Turbo Receiver Design for MIMO Relay ARQ · PDF fileRelay ARQ System Information ... Zakaria El-Moutaouakkil (NSN, Morocco) October 3, 2012 ... Constraints posed by 3G & 4G Progress

Cooperative CommunicationsRelay ARQ System

Information-Theoretic AnalysisSimulation Results I

Signal-Level Sub-Packet CombiningSimulation Results II

Conclusion and PerspectivesRelated Works

Turbo Receiver Design for MIMO Relay ARQTransmissions

Halim Yanikomeroglu

Carleton University, Canada

A joint work with

Zakaria El-Moutaouakkil (Telecom Bretagne, France)

Tarik Ait-Idir (ExceliaCom Solutions, Morocco)

Samir Saoudi (Telecom Bretagne, France)

Global Communications Conference (GLOBCOM) 2012

5th December 2012

October 3, 2012Zakaria El-Moutaouakkil (NSN, Morocco) Receiver Design for Throughput-Efficient Relay ARQ Transmissions (1)





Outline

1 Cooperative Communications

2 Relay ARQ System

3 Information-Theoretic Analysis

4 Simulation Results I

5 Signal-Level Sub-Packet Combining

6 Simulation Results II

7 Conclusion and Perspectives

8 Related Works

Zakaria El-Moutaouakkil (NSN, Morocco) Receiver Design for Throughput-Efficient Relay ARQ Transmissions (2)





Progress of wireless communications5G Requirements Impacting on Physical LayerConstraints posed by 3G & 4G

Progress of wireless communications

1G : (1980s ∼ 1990s) wireless communications were based on analoguesystems.

2G : (1990s ∼ 2000) such systems as GSM and IS-95 were defined, thesesystems were essentially designed for voice and low data rate applications.

3G : (2000 ∼ 2010) it addresses costumer demands for high-speed datacommunications while the business focus has shifted from voice services tomultimedia communication applications over Internet.

4G : (Next fewmonths) moving from standardization to deployment phase withthe promise of providing faster and more affordable wireless Internetconnectivity.

5G (beyond-4G) !?







5G Requirements Impacting on Physical Layer

Very high bit rates (e.g. 100 Mb/s to 1 Gb/s) with high user densities.

Ubiquitous coverage.

Adaptive and self configuring to user needs and transmission environment.

Moderate cost: terminal cost, power and battery requirements commensuratewith required performance and data rate.













































Goal ⇒ enabling the 4A paradigm

“any rate, anytime, anywhere, affordable”












⇒ Cooperative Relaying Concept












⇒ Cooperative Relaying Concept







Constraint posed by 3G & 4G mobile terminals

Tx RxH

Mobile TerminalBase Station

infeasible !?

3 × 3 MIMO System

Tx

RxH

MT

BS

Relay

3 × 3 Virtual MIMO System

In cellular Networks, it is not feasibleto deploy several antennas at ourmobile terminals !!

Solution

Virtual MIMO has been proposed.

⇒ Cooperative Communication







Constraint posed by 3G & 4G mobile terminals

Tx RxH

Mobile TerminalBase Station

infeasible !?

3 × 3 MIMO System

Tx

RxH

MT

BS

Relay

3 × 3 Virtual MIMO System

In cellular Networks, it is not feasibleto deploy several antennas at ourmobile terminals !!

Solution

Virtual MIMO has been proposed.

⇒ Cooperative Communication






Brief Description of the ConceptRelay ARQ ProtocolRelay ARQ with Slot Mapping ReversalSub-Packets ARQ Transmission Model

Relay ARQ System Model

Source

Relay

Destination

ND

NR

NSARQ

1 2

3

Fig. 1: Relay ARQ System Model.







Brief Description of the Concept

Source

Relay

Destination

ND

NR

NSARQ

1 2

3

Fig. 1: Relay ARQ System Model

Channel 1, channel 2, and channel 3 are regarded at kth transmission as a frequencyselective fading MIMO channels having LSR, LRD , and LSD independent paths,respectively.

Each path is characterized by its quasi-static flat fading MIMO channel matrix

HAB(k)

l ∈ CNA×NB , for l ∈ {0, . . . , LAB − 1} where A ∈ {S,R} and B ∈ {R,D}.Relaying works under the framework of half-duplex amplify-and-forward protocol.

Packet re-transmissions follows the Chase-type ARQ mechanism.








Source

Relay

Destination

ND

NR

NSARQ

1 2

3




HAB(k)










Source

Relay

Destination

ND

NR

NSARQ

1 2

3




HAB(k)










Source

Relay

Destination

ND

NR

NSARQ

1 2

3




HAB(k)










Fig. 2: Source node transmitter scheme.

Splitting Rule

Upon the 1st transmission, node S generates according to an STBICM encoder the symbolpacket

x , [x0, . . . , xT−1] ∈ CNS×T. (1)

It is then splitted into two equally sized NS × T2 sub-packets z1 and z2 constructed as

{z1,t = x2t , 0 ≤ t ≤ T

2 − 1

z2,t = x2t+1 , 0 ≤ t ≤ T2 − 1

. (2)








Fig. 2: Source node transmitter scheme.

Splitting Rule

Upon the 1st transmission, node S generates according to an STBICM encoder the symbolpacket

x , [x0, . . . , xT−1] ∈ CNS×T. (1)

It is then splitted into two equally sized NS × T2 sub-packets z1 and z2 constructed as

{z1,t = x2t , 0 ≤ t ≤ T

2 − 1

z2,t = x2t+1 , 0 ≤ t ≤ T2 − 1

. (2)







Relay ARQ Protocol

Transmission Period Reception Period

(S)

(R)

(D)

1st TS 2nd TS

Trans. (k)

(S)

(R)

(D)

(b)(a)

yR

(k)y

R

(k)

Z1 Z2

yD

1,(k)y

D

2,(k)

1st TS 2nd TS

Trans. (k odd)

yR

(k)y

R

(k)

Z1 Z2

yD

1,(k)y

D

2,(k)

1st TS 2nd TS

Trans. (k even)

yR

(k)y

R

(k)

Z2 Z1

yD

1,(k)y

D

2,(k)

Fig. 3: Relay ARQ Protocol (a), Relay ARQ with Slot-Mapping Reversal (b) for k = 1, . . . , K.

Sub-Packets Slot Mapping is Fixed Fig. 3(a)

z1 followed by z2 during the first and the second TS, respectively, for all the ARQ rounds.







Relay ARQ with Slot Mapping Reversal

Transmission Period Reception Period

(S)

(R)

(D)

1st TS 2nd TS

Trans. (k)

(S)

(R)

(D)

(b)(a)

yR

(k)y

R

(k)

Z1 Z2

yD

1,(k)y

D

2,(k)

1st TS 2nd TS

Trans. (k odd)

yR

(k)y

R

(k)

Z1 Z2

yD

1,(k)y

D

2,(k)

1st TS 2nd TS

Trans. (k even)

yR

(k)y

R

(k)

Z2 Z1

yD

1,(k)y

D

2,(k)

Fig. 3: Relay ARQ Protocol (a), Relay ARQ with Slot-Mapping Reversal (b) for k = 1, . . . , K.

Sub-Packets Slot Mapping is Reversed Fig. 3(b)

Depending on the transmission index parity, sub-packets z1 and z2 are mapped onto eitherthe first or the second time slot.







Sub-Packets ARQ Transmission Model (I)

During the 1st TS of ARQ round k:

y(k)R,t =

√ESR

LSR−1∑l=0

HSR(k)

l z1,(t−l)modT

2+ n

(k)R,t (3)

y1,(k)D,t =

√ESD

LSD−1∑l=0

HSD(k)

1,l z1,(t−l)modT

2+ n

1,(k)D,t (4)

ESR and ESD are the energies capturing the effects of path loss and shadowing in channel1 and 3, respectively.

n(k)B,t ∼ N (0NB×1, N0INB ) for B ∈ {R,D} .

A cyclic prefix (CP) portion of length Lcp = max {LSD, LSR, LRD} is appended to z1

and z2 upon their transmission.

AF function at the Relay node:{y(k)R,t = γy

(k)R,t, t = 0, ..., T2 − 1

γ = 1/√NSESR +N0

(5)







Sub-Packets ARQ Transmission Model (II)

During the 2nd TS of ARQ round k:

y2,(k)D,t =

Lmax−1∑l=0

H(k)l z

(t−l)modT2

+ n2,(k)D,t (6)

where zt ,

[z1,t

z2,t

]∈ X 2NS ,

Lmax , max(LSD , LSRD ), and LSRD = LSR + LRD − 1,

(7)

H(k)l =

[γ√

ESRERDHSRD(k)

l

√ESDH

SD(k)

2,l

],

n2,(k)D,t = γ

√ERD

LRD−1∑l=0

HRD(k)

l n(k)

R,(t−l)modT2

+ n2,(k)D,t . (8)







Sub-Packets ARQ Transmission Model (III)

At the end of the second slot node D builds up (jointly) the augmented size signalvector

yequ(k)

D,t

{[y1,(k)D,t

y2,(k)D,t

]=

Lmax−1∑l=0

Hequ(k)

l z(t−l)modT

2+ n

equ(k)

D,t , (9)

in which the k-parity 2ND × 2NS equivalent MIMO channel matrix Hequ(k)

l has beencarefully introduced with the following form

Hequ(k)

l =

[A 0ND×NSB C

], k odd

Hequ(k)

l =

[0ND×NS A

C B

], k even

(10)

where,

A =√

ESDHSD(k)

1,l , (11)

B = γ√

ESRERDL−1

HSRD(k)

l , (12)

C =√

ESDL−1

HSD(k)

2,l . (13)







Sub-Packets ARQ Transmission Model (III)

In a joint manner signal vector yequ(k)

D,t is grouped with all the previously

received signals yequ(k−1)

D,t , · · · ,yequ(1)

D,t to decode the data packet.

K ARQ rounds Transmission Model

This leads to the 2NDk × 2Ns block transmission model given byyequ

(1)

D,t

.

.

.

yequ(k)

D,t

︸︷︷︸

yequ,kD,t

=

Lmax−1∑l=0

Hequ(1)

l

.

.

.

Hequ(k)

l

︸︷︷︸

Hequ,kl

z(t−l)modT

2+

nequ

(1)

D,t

.

.

.

nequ(k)

D,t

︸︷︷︸

nequ,kD,t

. (14)






Outage ProbabilityAverage Throughput

Outage Probability

Definition (Pertaining to K=1)

The outage probability at a given signal-to-noise ratio (SNR) ρ, denoted by Pout, refers to the

probability half of the information rate I (the factor 12 comes from the fact that one channel use

of the equivalent received signal model (9) corresponds to two temporal channel uses), between

transmitted block z and received block yequ,1D

, is below a target rate R,

Pout (ρ,R) = Pr

{1

2I(z;yequ,1

D

∣∣∣{Hequ,1l

}, ρ)< R

}(15)

where

z =

z1...

zT2

, and yequ,1D

=

yequ,1D,1

...

yequ,1

D,T2−1

.







Outage Probability

Generalization

To extend the previous formula on our ARQ relay system, we use the renewal theory as well as theobservation that allows us to view the presented Chase-type ARQ mechanism, with a maximumnumber of rounds K, as a repetition coding scheme over K parallel sub-virtual channels.Accordingly, given the equivalent MIMO-ARQ channel model (14), (15) can be re-written as

Pout (ρ,R) =Pr

{1

2KI(

z; yequ,K

D

∣∣∣{Hequ,Kl

}, ρ)< R,A1, ...,AK−1

},

where Ak represents the event that a NACK feedback is sent back to the source node S at roundk = 1, ..., K − 1.







Average Throughput

The average throughput formula corresponding to the transmission over the equivalent Relay ARQMIMO channel is given by

η =E [R]

E [ν]. (16)

R is a discrete random variable equals either to R when successful packet decoding isdetected within the K rounds or 0 otherwise.

In an outage sense, these two values are taken with probabilities 1− Pout (ρ,R) andPout (ρ,R), respectively.

ν is a RV counting the number of rounds consumed to transmit one packet.

Thus, the average throughput (16) can be re-expressed as

η = Rν (1− Pout (ρ,R)) (17)

where Rν = R/E [ν].







Scenario 1

−4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 1010

−3

10−2

10−1

100

SNR(dB)

Out

age

Pro

babi

lity

Relay ARQ with SMR K=2Relay ARQ K=2Relay ARQ K=1Reference ProtocolDirect Transmission K=2Direct Transmission K=1

Fig. 4: Outage probability versus SNR for lSR = 0.3, NS = NR = ND = 2, LSR = LRD = LSD = 3, and κ = 3.







Scenario 2

−3 −2 −1 0 1 2 3 4 5 6 7 8 9 1010

−3

10−2

10−1

100

SNR(dB)

Out

age

Pro

babi

lity


Fig. 5: Outage probability versus SNR for lSR = 0.7, NS = NR = ND = 2, LSR = LRD = LSD = 3, and κ = 3.







Scenario 1

−8 −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

SNR(dB)

Ave

rage

Thr

ough

put (

bit/s

/Hz)


Fig. 6: Average throughput versus SNR for lSR = 0.3, NS = NR = ND = 2, LSR = LRD = LSD = 3, and κ = 3.







Scenario 2

−7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

SNR(dB)

Ave

rage

Thr

ough

put (

bit/s

/Hz)


Fig. 7: Average throughput versus SNR for lSR = 0.7, NS = NR = ND = 2, LSR = LRD = LSD = 3, and κ = 3.






Key IdeasTurbo Receiver Design

Key Ideas

One time slot ⇒ additional set of NS transmit and ND receive antennas atnode S and Node D, respectively.

One packet re(transmission) ⇒ additional set of 2ND receive antennas atnode D.

Our relay ARQ system at round k ∼ virtual 2NDk × 2NS MIMO system







Soft Sub-Packet Combiner Derivation

At ARQ round k, the NDkT ×NST sub-packet ARQ transmission model is gen by

yequ,k

= Hequ,k

z + nequ,k

, (18)

where

x = clmn0≤t≤T

2−1

(zt) = clmn0≤t≤T−1

(xt)

yequ,k = clmn0≤t≤T

2−1

(yequ,kD,t )

nequ,k = clmn0≤t≤T

2

(nequ,kD,t )

. (19)

Hequ,k can be block-diagonalized in the Fourier basis as

Hequ,k

= UHT/2,2NDk

∆(k)

UT/2,2NSk. (20)







Soft Sub-Packet Combiner Derivation

Applying the DFT to both sides of (18) yields the following multi-roundfrequency domain (FD) sub-packet ARQ transmission model

yequ,k

f= ∆

(k)xf + n

equ,kf . (21)

Unconditional MMSE Filter ⇒ x(k)f = Φ(k)yequ,k

f−Ψ(k)xf

The forward filter Φ(k) = diag{

Φ(k)0 , · · · ,Φ(k)

T/2−1

}, and the backward filter

Ψ(k) = diag{

Ψ(k)0 , · · · ,Ψ(k)

T/2−1

}are respectively expressed, for t = 0, · · · , T/2− 1,

as Φkt = 1

N0∆

(k)H

t

{I2NDk + ∆

(k)t C−1

t ∆(k)H

t

}C

−1

t = N0Θ(k)−1

x + ∆(k)H

t ∆(k)t

Ψkt = Φ(k)t ∆

(k)t − 2

T

∑T/2−1i=0 Φ

(k)t ∆

(k)t

.







Building Blocks of the Proposed Receiver

CP

del

etio

nC

P d

elet

ion

soft

sub-packet

combiner

soft de-mapper

interleaver

de-interleaver

soft mapper

SISO

decoder

+

CRC

ACK/NACK feedback

ARQ round k

ARQ round 1 virtual

second slot

ND receive antennas

b

+

previous rounds received signals and CFRs

Fig. : Building blocks of the proposed turbo receiver.







Recursive Implementation (Algorithm)

Two recursive variables: yequ,kt

and Γ(k) = diag{

Γ(k)0 , · · · ,Γ(k)

T/2−1

}are introduced

within the following new soft sub-packet combining structure

x(k)f = Φ

(k)yequ(k)

f− Ψ

(k)xf , (22)

where yequ

(k)

f= yequ

(k−1)

f+ Υ(k)Hyequ

(k)

f

yequ(0)

f= 02NS×1

Γ(k)t = Γ

(k−1)t + Υ

(k)H

t Υ(k)t

Γ(0)t = 02NS×2NS

.

The backward-forward filters have been adjusted to Φ(k) = diag{

Φ(k)0 , · · · , Φ(k)

T/2−1

},

and Ψ(k) = diag{

Ψ(k)0 , · · · , Ψ(k)

T/2−1

}with

Φ

(k)t = 1

N0

{I2NS − Γ

(k)t C

−1

t

}Ci = N0Θk−1

x + Γ(k)t

Ψ(k)t = Φ

(k)t Γ

(k)t − 2

T

∑T/2−1t=0 Φ

(k)t Γ

(k)t

.






Average Throughput

Scenario 1

1.6

0.0

1.4

1.2

1.0

0.8

1.8

-8.0 -4.0 -2.0 0.0 2.0 4.0 6.0

0.6

2.0

0.4

0.2

Av

era

ge

Th

rou

gh

pu

t (b

its

/s/H

z)

-6.0

SNR(dB)

Scenario 1

CR-Selective DF CR-AF

Relay ARQ with SMR

Fig. 6: Average throughput versus SNR for lSR = 0.3, NS = NR = 2, ND = 3, LSR = LRD = LSD = 3, and κ = 3.






Average Throughput

Scenario 2

2.0 4.0 6.0-2.0-4.0-6.0

Av

era

ge

Th

rou

gh

pu

t (b

its

/s/H

z)

0.0

1.6

2.0

1.8

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

SNR(dB)

Scenario 2

CR-AF

Relay ARQ with SMR CR-Selective DF

Fig. 7: Average throughput versus SNR for lSR = 0.6, NS = NR = 2, ND = 3, LSR = LRD = LSD = 3, and κ = 3.






ConclusionPerspectives

Conclusion

New throughput-efficient relay ARQ techniques are investigated.

The half-duplex constraint has been turned from a disadvantage causing a

multiplexing gain loss to an advantage providing significant improvement in

average throughput & outage probability performance.

Relay ARQ with SMR along with signal-level turbo sub-packet combiningprovides considerable gain in average throughput compared with conventionalARQ-based cooperative relaying over the entire SNR region.







Conclusion












Conclusion












Perspectives

Analytical results of the outage probability and average throughput instead of

Monte-Carlo based simulations should be investigated.

Extension of the proposed techniques to a multi-user environment whereseveral relays are deployed.







Perspectives










Perspectives









Related Works

Related Works

Zakaria El-Moutaouakkil, Tarik Ait-Idir, Halim Yanikomeroglu, and Samir Saoudi, “ReceiverDesign for Throughput-Efficient MIMO Relay ARQ Transmissions,” to be submitted, IEEETransactions on Signal Processing, 30 pp., December 2012.

Hatim Chergui, Tarik Ait-Idir, Mustapha Benjillali, Zakaria El-Moutaouakkil, and SamirSaoudi, “Joint-Over-Transmissions Project and Forward Relaying for Single CarrierBroadband MIMO ARQ Systems,” submitted, IEEE Vehicular Technology ConferenceVTC-Spring 2011, Budapest, Hungary, May 2011.

Zakaria El-Moutaouakkil, Tarik Ait-Idir, Halim Yanikomeroglu, and Samir Saoudi, “RelayARQ Strategies for Single Carrier MIMO Broadband Amplify-and-Forward CooperativeTransmission,” in Proc., 21th Annual IEEE Symposium on Personal Indoor and Mobile RadioCommunications PIMRC 2010, Istanbul, Turkey, Sep. 2010.

Tarik Ait-Idir, Houda Chafnaji, and Samir Saoudi, “Turbo Packet Combining for BroadbandSpace-Time BICM Hybrid-ARQ Systems with Co-Channel Interference,” IEEE Transactionson Wireless Communications, vol. 9, no. 5, pp. 1686-1697, May 2010.






Related Works

Perspectives & Conclusion

Thank you very much


Documents

Turbo Receiver Design for MIMO Relay ARQ · PDF fileRelay ARQ System Information ... Zakaria El-Moutaouakkil (NSN, Morocco) October 3, 2012 ... Constraints posed by 3G & 4G Progress