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A single source-destination pair communicating via a layer of parallel relay nodes under quasi-static slow fading environment is investigated. The time delays from the source to the destination via different relays are assumed to be different. For such an asynchronous environment, a new transmission scheme is constructed so as to achieve better diversity-multiplexing tradeoff (DMT). More specifically, both the source and the destination adopts orthogonal frequency division multiplexing technique
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TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES
Trans. Emerging Tel. Tech.
2013; 24:232–243
Published online 12 February 2013 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/ett.2618
RESEARCH ARTICLE
Achieving high diversity and multiplexing gains in the
asynchronous parallel relay network
Mingjun Dai
1
*
†
and Chi Wan Sung
2
1
College of Information Engineering (also with Shenzhen Key Lab of Advanced Communication and Information Processing),
Shenzhen University, Shenzhen, China
2
Dept. of Electronic Engineering, City University of Hong Kong, Hong Kong, China
ABSTRACT
A single source-destination pair communicating via a layer of parallel relay nodes under quasi-static slow fading environ-
ment is investigated. The time delays from the source to the destination via different relays are assumed to be different.
For such an asynchronous environment, a new transmission scheme is constructed so as to achieve better diversity-
multiplexing tradeoff (DMT). More specifically, both the source and the destination adopts orthogonal frequency division
multiplexing technique to solve the asynchronous problem; the relays cooperatively apply the distributed generalised
complex orthogonal design, a form of orthogonal space–time coding, for high-rate transmission. Each relay is assumed
to use the adaptive amplify-and-forward relaying strategy. To optimise its outage performance, a distributed on-off power
control rule applied to the relays is analytically derived and is proved to yield full spatial diversity order. Compared with
an existing protocol, our proposed scheme is shown to achieve the same DMT when there are four relay nodes and better
DMT when there are more. Besides, the DMT gap between our scheme and the existing one increases with the number of
relay nodes. Copyright © 2013 John Wiley & Sons, Ltd.
*Correspondence
M. Dai, College of Information Engineering (also with Shenzhen Key Lab of Advanced Communication and Information Processing),
Shenzhen University, Shenzhen, China.
E-mail: mingjundai@hotmail.com
The work was partly performed when he was with City University of Hong Kong.
Received 26 September 2012; Revised 9 December 2012; Accepted 3 January 2013
1. INTRODUCTION
Space–time block codes (STBC), in particular, orthogonal
STBC (OSTBC), is an effective technique to harvest
spatial diversity for point-to-point multi-input multi-output
system [1]. It can also be applied to relay networks with
each relay acts as a virtual antenna. Cooperative spatial
diversity can then be achieved, assuming the signals trans-
mitted from the relays can be superimposed at the desti-
nation in a synchronised way [2–4]. In practice, however,
the time delays from the source to the destination via
different relays are different, as the relays are not collo-
cated. Therefore, it is important to consider asynchronous
relay nodes.
Full asynchronous cooperative diversity for a parallel
relay network with single source-destination pair has been
studied in [5–10]. The work in [5] requires feedback
from destination to relays. When a feedback channel
is not available, the use of space–time trellis coding
may be used [6], but its detection complexity is high.
Some other transmission schemes have also been proposed
in the literature, namely, time-reversal distributed OSTBC
(TR-DOSTBC) with decode-and-forward (DF) relay nodes
[7], orthogonal frequency division multiplexing (OFDM)-
DOSTBC with fixed gain amplify-and-forward relay nodes
[8, 9] and shift-orthogonal STBC with either DF or FGAF
relay nodes [10]. In [7, 8], the proposed methods are
restricted to the case where there are only two relay nodes.
Although the schemes in [9, 10] are for more than two
relay nodes and are able to achieve full diversity, their
multiplexing gain is not high when the number of relay
nodes is large. In [11], the condition on the structure
of STBC to achieve full asynchronous diversity is iden-
tified. How to construct STBC that satisfies the condi-
tion, however, is not given. Besides, only the four group
decodable STBC is given, whose decoding complexity is
much higher than that of symbol-wise OSTBC. In [12],
the diversity-multiplexing tradeoff (DMT) in asynchronous
setting is analysed. Again, there is no explicit construc-
tion provided. Besides, the OFDM module is placed at
232
Copyright © 2013 John Wiley & Sons, Ltd.
M. Dai and C. W. Sung
the relay nodes that is quite energy-consuming for low-
cost relay nodes. Regarding the forwarding strategies of the
relays, it is well known that DF suffers from high encoding-
decoding complexity [13], which increases energy con-
sumption. FGAF does not require decoding and is thus
simpler to implement. However, as the amplifying gain of
each relay is fixed, it is possible that the transmit amplifiers
of the relay nodes are driven into saturation. In that case,
full diversity can no longer be guaranteed.
In this paper, we extend our work in [14], which can
only be applied to synchronous relay networks. We design
a new transmission scheme, which can achieve a good
DMT for asynchronous networks with large number of
relay nodes. In our design, we use the OFDM technology
to solve the asynchronisation problem. A high symbol-rate
DOSTBC matrix named distributed generalised complex
orthogonal design (DGCOD) matrix is adopted to provide
high multiplexing gain. We consider the use of adap-
tive amplify-and-forward (AAF), which is an AF scheme
whose amplifying factor is not fixed. It avoids the amplifier
saturation problem of FGAF. However, for AAF, it is
important to set the amplifying factor properly, for other-
wise, full diversity may be hampered [15]. We solve this
problem by deriving a power control law called on-off
power control (OOPC).
Our proposed scheme is attractive from a practical stand-
point, as the operations at each node is simple: The source
node performs fast fourier transform with cyclic prefix
(CP) addition. Each relay node performs either time rever-
sion or complex conjugate operation with simple OOPC.
Note that communication among relay nodes is not needed,
and the on-off decision is based only on local informa-
tion. The destination node performs fast fourier transform,
CP removal and orthogonalised fast symbol-wise detection
[16, 17]. Compared with the scheme in [9], our proposed
scheme achieves the same DMT when there are four relay
nodes and better DMT when there are more. Besides, the
gap between our scheme and that in [9] increases with the
number of relay nodes.
The rest of this paper is organised as follows: The
system model is presented in Section 2. Basic knowledge
on generalised orthogonal designs is given in Section 3.
The proposed scheme with corresponding power control
rule are illustrated in Sections 4 and 5, respectively. The
DMT comparison between our scheme with an existing
scheme is shown in Section 6. Finally, conclusion is drawn
in Section 7.
2. SYSTEM MODEL
We consider a single source communicating to a single
destination in a network over a layer of N parallel relay
nodes. There is no direct link from the source to the des-
tination. As shown in Figure 1, source A has a single
transmit antenna, and destination B has a single receive
antenna. The N relays are respectively denoted as relay
i 2f1; 2; ;Ng , N , each having a single antenna
Figure 1. The parallel relay network model.
that can transmit and receive in half-duplex manner. We
consider the slow-fading scenario where the link gains
are random but remain constant for a transmission block
of 2P transmission symbols, where the value of P is
determined in next section. Let h
Ai
and h
iB
be the link
gains from source A to relay i and from relay i to des-
tination B, respectively, where i 2 N .Defineh
B
as
the column vector .h
1B
; ;h
NB
/,andh as the column
vector .h
A1
; ;h
AN
;h
1B
; ;h
NB
/. We assume that
channel state information of a communication link is
available at its receiver but not at its transmitter. More
specifically, relay i knows h
Ai
, and the destination node
knows h
B
. Denote
i
as the overall relative delay from
source A to destination B via relay i, which is known
by destination B, where ‘relative’ means relative to relay
node 1,thatis,
1
D 0 (We assume relay 1 has the shortest
delay.) and
i
> 0 for i 2 N nf1g. For simplicity,
i
’s are
assumed to be integers. We leave it as a future direction for
i
’s being real numbers.
Let
N
X
i
Œm denote the transmitted codeword from node i
at time instant m, i 2fAg
S
N ,
N
Y
i
Œm and Nw
i
Œm denote
the received codeword and the thermal noise at node i at
time instant m, i 2fBg
S
N . The first and second hop’s
channel’s input–output relationship are represented by the
following formulas:
N
Y
i
Œm D h
Ai
N
X
A
Œm CNw
i
Œm for i 2 N (1)
N
Y
B
Œm D
N
X
iD1
h
iB
N
X
i
Œm C
i
CNw
B
Œm (2)
subject to the following power constraint: the power of
N
X
A
Œm, averaging over a transmission block of P symbol
times, is less than P
A
, and that of
N
X
i
Œm, averaging over
a transmission block of 2P symbol times, is less than P
i
for i 2 N . Note that the received signal at each relay
originates only from one source. We hence do not need to
consider the time delay in the first hop. We further assume
that P
i
, P
A
and w
i
Œm; w
B
Œm CN.0;
2
/, i 2 N .
The instantaneous received signal-to-noise ratio (SNR) at
relay i is denoted by
i
and is equal to jh
Ai
j
2
,where
SNR , P
A
=
2
. The instantaneous received SNR at des-
tination B is denoted by
B
.h/, whose value depends on
Trans. Emerging Tel. Tech.
24:232–243 (2013) © 2013 John Wiley & Sons, Ltd.
DOI: 10.1002/ett
233
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