(Rayleigh,Fast Fading)Cu Day1

7/31/2019 (Rayleigh,Fast Fading)Cu Day1

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Fundamentals of

Wireless Communication

David Tse

Dept of EECS

U.C. Berkeley


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Course Objective

Past decade has seen a surge of research activities inthe field of wireless communication.

Emerging from this research thrust are new points ofview on how to communicate effectively over wireless

channels. The goal of this course is to study in a unified way the

fundamentals as well as the new researchdevelopments.

The concepts are illustrated using examples fromseveral modern wireless systems (GSM, IS-95, CDMA2000 1x EV-DO, Flarion's Flash OFDM, ArrayCommsystems.)


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Course Outline

Day 1: Fundamentals

1. The Wireless Channel

2. Diversity

3. Capacity of Wireless Channels


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Course Outline (2)

Day 2: MIMO

4. Spatial Multiplexing and Channel Modelling

5. Capacity and Multiplexing Architectures

6. Diversity-Multiplexing Tradeoff


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Course Outline (3)

Day 3: Wireless Networks

7. Multiple Access and Interference Management: A

comparison of 3 systems.

8. Opportunistic Communication and Multiuser Diversity

9. MIMO in Networks


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1. The Wireless Channel


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Wireless Mulipath Channel

Channel varies at two spatial scales:

large scale fading

small scale fading


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Large-scale fading

In free space, received power attenuates like 1/r2.

With reflections and obstructions, can attenuate evenmore rapidly with distance. Detailed modelling

complicated.

Time constants associated with variations are very longas the mobile moves, many seconds or minutes.

More important for cell site planning, less forcommunication system design.


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Game plan

We wish to understand how physical parameters such as

carrier frequency, mobile speed, bandwidth, delay

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.


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Physical Models

Wireless channels can be modeled as linear time-

varying systems:

where ai(t) and i(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:


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Passband to Baseband Conversion

Communication takes place at [f_c-W/2, f_c+ W/2].

Processing takes place at baseband [-W/2,W/2].


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Baseband Equivalent Channel

The frequency response of the system is shifted from the

passband to the baseband.

Each path is associated with a delay and a complex

gain.


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Multipath Resolution

Sampled baseband-equivalent channel model:

where hl is the l th complex channel tap.

and the sum is over all paths that fall in the delay bin

System resolves the multipaths up to delays of 1/W .


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Flat and Frequency-Selective Fading

Fading occurs when there is destructive interference of

the multipaths that contribute to a tap.


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Time Variations

fci(t) = Doppler shift of the i th path


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Two-path Example

v= 60 km/hr, f_c = 900 MHz:

direct path has Doppler shift of + 50 Hz

reflected path has shift of - 50 Hz

Doppler spread = 100 Hz


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Types of Channels


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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

Complex circular symmetric Gaussian .

Rician model: 1 line-of-sight plus scattered paths


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Additive Gaussian Noise

Complete baseband-equivalent channel model:

Will use this throughout the course.


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Main story

Communication over a flat fading channel has poor

performance due to significant probability that channel is

in deep fading.

Reliability is increased by provide more signal paths that

fade independently.

Diversity can be provided across time, frequency and

space.

Name of the game is how to expoited the added diversity

in an efficient manner.


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Baseline: AWGN Channel

y = x+ w

BPSK modulation x = a

Error probability decays exponentially with SNR.


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Rayleigh Flat Fading Channel


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Rayleigh vs AWGN


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Typical Error Event


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BPSK, QPSK and 4-PAM

BPSK uses only the I-phase.The Q-phase is wasted. QPSK delivers 2 bits per complex symbol.

To deliver the same 2 bits, 4-PAM requires 4 dB more transmit power.

QPSK exploits the available degrees of freedom in the channel better.


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Time Diversity

Time diversity can be obtained by interleaving and coding over

symbols across different coherent time periods.


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Example:GSM

Amount of diversity limited by delay constraint and how fast

channel varies.

In GSM, delay constraint is 40ms (voice).

To get full diversity of 8, needs v > 30 km/hr at fc = 900Mhz.


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Repetition Coding


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Geometry


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Deep Fades Become Rarer


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Performance


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Beyond Repetition Coding

Repetition coding gets full diversity, but sends only one

symbol every L symbol times: does not exploit fully the

degrees of freedom in the channel.

How to do better?


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Example: Rotation code (L=2)


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Rotation vs Repetition Coding


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Product Distance


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Antenna Diversity

Receive Transmit Both


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Transmit Diversity

h1

h2


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Space-time Codes

Transmitting the same symbol simultaneously at the

antennas doesnt work.

Using the antennas one at a time and sending the same

symbol over the different antennas is like repetition

coding.

More generally, can use any time-diversity code by

turning on one antenna at a time.


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Alamouti Scheme


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Space-time Code Design


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Cooperative Diversity

Different users can form a distributed antenna array to

help each other in increasing diversity.

Distributed versions of space-time codes may be

applicable.

Interesting characteristics:

Users have to exchange information and this consumes

bandwidth.

Operation typically in half-duplex mode

Broadcast nature of the wireless medium can be exploited.


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Frequency Diversity


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Approaches

Time-domain equalization (eg. GSM)

Direct-sequence spread spectrum (eg. IS-95 CDMA)

Orthogonal frequency-division multiplexing OFDM (eg.

802.11a )


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ISI Equalization

Suppose a sequence of uncoded symbols are

transmitted.

Maximum likelihood sequence detection is performed

using the Viterbi algorithm.

Can full diversity be achieved?


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Reduction to Transmit Diversity


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MLSD Achieves Full Diversity


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OFDM


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OFDM


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Channel Uncertainty

In fast varying channels, tap gain measurement errors

may have an impact on diversity combining performance

The impact is particularly significant in channel with

many taps each containing a small fraction of the total

received energy. (eg. Ultra-wideband channels)


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3. Capacity of Wireless Channels


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Information Theory

So far we have only looked at uncoded or simple coding

schemes.

Information theory provides a fundamental

characterization of coded performance.

It succintly identifies the impact of channel resources on

performance as well as suggests new and cool ways to

communicate over the wireless channel.

It provides the basis for the modern development of

wireless communication.


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Capacity of AWGN Channel


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Power and Bandwidth Limited Regimes


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Frequency selective AWGN Channel


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Frequency-selective AWGN Channel


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Waterfilling in Frequency Domain


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Slow Fading Channel


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Outage for Rayleigh Channel


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Receive Diversity


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Transmit Diversity


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Repetition vs Alamouti


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Time Diversity


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Fast Fading Channel


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Waterfilling Capacity


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Transmit More when Channel is Good


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Performance


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Performance: Low SNR


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Summary

A slow fading channel is a source of unreliability: verypoor outage capacity. Diversity is needed.

A fast fading channel with only receiver CSI has a

capacity close to that of the AWGN channel: only a small

penalty results from fading. A fast fading channel with full CSI can have a capacity

greater than that of the AWGN channel: fading now

provides more opportunities for performance boost.

The idea of opportunistic communication is even morepowerful in multiuser situations, as we will see.

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