Improving performance of the asynchronous cooperative relay network with maximum ratio combining and transmit antenna selection technique
VNU Journal of Science: Comp. Science & Com. Eng., Vol. 33, No. 1 (2017) 28-36
Improving Performance of the Asynchronous Cooperative
Relay Network with Maximum Ratio Combining
and Transmit Antenna Selection Technique
The Nghiep Tran∗, Van Bien Pham, Huu Minh Nguyen
Faculty of Radio-Electronics, Le Quy Don Technical University,
236 Hoang Quoc Viet Street, Cau Giay, Hanoi, Vietnam
Abstract
In this paper, a new amplify and forward (AF) asynchronous cooperative relay network using maximum
ratio combining (MRC) and transmit antenna selection (TAS) technique is considered. In order to obtain a
maximal received diversity gain, the received signal vectors from all antennas of the each relay node are jointly
combined by MRC technique in the first phase. Then, one antenna of each relay node is selected for forwarding
MRC signal vectors to the destination node in the second phase. The proposed scheme not only offers to reduce
the interference components induced by inter-symbol interference (ISI) among the relay nodes, but also can
effectively remove them with employment near-optimum detection (NOD) at the destination node as compared
to the previous distributed close loop extended-orthogonal space time block code (DCL EO-STBC) scheme. The
analysis and simulation results confirm that the new scheme outperforms the previous cooperative relay
networks in both synchronous and asynchronous conditions. Moreover, the proposed scheme allows to reduce
the requirement of the Radio-Frequency (RF) chains at the relay nodes and is extended to general multi-antenna
relay network without decreasing transmission rate.
Received 17 October 2016; Revised 22 March 2017; Accepted 24 April 2017
Keywords: Maximum ratio combining, transmit antenna selection, near-optimum detection, distributed
space-time coding, distributed close-loop extended orthogonal space time block code.
1. Introduction*
node, and (2) decode and forward (DF) [7-12],
that decodes the received signal from the
source, re-encode the decoded data, and
transmit to the destination node. This paper
focuses on simple relaying protocols based on
amplify and forward strategy since it is easier to
implement them in the small relay nodes and
moreover, it does not require the knowledge of
the channel fading gains at the relay nodes.
Therefore, we can avoid imposing bottlenecks
on the rate by requiring some relays to decode.
The distributed close loop extended
orthogonal space time block code (DCL
EO-STBC) [1] and distributed close loop
quasi-orthogonal space time block code (DCL
Space-time block coding (STBC) can be
employed in the distributed manner, referred as
a distributed STBC (DSTC), to exploit the
spatial diversity available more efficiently and
provide coding gain in these networks.
Generally, there are two types of relaying
methods that were discussed in the literatures:
(1) amplify and forward (AF) [1-6], that is
linear process, in which the received signals are
amplified then transmitted to the destination
_______
* Corresponding author. E-mail.: nghiepsqtt@gmail.com
28
T.N. Tran et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 33, No. 1 (2017) 28-36
29
QO-STBC) [2] are proposed for two
dual-antenna relay nodes in the AF strategy. It
has been shown that both the DCL EO-STBC and
DCL QO-STBC achieve cooperative diversity
order of four with unity data transmission rate
between the relay nodes and the destination node.
G
Figure 1. Example number of ISI components for DCL EO-STBC [1] and DCL QO-STBC [2].
However, the existing research on DSTC
schemes [1-3], and [8], where each relay
antenna processes its received signal
independently, so that this received signal
combining is not optimal for multi-antenna
relay networks because the co-located antennas
of the each relay are treated as distributed
antennas.
ISI
components
than
the
DCL
QO-STBC one. Note that, they have the similar
configuration network and the imperfect
synchronous channel assumptions. Moreover, the
destination node uses the detection of interference
cancellation, called near-optimum detection
(NOD) [1, 9] and parallel interference
cancellation detection [2], to eliminate ISI
components, which is only solution at
the receiver.
As mentioned earlier, although a lot of
phase feedback schemes can be proved to
improve the distributed close loop system
performance, other problems of these systems
have to use all antennas of the relay node for
forwarding the signals to the destination node.
This improvement comes along with an
increase in complexity, size, and cost in
hardware design [5]. Moreover, the previous
DSTC schemes can not be directly applied on
the multi-antenna relay networks, where each
relay has more than two antennas.
Additionally, due to the distributed nature
of cooperative relay nodes, the received DSTC
symbols at the destination node will damage the
orthogonal feature by introducing inter-symbol
interference (ISI) components and degrade
significantly the system performance. In the
asynchronous cooperative relay networks, the
number of ISI components depends on both the
structure of the DSTC and the number of the
imperfect synchronous links [11]. The Fig. 1
illustrates a representation of ISI components at
the received symbols for the DCL EO-STBC [1]
and DCL QO-STBC [2]. It could be evident that
the DCL EO-STBC scheme has less number of
T.N. Tran et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 33, No. 1 (2017) 28-36
30
In this paper,
a
new asynchronous
In this paper, we propose the asynchronous
cooperative relay network with MRC and TAS
technique is considered as shown in Fig. 2. This
model consists of a source node, a destination
node and two relay nodes. Each terminal node,
i.e. the source node and the destination node, is
equipped with a single antenna while each relay
node is equipped with 푁푅 antennas. It is
assumed that there is no Direct Transmission
(DT) connection between the source and the
destination due to shadowing or too large
distance. The relay node operating is assumed
in half-duplex mode and AF strategy. The
channel coefficient from the source node to ꢀ푡ℎ
the antenna of the 푘푡ℎ relay node and the
channel coefficient from the ꢀ푡ℎ antenna of the
푘푡ℎ relay node to the destination node indicate
cooperative relay network using optimal MRC
technique for jointly combining received
signals from the source node. In the second
phase, the TAS technique utilizes at the relay
nodes which chooses the best antenna to
retransmit the resulting signals to the
destination. Different with all of the above-
mentioned papers, our proposed scheme uses
TAS technique to reduce the number of the ISI
components and the requirement of the RF
chains. Moreover, the destination node utilizes
the NOD to remove the ISI components
effectively.
The rest of the paper is organized as
follows: In the Sec. 2, we describe a new
asynchronous cooperative relay network with
the MRC and TAS technique (MRC/TAS) at
the relay nodes; the Sec. 3 represents the
application of the near-optimum detection
(NOD) at the destination node for the proposed
scheme; simulation results and performance
comparisons are represented in Sec. 4; finally,
the conclusion follows in Sec. 5.
푓
푖푘
and 푔푖푘 (for 푘 = 1,2; ꢀ = 1, . . . , 푁푅),
respectively. The noise terms of the relay and
destination node are assumed AWGN with
distribution 퐶푁(0,1). The total transmission
power of one symbol is fixed as 푃 (dB). Thus,
the optimal power allocation is adopted as
follows [12]
푃
푃
푃 = , 푃2 = ,
(1)
1
2
4
where
푃
1
and 푃2 are the average
Notations: the bold lowercase 푎 and bold
transmission power at the source and each relay
node, respectively.
uppercase
퐴
denote vector and matrix,
‖ ‖2
respectively; [. ]푇, [. ]∗, [. ]퐻 and
.
denote
transpose, conjugate, Hermitian (complex
conjugate) and Frobenius, respectively; 퐴
indicates the signal constellation.
2.1. In the first phase (broadcast phase)
The information symbols are transmitted
from the source node to the destination node via
two different phases. In the first phase, the
source node broadcasts the sequence of
quadrature phase-shift keying (QPSK), which is
2.fTheproposedasynchronouscooperativerela
ynetworkwith MRC/TAS technique
grouped
[
into
symbol
]
vector
퐬(푛) =
퐬(1, 푛) −퐬∗(2, 푛)
푇
The received symbol vector at ꢀ푡ℎ antenna
of the 푘푡ℎ relay node is given by
퐫 (푛) = 푃 푓 퐬(푛) + 퐯 (푛),
√
푖푘
1 푖푘
푖푘
for 푘 = 1, 2; ꢀ = 1, . . . , 푁푅(2)
where 퐯푖푘(푛) is the additive Gaussian noise
vector at each antenna of each relay node.
In the conventional DSTC scheme [1, 2], the
transmitted symbols from each relay antenna at
the same relay node is designed to be a linear
function of the received signal and its conjugate.
Figure 2. The proposed cooperative relay network
with MRC/TAS technique.
T.N. Tran et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 33, No. 1 (2017) 28-36
31
It is clear that this is not optimal for networks
whose relays have multiple antennas because the
co-located antennas of the same relay are treated
as distributed antennas. In order to achieve the
optimal received diversity gain, the received
symbols at the each relay node are combined by
using MRC technique as follow
This paper uses distributed matrices 퐀푘, 퐁푘
with Alamouti DSTC [13] to obtain a unity
transmission rate and linear complexity
detection. Note that, the factor 푃 /(푃 + 1) in
√
2
1
the equation (4) ensures that the average
transmission power at each relay node is 푃2.
2.2. In the second phase (cooperative phase)
퐫푘(푛)
푓∗
1푘
In the second phase, the transmit antenna of
each relay node can be selected by below
criterion [14], which achieves a maximal
transmitted diversity gain
1
푟 (푛) ⋯ 푟 (푛) ⋮
[
]
[
=
],
1푘
푁 푘
푅
‖ ‖
푓
푓푁∗ 푘
푘
퐹
푅
for 푘 = 1, 2; ꢀ = 1, . . . , 푁푅,
where 퐫푘(푛) is received symbol vector at 푘푡ℎ
‖ ‖
(3)
푢(푘) = max 푔푖푘 2; for 푘 = 1, 2; ꢀ =
|
|
푖=1,...,푁
푅
relay node after using MRC process and 푓
=
퐹
푘
1, . . . , 푁푅,
(5)
2
where 푢(푘) is the selected transmit antenna
index of the 푘푡ℎ relay node. 푔푘 (푘 = 1, 2)
denotes the channel gain from the selected
transmit antenna of the 푘푡ℎ relay node to the
destination node. The TAS technique allows to
achieve the transmitted diversity gain in the
second phase.
√
|
푓
2 + ⋯ + |푓푁 푘| . The transmitted symbol
|
1푘
푅
vector from selected transmit antenna 퐭푘(푛) is
described by a linear function of 퐫푘(푛) and its
conjugate 퐫푘∗(푛) as follow
푃
2
∗
(
)
퐭 (푛) =
푘
퐀푘퐫푘(푛) + 퐁푘퐫푘(푛) .(4)
√
푃 +1
1
G
Figure 3. Representation of ISI components between the selected transmit relay antenna
and the destination antenna.
As the previous mention in [1, 2], the
transmitted signals from the cooperative relay
nodes to the destination will undergo different
time delays due to different locations of the
relay nodes. Therefore, the received symbols at
the destination node may not align. Without
loss of generality, we assume that both antennas
of the first relay node (denotes 푅1) and the
destination node are synchronized perfectly,
whereas both antennas of the second relay node
(denotes 푅2) and the destination node are
synchronized imperfectly (푒. ꢀ. 휏2 = 휏12
=
휏22 ≠ 0) as shown in Fig.3. The received
symbols at the destination are written as follow
퐲(1, 푛) = 퐭1(1, 푛)푔1(푛) + 퐭2(1, 푛)푔2(푛)
+퐭2(2, 푛 − 1)푔2(푛 − 1) + 퐳(1, 푛), (6)
T.N. Tran et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 33, No. 1 (2017) 28-36
32
퐈i푛푡(1, 푛)
퐲(2, 푛) = 퐭1(2, 푛)푔1(푛) + 퐭2(2, 푛)푔2(푛) +
퐈i푛푡(푛) = [
]
퐭2(1, 푛)푔2(푛 − 1) + 퐳(2, 푛), (7)
퐈i푛푡(2, 푛)
퐹푔2(푛 − 1)퐬∗(1, 푛 − 1)
‖ ‖
푓
where 퐳(푛) is the additive Gaussian noise
vector at the destination. By substituting (4)
into (6) and (7), then taking the conjugate of
퐲(2, 푛), the received symbols at the destination
can be rewritten as
2
= [
],
푓
퐹푔2∗(푛 − 1)퐬∗(2, 푛)
‖ ‖
1
and
퐰(푛)
푔1(푛)퐯1(1, 푛) − 푔2(푛)퐯2∗(2, 푛)
푔1∗(푛)퐯1∗(2, 푛) + 푔2∗(푛)퐯2(1, 푛)
푃2
푃 푃
= √
[
]
2
1
(‖ ‖
퐹푔1(푛)퐬(1, 푛) +
퐲(1, 푛) =
푓
√
1 + 푃
1
1
1+푃
1
퐳(1, 푛)
‖ ‖
푓
)
퐹푔2(푛)퐬(2, 푛)
2
+ [
].
퐳∗(2, 푛)
푃2푃
1
+√
푓
퐹푔2(푛 − 1)퐬∗(1, 푛 − 1)
2
As similar literatures, the effects of ISIs
from the previous symbols in (8) and (9) are
represented by 푔2(푛 − 1). The strengths of
‖ ‖
1 + 푃
1
푃2
∗
푔2(푛 − 1) can be expressed as a ratio as [1]:
(
)
+√
푔1(푛)퐯1(1, 푛) − 푔2(푛)퐯2(2, 푛)
1
|
|2 |
|
2
1 + 푃
훽 = 푔2(푛 − 1) / 푔2(푛) .(11)
+퐳(1, 푛), (8)
The second term of (10), i.e. 퐈푖푛푡(, 푛) called
ISI components, and the Fig. 3 give that the
received symbols at the destination have two
ISI components. The ISI components of
proposed scheme are reduced in compared to
the previous DSTC schemes [1, 2] (See Fig. 1
in Section 1). It is important that the number of
ISI components of the proposed scheme always
equals two and is independent of the number of
the transmitted relay-antennas. Moreover, the
above analyses show that the TAS technique
not only allows to reduce the requirement of RF
chains at the relay nodes, but also increases at
twice the transmit power at each transmitted
antenna as comparison to the previous
cooperative relay networks. However, the
number of feedback bits of the proposed
scheme is quite larger than the DCL EO-STBC
scheme. It is a reasonable price for the
advantages of the proposed scheme.
푃2푃
1
퐲∗(2, 푛) = √
푓
퐹푔2∗(푛)퐬(1, 푛)
(‖ ‖
2
1 + 푃
1
∗
‖ ‖
)
− 푓 퐹푔1(푛)퐬(2, 푛)
1
푃2푃
1
+√
푔2∗(푛 − 1)퐬∗(2, 푛)
1 + 푃
1
푃2
∗
∗
∗
(
)
+√
1 + 푃
푔1(푛)퐯1(2, 푛) + 푔2(푛)퐯2(1, 푛)
1
+퐳∗(2, 푛), (9)
The equation (8) and (9) can be rewritten in
vector form as
퐲(1, 푛)
퐲∗(2, 푛)
퐲′(푛) = [
]
푃2푃
푃2푃
1
1
= √
퐇퐬′(푛) + √
퐈i푛푡(푛)
1 + 푃
1 + 푃
1
1
+퐰(푛),(10)
where
3.
Near-Optimumdetection
(NOD)
fortheproposedscheme
‖ ‖
푓
( ) ‖ ‖ ( )
퐹푔1 푛 퐹푔2 푛
푓
1
2
퐇 = [
] ;
‖ ‖ ∗( )
‖ ‖ ∗( )
푓
2
퐹푔2 푛 − 푓 퐹푔1 푛
1
As remarked above, although the number of
ISI components have been reduced by using
TAS technique, the ISI components have still
existed in the received symbol vector at the
퐬(1, 푛)
퐬(2, 푛)
퐬′(푛) = [
],
T.N. Tran et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 33, No. 1 (2017) 28-36
33
destination node. The existing ISI components
can lead to substantial degradation in system
performance. To the end this lack of the
asynchronous cooperative relay network, the
near-optimum detection (NOD) scheme is
employed at the destination node before the
information detection. In fact, the symbol
퐬(1, 푛 − 1) is known through the use of pilot
symbols at the start of the packet. Therefore, the
Step 3: Apply the Least Square (LS) at the
destination to estimate the transmitted signals
from the source node.
As seen the equation (14) 퐲′′(2, 푛) is only
related to 퐬(2, 푛). In addition, it can be proved
that 퐰퐷(2, 푛) is a circularly symmetric
Gaussian random variable with zero-mean and
covariance 휎퐖2 . Assuming the CSI at the
̃
destination node, 퐬(2, 푛)can be detected as
interference
components
퐈푖푛푡(1, 푛) =
follow
퐹푔2(푛 − 1)퐬∗(1, 푛 − 1) in the equation
‖ ‖
푓
̃
퐬(2, 푛) = arg min |퐲′′(2, 푛)
2
퐬(2,푛)∈퐴
(10) caneliminate as follows:
Step 1: Remove the ISI components
푃 푃2
1
− √
(휆퐬(2, 푛)
푃 + 1
1
퐲′(1, 푛) − 퐈푖푛푡(1, 푛)
+Λ(2, 푛)퐬∗(2, 푛))|2.
where 퐬(2, 푛) ∈ 퐴 is possible transmitted
symbol.
(16)
퐲̂(푛) = [
](12)
퐲′(2, 푛)
Step 2: Apply the matched filter by
multiplying the signals removed the ISI
components in (12) by 퐇퐻. Therefore, the
estimated signals can be represented as
퐲′′(1, 푛)
̃
Similarly, substituting 퐬(2, 푛) back to the
equation (15), 퐲′′(1, 푛) also is only related to
퐬(1, 푛). Therefore, 퐬(1, 푛) can be detected by
̃
퐲′′(푛) = [
] = 퐇퐻퐲̂(푛)
̃
퐬(1, 푛) = arg min |퐲′′(1, 푛)
퐲′′(2, 푛)
퐬(1,푛)∈퐴
푃 푃2
1
푃 푃
− √
(휆퐬(1, 푛)
1
2
=
푃 +1 (Δ퐬′(푛) + Λ퐬∗(2, 푛)) + 퐰퐷(푛),
√
푃 + 1
1
1
(13)
+Λ(1, 푛)퐬̃∗(2, 푛))|2.
(17)
Due to the presence of the interference
component 퐈푖푛푡(푛) in (10), which will destroy
the orthogonality of the received signal causing
a degradation in the system performance when
the conventional detector, e.g., the maximum
likelihood without interference cancellation,
uses at the destination node [1]. However, the
received symbol 퐲′′(2, 푛) in the equation (14)
has no ISI component via the using NOD. It is
noticeable from this equation that the
application of the NOD at the destination
where 퐲′′(1, 푛) and 퐲′′(2, 푛) are given by
푃 푃2
1
퐲′′(2, 푛) = √
(휆퐬(2, 푛)
푃 + 1
1
+ Λ(2, 푛)퐬∗(2, 푛))
+퐰퐷(2, 푛), (14)
퐲′′(1, 푛) = √
푃 푃2
1
(휆퐬(1, 푛)
푃 + 1
1
+ Λ(1, 푛)퐬∗(2, 푛))
+퐰퐷(1, 푛), (15)
effectively
removes
the
interference
with
Δ = 퐇퐻퐇 = [
components due to the impact of imperfect
synchronous among the relay nodes.
휆
0
] ,
0 휆
2
‖ ‖2 |
휆 = ∑ 푓
|
4. Comparisonresults
2
푔푘(푛) ,
푘
퐹
푘=1
In this section, we present some numerical
results to demonstrate the performance of our
proposed cooperative relay network with MRC
and TAS technique. In all figures, the bit error
0
‖ ‖
푓
Λ = 퐇퐻 [
],
퐹푔2∗(푛 − 1)퐬∗(2, 푛)
and 퐰퐷(푛) = 퐇퐻퐰(푛).
1
T.N. Tran et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 33, No. 1 (2017) 28-36
34
rates (BER) are shown as a function of the total
transmission rate between the relay and the
destination.
transmit power in the whole network. The
transmit information symbols are chosen
independently and uniformly from QPSK
constellation. It is assumed that all channels are
quasi-static Rayleigh fading channels. The
destination node completely acquires the
channel information states from the source to
the relays and from the relays to the destination.
The impact of imperfect synchronization is
performed by changing the value of 훽 = 0, −6
dB, which means adjusting the effect of
different time delays. Fig. 5 shows the BER
performance comparisons of the proposed
MRC/TAS DSTC scheme and the previous
DCL EO-STBC scheme [1] with the utilizing
NOD at the destination node. In this case, the
MRC/TAS DSTC scheme has similar
configuration network as comparison with DCL
EO-STBC scheme [1]. The BER performance
of the proposed scheme outweighs the previous
cooperative relay network. As shown in Fig. 5,
when the BER is 10−3 (at 훽 = −6 dB), the
proposed scheme can get an approximate 5 dB
gain over the DCL EO-STBC scheme. It could
be noticeable that the proposed MRC/TAS
DSTC scheme is more robust against the effect
of the asynchronous.
Figure 4. BER performance comparison
of the proposed MRC/TAS and DCL EO-STBC
scheme [1] in the perfect synchronous case.
Firstly, Fig.
4
illustrates the BER
performance of the proposed MRC/TAS DSTC
and DCL EO-STBC scheme [1] in the perfect
synchronous case where each relay node equips
two antennas. As seen the Fig. 4, the proposed
scheme outperforms the previous DCL
EO-STBC scheme. For example, to achieve a
BER = 10−3 we need 푃 of ~17 dB for the
proposed MRC/TAS DSTC scheme and ~21
dB for the DCL EO-STBC scheme. Secondly,
the system performance of the MRC/TAS
DSTC is simulated in the perfect synchronous
assumption and using three antennas at each
relay. The left curve of the Fig. 4 shows that the
system performance of proposed scheme is
improved considerably with increasing the
number of antennas of each relay node. The
improvement of the proposed scheme is
because that our scheme achieves both maximal
received diversity gain in the first phase and
cooperative transmit diversity gain in the
second phase. Moreover, the proposed scheme
has less requirement of RF chains of the relay
than the previous works and remains unity
Figure 5. BER performance comparison of the
MRC/TAS DSTC (푁푅 = 2) and the DCL
EO-STBC [1] with the utilizing NOD scheme.
In order to examine the advantages of
increasing the number of the relay-antennas, the
BER of the proposed scheme is performed with
three antennas at each relay node and various
asynchronous channel conditions. The Fig. 6
demonstrates that the MRC/TAS DSTC scheme
owning three relay-antennas has greater system
performance than, in the similar asynchronous
condition, the DCL EO-STBC one using two
antennas at each relay node. For example, at the
T.N. Tran et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 33, No. 1 (2017) 28-36
35
BER of 10−3 (at 훽 = −6 dB), the proposed
References
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performance is achieved as the MRC/TAS
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5. Conclusions
This paper proposes the AF asynchronous
cooperative relay network using MRC and TAS
technique. The use of MRC technique for
combining multiple received symbols is proved
to obtain maximal received diversity gain in
compared to conventional DSTC scheme [1,2].
In the second phase, the TAS technique allows
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The proposed scheme has less requirement of
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advantage of multi-antennas more effectively in
comparison to the previous one. We believe that
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the distributed relay networks using multi-
antennas at the relay nodes like sensor wireless
network or Ad hoc network under the
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