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1
Introduction to
Mobile Communications
Lecture 6 (Cellular II)
Dong In Kim
School of Info/Comm Engineering
Sungkyunkwan University
2
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.
3
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
4
Multipath Fading: Modern View
Classical view: fading channels are unreliable
Modern view: multipath fading can be exploited to
increase spectral efficiency.
16dB
5
Capacity of AWGN Channel
Capacity of AWGN channel
If average transmit power constraint is watts and
noise psd is watts/Hz,
6
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.
7
Capacity of Wireless Channels
7
8
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 .
9
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
10
Example 2: CDMA Uplink Capacity
• Single cell with K users.
• Capacity per user
• Cell capacity (interference-limited)
11
Example 2 (continued)
• If out-of-cell interference is a fraction f of in-cell interference:
12
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.
13
Uplink AWGN Capacity
successive cancellation:
cancel 1 before 2
cancel 2 before 1conventional
decoding
1 21 2 log 1
o
P PR R
N
14
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).
15
Orthogonal vs Capacity
20 dB power difference
between 2 users
Orthogonal achieves maximum throughput but may not be fair.
11
22
log 1
(1- ) log 1 (1 )
o
o
PR W
N
PR W
N
16
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
17
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.
18
Waterfilling in Frequency Domain
19
Slow Fading Channel
h random.
There is no definite capacity.
Outage probability:
outage capacity:
20
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
21
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
22
Receive Diversity
Diversity plus power gain.
23
Transmit Diversity
Transmit beamforming:
Alamouti (2 Tx):
Diversity but no power gain.
24
Repetition vs Alamouti
Repetition:
Alamouti:
Loss in degrees of freedom under repetition.
25
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:
26
Time Diversity (II)
Without channel knowledge,
Rate allocation cannot be done.
Coding across sub-channels becomes now necessary.
27
Fast Fading Channel
Channel with L-fold time diversity:
As
Fast fading channel has a definite capacity:
Tolerable delay >> coherence time.
28
Capacity with Full CSI
Suppose now transmitter has full channel knowledge.
What is the capacity of the channel?
29
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.
30
Transmit More When Channel is Good
31
Performance
At high SNR, waterfilling does not provide any gain.
But transmitter knowledge allows rate adaptation and
simplifies coding.
32
Performance: Low SNR
Waterfilling povides a significant power gain at low SNR.
33
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.
34
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.)
35
Rate Control
Mobile measures the channel based on the pilot and predicts the
SINR to request a rate.
36
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
37
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.
38
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.