Cooperative Diversity with MultipleAntenna Nodes in Fading
Relay Channels
Advisor : Yinman Lee
Speaker : Yen-Nan Chen
(s96325525)
Communication Signal Processing Lab
Graduate Institute of Communication Engineering
Tin Studio Established 07. In TAITUNG CITY
NCNU
Outline
•
•
•
•
•
Introduction
Transmission Model
Diversity Gain Analysis
Simulation Results And Discussion
Conclusion
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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
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Transmission Model
Fig. 1. Schematic representation of relay-assisted transmission.
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Transmission Model
• The received signals during the broadcasting
th
phase at the j  j  1, 2,..., N  receive antenna of
the destination terminal are given by
k
D, j
r
ESD M S i
k

h
x

n

SD , j i , k
D , j , k  1, 2,..., K ,
M S i 1
1
is the STBC-encoded modulation symbol
sent from the ith transmit antenna in time interval
k.
xi , k
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Transmission Model
• The received signals at the mth  m  1, 2,..., M R 
receive antenna of the relay terminal are given
by
k
R,m
r
ESR M S i
k

h
x

n

SR , m i , k
R , m , k  1, 2,..., K ,
M S i 1
 2
• In matrix notation, we can rewrite (2) as
rR ,m 
ESR
H SR,m x  nR,m ,
MS
 3
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Transmission Model
where H SR ,m is the S → RT link channel matrix with
xQ  denotes the codeword
size K × Q, x   x1
T
1
K
nR ,m  represents the noise
vector, and nR,m  nR,m
vector.
• During the relaying phase, the received signals
processed at the relay terminal are forwarded to
the destination terminal.
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Transmission Model
A. CSI-assisted AaF relaying
• The received signals at the destination terminal
are given by
l
D, j
r
ERD MT m
l

h
y

n

RD , j m ,l
D, j ,
M T m1
 4
ym ,l denote
the STBC-encoded modulation
symbols transmitted from the mth antenna at time
slot l .
l  K  1, K  2,..., 2 K and j  1, 2,...N
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Transmission Model
B. Blind AaF relaying
• The received signal at the destination terminal
from the t th t  1, 2,..., MT  antenna is given by
rDt ,,l j 
ERD t
hRD , j
MT
rRk,m
ESR M S  N 0
 nDt ,l, j
 5
l  tK  1,...t  K  1 , k  l  tK and j  1,..., N
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Transmission Model
C. DaF relaying
• The received signals at the destination terminal
can be written as
l
D, j
r
ERD MT m
l

h
y

n

RD , j m,l
D,
M T m1
 6
denotes the STBC-encoded modulation
symbol transmitted from the relay’s mth transmit
antenna in time slot l .
y m ,l
l  K  1,..., 2 K , and j  1,..., N
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Diversity Gain Analysis
• Defining the transmitted codeword vector from
the source and the erroneously-decoded
codeword vector at the destination terminal,
T
T
ˆ
ˆ
ˆ




x

x
,...,
x
x

x
,...,
x
respectively, as
Q  and
Q  , the
 1
 1
conditional PEP is given by

i
m
i
P x, xˆ hSR
,
h
,
h
,m
RD , j
SD , j , i  1,..., M S , m  1,..., M T ,
 d 2  x, xˆ  

j  1,..., N   Q 

2 N0 


7
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Diversity Gain Analysis
assuming ML decoding. Here, Q(.) is the
Gaussian-Q function and d 2  x, xˆ  denotes the
Euclidean distance between x and x̂ . Applying
the standard Chernoff bound to (7), we obtain

i
m
i
P x, xˆ hSR
,
h
,
h
,m
RD , j
SD , j , i  1,..., M S , m  1,..., M T ,
 d 2  x, xˆ  
j  1,..., N   exp  

4 N0 

8
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Diversity Gain Analysis
A. PEP for CSI-assisted AaF relaying
The Euclidean distance d 2  x, xˆ  for AaF relaying
can be written as
d 2  x, xˆ   d S2RD  x, xˆ   d S2 D  x, xˆ 

 ESD
MS
j 
N
MS
 h
j 1 i 1
M
i
SD , j
2

T SR  ESR
2
N
MT
j 1
m 1
   j  h
2
m
RD , j
2
 SR
,
9
 ESR N0  ERD
2
N 0   M S M T   M S  RD
, j  ESR
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N0 
Diversity Gain Analysis
  v x  xˆ  ...  v xQ  xˆQ
2
2
denotes the eigenvalue of
the codeword difference matrix, and
 SR  v
12

MR
m 1

MS
i 1

2 12
i
SR , m
h
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Diversity Gain Analysis
• Scenario 1 (Balanced S → D and R → D links
and high SNR in S → R link ):
we find PEP as
 ESD 
P  x, xˆ   

4
MN
0 

 N  M S  MT 
diversity order
 NM
S
 MT 
10
N  M S  MT   2 NM .
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Diversity Gain Analysis
• Scenario 2 (Balanced S → D and S → R links
and high SNR in R → D link):
we find PEP as
 ESD 
P  x, xˆ   

 4M S N 0 
diversity order
 NM S  M R M S 
  NM
S
M RM S 
11
M S  N  M R   NM  M 2.
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Diversity Gain Analysis
• Scenario 3 (Poor SNR in S → R link):
we find PEP as
 ESD

ˆ
P  x, x   

 4M S N 0 
diversity order
 NM S


ESR

1 
 4M S N 0 
MRMS
NM S .
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12 
Diversity Gain Analysis
• Scenario 4 (Non-fading R → D link):
 ESD 
ˆ
P  x, x   

4
M
N
S 0 

 NM S

 NM S

ESD 
exp   N 

4
N
0 

13
the diversity order is large and can not be
determined by an integer value anymore, i.e., an
AWGN-like performance is observed.
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Diversity Gain Analysis
B. PEP for blind AaF relaying
2
d
the Euclidean distance  x, xˆ  for blind AaF
relaying can be written as
N
d
2
MT
 x, xˆ    ERD   h
j 1 t 1

t
j
2
t
RD , j
 ESD
MS
N
MS
i
h
 SR ,t
2
i 1
MS
 h
j 1 i 1
2
i
SD , j
14 
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Diversity Gain Analysis
• Scenario 1 (Balanced S → D and R → D links
and high SNR in S → R link ):
we obtain the PEP expressions as
  N  MS  
P  x, xˆ   


N
  

MT
 MS  N  
P  x, xˆ   

 N  
P  x, xˆ  
log
 ESD
M
N 
MT
MT
  ESD 


4
MN
0 

 M S  N  MT 
  ESD 


4
MN
0 

N 0    ESD 


T
4
MN
0 

N  MS
15
MS  N
16 
 N  M S  MT 
 M S  N  MT 
MS  N
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17 
Diversity Gain Analysis
diversity order MT min  M S , N   M S N .
• Comparison to (10) further reveals that CSIassisted AaF and blind AaF relaying yield the
same diversity order, provided that M S  N .
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Diversity Gain Analysis
• Scenario 2 (Balanced S → D and S → R links
and high SNR in R → D link):
we find PEP as
 ESD

P  x, xˆ   

 4MN0 
diversity order
 M S  N  MT 
18
M S  MT  N  .
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Diversity Gain Analysis
• Scenario 3 (Poor SNR in S → R link):
we find PEP as
 ESD

ˆ
P  x, x   

 4MN 0 
 NM S

 ESR 
1 

4
MN
0 

 MT M S
19 
it can be easily concluded that the diversity order
in (19) is limited to NM S as observed for CSIassisted case.
i.e., direct transmission.
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Diversity Gain Analysis
• Scenario 4 (Non-fading R → D link):
we find PEP as
P  x, xˆ  
M S  MT  N 
M
N MT M S
diversity order
  ESD 


4
N
0 

 M S  MT  N 
M S  MT  N 
.
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Diversity Gain Analysis
C. PEP for DaF relaying
P  x, xˆ end to end



 PS  R  x, f  x   P  f  x  , xˆ   1  PS  R  x, f  x   P  x, xˆ  for  SR   th


 PS  D  x, xˆ  for  SR   th
we can upper bound P  x, xˆ end toend
P  x, xˆ 
 P  x, f  x    1  P  x, f  x    P  x, xˆ  for 
end to end
S R
S R
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SR
  th
Diversity Gain Analysis
• Scenario 1 (Balanced S → D and R → D links
and high SNR in S → R link ):
we find PEP as
 ESD 
ˆ
P  x, x end toend  

4
MN
0 

diversity order
 N  M S  MT 
 NM
S
 MT 
N  M S  MT  .
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Diversity Gain Analysis
• Scenario 2 (Balanced S → D and S → R links
and high SNR in R → D link):
we find PEP as
P  x, xˆ end to end
 ESD 


4
MN
0 

 NM S
  NM
S
diversity order MN.
i.e.,non-cooperative.
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Diversity Gain Analysis
• Scenario 3 (Poor SNR in S → R link):
we find PEP as
 ESD 
ˆ
P  x, x end to end  

4
MN
0 

 NM S
  NM
S
diversity order MN .
i.e.,non-cooperative.
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Diversity Gain Analysis
• Scenario 4 (Non-fading R → D link):
we find PEP as
 ESD 
ˆ
P  x, x end to end  

4
M
N
S 0 

 NM S

 NM S

ESD 
 exp   N 

4
N
0 

diversity order is large and provides an AWGNlike performance similar to our observation for
CSI-assisted AaF relaying.
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Diversity Gain Analysis
TABLE I
DIVERSITY ORDERS OF BLIND AaF,
CSI-ASSISTED AaF, AND DaF RELAYING.
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Simulation Results
And Discussion
Fig. 2. SER performance of blind AaF relaying.
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Simulation Results
And Discussion
Fig. 3. SER performance of blind AaF relaying assuming M = 2.
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Simulation Results
And Discussion
Fig. 4. SER performance of CSI-assisted AaF relaying.
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Simulation Results
And Discussion
Fig. 5. SER performance of CSI-assisted AaF relaying assuming M = 2.
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Simulation Results
And Discussion
Fig. 6. SER performance of DaF relaying.
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Simulation Results
And Discussion
Fig. 7. SER performance of DaF relaying assuming M = 2.
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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
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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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Thanks for your attention
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