Resource allocation for Hybrid ARQ [5pt] based Mobile … · Retransmission does not contradict forward error coding (FEC) Type-I HARQ : packet S is composed by coded symboles sn

Resource allocation for Hybrid ARQ

based Mobile Ad Hoc networks

Philippe Ciblat

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

Télécom ParisTech, France

Part 1 : Introduction to HARQ

Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 2 / 29

Standard communication scheme.

CODAGE010

bits d’info bits codés

001100DE

CANAL

MODULATION

00

0111

10

CANAL

.

No feedback about no-error or error at RX side

Adaptive Modulation and Coding if

− performance model available for considered channel

− model parameters known at TX side

Drawbacks

Lack of robustness to channel mis-knowledge

Limited number of Modulation and Coding Scheme (MCS) in

practice

More important, weak adaptability to the real propagation states

(noise, etc)


MCS design

Example : QAM size (according to target Symbol Error Rate).

BPSK4QAM

16QAM64QAM

SER

Cible

4Q

AM

16Q

AM

64Q

AM

BP

SK

10−1

10−2

10−3

10−4

10−5

0 5 10 15 20

SNR (dB)

Sym

nol

Err

or

Rat

eZONE

INTERDITE

.

AMC done on average performance, not on instantaneous one

Idea : try/error principle

− Send one (symbol) packet

− if OK (ACK), ր− if KO (NACK), ց 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

NON

OUI

T

.

Management for T :

Stop-and-Wait

Parallel Stop-and-Wait

Selective Repeat

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


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

Remark

Retransmission does not contradict forward error coding (FEC)

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

• first packet is more protected

• there is less retransmission

• transmission delay is reduced

• Efficiency is upper-bounded by the code rate


Type-II HARQ

Comments on Type-I HARQ

Each received packet is treated independently

Mis-decoded packet is thrown in the trash

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

NACK

ACK

TX RX

NON

OUI

S1(1)

S1(2)

S2(1)

.

Main examples :

Chase Combining (CC)

Incremental Redundancy (IR)


Examples : CC-HARQ and IR-HARQ

CC

Y1 = S1 + N1

Y2 = S1 + N2

then detection on

Y = (Y1 + Y2)/2

SNR-Gain equal to 3dB.

NACK

TX RX

=

+

OUIACK

S2

S1

S1

.

IR

Y1 = S1(1) + N1

Y2 = S1(2) + N2

then detection on

Y = [Y1,Y2]

Coding gain.

NACK

TX RX

=

OUIACK

S1(1)

S1(2)

S2(1)

.


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 efficiency

Voice on IP : delay

Vidéo 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)

∑Lk=1 p(k)

− d2

with

p(k) probability to receive information pacjket in exactly k

transmissions

L 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−π

L0

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) - (avec N=100 et L=3)

PEREfficaciteDelaiGigue


Part 2 : HARQ based resource allocation

2.1 Trade-off Retransmission-Physical Layer performance

2.2 Waterfilling-like algorithm

2.3 Application to Mobile Ad Hoc Networks (MANETs)


Trade-off Retransmission-Physical Layer performance

When only PHY layer is considered :

Power minimization with target SNR

Rate maximization with power constraint

#bits/pcu =

⌊

log2

(

1 +SNR

Γ

)⌋

with Γ SNR-gap wrt. Shannon capacity for one FEC and targetSER

Target PHY layer is required

When retransmission (HARQ) is considered :

Rate is replaced with Efficiency

Rate maximization leads to the optimal PHY layer performancethrough p(k)

PHY layer performance is not fixed in advance


Example : Type-I HARQ

Rayleigh channel :

Each packet is encoded with coding rate R

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

1 +

SNR1

log(

11−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)

Bes

t req

uire

d P

ER

ε*

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


Waterfilling-like algorithm : data rate optimization

σ2

σ2

|H(n)|2

σ2

|H(1)|2

|H(N)|2

...

...

RXTX

P (1)

P (n)

P (N)

− 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=symb, here).


Practical algorithms

Convex optimization problem (⇒ KKT conditions)

Capacity : “Waterfilling” [Sha48]

P(n)∗ =

(

ν − σ2

|H(n)|2)+

with

ν chosen s.t.∑N

n=1 P(n)∗ = Pmax.

(•)+ = max(0, •).

Efficiency : [unpublished]

P(n)∗ =

(2σ2

γ(n)|H(n)|2 log

(m(n)γ(n)|H(n)|2

µσ2

))+

with

µ chosen s.t.∑N

n=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)

Remark

The best subcarriers do not have necessary the highest powers (at

high SNR)


Mobile Ad Hoc Networks (MANETs)

Infrastructure-free

Highly flexible

Fast and short-lived communications deployment

Cluster HeadG1

Rx1

T x1

and Rx3

G3

G2

Rx2

Tx2

Tx3

Clusterization ⇒ Centralized coordination of the pairwisecommunications at CH

Feedback latency ⇒ Channel statistics known at CH


Communication scheme

OFDMA

− PHY layer : cancel ISI due to multipath spread

− Multiple access : cancel multiuser interference inside a cluster

HARQ

− manage fast channel variations

Statistical channel model : let us consider the k -th link

− Let hk (m) be the m-th filter tap. Ind. (but not i.d.) ∼ CN (0, ς2k,m)

− Hk (n) non-ind. wrt n but i.d. ∼ CN (0, ς2k ) with ς

2k =

∑m ς

2k,m

⇒ Rayleigh fading channel

⇒ Channel statistics (for Hk (n)) ind. of subcarrier n

⇒ Subcarriers are statistically equivalent

Consequence for the k -th link

Bandwidth proportion and identical energy per subcarrier


Resource allocation issue

Qk : Energy of link k in OFDM symbol

γk : Bandwidth proportion assigned to link k

Ek : Energy of link k in entire bandwidth ⇒ Qk = γk Ek

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

Goal [Mar13]

min

K∑

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, eff.+delay


Type-I HARQ case

PER expression

Pk (SNR) ∝ 1

SNRdmin

Valid for fast-fading channel model (BICM + FH)

Efficiency expression

ηk (γk ,Ek ) = γk mk Rk (1 − Pk (Gk Ek ))

Delay expression

dk (γk ,Ek ) =1

γk

(1

1 − Pk (Gk Ek )− L Pk (Gk Ek )

L

1 − Pk (Gk Ek )L

)


Optimization problem 1 : rate constrained

Write the problem in (γ,Q) instead of (γ,E)

min(γ,Q)

K∑

k=1

Qk s.t. ηk (γk ,Qk ) ≥ η(0)k , ∀k

K∑

k=1

γk ≤ 1

γk ≥ 0, Qk ≥ 0, ∀k

Results

Solution exists iff∑K

k=1 η(0)k /(mk Rk ) < 1

Problem is convex in (γ,Q)

Optimal solutions exhibited in closed-form (from KKT) givenmcsk = (mk ,Rk )


Numerical results

K = 4 links

Free-space path loss

Random distances in [50, 1000] m

L = 3

0 0.5 1 1.5 2 2.5 3 3.5 4 4.510

15

20

25

30

35

40

45

Total spectral efficiency (bit/s/Hz)

Tot

al tr

ansm

it po

wer

(dB

m)

Exhaustive MCS selection

Greedy MCS selection

Fixed same MCS for all linksMCSc1

MCSc2

MCSc3

MCSc4

MCSc5 MCSc6


Optimization problem 2 : rate + PER constrained

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110

-4

10-3

10-2

10-1

100


PE

R

Rate only (MAC,L=3)

PER 10-2 (MAC,L=3)

min(γ,Q)

K∑

k=1

Qk s.t. ηk (γk ,Qk) ≥ η(0)k , ∀k

Pk (Qk/γk ) ≤ P(0)k , ∀k

K∑

k=1

γk ≤ 1

γk ≥ 0, Qk ≥ 0, ∀k

Results

Pk is a quasi-convex function of (γk ,Qk )

KKT are optimal [Las10] but it is O(2K−1

). . .

. . .Suboptimal KKT resolution (SKA)

. . .Suboptimal alternate directional descent wrt. (γk ,Ek ) (SLA)


Numerical Results

0 0.2 0.4 0.6 0.8 1-15

-10

-5

0

5

10


Tot

al tr

ansm

it po

wer

(dB

m)

Optimal (10-2 )

SKA (10-2 )

SLA (10-2 )

Optimal (10-4 )

SKA (10-4 )

SLA (10-4 )

0 0.2 0.4 0.6 0.8 1-20

-15

-10

-5

0

5


Tot

al tr

ansm

it po

wer

(dB

m)

Rate constraint only

PER constraint (10-2 )

Remarks

SLA offers almost the same performance as KKT

Constraining the PER to 10−2 adds an energy cost of about 2 dB


Optimization problem 3 : rate + delay constrained

min(γ,E)

K∑

k=1

γk Ek s.t. ηk (γk ,Ek ) ≥ η(0)k , ∀k

dk (γk ,Ek ) ≤ d(0)k , ∀k

K∑

k=1

γk ≤ 1

γk ≥ 0, Ek ≥ 0, ∀k

Results

Solution exists iff∑K

k=1 max(

η(0)k /(mk Rk ), 1/d

(0)k

)

< 1

dk quasi-convex in Ek , convex in γk , no information in joint

directions

KKT-based algo. (KBA) : KKT solved, but no optimality theorem

Ping-Pong algo. (PPA) : optimization alternately in both directions


Numerical Results

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-12

-10

-8

-6

-4

-2

0

2

4


Tot

al tr

ansm

it po

wer

(dB

m)

KBA (dk(0) τ = 1 ms)

PPA (dk(0) τ = 1 ms)

KBA (dk(0) τ = 2.5 ms)

PPA (dk(0) τ = 2.5 ms)

Remark

KBA is optimal when the delay constraint is strictly satisfied


Type-II HARQ case

Much more complicated : see efficiency expression in Slide 9

Actually, the efficiency for any Type-II HARQ writes as follows

ηk (γk ,Ek ) = mk Rkγk

1 − qk ,L(Gk Ek )

1 +∑L−1

l=1 qk ,l(Gk Ek )

where qk ,l(SNRk ) is the probability that the first l transmissions of a

HARQ round are all received in error.Let πk ,l be the probability for not decoding the information packet

based on the first l transmissions.

πk ,l ≈gk ,l(mk ,Rk )

SNRdk,l (Rk )k

where dk ,l represents a minimal Hamming distance.

Remark

qk ,l can be upper-bounded by πk ,l [Duc10]


Optimization problem : rate

minγ,E

K∑

k=1

γk Ek s.t. γk1 − πk ,L(Gk Ek )

1 +∑L−1

l=1 πk ,l(Gk Ek )≥ η

(0)k

mk Rk

, ∀k

K∑

k=1

γk ≤ 1

γk > 0,Ek > 0, ∀k

Results

It is a geometric program [Ksa13]

Transformation into a convex optimization problem by γk = exk

and Ek = eyk

KKT solved


Numerical results

K = 10 links, Bandwidth W = 5 MHz , QPSK

Feasability 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 su

m-p

ower

(dB

m)

CC-HARQ R1=1/2

Type-I HARQ R1=1/2

IR-HARQ R1=8/10

IR-HARQ R1=1/2

Remarks

Nested-codes IR-HARQ outperforms RCP-codes IR-HARQ

4/5-rate IR-HARQ outperforms 1/2-rate Type-I and CC-HARQ

up to 3.3 Mbps. For higher target rates, its worse pre-HARQ

performance (πk ,1) plays a role.


Conclusion

Extension done to per-link power constraint

Applications : HSPA, Wimax, LTE

New metrics for resource allocation

References :

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

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

[Las10] J. B. Lasserre, “On representations of the feasible set in convex optimization,” Optim. Lett.,

2010.

[Duc10] A. Le Duc, ”Derivations and analysis of HARQ schemes in a cross-layer context,” Telecom

ParisTech PhD thesis, 2010.

[Mar13], S. Marcille, “Resource allocation for HARQ based mobile ad hoc network,” Telecom

ParisTech PhD thesis, 2013.

[Ksa13], N. Ksairi, P. Ciblat, and C. Le Martret, “Optimal Resource Allocation for Type-II

HARQ-based OFDMA Ad Hoc Networks,” submitted to IEEE GlobaSIP Conference, Dec. 2013.


Documents

Resource allocation for Hybrid ARQ [5pt] based Mobile … · Retransmission does not contradict forward error coding (FEC) Type-I HARQ : packet S is composed by coded symboles sn