Combined Cross-Layer Design and
HARQ for TDD Multiuser systems
with Outdated CSIT
Rui Wang & Vincent K. N. Lau
Dept. of ECE
The Hong Kong University of Science & Technology
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Outline
Model of Multiuser System with HARQ-IR
Cross-Layer Problem Formulation
Cross-Layer Scheduler Design
Discussions & Simulation Results
Conclusions
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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.
Encoder:
–
Encoder:
Information
Tx:
1st Tx
Rx:
MRC Combining
2nd Tx
3rd Tx
4th Tx
Achieve larger receiving SNR
Incremental Redundancy (IR): the information is first encoded into a long mother code, and
then punctured into multiple blocks where the blocks will be sent in subsequent retransmission.
Information
Tx:
1st Tx
Rx:
Subpacket
•
Coded Packet
Subpacket
Subpacket
2nd Tx
Subpacket
Subpacket
3rd Tx
Subpacket
Subpacket
4th Tx
Subpacket
We consider the scheme of incremental redundancy in this paper.
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.
User 1
st
Transmission
event scheduled
to user Z
Time
1 Transmission
nd
2 Transmission
st
Transmission
event scheduled
to user Y
1 Transmission
st
2 Transmission
st
1 Transmission
rd
Transmission
event scheduled
to user X
3 Transmission
nd
– We consider slow fading channel where
the channel gain is quasi-static within a
transmission event (the duration one
packet transmission).
User 3
2 Transmission
Let X be the transmitted symbol, the
receiver symbol of the user k is given by
the following equation.
User 2
st
•
BS
1 Transmission
– 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 packet
until the ACK feedback is received or the
maximum number of transmission is
reached.
...
Transmission
event scheduled
to user X
Yk  H k X  Z k
Received symbol
Channel gain
Noise
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Model of Outdated CSIT --- Practical Issues
• In order to perform scheduling in the downlink
transmission, the BS should have the knowledge of
channel state information (CSIT).
• However, the CSIT estimated at the BS is usually outdated.
Downlink
Pilot
Uplink
Data
Pilot
Downlink
Data
Delay
Estimate the
downlink channel
Pilot
Data
Use the channel
estimation to do the
scheduling
• A general model of CSIT error is given below:
Hˆ k  H k   k
Estimated CSIT
CSIT Error
Actual CSI
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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}.  the effect
of channel noise can be ignored with strong coding.
• Yet, the second factor (channel outage) is systematic and will be the
major 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

| H A |2

CL   log 2 1  p j
 z2
j 1

L
g  r  I(r  CL )
Date rate
I[] is 1 when the event is true and 0 otherwise.




Summation due to IR retransmission
• The average system throughput of a transmission event is
G  EHˆ [ EH ( g ) | Hˆ ]  EHˆ [r  Pr(r  CL | Hˆ )]
• Since each transmission event may contain multiple channel use, we
use the normalized average throughput (named as average goodput) as
the system optimization objective.
~
G
G
EH , Hˆ [T ]
Average number of transmissions per transmission event
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Outline
Model of Multiuser System with HARQ-IR
Cross-Layer Problem Formulation
Cross-Layer Scheduler Design
Discussions & Simulation Results
Conclusions
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Diagram of Scheduler
Selected user
CSIT
A
{Hˆ 1 , Hˆ 2 ,..., Hˆ K }
{ p1, p2 ,..., p L }
Cross-Layer Scheduler
r
Data rate
Power for each transmission
We shall formulate this box as an optimization problem
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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 packet
transmission according to the CSIT
A   Hˆ
 
• Power allocation policy P: determine the transmit power for active
users according to the CSIT.
 
{ p1 ,..., pL }  P Hˆ
• Rate allocation policy R: determine the transmit data rate for active
users according to the CSIT.
r  R Hˆ
 
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Problem Formulation
• The optimal user selection policy A*, the optimal
power allocation policy P* as well as the optimal
rate allocation policy R* are given by:
~
(A* , P* , R * )  arg max G (A, P, R )
( A,P,R )
– 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.
Average power per transmission event
Maximum number of transmission
L
E Hˆ [ p j q j 1 ]  P0
j 1
Packet error rate after j-1 transmissions
Power of j-th transmission
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Outline
Model of Multiuser System with HARQ-IR
Cross-Layer Problem Formulation
Cross-Layer Scheduler Design
Discussions & Simulation Results
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 each
transmission is given by:
– User selection:
A  arg max | Hˆ k |2
– Power allocation (power for j-th transmission):
Power constraint
pj 
P0
jq j 1
j  1,2,..., L
Outage probability of the j-1 th transmission
Constant related to L
– Rate allocation:
r  log[ 1  a
1/ L
L
(
2 | Hˆ A |2 /  e2
e
P0 e
Target outage probability
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
) ]
Estimation error
HKUST
Outline
Model of Multiuser System with HARQ-IR
Cross-Layer Problem Formulation
Cross-Layer Scheduler Design
Discussions & Simulation Results
Conclusions
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Discussions
• The average system goodput is given by
 1  P 2
~
G  log 2 aLL  0 e

 




K
  (1   2 )
1
e

(log 2 e)
2


n 1 n
e
O(lnL)
O(lnK)
– Goodput vs. Number of users K: The average system
goodput 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).
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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 TDD
multiuser systems with outdated CSIT in slow
fading channel.
• We obtain the closed-form expressions for the
average 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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Thank You !
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