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An Interleaver-based Asynchronous Cooperative
Diversity Scheme for Wireless Relay Networks
Zhaoxi Fang, Liangbin Li, Zongxin Wang
Department of Communications Science and Engineering
Fudan University
Shanghai, P.R.China
Email: fangzhaoxi@hotmail.com, rainnysun@gmail.com, zxwang@fudan.ac.cn
Abstract—Distributed space time coding can a chieve full spatial
diversity in wireless relay networks. However, it requires
accurate symbol-level synchronization and priori coordination
between cooperative relay terminals, which is difficult to
implement in distributed networks. In this paper, we propose a
novel scheme based on interleaving to achieve cooperative
diversity in both synchronous and asynchronous networks with
little protocol overhead. A low compl exity iterative detection
algorithm is also proposed to combine signals from different
relays at the receiver. The simulation results demonstrate the
comparable performance to space-time codes based cooperative
schemes which require perfect synchronization and
coordi nat ion.
I. INTRODUCTION
It is generally acknowledged that MIMO technology is an
important means to improve the performance in wireless
systems through space time coding, and/or to increase data rate
through spatial multiplexing. However, in a practical scenario,
due to the size, cost or hardware complexity limitations,
mobile terminals may not be able to support multiple transmit
antennas. Recently, cooperative communication [1-4] is
proposed to improve transmission reliability in fading channels
by exploiting the broadcasting features of wireless channels,
where mobile terminals share their antennas and resources to
create a virtual array to achieve spatial diversity.
In [2], the authors developed and analyzed several
cooperative diversity protocols, namely, amplify-and-forward
(AF), fixed decode-and-forward (FDF) and selection decode-
and-forward (SDF). It was shown that except fixed decode-
and-forward protocol, all the others can achieve full transmit
diversity. A bandwidth efficient cooperative protocol was
proposed in [3] by directly using the existing orthogonal space-
time block codes (OSTBC) [5]. In order to keep the
orthogonality of the space time codes, perfect synchronization
of various signals from different cooperative terminals (or
relays) is required at the receiver. However, unlike
conventional point-to-point MIMO systems where multiple
transmit antennas are co-located at the same place, the
terminals in a wireless relay network are geographically
dispersed. As a result, the received signals at the destination
terminal are asynchronous in nature. In such asynchronous
networks, the orthogonality of space time codes is hard to
maintain that a diversity loss is inevitable, thus giving birth to
some recent works to explore cooperative diversity in
asynchronous networks [6-7].
All of the previous space-time cooperative diversity
protocols require a central control unit or prior coordination
between the terminals. In a large-scale wireless network, the
number of cooperative terminals is not fixed and is presumably
unknown, making it essential for all the terminals, apart from
the destination, to have the instantaneous knowledge of the
other terminals in cooperation in order to select the
corresponding space time code matrix. This causes a large
protocol overh ead.
In [8], a novel multiple access scheme named as interleave-
division multiple-access (IDMA) was proposed. In IDMA,
each user i s assigned a unique interleaver t o enabl e low
complexity multiuser detection at the receiver. Inspired by
IDMA, we propose a simple uncoordinated cooperation
scheme based on interleaving, where each cooperating
terminal simply interleaves the detected bits using a pre-
allocated interleaver. Compared with the protocols pr oposed in
[3, 4, 6, 7], the proposed scheme shares several advantages:
1. The cooperatin g terminals are not required to know who
their partners are.
2. This protocol supports arbitrary number of cooperative
terminals, whereas full rate full diversity orthogonal space
time codes does not exist in most cases [5].
3. The spatial diversity can be achieved through a low
complexity symbol-by-symbol iterative detection
algorithm at the receiver even if the received signal is
asynchronous.
The remainder of this paper is organized as follows Section
II describes the system and channel model. Section III presents
the iterative multi-relay detection algorithm. Some numeric
results are presented in Section IV. Finally, some concluding
remarks are given in Section V.
II. SYSTEM MODEL
Considering a wireless communication system shown in
Fig. 1 with M+2 terminals, wh ere S is the source terminal, D is
the destination terminal, and all the other M terminals Rm,
m=1,2,…,M, serve as the potential relays. Similar to [2], a time
division scheme is adopted. There are two phases during the
cooperative communication: broadcasting phase and
cooperative phase, each phase occupying one slot in
transmission. In Phase one (broadcasting phase), terminal S
broadcasts its information bits to the destination terminal D as
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2008 proceedings.
978-1-4244-2075-9/08/$25.00 ©2008 IEEE
well as M other potential relays Rm,m=1,2,…,M. In the second
phase (cooperative phase), relay Rm decides whether to
forward the detected signal according to the adopted
cooperative protocols, while terminal S continues its
transmission and terminal D keeps receiving signal. In this
paper, we will consider two interleaver-based cooperative
communication protocols: fixed decode-interleave-and-
forward (FDIF) protocol and selection decode-interleave-and-
forward (SDIF) protocol. Since not all of the M relay terminals
are active in cooperative phase, it is convenient to denote Ra as
the set of the terminals being active in cooperative phase and
Ma as the size of the set, Ma=|Ra|.
In the broadcasting phase, terminal S transmits a modulated
symbol sequence with length N,xs(n), n=0,1,...,N-1, containing
information bits b(n), n=0,1,,…,Nb-1, and several cyclic
redundancy check (CRC) bits, which helps to detect the signals
received at the relays in SDIF protocol. Assuming the channels
are flat fading and remain constant in the consecutive two
slots, the received signal at terminal D in the broadcasting
phase can be expressed as
,1 ,1
() () ()
dsdsd
rn hxn n
η
=+ (1)
and the signal at relay Rm , m=1,2,…,M, can be written as
() () ()
msmsm
rn hxn n
η
= + (2)
where hij,i,j=s,d,1,2,…,M, are the channel coefficients
between terminal iand j, which are Rayleigh distributed with
mean-square Gij=E(|hij|2); ,1()
dn
η
and ( )
mn
η
are the AWGN at
destination D during phase one and at relay terminal m,
respectively, both have zero mean and variance 2
σ
per
dimension.
During the cooperative phase, terminal Rm first
demodulates and decodes the received signal rm to get an
estimate of the transmitted information bits: ˆ()
m
bn ,
n=0,1,…,Nb-1. If FDIF protocol is used, the decoded bit stream
is first interleaved by a random interleaver m
π
, then re-
modulated to produce symbol sequence xm(n), n=0,1,...,N-1.
The relay terminal Rm will forward xm to the destination D
without any CRC checking, i.e., the relay Rm is always active
during phase two if FDIF protocol is adopted, i.e., Ra ={ Rm |
m=1,2,…,M}, Ma=M.
On the other hand, if SDIF protocol is adopted, The relay
Rm first performs CRC check to see if the whole frame has
been received correctly. If so, the relay Rm then forwards the
interleaved and re-modulated signal xm to the destination D as
in the FDIF protocol. Otherwise, Rm will keep idle, i.e. doesn’t
participate in the second phase. In this case,
ˆ
{|() (),}
amm
RRbnbnn==∀. Meanwhile, terminal S transmits
xs again regardless of which protocol is adopted by the relay
terminals. The signal received at terminal D in the cooperative
phase can be expressed as
,2 ,2
() ( ) ( ) ()
ma
d mdm m sds s d
RR
rn hxn hxn n
ττη
∈
=−+−+
¦ (3)
where ,2 ()
dn
η
is the AWGN at destination D during phase two
with the same statistical properties as ,1 ()
dn
η
, and S
τ
,m
τ
is
the asynchronous delay for terminal S and terminal Rm,
respectively.
III. LOW COMPLEXITY ITERATIVE DETECTION
Relying on (1), (3), a low complexity symbol-by-symbol
iterative detection method can be applied at receiver to achieve
cooperative diversity. With out loss of generality, we assume
QPSK modulation and each modulated symbol can be
expressed as ( ) { 1 }
x
nj∈±± ,1j=−. Note that destination
terminal D processes signal received at two distinctive slots.
Terminal D first extracts initial prior information of xs(n) from
signal received at the first slot, then employs symbol-by-
symbol iterative detection based on the signal received at the
second slot, the detail algorithm is listed below:
Initialization:
The initial log likelihood ratio (LLR) information of xscan
be derived according to the received signal rd,1 during the
broadcasting phase:
Re * 2
1,1
Im * 2
1,1
(())2Re[ ()] ,
(())2Im[ ()] , .
ssdd
ssdd
L
xn hrn n
L
xn hrn n
σ
σ
=∀
=∀
(4)
L1(xs(n)) serves as the initial prior information for iterative
detection at the cooperative phase, i.e,
1
1
(()) (())
as s
L
xn Lxn=, )))((())(( 1
1nxLnxL msma
π
=, nm,∀
where the superscript 1 denotes the first iteration, the subscript
1 denotes the first slot, and )(⋅
m
π
denotes the interleaving
operation.
The i-th iteration:
S D
R
1
R
M
…
Figure 1. A wireless relay network with M potential relays.
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2008 proceedings.
Firstly, calculate the expectation and variance of xm(n)
from the prior information ))(( nxL m
i
aderived at the previous
iteration:
Re Re
Im Im
Re Re 2
Im Im 2
E( ( )) tanh( ( ( )) / 2), ,
E( ( )) tanh( ( ( )) / 2), ,
Var( ( )) 1 | E( ( )) | , ,
Var( ( )) 1 | E( ( )) | , ,
i
mam
i
mam
mm
mm
x
nLxnmn
x
nLxnmn
x
nxnmn
x
nxnmn
=∀
=∀
=− ∀
=− ∀
(5)
where E(x) and Var(x) denotes the mean and variance of the
variable x. The derivation of the mean and variance of xs(n) is
similar.
While detecting symbol xk(n), k=1,2,…,M, forwarded by
the kth relay Rk , (3) can be rewritten as
,2() ()()
dkkdkk
rn hxn n
τξ
+= + (6)
where ( )
kn
ξ
is the interference to ( )
k
x
n, Due to interleaving,
()
kn
ξ
is uncorrelated with ( )
k
x
n and can be assumed
Gaussian distributed for large M according to the central limit
theorem. ( )
kn
ξ
can be written as
,2
,
,2
()() ()
()
()().
mamk
kd kkdk
md m k m
RRRR
s
ds k s d k
nrn hxn
hxn
hn n
ξ
τ
ττ
ττ η τ
∈≠
=+−
=+−
++−++
¦
x
(7)
The phase offset due to hkd in (6) can be cancelled out by
multiplying both sides of (6) with *
kd
h, thus the detection of
the real part and imaginary part of ()
k
x
n can be treated
separately as [8]
2*
,
Re
2*
2*
,
Im
2*
2 (Re[ ( )]-E[Re[ ( )]])
(()) V[Re[ ()]]
2 (Im[ ( )]-E[Im[ ( )]])
(()) V [Im[ ( )]]
kd k d kd k
i
k
kd k
kd k d kd k
i
k
kd k
hynhn
Lx n ar h n
hynhn
Lx n ar h n
ξ
ξ
ξ
ξ
=
=
(8)
where *
,d,2
() ( )
kd kd k
ynhrnIJ=+.
After de-interleaving, the LLRs derived from the signal
forwarded by all the active relays and by the source terminal S
during phase two are combined with the LLR derived from the
signal transmitted at the first phase as
1
221
(()) ( ( ())) (()) (())
ma
ii i
smmss
RR
L
xn Lx n Lxn Lxn
π
−
∈
=++
¦ (9)
Hence, the prior information for next iteration can be
updated as
1
2
1
2
( ( )) ( ( )) ( ( ))
(()) ((())) (()) ,.
iii
as s s
ii i
am sm m
LnLnLn n
L
nL n L n mn
π
+
+
=− ∀
=−∀
xxx
xx x (10)
Then go back to equation (5) for next iteration. A hard
decision is made based on L(xs(n)) in the last iteration. This
symbol by symbol iterative detection shares the advantage of
low complexity [8], the cost per information symbol per
iteration involved in (5) ~ (10) is proportional to the total
number of active terminals, Ma.
IV. SIMULATION RESULTS
During simulation, the channels are assumed to be
Rayleigh flat fading and to maintain unchanged in the
consecutive two slots. The bit SNR in the simulation results is
defined as
00
bssd
c
EEG
NKN
β
= (11)
where Kc,Es and ȕ are denoted as the number of information
bits represented by each modulation symbol, the energy of
each modulation symbol and transmission rate, respectively.
Specifically, ȕ=1 for direct transmission and ȕ=0.5 for
interleaver-based cooperative transmission due to the fact that
one data frame occupies two consecutive slots. Furthermore,
we assume that the maximum asynchronous delay is LTs,
where Tsis symbol duration, and the asynchronous delay for
each terminal is uniformly generated from [0, LTs]. A random
interleaver is employed in th e protocol, with each frame
containing 2048 QPSK symbols. Th e relative channel gain is
defined as Bsm=Gsm/Gsd ˈBmd=Gmd/Gsd, m=1,2,…,M. In this
simulation, we assume that relays Rm,m=1,2,…,M, are cl ose to
terminal S, Bmd = 1, m=1,2,…,M, and that the channel gains
between the relays and the terminal S are equivalent, Bsm=Bˈ
m= 1,2,…,M.
We first consider the synchronous case, i.e., L=0. Fig. 2
illustrates the frame error rate (FER) performance when
different cooperative diversity protocols are employed with
one relay in the system. In Fig.2, B=inf. indicates that the
channels between source terminal S and relays are error-free;
hen ce no err ors occur during pha se on e transmission. For
comparison, Fig. 2 also includes the performance of direct
transmission (labeled as ‘Direct Tran s.’ in the figure) and that
of the OSTBC based cooperative transmission[3] employing
the Alamouti space time code[9] under B=inf. Th e iteration
number is 2 for the proposed cooperative diversity scheme. It
is shown in the figure that interleaver-based cooperative
diversity protocols provide significant performance
improvement to the direct transmission. Specifically, the
transmission scheme employing SDIF protocol achieves the
same diversity order as that using Alamouti space time code,
while the performance of FDIF protocol is worse than that of
SDIF. This is due to the fact that the relay will always forward
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2008 proceedings.
the signals even if it fails to decode the received frame
correctly in FDIF. It can be seen from Fig.2 that the diversity
order of the fixed relaying protocol FDIF is 1 as the direct
transmission scheme.
The FER performance under the different number of relay
terminals with synchronous receiving is shown in Fig. 3. The
proposed Selection Decode-Interleave-and-Forward protocol is
employed and the iteration number is six for M=3 and 8.
Obviously, the achievable diversity order increments with the
number of relays.
Fig.4 demonstrates a comparison of the performances
related to synchronous receiving and asynchronous receiving,
both employin g SDIF protocol and the relative chann el gain is
set to be B=10. It is shown that the FER performance of the
asynchronous case is the same as that of synchronous
receiving, indicating the effectiveness of the proposed
interleaver-based cooperative diversity protocol.
V. CONCLUSION
A novel interleaver-based cooperative diversity protocol is
introduced in this literature. Furthermore, a low complexity
iterative symbol-by-symbol detection algorithm is proposed to
combine signals from all active relays. In contrast to
conventional space-time coded cooperative diversity protocol,
the proposed scheme is more attractive for distributed
implementation since the cooperating relays do not have to
know which other relays ar e active, and full cooperative
diversity is achievable in both synchronous and asynchronous
networks.
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Figure 3. FER performance under different number of relays with
synchr onous receiving. SDIF protocol is employed.
Figure 2. Comparison am ong the sy stems employi ng vari ous prot ocol s
with 1 r elay and synchron ous r eceiving.
Figure 4. Comparison with synchronous and asynchronous receiving
with multipl e rela ys. SDIF prot ocol i s employed.
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2008 proceedings.
