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)
Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 2 / 29
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)
Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 3 / 29
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)
Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 4 / 29
... 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
Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 5 / 29
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)
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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)
.
Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 7 / 29
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
Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 8 / 29
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
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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
Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 10 / 29
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)
Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 11 / 29
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
Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 11 / 29
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) !
Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 12 / 29
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).
Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 13 / 29
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
Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 14 / 29
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)
Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 15 / 29
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
Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 16 / 29
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
Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 17 / 29
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
Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 18 / 29
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
)
Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 19 / 29
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 )
Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 20 / 29
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
Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 21 / 29
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
Total spectral efficiency (bit/s/Hz)
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)
Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 22 / 29
Numerical Results
0 0.2 0.4 0.6 0.8 1-15
-10
-5
0
5
10
Total spectral efficiency (bit/s/Hz)
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
Total spectral efficiency (bit/s/Hz)
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
Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 23 / 29
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
Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 24 / 29
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
Total spectral efficiency (bit/s/Hz)
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
Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 25 / 29
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]
Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 26 / 29
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
Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 27 / 29
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.
Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 28 / 29
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.
Philippe Ciblat Resource allocation for Hybrid ARQ based Mobile Ad Hoc networks 29 / 29
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