Resource allocation for Hybrid ARQ [5pt] based wireless ......Resource allocation for Hybrid ARQ based wireless networks Philippe Ciblat Joint work with N. Ksairi, A. Le Duc, C. Le

Resource allocation for Hybrid ARQ

based wireless networks

Philippe Ciblat

Joint work with N. Ksairi, A. Le Duc, C. Le Martret, S. Marcille

Télécom ParisTechFrance

Introduction to HARQ Resource allocation

Part 1 : Introduction to HARQ

Philippe Ciblat Resource allocation for Hybrid ARQ based wireless networks 2 / 28


Standard communication scheme.

010 001100MODULATION

00

0111

10

info bits

CHANNELCODING coded bits

CHANNEL

.

No feedback about no-error or error at RX sideAdaptive Modulation and Coding if− channel model− theoretical performance available for channel model− channel model parameters known at TX side

DrawbacksLack of robustness to channel mis-knowledgeLimited number of Modulation and Coding Scheme (MCS) inpracticeMore important, weak adaptability to the real propagation states(noise, etc)



MCS designExample : QAM size (according to target Symbol Error Rate)

.

BPSK4QAM

16QAM64QAM

4QA

M

16Q

AM

64Q

AM

BPS

K

10−1

10−2

10−3

10−4

10−5

0 5 10 15 20

SNR (dB)

Sym

nolE

rror

Rat

e

TargetSER

AREA

FORBIDDEN

.

AMC done on average performance, not on instantaneous oneIdea : try/error principle− Send one (symbol) packet− if OK (ACK),↗− if KO (NACK),↘ send it again

Need for one-bit feedback way (providing information on theinstantaneous channel)



From ARQ (Automatic ReQuest) ...

Let S = [s0, · · · , sN−1] be a packet composed by N uncoded symbols.

S1

S1

S2

NACK

ACK

TX RX

T NO

YES

.

Management for T :Stop-and-WaitParallel Stop-and-WaitSelective Repeat

Assumption : perfect feedback (neither error, nor delay T = 0)



... Towards Hybrid ARQ (HARQ) : Type-I HARQ

RemarkRetransmission does not contradict forward error coding (FEC)

Type-I HARQ : packet S is composed by coded symbols sn

• first packet is more protected• there is less retransmission• transmission delay is reduced

• Efficiency is upper-bounded by the code rate

DrawbacksEach received packet is treated independentlyMis-decoded packet is thrown in the trash



Type-II HARQ

Memory at RX side is considered⇒ Type-II HARQ.

NACK

ACK

TX RX

S1(1)

S1(2)

S2(1)

NO

YES

.

Main examples :Chase Combining (CC)Incremental Redundancy (IR)



Examples : CC-HARQ and IR-HARQ

CC

Y1 = S1 + N1Y2 = S1 + N2

then detection on

Y = (Y1 + Y2)/2

SNR-Gain equal to 3dB.

NACK

TX RX

=

+

ACK

S2

S1

S1

YES.

IR

Y1 = S1(1) + N1Y2 = S1(2) + N2

then detection on

Y = [Y1,Y2]

Coding gain.

NACK

TX RX

=

ACK

S1(1)

S1(2)

S2(1)

YES.



Performance metrics

Packet Error Rate (PER) :

PER = Prob(information packet is not decoded)

Efficiency (Throughput/Goodput/etc) :

η =information bits received without error

transmitted bits(Mean) delay :

d = # transmitted packets when information packet is received

Jitter :σd = delay standard deviation

Quality of Service (QoS)

Data : PER and efficiencyVoice on IP : delayVidéo Streaming : efficiency and jitter



Closed-form expressions for metrics

PER = 1−L∑

k=1

p(k)

η ∝∑L

k=1 p(k)

L(1−∑Lk=1 p(k)) +

∑Lk=1 kp(k)

d =

∑Lk=1 kp(k)∑Lk=1 p(k)

σd =

√√√√∑Lk=1 k2p(k)∑L

k=1 p(k)− d2

with [Duc12]p(k) probability to receive information packet in exactly ktransmissionsL maximum number of transmissions per information packet



Example : Type-I HARQ

Let π0 be the probability the information packet is mis-decoded(in one transmission). Then

p(k) = (1− π0)πk−10

Let an information packet composed by N BPSK uncodedsymbols. Then

π0 = 1−(

1−Q(√

2SNR))N

Results

PER = πL0

η = 1− π0

d = L + 11−π0

− L1−πL

0

σd = too long

0 2 4 6 8 10 12 14 16 18 200

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

SNR (dB) − (with N=100 and L=3)

PER

Efficiency

Delay

Jitter


Introduction to HARQ Resource allocation Trade-off Waterfilling Statistical CSIT Outdated CSIT

Part 2 : HARQ based resource allocation

2.1 Trade-off between HARQ and physical layer2.2 Waterfilling-like algorithm2.3 Statistical CSIT based resource allocation2.4 Outdated CSIT based resource allocation



2.1 - Trade-off between HARQ and physical layer

If PHY layer is designed in advance based on averaged channelperformance

Amount of retransmission is quite weak : only when channelrealization is badbut resource is wasted : when channel realization is good

What is the best trade-off between retransmission and physical layer ?

If HARQ is employedwhat is the PHY layer performance leading to the maximumrate/efficiencywhere the PHY layer performance is described through p(k)



Example : Type-I HARQ in Rayleigh channel

Each packet is encoded with coding rate R

π0 = Probh(log2(1+|h|2SNR) < R)⇔ Rπ0 = log2

1 +SNR

1log

(1

1−π0

)

Best PHY layer is given by [Jin09]

π∗0 = arg maxπ0

Rπ0(1− π0)︸︷︷︸ηπ0 : efficiency

0 5 10 15 20 25 300

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

SNR (dB)

Best re

quired P

ER

π0*

Reliable PHY layer is not requiredat all (thanks to retransmission) !



2.2 - Waterfilling-like algorithm

σ2

σ2

|H(n)|2

σ2

|H(1)|2

|H(N)|2

...

...

RXTX

P (1)

P (n)

P (N)

− Data rate maximization− Power constraint :

N∑n=1

P(n) = Pmax

with maximum power Pmax.− Perfect CSIT

Problem : which data rate criterion to be used ?

(Shannon) sum-capacity : [P(1)∗, · · · ,P(N)∗] =

arg maxP(1),··· ,P(N)

∑Nn=1 log2

(1 + |H(n)|2 P(n)

σ2

)(HARQ) sum-efficiency : [P(1)∗, · · · ,P(N)∗] =

arg maxP(1),··· ,P(N)

∑Nn=1 m(n) · (1− Pe(n))

with 2m(n)-QAM and Pe(n) SER (packet=symbol, here).



Practical algorithmsConvex optimization problem (⇒ KKT conditions)

Capacity : “Waterfilling” [Sha48]

P(n)∗ =(ν − σ2

|H(n)|2)+

withν chosen s.t.

∑Nn=1 P(n)∗ = Pmax.

(•)+ = max(0, •).

Efficiency : [unpublished]

P(n)∗ =(

2σ2

γ(n)|H(n)|2 log(

m(n)γ(n)|H(n)|2µσ2

))+

withµ chosen s.t.

∑Nn=1 P(n)∗ = Pmax.

γ(n) modulation gain at channel #n



Numerical illustrations

N = 16, SNR = 0dB (left), SNR = 20dB (right)

2 4 6 8 10 12 14 1610

−2

10−1

100

101

subcarrier index

Power optimization

abs(H)

2 4 6 8 10 12 14 1610

−3

10−2

10−1

100

101

102

103

subcarrier index

Power optimization

abs(H)

RemarkThe best subcarriers do not have necessary the highest powers (athigh SNR)



2.3 - Statistical CSIT based resource allocation

Channel statistics known at the transmitter

− fast-varying Rayleigh fading channel− costly to report instantaneous channel realizations− cheap to report statistics due to its coherence time

HARQ to handle channel variation and mis-knowledge

Applications

Mobile Ad Hoc networks (MANET)Cellular networks with high mobility



Communication model

PHY layer− OFDMA : cancel ISI due to multipath spread− Multiple access : cancel multiuser interference within a cell

Statistical channel model (for the k -th link)− Let hk (m) be the m-th filter tap.

Independent but not identically distributed ∼ CN (0, ς2k,m)

− Let Hk (n) be the n-th Fourier componentnon-independent wrt n but identically distributed ∼ CN (0, ς2

k ) withς2

k =∑

m ς2k,m

⇒ Subcarriers are statistically equivalent⇒ Rayleigh fading channel

Consequence for the k -th link

Bandwidth proportion and identical energy per subcarrier



Resource allocation issue

Qk : Energy of link k in OFDM symbolγk : Bandwidth proportion assigned to link kEk : Energy of link k in entire bandwidth⇒ Qk = γk Ek

Modulation (order 2mk ) and coding scheme (rate Rk )

Goal [Mar12,Ksa14]

minK∑

k=1

Qk ⇔ min(γ,E)

K∑k=1

γk Ek

s.t. QoSk (γk ,Ek ) ≥ QoS(0)k , ∀k

K∑k=1

γk ≤ 1

γk ≥ 0, Ek ≥ 0, ∀k

for various Quality of Service (QoS) : eff., eff.+PER, ...



Type-II HARQ case

Efficiency

ηk (γk ,Ek ) = mk Rkγk1− qk,L(SNRk )

1 +∑L−1`=1 qk,`(SNRk )

withqk,` probability the first ` transmissions of a HARQ all in errorSNRk ∝ Ek

qk,` can be upper-bounded by πk,l with πk,` probability for notdecoding information packet based on the first ` transmissions.[Duc12]

Bit-Interleaved Coded Modulation (BICM)Random Subcarrier Assignment Scheme (SAS)

πk,`(SNRk ) ≈gk,`(mk ,Rk )

SNRdk,`(Rk )k

where dk,` represents a minimal Hamming distance and the diversity.Philippe Ciblat Resource allocation for Hybrid ARQ based wireless networks 19 / 28


Optimization problem

minγ,E

K∑k=1

γk Ek

s.t. γk1− πk,L(SNRk )

1 +∑L−1`=1 πk,`(SNRk )

≥ η(0)k

mk Rk,∀k

K∑k=1

γk ≤ 1

γk > 0,Ek > 0,∀k

ResultsIt is a geometric program [Ksa14]Transformation into a convex optimization problem by γk = exk

and Ek = eyk

KKT solved



Algorithm

λ← 0REPEATFORALL k ∈ {1,2, . . . ,K}

γk ← η(0)k

mk RkFk (λ)

Ek ← Gk (λ)

ENDFORIncrement λUNTIL

∑Kk=1 γk ≤ 1

{γ∗k = γk}k=1...K

{E∗k = Ek}k=1...K

where Fk and Gk are well defined in closed-form.



Numerical results

K = 10 links, Bandwidth W = 5 MHz , QPSKFeasability condition satisfies for sum rates up to 5 Mbps.

2800 3000 3200 3400 3600 3800 4000 420018

19

20

21

22

23

24

25

26

27

28

Target sum−rate (kbps)

Tra

nsm

it s

um

−pow

er

(dB

m)

CC−HARQ R1=1/2

Type−I HARQ R1=1/2

IR−HARQ R1=8/10

IR−HARQ R1=1/2



2.4 - Outdated CSIT based resource allocation

.

tHARQ round

One-bit feedback Section 2.4 : outdated instantaneous/multi-bits CSIT

Section 2.3 : long-term statistical CSIT .

At each retransmission, instantaneous CSIT (via multi-bitsfeedback)Problem : outdated CSIT

Goal [Taj13]

How allocating power between retransmission packets based onoutdated instantaneous CSIT under long-term power constraint



Mathematical tools

Generic expressions from Slide 9 can not be used since− long-term power constraints is not round per round,− and instantaneous CSIT can not be incorporated

An other tool has to be used : Markov Decision Process (MDP)

Go back to the original problemAfter the n-th transmission, if NACK is received, we have

New action An+1 to do : here choosing Pn+1

Available information : accumulated mutual information equal toIn =

∑n`=1 log2(1 + G`P`) if IR-HARQ

Kn ∈ {ACK and new round,1 attempt and NACK received,· · · ,L attempts and NACK received}

P(Kn+1, In+1|Kn, In, · · · ) = P(Kn+1, In+1|Kn, In)⇒We have a Markov Chain : Sn = (Kn, In)



Optimization problem

A policy π = how selecting Pn+1 given Sn

deterministic : π(•|Sn) = δ(• − f (Sn)) with function frandom : π(•|Sn) = p(•|Sn) with pdf p

Optimisation issue

π∗ = arg maxπ

ηπ, with ηπ = limN→∞

1N

N−1∑n=0

rewardπ(Sn,An)︸︷︷︸#information bits after ACK

s.t.

limN→∞

1N

N−1∑n=0

P(Sn,An) ≤ Pmax

SolutionUnder mild conditions, optimal random policy existsOptimal pdf leads to linear programming



Numerical results

Setup : IR-HARQ, L = 5, Rayleigh channel

−10 −8 −6 −4 −2 0 2 4 6 8 100

0.5

1

1.5

2

2.5

SNR (dB) [source: Tajan’s PhD]

Thro

ughput (in b

cpu)

constant power

optimal random policy based power



Open issues

Single-user

Correlated channels : a mixture of outdated and known channels

Multi-userSubcarrier allocation (number of states too huge)Performance on real MCS (not information-theoretic tools)



References

[Jin09] P. Wu and N. Jindal, “Coding Versus ARQ in Fading Channels : How reliable should the PHY

be ?,” IEEE Globecom Conference, Nov. 2009.

[Duc12] C. Le Martret, A. Le Duc, S. Marcille, and P. Ciblat, “Analytical Performance derivation of

Hybrid ARQ Schemes at IP layer,” IEEE Trans. on Communications, May 2012.

[Mar12] S. Marcille, , P. Ciblat, and C. Le Martret, “Resource Allocation for Type-I HARQ-based

wireless ad hoc networks,” IEEE Wireless Communications Letters, Dec. 2012.

[Ksa14] N. Ksairi, P. Ciblat, and C. Le Martret, “Near-Optimal Resource Allocation for Type-II

HARQ-based OFDMA Ad Hoc Networks under rate and power constraints,” IEEE Trans. on

Wireless Communications, Oct. 2014.

[Taj13] R. Tajan, “HARQ retransmission scheme in cognitive radio,” PhD thesis, Univ.

Cergy-Pontoise, France, 2013.


Documents

Resource allocation for Hybrid ARQ [5pt] based wireless ......Resource allocation for Hybrid ARQ based wireless networks Philippe Ciblat Joint work with N. Ksairi, A. Le Duc, C. Le