Design of Distributed Space-Time Block Code for Two-Relay System over Frequency Selective Fading Channels

Abstract

This paper proposes the distributed space-time block code (D-STBC) over frequency selective fading channel that achieves both spatial diversity gain and low decoding complexity with decoupling property in amplify-and-forward (AF) relay networks. These two goals are simultaneously achieved by our proposed code design, where the source permutates and conjugates the transmitted data before sending to the second relay. The diversity gain is investigated by analyzing the pairwise error probability (PEP) of the proposed scheme. In the analysis, we assume that one hop is line-of-sight (LOS) transmission modeled by Rician fading and the other hop is non-line-of-sight (NLOS) transmission experienced by Rayleigh fading. For each case, the PEP is derived based on the corresponding fading channel model.

Full text

Design of Distributed Space-Time Block Code for
Two-Relay System over Frequency Selective
Fading Channels
Quoc-Tuan Vien, Le-Nam Tran, and Een-Kee Hong
School of Electronics and Information
Kyung Hee University
Yongin, Geonggi, Rep. of Korea, 446-701
Email: {tuanvq;nltran;ekhong}@khu.ac.kr
Abstract—This paper proposes the distributed space-time
block code (D-STBC) over frequency selective fading channel
that achieves both spatial diversity gain and low decoding
complexity with decoupling property in amplify-and-forward
(AF) relay networks. These two goals are simultaneously achieved
by our proposed code design, where the source permutates and
conjugates the transmitted data before sending to the second
relay. The diversity gain is investigated by analyzing the pairwise
error probability (PEP) of the proposed scheme. In the analysis,
we assume that one hop is Line-Of-Sight (LOS) transmission
modeled by Rician fading and the other hop is Non-Line-Of-
Sight (NLOS) transmission experienced by Rayleigh fading. For
each case, the PEP is derived based on the corresponding fading
channel model.
Index Terms—Distributed space-time block code (D-STBC),
relay networks, multipath fading, Rayleigh fading, Rician fading.
I. INTRODUCTION
The quality and the data rates of wireless communications
over fading channels can be improved greatly by using space-
time block codes (STBC) applied for multiple transmit an-
tennas [1]. The conventional STBCs are designed for co-
located antennas, and can be easily implemented at the base
station in a cellular network to improve the performance of
the downlink transmission. However, the deployment of STBC
is impractical in the uplink transmission due to the inherent
hardware limitation of current mobile handsets. Recently, it
has been demonstrated that cooperative diversity, also known
as user cooperation, provides an effective means of improving
spectral and power efficiency of wireless networks as an
alternative to multiple-antenna transmission schemes [2-5].
This form of diversity allows single-antenna mobiles to reap
some of the benefits of multi-input multi-output (MIMO)
systems. Many distributed STBCs have been proposed, but
most of research works on this area assumed the frequency flat
fading channels. This situation occurs when the channel delay
spread is relatively small compared to the symbol duration. In
many current wireless communication standards, the system
is designed to communicate at a high date rate. Thus, the
communication channels become frequency selective fading,
and cause intersymbol interference. The problem of apply-
ing D-STBC to frequency selective fading channels becomes
challenging. The work in [6] introduced the application of D-
STBC for single-relay system in frequency selective Rayleigh
fading channels.
In this paper, a new D-STBC is proposed for two-relay
networks over frequency selective fading channels with AF
protocol. The proposed D-STBC operates as follow. In the
first time slot, the source sends two symbol blocks to the first
relay. The remark of our proposed D-STBC is that the source
permutates and conjugates the transmitted data that will be
sent to the second relay in the next time slot. It means that
the source creates a distinct column of the block Alamouti
scheme [7,8]. This idea allows the proposed D-STBC to obtain
the maximal diversity gain and decoupling detection of data
blocks for low complexity of receiver structure. The analysis
of the proposed design is performed for the scenario where
one hop (source to relay or relay to destination) is in LOS
condition, while the other hop (relay to destination or source to
destination) is in NLOS condition to evaluate many conditions.
That is, the relay locates near by the mobile station or the base
station, the receiver is in LOS condition with the transmitter.
Therefore, the channel of one hop in LOS condition can be
modeled as Rician fading and the other hop in NLOS condition
is Rayleigh fading.
Our work is different from published papers from two
aspects. First, two relays are considered, instead of one.
Second, the diversity gain is analyzed with the mixed Rayleigh
and Rician channel model, allowing us to study two typical
cases. The difficulty in dealing with the mixed channel model
is the appearance of moment generating function of Rician
fading in the analysis.
The rest of this paper is organized as follows: In Section II,
we describe the system model of the proposed D-STBC and
the proof of decoupling capability. Performance analyses are
presented in Section III. We present the numerical results in
Section IV and Section V concludes this paper.
Notation: Bold lower case letters represent vectors while
bold upper letters denote matrices; (.)T,(.)∗, and (.)Hdenote
transpose, complex conjugate, and Hermitian transpose oper-
ations, respectively; IMand 0Mdenote an identity matrix
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2009 proceedings.
978-1-4244-4148-8/09/$25.00 ©2009

1
2
⎡⎤
⎢⎥
⎣⎦
s
s
1
1
()
1
()
2
R
R
⎡⎤
⎢⎥
⎣⎦
r
r
()
1
()
2
D
D
⎡
⎤
⎢
⎥
⎣
⎦
r
r
2
2
()
1
()
2
R
R
⎡⎤
⎢⎥
⎣⎦
r
r
2
SR
h
1
SR
h
1
RD
h
2
RD
h
S
R1
R2
D
Fig. 1. Cooperative communication model.
and an all-zero matrix of size M×M;E[.]denotes the
expectation; .denotes the Euclidean norm of a vector;
FMstands for a fast Fourier transform (FFT) matrix of size
M×M;P(n)
Jis the J×Jpermutation matrix carrying the
reverse operation followed by a right cyclic shift of over n
positions of a given vector of length J;S→R
iand Ri→D
represent the links from the source to the i-th relay and from
the i-th relay to the destination, respectively.
II. SYSTEM MODEL
We consider a cooperative communication system with
two relays as shown in Fig. 1. The data transmis-
sion from the source to the destination is accomplished
with the two-hop protocol. The channel impulse responses
(CIR) for S→R
iand Ri→Dlinks are given
by hSRi=[hSRi(0), ..., hSRi(LSRi)]Tand hRiD=
[hRiD(0), ..., hRiD(LRiD)]T, respectively, where LSRiand
LRiDare the corresponding channel memory order. In this
scheme, the source transmits two data blocks continuously:
in the first time slot, Stransmits the signal to relay R1,
in the second time slot, the source reorders the transmitted
data blocks and transmits its processed signals to relay R2.
Both relays amplify and forward their received signals to the
destination D(see Fig. 1).
The data symbol stream is serial-to-parallel converted into
blocks of length B. In order to perform block-wise transmis-
sion for frequency selective channels, two consecutive symbol
blocks s1,s2, in which a zero sequence of length Lis added to
form a transmitted block of size M=B+L. This operation
is represented by multiplying the vector of data block with a
zero-padding matrix given by Tzp =[IB,0B×L]T. Since
each data block is transmitted to the eventual destination
through two-hop paths, the length of the zero sequence must
satisfy L≥max(LSR1+LR1D,L
SR2+LR2D). The purpose
of inserting zero sequence is to make the channel matrix
circulant. In the second time slot, the source multiplies each
of the transmitted signal vector with the permutation matrix
P(B)
M(or −P(B)
M, depending on the block index) to reorder the
signals. Furthermore, the second signal vector is conjugated
before being transmitted. The received signals at the relay R1
and R2are given by
r(R1)
i=HSR1Tzpsi+η
η
η(R1)
i,i=1,2,(1)
r(R2)
1=−HSR2P(B)
MTzps∗
2+η
η
η(R2)
1
r(R2)
2=HSR2P(B)
MTzps∗
1+η
η
η(R2)
2
,(2)
where si,i=1,2is the i-th data block, η
η
η(Rj)
iis the samples
of the white Gaussian noise process at the relay Rjwith each
entry having zero-mean and variance of N0/2per dimension,
and HSRjis the circulant matrix.
The relays amplify and forward the received signals to the
destination. The received signals at the destination are written
by
r(D)
1=HR1Dr(R1)
1+HR2Dr(R2)
1+η
η
η(D)
1,(3)
r(D)
2=HR1Dr(R1)
2+HR2Dr(R2)
2+η
η
η(D)
2,(4)
where η
η
η(D)
i,i =1,2, are the samples of the white Gaussian
noise process at the destination with each entry having zero-
mean and variance of N0/2, and HRjDis the circulant matrix.
We now proceed to prove the decoupling property of our
design at the destination. Regarding to equations (1) and (2),
we can rewrite (3) and (4) as
r(D)
1=HR1DHSR1Tzps1−HR2DHSR2P(B)
MTzps∗
2+´
η
η
η(D)
1,
(5)
r(D)
2=HR1DHSR1Tzps2+HR2DHSR2P(B)
MTzps∗
1+´
η
η
η(D)
2,
(6)
where ´
η
η
η(D)
1and ´
η
η
η(D)
2include the Gaussian noise of relays
and destination. The noise of the relay is also transmitted
to the relay, and the total noise variance is increased at
the destination. Thus, the normalization procedure should be
carried out as in [6]. After normalization, we have
r(D)
1=α1HR1DHSR1Tzps1−α2HR2DHSR2P(B)
MTzps∗
2+η
η
η1
,
(7)
r(D)
2=α1HR1DHSR1Tzps2+α2HR2DHSR2P(B)
MTzps∗
1+η
η
η2
,
(8)
where η
η
ηj,j =1,2is the complex Gaussian with zero mean
and variance of N0/2, and αiis defined by
αi=⎡
⎢
⎢
⎢
⎣
βj=iγiESRi
β1β2+β2γ1
LR1D

l=0
|hR1D(l)|2+β1γ2
LR2D

l=0
|hR2D(l)|2
⎤
⎥
⎥
⎥
⎦
1
2
,
(9)
where βi=1+ESRi/N0, and γi=ERiD/N0for i, j ∈
{1,2}.
Conjugating and multiplying both sides of (8) with the
permutation matrix P(B)
M,wehave
˜
r(D)
2=α1P(B)
MH∗
R1DH∗
SR1Tzps∗
2
+α2P(B)
MH∗
R2DH∗
SR2P(B)
MTzps1+P(B)
Mη
η
η∗
2.(10)
We notice the property that P(B)
MP(B)
M=IMand
P(B)
MH∗P(B)
M=HHfor a circulant matrix H. Thus, (10)
is equivalently rewritten as
˜
r(D)
2=α1HH
R1DHH
SR1˜s2+α2HH
R2DHH
SR2˜s1+˜η
˜η
˜η2,(11)
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2009 proceedings.
978-1-4244-4148-8/09/$25.00 ©2009

where ˜s2=P(B)
MTzps∗
2,˜s1=Tzps1, and ˜η
˜η
˜η2=P(B)
Mη
η
η∗
2.
Similarly, we can rewrite (7) as
r(D)
1=α1HR1DHSR1˜s1−α2HR2DHSR2˜s2+η
η
η1.(12)
Let us define r(D)=[(r(D)
1)T,(˜r(D)
2)T]T,s=
[(˜s1)T,(˜s2)T]T, and η
η
η=[(η
η
η1)T,(˜η
˜η
˜η2)T]T. Then, we have
the following equality
r(D)=α1HR1DHSR1−α2HR2DHSR2
α2HH
R2DHH
SR2α1HH
R1DHH
SR1s+η
η
η. (13)
The equivalent matrix Λis defined by
Λ=α1HR1DHSR1−α2HR2DHSR2
α2HH
R2DHH
SR2α1HH
R1DHH
SR1.(14)
Thus, (13) can be simply rewritten as
r(D)=Λs +η
η
η. (15)
In equation (15), the equivalent matrix Λis orthogonal in
the sense that the product ΛHΛbecomes a block-diagonal
matrix. That is
ΛHΛ=Ω0
M
0MΩ,(16)
where Ω=α2
1|HSR1|2|HR1D|2+α2
2|HSR2|2|HR2D|2.
Multiplying both sides of (16) with Ψ=(I2⊗Ω−1/2)ΛH
, we can decouple the received signals as
z=z1
z2=Ω1/2Tzps1
Ω1/2P(B)
MTzps∗
2+˙η
˙η
˙η1
˙η
˙η
˙η2,(17)
where [( ˙η
˙η
˙η1)T,(˙η
˙η
˙η2)T]T=Ψη
Ψη
Ψη.
We infer from equation (17) that the blocks s1and s2can be
demodulated separately by linear receiver processing. Further-
more, each can be detected by applying standard equalization
techniques such as minimum mean square error or maximum
likelihood sequence estimation equalizers.
III. PERFORMANCE ANALYSIS
In this paper, we derive the PEP expression of the proposed
D-STBC model over frequency selective fading channels,
where the links S→Rand R→Dexperience Rician fading
and Rayleigh fading, respectively. For the case S→Rand
R→Dare Rayleigh fading and Rician fading, the PEP is
quite similarly derived by interchanging some parameters.
Let us define the decoded codeword vector as ˆs and the
Euclidean distance between sand ˆs as d(s,ˆs). Based on the
mixed Rayleigh and Rician channel model given by (13), the
conditional PEP is given by
P(s→ˆs|hSR1,hSR2,hR1D,hR2D)=Q⎛
⎝d2(s,ˆs)
2N0⎞
⎠,
(18)
where Q(.)is the Qfunction. By applying Chernoff bound to
Qfunction, this PEP is upper bound as
P(s→ˆs|hSR1,hSR2,hR1D,hR2D)≤exp −d2(s,ˆs)
4N0.
(19)
The Euclidean distance in equation (19) is calculated as
d2(s,ˆs)=α2
1||HR1DHSR1Tzp(s1−ˆs1)||2
+α2
2||HR2DHSR2P(B)
MTzp(s2−ˆs2)||2.(20)
To simplify analysis, we can approximate (20) as
d2(s,ˆs)≈α2
1
M||HR1D||2||HSR1e1||2+α2
2
M||HR2D||2
×||HSR2e2||2
≈α2
1
M||HSR1||2||HR1De1||2+α2
2
M||HR2D||2||HSR2e2||2
≈α2
1
M||HR1D||2||HSR1e1||2+α2
2
M||HSR2||2||HR2De2||2
≈α2
1
M||HSR1||2||HR1De1||2+α2
2
M||HSR2||2||HR2De2||2,
(21)
where ei=Tzp(si−ˆsi),i =1,2. We note that ||Hk||2=
MLk
lk=0 |hk(lk)|2and ||Hkei||2=Lk
lk=0 λ
λ
λi(lk)|ν
ν
νi(lk)|2,
where k=SR1,SR
2,R
1D, R2D,i=1,2.λ
λ
λi(lk)denotes
the eigenvalue of codeword difference matrix and ν
ν
νis zero-
mean complex Gaussian vectors with unit variance. Thus, we
can rewrite the equation (21) by dividing into two parts as
follows
d2
1=
LRD

lRD=0
|hRD(lRD )|2
LSR

lSR=0
λ
λ
λ(lSR)|ν
ν
ν(lSR)|2,(22)
d2
2=
LSR

lSR=0
|hSR(lSR)|2
LRD

lRD=0
λ
λ
λ(lRD)|ν
ν
ν(lRD)|2.(23)
In the following, we will derive the PEP for three cases
based on the relation of LRD and LSR because of the different
characteristics of fading S→Rand R→D.
Case 1:LRD >L
SR: We consider (22) and define
Z1=d2
1=X1Y1where X1=LRD
lRD=0 |hRD (lRD )|2
and Y1=LSR
lSR=0 λ
λ
λ(lSR)|ν
ν
ν(lSR)|2. The PEP correspond-
ing to d2
1can be calculated as EZ1[exp(−α2Z1/4N0)] =
ΦZ1(s)|s=−α2/4N0, where Φ(.)denotes the moment gener-
ating function. ΦZ1(s)can be evaluated as
ΦZ1(s)=
∞

0
fX1(x1)ΦY1(sx1)dx1,(24)
where f(.)is the probability density function. Since the fading
channels S→Rand R→Dare frequency-selective Rician
and Rayleigh fading respectively,
fX1(x1)=(LRD +1)
LRD+1
Γ(LRD +1) xLRD
1e−(LRD+1)x1,(25)
ΦY1(s)=
LSR

lSR=0 1+n2
1+n2−sλ
λ
λ(lSR)en2sλ
λ
λ(lSR)
1+n2−sλ
λ
λ(lSR).(26)
Substituting (25) and (26) to (24) and assuming high SNR,
i.e. α2/4N01and (1 + n2)/n2≈1, (24) can be evaluated
as
ΦZ1(s)|s=−α2
4N0
=(LRD+1)(1+n2)
en2LSR+1
×Γ(LRD−LSR )
Γ(LRD+1) α2
4N0−(LSR+1) LSR

lSR=0
1
λ
λ
λ(lSR).
(27)
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2009 proceedings.
978-1-4244-4148-8/09/$25.00 ©2009

Case 2:LSR >L
RD : We consider (23) and define
similarly Z2=d2
2=X2Y2where X2=LSR
lSR=0 |hSR(lSR)|2
and Y2=LRD
lRD=0 λ
λ
λ(lRD)|ν
ν
ν(lRD)|2. The PEP correspond-
ing to d2
2can be calculated as EZ2[exp(−α2Z2/4N0)] =
ΦZ2(s)|s=−α2/4N0,where
ΦZ2(s)=
∞

0
fX2(x2)Φ
Y2(sx2)dx2,(28)
where
fX2(x2)=(LSR+1)1−
LSR
2
nLSR
x
LSR
2
2ILSR [2(LSR+1) 3
2nx
1
2
2]
e(LSR+1)2n2−(LSR+1)x2,
(29)
and
ΦY2(s)=
LRD

lRD=0
1
1−sλ
λ
λ(lRD).(30)
The function Iα(β)is defined as Iα(β)Δ
=
(β/2)α∞
k=0 (β2/4)k[k!Γ(α+k+ 1)]−1,α ∈R.
Substituting (29) and (30) to (28) under assumption of
high SNR, we get
ΦZ2(s)|s=−α2
4N0
=α2
4N0−(LRD+1) (LSR +1)1−
LSR
2
nLSR e(LSR+1)2n2
×
LRD

lRD=0
1
λ
λ
λ(lRD)
∞

0
x
LSR
2
−LRD−1
2ILSR [2(LSR+1) 3
2nx
1
2
2]
e(LSR+1)x2dx2
(31)
After some mathematical manipulations, we obtain
ΦZ2(s)|s=−α2
4N0
=(LSR+1)LRD +1 Γ(LSR−LRD)
e(LSR+1)2n2
×1˜
F1(LSR −LRD;LSR +1;(LSR +1)
2n2)
×α2
4N0−(LRD+1) LRD

lRD=0
1
λ
λ
λ(lRD).
(32)
where 1˜
F1(a;b;z)is the hypergeometric 1F1
regularized function defined as 1˜
F1(a;b;z)Δ
=
∞
k=0 [(a)k/(b)k](zk/k!)/Γ(b).
Case 3:LSR =LRD: We consider (22), ΦZ1(s)can be
calculated as following:
ΦZ1(s)|s=−α2
4N0
=(LSR+1)LSR+1 (1+n2)LSR+1
Γ(LSR+1)e(LSR+1)n2
×α2
4N0−(LSR+1) LSR

lSR=0
1
λ
λ
λ(lSR)
∞

0
tLSR
1e−(LSR+1)(1+n2)t1
LSR

lSR=0 t1+1
α2
4N0λ
λ
λ(lSR)dt1.
(33)
For easy calculation, we define BΔ
=
LSR
lSR=0 (λ
λ
λ(lSR))−1∞
0
tLSR
1e−(LSR+1)(1+n2)t1
LSR
lSR=0 (t1+[(α2/4N0)λ
λ
λ(lSR)]−1)dt1
. By using some mathematical expansions, we can represent
Bas
B=
LSR

lSR=0 α2
4N0LSR plSR
λ
λ
λ(lSR)
∞

0
tLSR
1e−(LSR+1)(1+n2)t1
t1+1
α2
4N0λ
λ
λ(lSR)
dt1,
(34)
where plSR
Δ
=LSR
l=0,l=lSR λ
λ
λ(lSR)/[λ
λ
λ(lSR)−λ
λ
λ(l)]. Calculat-
ing the integral in (34) and substituting Bto (33), we get
ΦZ1(s)|s=−α2
4N0
=(LSR+1)(1+n2)
en2LSR+1 α2
4N0−(LSR+1)
×
LSR

lSR=0
⎡
⎣plSR
[λ
λ
λ(lSR)]
LSR+1 e
(LSR+1)(n2+1)
α2
4N0λ
λ
λ(lSR)Γ
−LSR,(LSR+1)(n2+1)
α2
4N0λ
λ
λ(lSR)⎤
⎦.
(35)
Through three above cases with equations (27), (32) and
(35), we can conclude that the diversity gain of our proposed
D-STBC is min(LSR1,L
R1D) + min(LSR2,L
R2D)+2.The
value of nin Rician fading channels causes the reduction
of the PEP and does not have any effects on the diversity
gain. One example of PEP calculation is given for the case
LR1D>L
SR1and LR2D>L
SR2. With the assump-
tion that ESR2/N0=ER1D/N0=ER2D/N 01and
ESR1/N0>E
SR2/N0, the normalization factor in (9) can
be approximated as α2
1≈α2
2≈ESR2. The PEP is calculated
as
PEP =(1+n2)LSR1+LSR2+2e−(LSR1+LSR2+2)n2
×(LR1D+1)
LSR1+1(LR2D+1)
LSR2+1
×Γ(LR1D−LSR1)
Γ(LR1D+1)
Γ(LR2D−LSR2)
Γ(LR2D+1) ESR2
4N0−(LSR1+LSR2+2)
×
LSR1

lSR1=0
1
λ
λ
λ(lSR1)
LSR2

lSR2=0
1
λ
λ
λ(lSR2).
(36)
IV. NUMERICAL RESULTS
We consider block transmission with each data block con-
sisting of 64 QPSK symbols and MMSE frequency domain
equalizer is used in our simulations for the D-STBC model. We
assume that the receiver has perfect channel state information.
The fading S→Ris characterized by a Rician distribution,
while the fading R→Dis characterized by a Rayleigh
distribution. The key parameter of the Rician distribution or
Nakagami-n distribution is the K-factor (K=n2), defined
as the ratio of the ”fixed” component power and the ”scatter”
component power.
The performance of D-STBC is shown in Fig.2 with differ-
ent values of K-factor and the assumption of channel memory
order of LSR1=4,L
SR2=6,L
R1D=4,L
R2D=6.We
assume that the value of ESR1/N0is fixed at 25dB, and
ER1D=ER2D= 10dB, and plot the BER curves as a
function of ESR2/N0. We remark that the K-factor of Rician
fading increases, the better performance is achieved. However
the diversity gain is maintained, since the term Kjust only
affects the value of PEP and it is independent of α2/4N0as
proved in the above performance analysis. When K=0,the
performance is identical with the case of Rayleigh fading.
Fig.3 shows the BER performances of two cases K=0
and K=25for various combinations of channel memory
order. For each K-factor, with the same value of LSR1and
LSR2, the better performance is achieved as the number of
paths from the relays to destination increases, and the best
performance is obtained when such channels become non-
fading, i.e. AWGN channel. Although, there are differences
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2009 proceedings.
978-1-4244-4148-8/09/$25.00 ©2009

0 2 4 6 8 1012141618202224
10
-8
10
-7
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
BER
E
SR2
/ N
0
[dB ]
K = 0
K = 1
K = 10
K = 25
K = 100
Fig. 2. Performance comparison for different values of K-factor over Rician
fading channels.
02468101214161820
10
-8
10
-7
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
BER
E
SR2
/ N
0
[dB ]
L
SR1
= L
SR2
= L
R1D
= L
R2D
= 1
L
SR1
= 1, L
SR2
= 2, L
R1D
= 1, L
R2D
= 2
L
SR1
= 1, L
SR2
= L
R1D
= L
R2D
= 2
L
SR1
= 2, L
SR2
= 4, L
R1D
= 2, L
R2D
= 4
L
SR1
= 4, L
SR2
= 6, L
R1D
= 4, L
R2D
= 6
L
SR1
= L
SR2
= L
R1D
= 4, non-fading R
2
->D
L
SR1
= L
SR2
= 4, non-fading R
1
->D , non-fading R
2
->D
K = 0
K = 25
Fig. 3. Performance of D-STBC with different values of channel memory
orders and K-factor over Rician fading channels.
on BER performances, the slopes of BER curves at high
ESR2/N0are identical, provided that LSR1=LSR2.Thisis
because the achievable diversity gain of our proposed DSTBC
is min(LSR1,L
R1D) + min(LSR2,L
R2D)+2.
V. C ONCLUSION
In this paper, we propose a D-STBC scheme for two-relay
system over frequency selective fading channels that achieve
both maximal diversity gain and low decoding complexity with
decoupling property. The performance analysis of the proposed
D-STBC is derived for the fading channel model in which
two links S→Rand R→D areassumedtobeRicianand
Rayleigh fading, respectively.
REFERENCES
[1] V. Tarokh, H. J. Jafarkhani, and A. R. Calderbank, ”Space-time block
codes from orthogonal designs,” IEEE Trans. Inf. Theory, vol. 45, no. 5,
pp. 1456-1467, Jul. 1999.
[2] A. Sendonaris, E. Erkip, and B. Aazhang, ”User cooperation diversity-
Part I: System description,” IEEE Trans. Commun., vol. 51, no. 11, pp.
1927-1938, Nov. 2003.
[3] –, ”User cooperation diversity-Part II: Implementation aspects and perfor-
mance analysis,” IEEE Trans. Commun., vol. 51, no. 11, pp. 1938-1948,
Nov. 2003.
[4] J. N. Laneman and G. W.Wornell, ”Distributed space-time-coded pro-
tocols for exploiting cooperative diversity in wireless networks,” IEEE
Trans. Inf. Theory, vol. 49, no. 10, pp. 2415-2425, Oct. 2003.
[5] J. N. Laneman, D. N. C. Tse, and G. W. Wornell, ”Cooperative diversity in
wireless networks: Efficient protocols and outage behavior,” IEEE Trans.
Inf. Theory, vol. 50, no. 10, pp. 3062-3080, Dec. 2004.
[6] H. Mheidat, M.Uysal, and N. Al-Dhahir, ”Equalization Techniques for
Distributed Space-Time Block Codes With Amplify-and-Forward Relay-
ing,” IEEE Trans. Signal Process., vol. 55, no. 5, pp. 1839-1852, May
2007.
[7] S. Zhou and G. B. Giannakis, ”Space-time coding with maximum
diversity gains over frequency-selective fading channels,” IEEE Signal
Processing Lett., vol. 8, no. 10, pp. 269-272, Oct. 2001.
[8] N. Al-Dhahir, ”Single carrier frequency domain equalization for space
time block coded transmissions over frequency selective fading channels,”
IEEE Commun. Lett., vol. 5, pp. 304, Jul. 2001.
[9] J. G. Proakis, ”Digital Communications,” 4th Ed. New York: McGraw-
Hill, Inc., 2001.
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2009 proceedings.
978-1-4244-4148-8/09/$25.00 ©2009