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HKUST- 1 -

Combined Cross-Layer Design and

HARQ for TDD Multiuser systems

with Outdated CSIT

Rui Wang & Vincent K. N. Lau

Dept. of ECEThe Hong Kong University of Science & Technology

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HKUST- 2 -

Outline

Model of Multiuser System with HARQ-IR

Cross-Layer Problem Formulation

Cross-Layer Scheduler Design

Discussions & Simulation Results

Conclusions

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HKUST- 3 -

HARQ• Generally speaking, HARQ (Hybird Automatic Retransmission reQuest) is a

retransmission technique to improve the packet receiving.• There are two schemes of HARQ retransmission:

– Chase Combining (CC): the retransmit packets are exactly the same, while the receiver combines the multiple copies of the packet to obtain a higher post-combining SNR.

– Incremental Redundancy (IR): the information is first encoded into a long mother code, andthen punctured into multiple blocks where the blocks will be sent in subsequent retransmission.

• We consider the scheme of incremental redundancy in this paper.

Information Coded Packet

2nd

Tx 3rd

Tx1st

Tx 4th

Tx

MRC Combining

Encoder:

Tx:

Rx: Achieve larger receiving SNR

Information Subpacket

2nd Tx 3rd Tx1st Tx 4th Tx

Encoder:

Tx:

Rx:

Subpacket SubpacketSubpacket

Subpacket Subpacket SubpacketSubpacket

Protect the packet by

redundancy

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System Model• We consider downlink transmission of a

multiuser system with one BS and K mobile users. – At each packet transmission, BS should

select one mobile as target receiver. – HARQ-IR is supported, hence, if the target

receiver cannot decode the packet, a NAK will be feed back to the BS.

– The BS should retransmit the failed packetuntil the ACK feedback is received or themaximum number of transmission isreached.

• Let X be the transmitted symbol, thereceiver symbol of the user k is given bythe following equation. – We consider slow fading channel where the

channel gain is quasi-static within atransmission event (the duration one packettransmission).

BS

User 1

User 2

User 3

k k k Z X H Y +=

Received symbol Channel gain Noise

1 s t Tr an s mi s s i on


1r d

Tr an s mi s s i on

1n d Tr an s mi s s i on


1n d

Tr an s mi s s i on

...


Transmission

event scheduled

to user X

Transmission

event scheduled

to user Z

Transmission

event scheduled

to user X

Transmission

event scheduled

to user Y

Time


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HKUST- 5 -

Model of Outdated CSIT --- Practical Issues

• In order to perform scheduling in the downlink transmission, the BS should have the knowledge of channelstate information (CSIT).

• However, the CSIT estimated at the BS is usually outdated.

• A general model of CSIT error is given below:

k k k H H ∆+=ˆ

CSIT Error

Actual CSI

Estimated CSIT

Pilot Data Pilot Data

Downlink Uplink

Pilot Data

Downlink

Estimate the

downlink channel

Use the channel

estimation to do the

scheduling

Delay

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Packet Error Model --- Subsequent of Outdated CSIT

• In slow fading channels, there are two reasons of packet error – Finite block length of channel coding [channel noise effect]

– Transmitted data rate exceeding the instantaneous mutual information of the channel [channel outage]

• By applying strong channel coding (e.g. LDPC) with reasonable

block length (e.g. 2k byte), it can be shown that Shannon’s limit can be achieved to within 0.05dB for a target FER of 10^{-2}. theeffect of channel noise can be ignored with strong coding.

• Yet, the second factor (channel outage) is systematic and will be themajor contributor of packet error (esp when strong coding is used).Hence, we assume Packet Error Rate = Pr [r > mutual

information].• To account for penalty of packet errors, we shall consider system

goodput (b/s/Hz successfully delivered to the mobiles) as our optimization objective.

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Average System Goodput• The instantaneous throughput of a transmission event is

• The average system throughput of a transmission event is

• Since each transmission event may contain multiple channel use, we

use the normalized average throughput (named as average goodput) as

the system optimization objective.

)]ˆ|(Pr []ˆ|)([ ˆˆ H C r r E H g E E G L H H H ≤×==

][

~

ˆ,T E

GG

H H

=

Average number of transmissions per transmission event

)(I LC r r g ≤×= ∑=

+=

L

j z

A j L

H pC

1

1

1

1

||1log

σ

Date rate I[] is 1 when the event is true and 0 otherwise. Summation due to IR retransmission

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Outline





Conclusions

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Diagram of Scheduler

}ˆ,...,ˆ,ˆ{ 11 K H H H Cross-Layer Scheduler

r

p p p

A

L},...,{ 1,1

CSIT

Data rate

Power for each transmission

We shall formulate this box as an optimization problem

Selected user

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Policies --- Actions of Scheduler • The average system goodput is a function of the user selection

policy A, power allocation policy P and rate allocation policy R.

• User selection policy A: determine the active user for each packettransmission according to the CSIT

• Power allocation policy P: determine the transmit power for activeusers according to the CSIT.

• Rate allocation policy R: determine the transmit data rate for activeusers according to the CSIT.

( ) H AˆΑ=

( ) H p p LˆP},...,{

1=

( ) H r ˆR =

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Problem Formulation

• The optimal user selection policy A*, the optimal power allocation policy P* as well as the optimalrate allocation policy R* are given by:

– Subject to the following constraint:• PER constraint: the packet error probability after the

maximum number of transmissions should be ε.

• Average power constraint: the average transmit power cannot be large than P0.

)R P,A,(

~

maxarg)R ,P,A( )R P,A,(

***

G=

1

1

1ˆ ][E P q p L

j

j j H ≤∑

=

−

Maximum number of transmission

Power of j-th transmission

Packet error rate after j-1 transmissions

Average power per transmission event

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Outline





Conclusions

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Cross-layer Scheduler Design• The asymptotical optimally scheduler design for sufficiently small

target outage probability and sufficiently large SNR on eachtransmission is given by:

– User selection:

– Power allocation (power for j-th transmission):

– Rate allocation:

1|ˆ|maxarg k H A =

L jq j

P p

j

j ,...,1,1 1

1==

−δ

Outage probability of the j-1 th transmission

Power constraint

Constant related to L

])(1log[

11/|ˆ|1

1/1 δ

σ

δ

σ ε

e A H

e L

L

e P ar +=

Target outage probability Estimation error

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Outline





Conclusions

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Discussions

• The average system goodput is given by

– Goodput vs. Number of users K : The average systemgoodput scales in the order of ln(K), for small number

of users K. – Goodput vs. Maximum number of transmissions L: The

average system goodput scales in the order of ln(L).

O(lnL) O(lnK)

∑=

−+

=

K

ne

ee L L

n

e P

aG1

11

11

1

1

1

1)(log

)1(log

~

σ

σ δ

δ

σ ε

δ

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Simulations

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Conclusions

• In this paper, we study the combined design of cross-layer scheduling and HARQ for TDDmultiuser systems with outdated CSIT in slowfading channel.

• We obtain the closed-form expressions for theaverage system goodput. – average system goodput scales in the order of O(ln L) at

small K and target PER ε.

– the average system goodput also scales in the order of O(ln K) for small K.

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