Unit 1 Introduction to Cooperative
Communications Systems
Department of Communication Engineering, NCTU
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Unit 1: Introduction to Cooperative Communications
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Sau-Hsuan Wu
What are cooperative communications?
Adopted from, “Cooperative Communication in Wireless Networks,’
by Nostratinia et al, IEEE Comm. Magazine, 2004
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Unit 1: Introduction to Cooperative Communications
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Sau-Hsuan Wu
Why do we need cooperation?
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Recent developments on MIMO systems show that the
channel capacity can dramatically increases by using
multiple transmit and receive antenna pairs
Y = HX + N,
Y: Mr  1, X : Mt  1 and H : Mr  Mt
I(X : Y) = E{log det ( Ir + (P / Mt2) HHH) }
=
where m = min {Mr, Mt} and
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Given perfect CSI:
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Unit 1: Introduction to Cooperative Communications
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Sau-Hsuan Wu
Adopted from I. Emre Telatar, “Capacity of multiple
antenna Gaussian channels.’ -Bell Lab Report, 1999
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Unit 1: Introduction to Cooperative Communications
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Sau-Hsuan Wu
The capacity advantage of MIMO is an appealing solution
to further increase available throughput (more precisely,
degrees of transmission freedom) in limited wireless
resources
However, deployment of multiple transmit and receive
antennas in a limited space is difficult and costly
This makes people to reconsider using relays to create a
virtual MIMO channels for wireless communications
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Unit 1: Introduction to Cooperative Communications
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Are there any other advantages than capacity for
cooperative communications?
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Sau-Hsuan Wu
Despite the achievable capacity of MIMO systems, a more
practical performance criterion is the probability of error
This is particularly important when coding over a small
number of blocks where the Shannon capacity is zero
Consider communications over Rayleigh fading channels
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For BPSK over a Rayleigh channel with variance E{2}=1
 Pe  1/ (4Eb/N0)
For DPSK
 Pe  1/ (2Eb/N0)
For coherent FSK
 Pe  1/ (2Eb/N0)
For non-coherent FSK  Pe  1/ (Eb/N0)
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Unit 1: Introduction to Cooperative Communications
Department of Communication Engineering, NCTU
Sau-Hsuan Wu
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Unit 1: Introduction to Cooperative Communications
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Sau-Hsuan Wu
How do people usually do to combat fading?
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Diversity techniques
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Frequency diversity  maximal ratio combining (MRC)
For BPSK with MRC
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Temporal diversity  interleaving
Spatial diversity using multiple TX and/or RX antennas
 beamforming
 antenna selection
Spatial plus temporal diversity using multiple TX and/or RX
antennas and multiple time slots
 space-time codes
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Unit 1: Introduction to Cooperative Communications
Department of Communication Engineering, NCTU
Sau-Hsuan Wu
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Unit 1: Introduction to Cooperative Communications
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Sau-Hsuan Wu
How to use multiple antennas to increase diversity?
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Alamouti’s scheme
y1
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y2   h1
-JSAC, 1998
 x1
h2 
 x2
 x2* 
 n1 n2 
* 
x1 
A simple codeword over two consecutive channels
Rearrange the received signals into
 y1   h1 h2   x1   n1 
 y *   h *  h *   x   n * 
1  2 
 2  2
 2
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*

h
h2   y1 
2
2
 1

|
h
|

|
h
|
1
1
 *
 * 
y
h

h
1  2 
 2
*
x

h
h2   n1 
 1
1
 * 
x    *
n
h

h
 2  2
1  2 
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Unit 1: Introduction to Cooperative Communications
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Adopted from, “A simple transmit diversity technique for wireless
communications,’ by S. M. Almouti, JSAC, 1998
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Unit 1: Introduction to Cooperative Communications
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Is there a formal definition for diversity?
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Sau-Hsuan Wu
We look at this from the sense of outage probability
To achieve capacity, a coding is assumed to take place
across fading blocks, which entails large delays
We consider a coding scheme which is done just across one
fading block
Def 1: The outage probability for a transmission rate of R
and a given transmission strategy p(X)
Poutage(R, P(X)) = P{H: I(X,Y|H(k)=H) < R }
When one use a white Gaussian codebook
Poutage(R) =P{log det ( Ir + (P/ t2) HHH ) < R}
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Unit 1: Introduction to Cooperative Communications
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At high SNR, the outage probability is the same as frame
error probability (FER) in terms of the SNR exponent
- L. Zheng and D. N. C. Tse, IEEE-IT, 2003
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Def 2: A coding scheme which has an average error
probability Pe (or an outage probability Pout) as a function
of SNR that behave as
log( Pe )
lim
 d
SNR log( SNR)
is said to have a diversity of order d
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Unit 1: Introduction to Cooperative Communications
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Sau-Hsuan Wu
A systematic way to exploit space-time diversity
- by Tarokh et al. IEEE-IT 1999
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Consider a codeword sequence x = [xT(0),…,xT(N)],
where x (k)=[x1(k),… xMt(k)]T.
Given the perfect CSI, the pair-wise error probability (PEP)
between x and e can be bounded from above by
where Km,n is the Ricean coefficient, Es=P/Mt, i are the
eigenvalues of A(x,e)=B(x,e)HB(x,e), and
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Unit 1: Introduction to Cooperative Communications
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For Rayleigh fading channels (Km,n =0), we have
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Let q denote the rank of A(x,e), then we have
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According to Def 2 for the diversity order, the diversity
order using space-time coding is qMr
 B(x,e) has to be full row rank for any codewords x and
e to achieve the maximum diversity Mt Mr
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Unit 1: Introduction to Cooperative Communications
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Examples of space-time trellis codes
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4-PSK, Mt =2 at 2 b/s/Hz
Sau-Hsuan Wu
32-state
16-state
4-state
8-state
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Unit 1: Introduction to Cooperative Communications
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Sau-Hsuan Wu
FER for two transmit antennas and one receive antenna
Diversity order = 2
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Unit 1: Introduction to Cooperative Communications
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Sau-Hsuan Wu
FER for two transmit antennas and two receive antennas
Diversity order = 4
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Unit 1: Introduction to Cooperative Communications
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Example of space-time trellis code
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Sau-Hsuan Wu
32-state
8-PSK, Mt =2 at 3 b/s/Hz
16-state
8-state
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Unit 1: Introduction to Cooperative Communications
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Sau-Hsuan Wu
FER for two transmit antennas and one receive antenna
Diversity order = 2
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Unit 1: Introduction to Cooperative Communications
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Sau-Hsuan Wu
FER for two transmit antennas and two receive antennas
Diversity order = 4
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Unit 1: Introduction to Cooperative Communications
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Sau-Hsuan Wu
A natural question that arises is, how many codewords
can we have that allows us to attain a certain diversity
order?
Def 3: A coding scheme which has a transmission rate of
R(SNR) as a function of SNR is said to have a
multiplexing gain r if
R( SNR)
lim
r
SNR log( SNR)
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The constellation size is also allowed to become larger with
SNR
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Unit 1: Introduction to Cooperative Communications
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Theorem 1: For N > Mt + Mr -1, and K = min(Mt, Mr),
the optimal tradeoff curve d*(r) is given by the piecewise
linear function connecting points in (k, d*(k)), k = 0,…,K,
where
d*(k) = (Mr – k) (Mt – k)
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If r = k is an integer,
this can be interpreted as
using (Mr – k) receive and
(Mt – k) transmit antennas
to provide diversity, while
using k antennas to provide
multiplexing gain
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Unit 1: Introduction to Cooperative Communications
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Sau-Hsuan Wu
How do we do cooperation?
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By Sendonaris, Stefanov, Erkip, and Ashang
Y0 = K10X1 + K20X2 + Z0
Y1 = K21X2 + Z1
Y2 = K12X1 + Z2
Assume perfect
echo cancellation
Channel phases of
K10 and K20
are given
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Unit 1: Introduction to Cooperative Communications
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Sau-Hsuan Wu
Consider transmission of B blocks, each of length n.
Both B and n are assumed to be large to make
observations over different fading levels
X1(j) = X10(j) + X12(j) + U1(j)
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X10(j) = P101/2 X10 [W10(j) + W12(j-1) + W21(j-1)]
X12(j) = P121/2 X12 [W12(j) + W12(j-1) + W21(j-1)]
U1(j) = PU11/2 exp(-j10)U [W12(j-1) + W21(j-1)]
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Unit 1: Introduction to Cooperative Communications
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Theorem 2 : An achievable region for the cooperative
system is the closure of the convex hull of all rate pairs
(R1, R2) such that R1 = R10+ R12 and R2 = R20+ R21
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P1= P10+P12+PU1 , P2= P20+P21+PU2 and C (x) = log(1+x)
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Unit 1: Introduction to Cooperative Communications
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Sau-Hsuan Wu
Assume perfect recovery of W12 at (Terminal 2, T2)
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X1(j) = X10(j) + X12(j) + U1(j)
X12(j) = P121/2 X12 [W12(j) + W12(j-1) + W21(j-1)]
Starting from j=1, assume W12(0) and W21(0) are given
X10(1) is treated as noise to X12(1)
For perfect recovery of W12 at T2
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For multiple access channel, we have

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Unit 1: Introduction to Cooperative Communications
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Sau-Hsuan Wu
Perform backward decoding and assume
[W10(B), W12(B), W20(B), W21(B)] = [0,0,0,0]
Assume prior knowledge for the channel phase 10 and
20 at the transmitter T1 and T2 , respectively
The aiding signal is sent from T1 with |K10|U(B) and sent
from T2 with |K20|U(B)
Since W10(B), W12(B), W20(B), W21(B) and U(B-1) given,
X= P121/2K10W12(B-1)+P211/2 K20W21(B-1)
+ (|K10|PU11/2 +|K20|PU21/2) U(B)
 For perfect recovery of W12(B-1) and W21(B-1)
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Unit 1: Introduction to Cooperative Communications
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Moving into block B-1,
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Sau-Hsuan Wu
X1 (B-1) = K10 [P101/2X10(B-1)+P121/2X12(B-1)]
+ |K10|PU11/2 U(B-1)
X2 (B-1) = K20 [P201/2X10(B-1)+P211/2X21(B-1)]
+ |K20|PU21/2 U(B-1)
X10(B-1) = P101/2 X10 [W10(B-1) + W12(B-2) + W21(B-2)]
X12(B-1) = P121/2 X12 [W12(B-1) + W12(B-2) + W21(B-2)]
U1(B-1) = PU11/2 exp(-j10)U [W12(B-2) + W21(B-2)]
Since W12(B-1) and W21(B-1) are given
To recover W10(B-1),W12(B-2), W20(B-1) and W21(B-2)
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Unit 1: Introduction to Cooperative Communications
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Symmetric
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P1= 2.0
P2= 2.0
E{K1}= .63
E{K2}= .63
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Unit 1: Introduction to Cooperative Communications
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Asymmetric
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P1= 2.0
P2= 2.0
E{K1}= .95
E{K2}= .30
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Unit 1: Introduction to Cooperative Communications
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Outage probability Pout=P(Rmax< r )
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R1= R2= Rmax
P1= 2.0
P2= 2.0
E{K1}= .63
E{K2}= .63
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Unit 1: Introduction to Cooperative Communications
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Sau-Hsuan Wu
Outage probability Pout=P(Rmax< r )
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R1= R2= 0.18
P1= 2.0
P2= 2.0
E{K1}= .63
E{K2}= .63
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Unit 1: Introduction to Cooperative Communications
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Sau-Hsuan Wu
A coding scheme for a cooperative system
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A node is not allowed to transmit and listen at the same time
Time division multiple access between T1 and T2
Each link has a constant fading level for N symbols
Each terminal has a separate time slot consisting N uses of
the channel
T2
T1
No cooperation
N channel uses
Cooperation
T1
N /2
N channel uses
T2 : if success
T1 : otherwise
T2
T1 : if success
T2 : otherwise
N /2
N /2
N /2
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Unit 1: Introduction to Cooperative Communications
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If T2 successively decode the
message at phase I
Cooperative scheme
Phase I
Sau-Hsuan Wu
Phase II
T1
D
T2
T1
If T2 fails decoding the
message at phase I
D
T2
T1
D
T2
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Unit 1: Introduction to Cooperative Communications
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Coding scheme
Convolutional
code, rate 1/4
Phase I
C1 C2
CN/2
C1 C2
CN/2
Phase II
T2
D
T1
D
T1
D
or
T2
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Unit 1: Introduction to Cooperative Communications
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Sau-Hsuan Wu
Simulation results for the symmetric scenario
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Rate ¼, (13,15,15,17) convolutional code
FER(T1 T2)=0.01,
Diversity order = 2
FER(T1 T2)=0. 5,
Diversity order = 1,
but 3dB coding gain
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Unit 1: Introduction to Cooperative Communications
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Sau-Hsuan Wu
Simulation results for the asymmetric scenario
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Rate ¼, (13,15,15,17) convolutional code
SNR1=15dB
FER1  0.01
FER(T1 T2)=0.5
FER2 has a 3dB
coding gain in
comparison with the
non-cooperative case
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Unit 1: Introduction to Cooperative Communications
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The development of cooperative communications
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Cover and El Gamal analyzed the capacity of the three-node
relay network in AWGN channels
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Did not consider the fading
effects
The relay node only helps
the main channel
Sendonaris et al extend the
idea to a cooperative mode
where the users can act both
as information sources and
relays
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Unit 1: Introduction to Cooperative Communications
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Laneman et al extends the above ideas to more general
cooperative communication scenarios
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Sau-Hsuan Wu
Decode-and-Forward
Amplify-and-Forward
Selection relaying
Devroye et al further extend the cooperative idea to a more
generic sense of cognitive radio consisting behaviors of
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Competitive behavior
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Cognitive behavior
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Cooperative behavior
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Unit 1: Introduction to Cooperative Communications
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Sau-Hsuan Wu
Deployment Concepts for the Relay Network
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Transmission rates for 4G system are two orders of 3G
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Spectrum for 4G system will be allocated above the 2GHz
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More vulnerable to non-line-of-sight transmission
The brute force solution to these two problems
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1 GHz for fixed stations
100Mhz for mobile stations
To increase the density of base stations unlikely
Alternative solution  Relays
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Lower cost
Relays do not have a wired connection to the backhaul
The relay-to-user link could use a different spectrum than the
BS-to-user link
Diver traffic from congested areas to cells with a lower load
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Unit 1: Introduction to Cooperative Communications
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Sau-Hsuan Wu
Multihop Relaying
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Simple decode-and-forward operation
Use relays at street corners to combat shadowing
To extend coverage range
To use a higher link capacity
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Unit 1: Introduction to Cooperative Communications
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Sau-Hsuan Wu
Examples of fixed relaying
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APs and Relays operate at the same carrier frequency
APs and Relays operate at different carrier frequencies
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Unit 1: Introduction to Cooperative Communications
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Sau-Hsuan Wu
Throughput vs.. the radio range improvement using relays
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Unit 1: Introduction to Cooperative Communications
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Two-Stage Relaying
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A fixed mounted relay in between the AP and the second
relay connects the AP and the relay by store-and-forward
The first relay only serves as a bridge
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Unit 1: Introduction to Cooperative Communications
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Left: use a relay to combat shadowing
Right: use a relay to extend the range of an AP
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Unit 1: Introduction to Cooperative Communications
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A cellular relay network (Wireless Media System, WMS)
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Make use of a wireless or mobile broadband air interface to
link low-power pico BSs, APs, and relays
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Unit 1: Introduction to Cooperative Communications
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References
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Diggavi et al, “Great expectations-The value of spatial
diversity in wireless networks,” Proceeding of IEEE 1994
I. E. Teltar, “Capacity of multi-antenna Gaussian channels,”
Bell Lab report
Erkip et al, “Cooperative Communication in Wireless
Systems” Advances in Network Information Theory 2004
Laneman et al, “Cooperative diversity in wireless networks:
Efficient protocols and outage behavior
Pabst et al, “Relay-Based development concepts for
wireless and mobile broadband radio,” IEEE
Communication Magazine, 2004
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