1

Introduction to

Mobile Communications

Lecture 6 (Cellular II)

Dong In Kim

School of Info/Comm Engineering

Sungkyunkwan University

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Information Theory

• So far we have only looked at specific communication

schemes.

• Information theory provides a fundamental limit to (coded)

performance.

• It succinctly 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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Historical Perspective

Wireless communication

has been around since

1900’s.

Ingenious but somewhat

adhoc design techniques

Claude ShannonGugliemo Marconi

•Information theory says every

channel has a capacity.

• Many recent advances based

on understanding wireless

channel capacity.

New points of views arise.

1901 1948

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Multipath Fading: Modern View

Classical view: fading channels are unreliable

Modern view: multipath fading can be exploited to

increase spectral efficiency.

16dB

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Capacity of AWGN Channel

Capacity of AWGN channel

If average transmit power constraint is watts and

noise psd is watts/Hz,

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Power and Bandwidth Limited Regimes

Bandwidth limited regime capacity logarithmic

in power, approximately linear in bandwidth.

Power limited regime capacity linear in power,

insensitive to bandwidth.

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Capacity of Wireless Channels

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Example 1: Impact of Frequency Reuse

• Different degree of frequency reuse allows a tradeoff

between SINR and degrees of freedom per user.

• Users in narrowband systems have high link SINR but

small fraction of system bandwidth.

• Users in wideband systems have low link SINR but full

system bandwidth.

• Capacity depends on both SINR and d.o.f. and can

provide a guideline for optimal reuse.

• Optimal reuse depends on how the out-of-cell

interference fraction f() depends on the reuse factor .

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Numerical Examples

Linear cellular system Hexagonal system

2 2

1log 1 log 1 (high SNR),

o

SNR PR W W SNR

f SNR f N Wd

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Example 2: CDMA Uplink Capacity

• Single cell with K users.

• Capacity per user

• Cell capacity (interference-limited)

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Example 2 (continued)

• If out-of-cell interference is a fraction f of in-cell interference:

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Uplink and Downlink Capacity

• CDMA and OFDM are specific multiple access schemes.

• But information theory tells us what is the capacity of the

uplink and downlink channels and the optimal multiple

access schemes.

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Uplink AWGN Capacity

successive cancellation:

cancel 1 before 2

cancel 2 before 1conventional

decoding

1 21 2 log 1

o

P PR R

N

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Conventional CDMA vs Capacity

20 dB power difference

between 2 users

Successive cancellation allows the weak user to have a good

rate without lowering the power of the strong user (e.g., NOMA).

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Orthogonal vs Capacity

20 dB power difference

between 2 users

Orthogonal achieves maximum throughput but may not be fair.

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22

log 1

(1- ) log 1 (1 )

o

o

PR W

N

PR W

N

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Downlink Capacity

20 dB gain

difference

between 2 users

superposition coding

orthogonal

2 2

1 2 1 2

1 2

, / 0 , / 20 (asymmetric)

user 1 (far) and user 2 (near)

o oP P P P h N dB P h N dB

P P

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Frequency-selective Channel

's are time-invariant.

OFDM converts it into a parallel channel:

where is the waterfilling allocation:

with chosen to meet the power constraint.

Can be achieved with separate coding for each sub-carrier.

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Waterfilling in Frequency Domain

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Slow Fading Channel

h random.

There is no definite capacity.

Outage probability:

outage capacity:

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Outage for Rayleigh Channel

Pdf of log(1+|h|2SNR) Outage cap. as fraction of AWGN cap.

at high SNR Note: more severe at low SNR

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Outage for Rayleigh Channel

1

1

1 1

2

2 1

2

1log 1 1 log (high SNR)

1

1 log 1 (low SNR)

Note: i) ( ) Pr , ii) 1 for Rayleigh ( 1)

With receive diversity,

i) ( ) Pr , ii)

awgn

awgn

C F SNR CF

F SNR e F C

F x h x F

L

F x x

h

/

2

1/1

2 1( ) (high SNR),

!

iii) ! log (low SNR)

LR

out L

LL

P RL SNR

C L SNR e

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Receive Diversity

Diversity plus power gain.

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Transmit Diversity

Transmit beamforming:

Alamouti (2 Tx):

Diversity but no power gain.

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Repetition vs Alamouti

Repetition:

Alamouti:

Loss in degrees of freedom under repetition.

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Time Diversity (1)

Coding done over L coherence blocks, each of many

symbols.

This is a parallel channel. If transmitter knows the

channel, can do waterfilling.

Can achieve:

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Time Diversity (II)

Without channel knowledge,

Rate allocation cannot be done.

Coding across sub-channels becomes now necessary.

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Fast Fading Channel

Channel with L-fold time diversity:

As

Fast fading channel has a definite capacity:

Tolerable delay >> coherence time.

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Capacity with Full CSI

Suppose now transmitter has full channel knowledge.

What is the capacity of the channel?

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Fading Channel with Full CSI

This is a parallel channel, with a sub-channel for each

fading state.

is the waterfilling power allocation as a function of

the fading state, and is chosen to satisfy the

average power constraint.

where

Can be achieved with separate coding for each fading

state.

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Transmit More When Channel is Good

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Performance

At high SNR, waterfilling does not provide any gain.

But transmitter knowledge allows rate adaptation and

simplifies coding.

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Performance: Low SNR

Waterfilling povides a significant power gain at low SNR.

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Waterfilling vs Channel Inversion

• Waterfilling and rate adaptation maximize long-term

throughput but incur significant delay.

• Channel inversion (“perfect” power control in CDMA

jargon) is power-inefficient but maintains the same data

rate at all channel states.

• Channel inversion achieves a delay-limited capacity.

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Example of Rate Adaptation

1xEV-DO Downlink

Multiple access is TDMA via scheduling. (More on this

later.)

Each user is rate-controlled rather than power-controlled.

(But no waterfilling.)

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Rate Control

Mobile measures the channel based on the pilot and predicts the

SINR to request a rate.

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SINR Prediction Uncertainty

3 km/hr 30 km/hr 120 km/hr

accurate prediction

of instantaneous

SINR.

conservative

prediction of

SINR.

accurate prediction

of average SINR for

a fast fading channel

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Incremental ARQ

• A conservative prediction leads to a lower requested rate.

• At such rates, data is repeated over multiple slots.

• If channel is better than predicted, the number of

repeated slots may be an overkill.

• This inefficiency can be reduced by an incremental ARQ

protocol.

• The receiver can stop transmission when it has enough

information to decode.

• Incremental ARQ also reduces the power control

accuracy requirement in the reverse link in Rev A.

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Summary

• A slow fading channel is a source of unreliability: very

poor outage capacity. Diversity is needed.

• A fast fading channel with only receiver CSI has a

capacity close to that of the AWGN channel. Delay is

long compared to channel coherence time.

• 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 more

powerful in multiuser situations, as we will see.