Tin Studio Established 07. In TAITUNG CITY Communication Signal Processing Lab Graduate Institute of Communication Engineering NCNU Cooperative Diversity

Communication Signal Processing LabGraduate Institute of Communication Engineering

NCNU Tin Studio Established 07. In TAITUNG CITY

Cooperative Diversity with Multiple-Antenna Nodes in Fading

Relay Channels

Advisor : Yinman Lee

Speaker : Yen-Nan Chen

(s96325525)



Outline

• Introduction• Transmission Model• Diversity Gain Analysis• Simulation Results And Discussion• Conclusion



Introduction

• We investigate the performance of a single-relay cooperative scenario where the source, relay and destination terminals are equipped with multiple transmit/receive antennas.

A. CSI-assisted AaF relaying

B. Blind AaF relaying

C. DaF relaying



Transmission Model

Fig. 1. Schematic representation of relay-assisted transmission.



Transmission Model

• The received signals during the broadcasting phase at the receive antenna of the destination terminal are given by

is the STBC-encoded modulation symbol sent from the transmit antenna in time interval k.

,i kxthi

, , , ,1

, 1, 2,..., , 1SM

k i kSDD j SD j i k D j

iS

Er h x n k K

M

1, 2,...,thj j N



Transmission Model

• The received signals at the receive antenna of the relay terminal are given by

• In matrix notation, we can rewrite (2) as , , , ,

1

, 1, 2,..., , 2SM

k i kSRR m SR m i k R m

iS

Er h x n k K

M

1,2,...,thRm m M

, , , , 3SRR m SR m R m

S

Er H x n

M



Transmission Model

where is the S → R link channel matrix with size K × Q, denotes the codeword vector, and represents the noise vector.

• During the relaying phase, the received signals processed at the relay terminal are forwarded to the destination terminal.

,SR mH

1 T

Qx x x 1

, , , TK

R m R m R mn n n



Transmission Model

A. CSI-assisted AaF relaying• The received signals at the destination terminal

are given by

denote the STBC-encoded modulation symbols transmitted from the antenna at time slot .

,m ly

, , , ,1

, 4TM

l m lRDD j RD j m l D j

mT

Er h y n

M

l

thm

1, 2,..., 2 and 1,2,...l K K K j N



Transmission Model

B. Blind AaF relaying• The received signal at the destination terminal fr

om the antenna is given by

,, ,, , ,

0

5kR mt l t t lRD

D j RD j D jT SR S

rEr h n

M E M N

1,2,...,thTt t M

1,... 1 , and 1,...,l tK t K k l tK j N



Transmission Model

C. DaF relaying• The received signals at the destination terminal

can be written as

denotes the STBC-encoded modulation symbol transmitted from the relay’s transmit antenna in time slot .

,m lythm

, , ,1

, 6TM

l m lRDD j RD j m l D

mT

Er h y n

M

1,..., 2 , and 1,...,l K K j N

l



Diversity Gain Analysis

• Defining the transmitted codeword vector from the source and the erroneously-decoded codeword vector at the destination terminal, respectively, as and , the conditional PEP is given by

1,...,T

Qx x x 1ˆ ˆ ˆ,...,T

Qx x x

, , ,

2

0

ˆ, , , , 1,..., , 1,..., ,

ˆ, 1,..., 7

2

i m iSR m RD j SD j S TP x x h h h i M m M

d x xj N Q

N




assuming ML decoding. Here, Q(.) is the Gaussian-Q function and denotes the Euclidean distance between and . Applying the standard Chernoff bound to (7), we obtain

x

2 ˆ,d x x

x̂

, , ,

2

0

ˆ, , , , 1,..., , 1,..., ,

ˆ, 1,..., exp 8

4

i m iSR m RD j SD j S TP x x h h h i M m M

d x xj N

N




A. PEP for CSI-assisted AaF relaying

The Euclidean distance for AaF relaying can be written as

2 ˆ,d x x

2 2 2

2 2 2, ,

1 1 1 1

ˆ ˆ ˆ, , ,

, 9S T

S R D S D

M MN Ni mSDSD j j RD j SR

j i j mS

d x x d x x d x x

Eh h

M

0

2 20 , 0

SR RDj

T SR SR S T S RD j SR

E N E

M E N M M M E N




denotes the eigenvalue of the codeword difference matrix, and

22ˆ ˆ... Q Qv x x v x x

1 221 2,1 1

R SM M iSR SR mm i

v h




• Scenario 1 (Balanced S → D and R → D links and high SNR in S → R link ):

we find PEP as

diversity order .

0

ˆ, 104

S T

S T

N M M

N M MSDEP x xMN

2S TN M M NM




• Scenario 2 (Balanced S → D and S → R links and high SNR in R → D link):

we find PEP as

diversity order .

0

ˆ, 114

S R S

S R S

NM M M

NM M MSD

S

EP x x

M N

2S RM N M NM M




• Scenario 3 (Poor SNR in S → R link):

we find PEP as

diversity order .

0 0

ˆ, 1 124 4

S R SNM M M

SD SR

S S

E EP x x

M N M N

SNM




• Scenario 4 (Non-fading R → D link):

the diversity order is large and can not be determined by an integer value anymore, i.e., an AWGN-like performance is observed.

0 0

ˆ, exp 134 4

S

S

NM

NMSD SD

S

E EP x x N

M N N




B. PEP for blind AaF relaying

the Euclidean distance for blind AaF relaying can be written as

2 22, ,

1 1 1

2

,1 1

ˆ,

14

ST

S

MMNt t i

RD j RD j SR tj t i

MNiSDSD j

j iS

d x x E h h

Eh

M

2 ˆ,d x x





we obtain the PEP expressions as

0

ˆ, 154

T S TM M N M

S SDS

N M EP x x N M

N MN

0

ˆ, 164

T S TM N M M

S SDS

M N EP x x M N

N MN

0

0

logˆ, 17

4

S TT

T

M N MMSD SD

SM

E N EP x x M N

MNN




diversity order .• Comparison to (10) further reveals that CSI-assi

sted AaF and blind AaF relaying yield the same diversity order, provided that .

min ,T S SM M N M N

SM N





we find PEP as

diversity order .

0

ˆ, 184

S TM N M

SDEP x xMN

S TM M N





we find PEP as

it can be easily concluded that the diversity order in (19) is limited to as observed for CSI-assisted case.

i.e., direct transmission.

0 0

ˆ, 1 194 4

S T SNM M M

SD SRE EP x x

MN MN

SNM





we find PEP as

diversity order .

0

ˆ,4

S TS T

T S

M M NM M NSD

M M

EMP x x

N N

S TM M N




C. PEP for DaF relaying

we can upper bound

ˆ ˆ, , 1 , , for

ˆ,ˆ, for

S R S R SR th

end to end

S D SR th

P x f x P f x x P x f x P x xP x x

P x x

SRˆ ˆ, , 1 , , for S R S R thend to endP x x P x f x P x f x P x x

ˆ,end to end

P x x





we find PEP as

diversity order . S TN M M

0

ˆ,4

S T

S T

N M M

N M MSDend to end

EP x x

MN





we find PEP as

diversity order .

i.e.,non-cooperative.

MN

0

ˆ,4

S

S

NM

NMSDend to end

EP x x

MN





we find PEP as

diversity order .

i.e.,non-cooperative.

0

ˆ,4

S

S

NM

NMSDend to end

EP x x

MN

MN





we find PEP as

diversity order is large and provides an AWGN-like performance similar to our observation for CSI-assisted AaF relaying.

0 0

ˆ, exp4 4

S

S

NM

NMSD SDend to end

S

E EP x x N

M N N




TABLE IDIVERSITY ORDERS OF BLIND AaF,

CSI-ASSISTED AaF, AND DaF RELAYING.



Simulation Results And Discussion

Fig. 2. SER performance of blind AaF relaying.




Fig. 3. SER performance of blind AaF relaying assuming M = 2.




Fig. 4. SER performance of CSI-assisted AaF relaying.




Fig. 5. SER performance of CSI-assisted AaF relaying assuming M = 2.




Fig. 6. SER performance of DaF relaying.




Fig. 7. SER performance of DaF relaying assuming M = 2.



Conclusion

• In this paper, we have investigated performance of three relaying schemes in a cooperative scenario in which the cooperating nodes are equipped with multiple antennas and operating over frequency-flat Rayleigh fading channels.

• We have analyzed the diversity gains of blind AaF, CSI-assisted AaF, and DaF schemes



References

• [1] S. Alamouti, “A simple transmit diversity technique for wireless communications,” IEEE J. Select. Areas Commun., vol. 16, no. 8, pp. 1451–1458, 1998.

• [2] A. Sendonaris, E. Erkip, and B. Aazhang, “User cooperation diversity-Part I: System description,” IEEE Trans. Commun., vol. 51, pp. 1927-1938, Nov. 2003.

• [3] A. Sendonaris, E. Erkip, and B. Aazhang, “User cooperation diversity-Part II: Implemen taion aspects and performance analysis,” IEEE Trans. Commun., vol. 51, pp. 1939-1948, Nov. 2003.

• [4] M. K. Simon and M. S. Alouini, Digital Communication Over Fading Channels: A Unified Approach to Performance Analysis. NewYork: Wiley-Interscience, 2000.



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Tin Studio Established 07. In TAITUNG CITY Communication Signal Processing Lab Graduate Institute of Communication Engineering NCNU Cooperative Diversity