel
Time Variations
Fundamentals of Wireless Communication, Tse&Viswanath 21
Doppler shift of the i th path
Doppler spread
Coherence time
2: The Wireless Channel
Two-path Examplev= 60 km/hr, fc = 900 MHz:
direct path has Doppler shift of -50 Hz
reflected path has shift of +50 Hz
Doppler spread = 100 Hz
Fundamentals of Wireless Communication, Tse&Viswanath 22
2: The Wireless Channel
Doppler Spread
Doppler spread is proportional to:
• the carrier frequency fc;
Fundamentals of Wireless Communication, Tse&Viswanath 23
• the carrier frequency fc;
• the angular spread of arriving paths.
where θi is the angle the direction of motion
makes with the i th path.
2: The Wireless Channel
Fundamentals of Wireless Communication, Tse&Viswanath 24
2: The Wireless Channel
Types of Channels
Fundamentals of Wireless Communication, Tse&Viswanath 25
2: The Wireless Channel
Typical Channels are Underspread
• Coherence time Tc depends on carrier frequency
and vehicular speed, of the order of milliseconds
or more.
• Delay spread Td depends on distance to
scatterers, of the order of nanoseconds (indoor)
Fundamentals of Wireless Communication, Tse&Viswanath 26
scatterers, of the order of nanoseconds (indoor)
to microseconds (outdoor).
• Channel can be considered as time-invariant
over a long time scale.
2: The Wireless Channel
Statistical Models• Design and performance analysis based on statistical
ensemble of channels rather than specific physical
channel.
• Rayleigh flat fading model: many small scattered paths
Fundamentals of Wireless Communication, Tse&Viswanath 27
Complex circular symmetric Gaussian .
Squared magnitude is exponentially distributed.
• Rician model: 1 line-of-sight plus scattered paths
2: The Wireless Channel
Correlation over Time• Specified by autocorrelation
function and power spectral density of fading process.
• Example: Clarke’s (or Jake’s) model.
Fundamentals of Wireless Communication, Tse&Viswanath 28
2: The Wireless Channel
Additive Gaussian Noise
• Complete baseband-equivalent channel model:
Fundamentals of Wireless Communication, Tse&Viswanath 29
• Special case: flat fading:
• Will use this throughout the course.
2: The Wireless Channel
Summary
• We have understood how time and frequency
selectivity of wireless channels depend on key
physical parameters.
• We have come up with statistical channel
Fundamentals of Wireless Communication, Tse&Viswanath 30
• We have come up with statistical channel
models that are useful for analysis and design.