A low complexity distributed differential scheme based on orthogonal space time block coding for decode-and-forward wireless relay networks

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 13, No. 1, February 2023, pp. 1180~1188
ISSN: 2088-8708, DOI: 10.11591/ijece.v13i1.pp1180-1188  1180
Journal homepage: http://ijece.iaescore.com
A low complexity distributed differential scheme based on
orthogonal space time block coding for decode-and-forward
wireless relay networks
Samer Alabed1
, Nour Mostafa2
, Wael Hosny Fouad Aly2
, Mohammad Al-Rabayah2
1
Biomedical Engineering Department, School of Applied Medical Sciences, German Jordanian University, Amman, Jordan
2
College of Engineering and Technology, American University of the Middle East, Egaila, Kuwait
Article Info ABSTRACT
Article history:
Received Feb 16, 2022
Revised May 24, 2022
Accepted Jul 2, 2022
This work proposes a new differential cooperative diversity scheme with
high data rate and low decoding complexity using the decode-and-forward
protocol. The proposed model does not require either differential encoding
or channel state information at the source node, relay nodes, or destination
node where the data sequence is directly transmitted and the differential
detection method is applied at the relay nodes and the destination node. The
proposed technique enjoys a low encoding and decoding complexity at the
source node, the relay nodes, and the destination node. Furthermore, the
performance of the proposed strategy is analyzed by computer simulations in
quasi-static Rayleigh fading channel and using the decode-and-forward
protocol. The simulation results show that the proposed differential
technique outperforms the corresponding reference strategies.
Keywords:
Cooperative techniques
Decode and forward protocol
Differential techniques
Distributed systems
Diversity techniques
Space-time coding
Wireless relay networks
This is an open access article under the CC BY-SA license.
Corresponding Author:
Samer Alabed
Biomedical Engineering Department, School of Applied Medical Sciences, German Jordanian University
Amman 11180, Jordan
Email: samer.alabed@gju.edu.jo
1. INTRODUCTION
Transmit diversity, a form of spatial diversity, has been studied extensively as a method of
combating detrimental effects in wireless fading channels [1]–[4] instead of using time and frequency
diversity. In the last years, space diversity using multiple input multiple output (MIMO) systems [5], [6] has
received much attention because it can be combined with other forms of diversity [7]–[10] and, additionally,
it improves the overall performance in terms of bite error rate and data rate without requiring extra bandwidth
or transmission power [11], [12]. MIMO systems have been suggested to increase the channel capacity
linearly with the minimum number of transmitting and receiving antennas.
Advances made in MIMO signal processing techniques have shown tremendous improvements in
reliability and throughput [13]–[19]. However due to size, cost, and hardware constraints, the use of MIMO
techniques in ad-hoc networks may not always be feasible especially in small devices. Hence, it might not be
practical to use multiple-antennas for certain applications. As a solution to this problem, cooperative
communication, a spatial diversity method, becomes a practical alternative to MIMO when the size of the
wireless device is limited [20]–[22]. Recently, there has been a growing interest in the so-called cooperative
diversity techniques where multiple terminals in a network cooperate to form a virtual antenna array in order
to exploit spatial diversity in a distributed fashion [23], [24]. Hence, node cooperation can yield significant
performance gains in wireless networks [23], [24]. In particular, cooperating nodes can achieve a diversity
gain in fading channels [20]–[24]. Recently, several cooperative transmission techniques and protocols have

Int J Elec & Comp Eng ISSN: 2088-8708 
A low complexity distributed differential scheme based on orthogonal space time … (Samer Alabed)
1181
been proposed. These protocols can be categorized into two principal classes: the amplify-and-forward (AF)
protocol [13], [21] and the decode-and-forward (DF) protocol [7], [23]. Early transmit diversity schemes
were designed for coherent detection [7]–[12] with channel estimates assumed available at the receiver.
However, the complexity and cost of channel estimation grow with the number of transmit and receive
antennas. As a solution to this problem, transmit diversity techniques that do not require channel estimation
are desirable such as differential techniques. Recently, different approaches of differential space-time
modulation techniques have been proposed [25]–[32]. At this end, differential space-time block coding
(DSTBC) techniques are useful for wireless communications with multiple transmitting antennas [25]–[27].
With DSTBC, the channel state information (CSI) is not required either at the transmitters or at the receivers
which is important for applications when the CSI changes too fast to be estimated and utilized. The design of
DSTBC has attracted the attention of many researchers in recent years [15], [16]. For two transmitters, the
design of DSTBC is well established because of the existence of full rate complex orthogonal code. But for
more than two transmitters, the design of DSTBC is still an active area of research. For practical use, there is
a strong interest to reduce the decoding complexity of DSTBC with as little loss of coding gain as possible.
In many papers, their authors considered cooperative networks employing the differential unitary space time
coding (DUSTC) technique which does not require CSI at source node, relay nodes, or destination node [25]–
[32], however using DUSTC in broadcast phase and relay phase increases the decoding complexity at relay
nodes and destination node exponentially with the increase of the number of relay nodes or the data rate, i.e.,
spectral efficiency, r bps/Hz [31].
In this paper, a new cooperative diversity technique with full rate and low complexity is proposed.
This model also does not require either a differential encoding at the source node or relay nodes or the CSI at
the source node, relay nodes or destination node like [1], [13]–[19], [21]. In this system, more than two relay
nodes are considered. Moreover, the complexity in the proposed system is very low at source node, relay
nodes, and destination node where the proposed system of L nodes operating at a data rate, i.e., spectral
efficiency, r bps/Hz requires a symbol-wise decoder with decoding search space of 2r
search for each symbol
at the destination node while cooperative networks of L nodes employing DUSTC and operating at a data rate
r bps/Hz requires a decoding search space of 2rL
for L symbols at each relay node and at the destination node.
Furthermore, the bit error performance of the proposed system is analyzed by computer simulation and it is
shown that it outperforms the DUSTC system given in [25]–[32] for two, three, and four relay nodes.
2. METHOD
In this work, a novel distributed space-time coding approach using the DF protocol and M-ary phase
shift keying (MPSK) constellations is suggested. The proposed approach does not require any channel
knowledge at any part of the system. Moreover, it enjoys a high error performance and a low encoding and
decoding complexity at all nodes in the whole network.
2.1. System model
We consider a wireless network with L+2 nodes, a source node {S}, a destination node {D} and L
relay nodes {Rk}l=1
L
which are randomly and independently distributed as shown in Figure 1. The source
node intends to send its information symbols to the destination node while the L other nodes serve as relays.
We also assume that the total transmit power 𝑃𝑡 is divided equally between the source node and the relay
nodes. Moreover, the power of the relay nodes is equally distributed among the relays, so that the power of
the source node is 𝑃𝑠 =
1
2
𝑃𝑡 and the power of each relay is 𝑃𝑟 =
1
2𝐿
𝑃𝑡 where 𝑃𝑡 is the total transmitted power.
Each relay processes the received signals independently. All nodes in the whole network, i.e., the source
node, destination node, and all relay nodes, are equipped with single antennas. It is assumed that each node
can transmit and receive, but not simultaneously, i.e., half duplex operation. The channel from the source
node to the lth
relay is denoted by 𝑓𝑙, while the one from the lth
relay node to the destination node, is denoted
by 𝑔𝑙 as shown in Figure 1. Moreover, it is assumed that the CSI is unknown either at the transmitting node
or at the receiving node. Both channels, 𝑓𝑙 and 𝑔𝑙, are assumed as quasi-static flat Rayleigh fading. The
cooperation process can be divided into two phases, broadcast phase and relay phase. During the first phase,
broadcast phase, the information is transmitted from the source node to the relay nodes as shown in Figure 2.
In the second phase, relay phase, each relay node decodes and transmits the signal to the destination nodes as
shown in Figure 3.
We further assume that there are (2L-2) symbols s(𝑙), 𝑙 = {0,1,2, . . .2𝐿 − 3} drawn from MPSK
constellation. In this article, (. )∗
denotes complex conjugate of (. ) and ‖. ‖ denotes the Frobenious norm. It is
assumed that the channel coefficients 𝑓𝑙 and 𝑔𝑙 are independent, zero mean complex Gaussian random
variables of variance one but they remain unchanged during each block.

 ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 13, No. 1, February 2023: 1180-1188
1182
Figure 1. Wireless relay network with L relay nodes
Figure 2. Broadcast phase Figure 3. Relay phase
2.2. Broadcast phase
The source-relay channel and relay-destination channel are assumed independent of each other. All
channels are assumed as quasi static flat Rayleigh fading, i.e., they are constant during each block which
consists of several frames and change independently from one block to another. In Figure 1, 𝑓𝑖,𝑘 is the
complex channel coefficient from source node to the lth
relay node of the kth
transmission frame, and 𝑔𝑖,𝑘 is
the complex channel coefficient from the lth
relay node to the destination node of the kth
transmission frame.
Let us assume that each frame has two phases where during each frame, the source node sends (2L-2)
information symbols. Let also assume that s(𝑘)
is the source symbol sequence with elements s(𝑘)(𝑖), 𝑖 ∈
{0,1,2, . . . ,2𝐿 − 3}. In the first phase, broadcast phase, the source node transmits (2L-2) symbols to the relay
terminals where the initial (2L-2) symbols of the initial frame are known at the source node, relay nodes and
destination node, and they are assumed to be ones, s(0)
= [1, 1, . . , 1], to initialize the differential encoding. At the
end of transmission, the received signal vector at the lth
relay node of the kth
frame is given by (1):
r𝑙
(𝑘)
= 𝑓𝑙,𝑘 s(𝑘)
+ n𝑙
(𝑘)
, (1)
where r𝑙
(𝑘)
= [𝑟𝑙
(𝑘)
(0), 𝑟𝑙
(𝑘)
(1), … … , 𝑟𝑙
(𝑘)
(2L − 3)], s(𝑘)
= [𝑠(𝑘)
(0), 𝑠(𝑘)
(1), . . . … , 𝑠(𝑘)(2L − 3)],
n𝑙
(𝑘)
= 𝑛𝑙
(𝑘)
(0), 𝑛𝑙
(𝑘)
(1), . . , 𝑛𝑙
(𝑘)
(2L − 3)], and 𝑛𝑙
(𝑘)
(𝑖) is the additive channel noise of the ith
time slot at the
lth
relay node with independent, zero mean, complex Gaussian random variables of unity variances. At the
relay nodes, the received signals in the kth
transmission frame are combined as in (2).
𝑝𝑙
(𝑘)
(𝑖 − 1) = 𝑟𝑙
(𝑘)
(𝑖 − 1) 𝑟𝑙
(𝑘)
(𝑖), (2)
Note that |𝑠(𝑘)
(𝑖)| = 1 since the symbols are drawn from MPSK constellations. If we consider a noise-free
scenario, then |𝑝𝑙
(𝑘)
(𝑖)| = |𝑓𝑙,𝑘|
2
. Therefore, the information symbol 𝑠(𝑘)
(𝑖) can be reconstructed by applying
the following maximum likelihood (ML) decoder:
𝑠̂𝑙
(𝑘)
(𝑖) = arg min𝑠∈𝑆𝑖
‖𝑝𝑙
(𝑘)
(𝑖) − |𝑝𝑙
(𝑘)
(𝑖)| 𝑠‖, (3)
where 𝑖 = {0,1,2,3, . . .2𝐿 − 3}, 𝑆𝑖 denotes all possible symbols of MPSK constellation transmitted over one
frame. At the end of the transmission, the lth
relay contains the estimated data sequence 𝑠
̂𝑙
(𝑘)
(𝑖). Basically, we
search for the symbol that minimizes the cost-function given in (3) by substituting all possible symbols of MPSK
constellation.

1183
2.3. Relay phase
By using L relay nodes, a low complexity and full rate space time coding scheme with complex
orthogonal design is performed. An orthogonal design is used to minimize the decoding complexity by
applying a symbolwise decoder at the receiver side. During the second phase, relay phase, the estimated
symbol sequence of the relays is space time block coded in the following designed code matrices.
2.3.1. Two relay system
In the orthogonal design, there are several codes. For two relay-node system, Alamouti’s code is the
optimal one. Therefore, if the system contains only two relays, the relay detected symbol sequence is
orthogonally space time block coded using the Alamouti's matrix as (4):
X(𝑘)
= [
𝑠̂1
(𝑘)
(0) 𝑠̂2
(𝑘)
(1)
−{𝑠̂2
(𝑘)
(3)}
∗
{𝑠̂3
(𝑘)
(2)}
∗], (4)
where 𝑠̂𝑙
(𝑘)
(𝑖) is the ith
estimated symbol in the kth
frame on the lth
relay.
2.3.2. Three relay system
If the system contains three relay nodes, there are several orthogonal designs. The best choice is to
find an orthogonal code with full-rate. Therefore, in three relay system, the estimated symbol sequence at the
relays is space time block coded in terms of the following full rate, low complexity orthogonal matrix.
X(𝑘)
=
[
𝑠̂1
(𝑘)
(0) 𝑠̂2
(𝑘)
(1) 0
−{𝑠̂1,𝑘
(𝑘)
(1)}
∗
{𝑠̂2
(𝑘)
(0)}
∗
0
0 𝑠̂2
(𝑘)
(2) 𝑠̂3
(𝑘)
(3)
0 −{𝑠̂2
(𝑘)
(3)}
∗
{𝑠̂3
(𝑘)
(2)}
∗
]
. (5)
2.3.3. L relay system
Similar to section 2.3.2, if the system contains L relay nodes, there are several orthogonal designs.
The best choice is to find an orthogonal code with full-rate. Therefore, in L relay system, the estimated
symbol sequence at the relays is space time block coded in terms of the following full rate, low complexity
orthogonal matrix.
𝐗(𝑘)
=
[
{𝑠̂1
(𝑘)
(0)} {𝑠̂2
(𝑘)
(1)} 0 . . 0 0
−{𝑠̂1
(𝑘)
(1)}
∗
{𝑠̂2
(𝑘)
(0)}
∗
0 . . 0 0
0 {𝑠̂2
(𝑘)
(2)} {𝑠̂3
(𝑘)
(3)} . . 0 0
0 −{𝑠̂2
(𝑘)
(3)}
∗
{𝑠̂3
(𝑘)
(2)}
∗
. . 0 0
. . . . . . .
. . . . . . .
0 0 0 . . {𝑠̂𝐿−1
(𝑘)
(2𝐿 − 4)} {𝑠̂𝐿
(𝑘)
(2𝐿 − 3)}
0 0 0 . . −{𝑠̂𝐿−1
(𝑘)
(2𝐿 − 3)}
∗
{𝑠̂𝐿
(𝑘)
(2𝐿 − 4)}
∗
]
(6)
2.4. Differential detection technique
The received signal vector, r𝑑
(𝑘)
= [𝑟𝑑
(𝑘)
(0), 𝑟𝑑
(𝑘)
(1), … 𝑟𝑑
(𝑘)
(2𝐿 − 3)]𝑇
, at the destination terminal in
the kth
frame is given by (7):
r𝑑
(𝑘)
= X(𝑘)
g𝑘 + n𝑑
(𝑘)
, (7)
where g𝑘 = [𝑔1,𝑘, 𝑔2,𝑘, … , 𝑔𝐿,𝑘] is the channel state information (CSI) between the relay nodes and
destination terminal and n𝑑
(𝑘)
= [𝑛𝑑
(𝑘)
(0), 𝑛𝑑
(𝑘)
(1), … 𝑛𝑑
(𝑘)
(2𝐿 − 3)]𝑇
is the noise vector in the kth
frame at the
destination terminal. In case of two relay system, the received signals in the kth
frame at the destination node,
assuming that the destination node does not receive a copy from the source node, are given by (8).
𝑟𝑑
(𝑘)
(0) = 𝑔1,𝑘 𝑠̂1
(𝑘)
(0) + 𝑔2,𝑘 𝑠̂2
(𝑘)
(1) + 𝑛𝑑
(𝑘)
(0),
𝑟𝑑
(𝑘)
(1) = −𝑔1,𝑘{𝑠̂1
(𝑘)
(1)}
∗
+ 𝑔2,𝑘{𝑠̂2
(𝑘)
(0)}
∗
+ 𝑛𝑑
(𝑘)
(1). (8)

 ISSN: 2088-8708
1184
For three-relay system and at the destination node, the received signals in the kth
frame are given by (9).
𝑟𝑑
(𝑘)
(0) = 𝑔1,𝑘 𝑠̂1
(𝑘)
(0) + 𝑔2,𝑘 𝑠̂2
(𝑘)
(1) + 𝑛𝑑
(𝑘)
(0),
𝑟𝑑
(𝑘)
(1) = −𝑔1,𝑘{𝑠̂1
(𝑘)
(1)}
∗
+ 𝑔2,𝑘{𝑠̂2
(𝑘)
(0)}
∗
+ 𝑛𝑑
(𝑘)
(1),
𝑟𝑑
(𝑘)
(2) = 𝑔2,𝑘 𝑠̂2
(𝑘)
(2) + 𝑔3,𝑘 𝑠̂3
(𝑘)
(3) + 𝑛𝑑
(𝑘)
(2),
𝑟𝑑
(𝑘)
(3) = −𝑔2,𝑘{𝑠̂2
(𝑘)
(3)}
∗
+ 𝑔3,𝑘{𝑠̂3
(𝑘)
(2)}
∗
+ 𝑛𝑑
(𝑘)
(3). (9)
For L-relay system and at the destination node, the received signals in the kth
frame are given by (10).
𝑟𝑑
(𝑘)
(0) = 𝑔1,𝑘 𝑠̂1
(𝑘)
(0) + 𝑔2,𝑘 𝑠̂2
(𝑘)
(1) + 𝑛𝑑
(𝑘)
(0),
𝑟𝑑
(𝑘)
(1) = −𝑔1,𝑘{𝑠̂1
(𝑘)
(1)}
∗
+ 𝑔2,𝑘{𝑠̂2
(𝑘)
(0)}
∗
+ 𝑛𝑑
(𝑘)
(1),
𝑟𝑑
(𝑘)
(2) = 𝑔2,𝑘 𝑠̂2
(𝑘)
(2) + 𝑔3,𝑘 𝑠̂3
(𝑘)
(3) + 𝑛𝑑
(𝑘)
(2),
𝑟𝑑
(𝑘)
(3) = −𝑔2,𝑘{𝑠̂2
(𝑘)
(3)}
∗
+ 𝑔3,𝑘{𝑠̂3
(𝑘)
(2)}
∗
+ 𝑛𝑑
(𝑘)
(3),
𝑟𝑑
(𝑘)
(2𝐿 − 4) = 𝑔𝐿−1,𝑘 𝑠̂𝐿−1
(𝑘)
(2𝐿 − 4) + 𝑔𝐿,𝑘 𝑠̂3
(𝑘)
(2𝐿 − 3) + 𝑛𝑑
(𝑘)
(2𝐿 − 4),
𝑟𝑑
(𝑘)
(2𝐿 − 3) = −𝑔𝐿−1,𝑘{𝑠̂2
(𝑘)
(2𝐿 − 3)}
∗
+ 𝑔𝐿,𝑘{𝑠̂3
(𝑘)
(2𝐿 − 4)}
∗
+ 𝑛𝑑
(𝑘)
(2𝐿 − 3). (10)
For the sake of simplicity and in order to reconstruct the data sequence, let us assume that 𝑔𝑙,𝑘 = 𝑔𝑙,𝑘−1 =
𝑔𝑙 , ∀𝑙 ∈ {1,2,3, . . . , 𝐿} and consider noise-free case, therefore, the received signals in the kth
frame given by
(10) are combined as (11).
𝐲𝟏
(𝑘)
= [
𝐲𝟏
(𝑘)
(0)
𝐲𝟏
(𝑘)
(1)
] = [
𝑟𝑑
(𝑘)
(0)
(𝑟𝑑
(𝑘)
(1))
∗] = [
𝑠̂1
(𝑘)
(0) 𝑠̂2
(𝑘)
(1)
−𝑠̂1
(𝑘)
(1) 𝑠̂2
(𝑘)
(0)
] [
𝑔1
(𝑔2)∗],
𝐲𝟐
(𝑘)
= [
𝐲𝟐
(𝑘)
(0)
𝐲𝟐
(𝑘)
(1)
] = [
𝑟𝑑
(𝑘)
(2)
(𝑟𝑑
(𝑘)
(3))
∗] = [
𝑠̂1
(𝑘)
(2) 𝑠̂2
(𝑘)
(3)
−𝑠̂1
(𝑘)
(3) 𝑠̂2
(𝑘)
(2)
] [
𝑔2
(𝑔3)∗],
𝐲𝐋−𝟏
(𝑘)
= [
𝐲𝐋−𝟏
(𝑘)
(0)
𝐲𝐋−𝟏
(𝑘)
(1)
] = [
𝑟𝑑
(𝑘)
(2𝐿 − 4)
(𝑟𝑑
(𝑘)
(2𝐿 − 3))
∗] = [
𝑠̂1
(𝑘)
(2𝐿 − 4) 𝑠̂2
(𝑘)
(2𝐿 − 3)
−𝑠̂1
(𝑘)
(2𝐿 − 3) 𝑠̂2
(𝑘)
(2𝐿 − 4)
] [
𝑔𝐿−1
(𝑔𝐿)∗]. (11)
To reconstruct the original information symbols, the following ML decoders can be used
[𝑠̂(𝑘)
(0) 𝑠̂(𝑘)
(1)] = arg min𝑠𝑖∈𝑆𝑖
‖y1
(𝑘)
− [𝑠1 𝑠2] y1
(0)
‖,
[𝑠̂(𝑘)
(2) 𝑠̂(𝑘)
(3)] = arg min𝑠𝑖∈𝑆𝑖
‖y2
(𝑘)
− [𝑠1 𝑠2] y2
(0)
‖,
[𝑠̂(𝑘)
(2𝐿 − 4) 𝑠̂(𝑘)
(2𝐿 − 3)] = arg min𝑠𝑖∈𝑆𝑖
‖yL−1
(𝑘)
− [𝑠1 𝑠2] yL−1
(0)
‖, (12)
where y𝑙
(0)
, which is used to detect the signals differentially, is the received signal vector for the arbitrary
initial symbols s(0)
. Note that 𝑔𝑙
̂ =
y𝑙
(𝑘)
(0)+y𝑙
(𝑘)
(1)
2
and 𝑔𝑙+1
̂ = (
y𝑙
(𝑘)
(0)−y𝑙
(𝑘)
(1)
2
)
∗
where 𝑙 = [1,2,3, … 𝐿 − 1].
Therefore, the previous ML decoder expressed in (12) can be simplified to be a fast symbol-wise decoder,
given by (13)
𝑠̂(𝑘)
(2𝑙 − 2) = arg min𝑠∈𝑆𝑖
‖(𝑔𝑙
̂ 𝐲𝑙
(𝑘)
(0) + 𝑔𝑙+1
∗
̂ 𝐲𝑙
(𝑘)
(1)) − (|𝑔𝑙
̂ |2 + |𝑔𝑙+1
̂|2) 𝑠 ‖,
𝑠̂(𝑘)
(2𝑙 − 1) = arg min𝑠∈𝑆𝑖
‖(𝑔𝑙+1
̂ 𝐲𝑙
(𝑘)
(0) − 𝑔𝑙
∗
̂ 𝐲𝑙
(𝑘)
(1)) − (|𝑔𝑙
̂ |2
+ |𝑔𝑙+1
̂|2) 𝑠 ‖. (13)
3. RESULTS AND DISCUSSION
Our simulation results show the performance of a half-duplex wireless relay network using
independent quasi-static flat Rayleigh fading channels. As explained in section 2.1, it is assumed that the
total power 𝑃𝑡 is distributed equally between the source node and relay nodes. The relay power is equally
distributed among all relays as well such that 𝑃s = 𝐿 𝑃𝑟 =
1
2
𝑃𝑡 and 𝑃𝑟 =
1
2𝐿
𝑃𝑡 where 𝑃𝑡 is the power of the rth

1185
relay and 𝑃s is the power of the source node. In this section, we use a Monte Carlo simulation with 106
runs
to compare the symbol error rate (SER) performance of the proposed DF distributed differential cooperative
space time coding technique with the SER performance of the DF cooperative distributed unitary space time
coding technique suggested in [25]–[32] as function of total signal-to-noise (SNR), where the total SNR is
the ration between the total transmitted power to the total power of the noise. In our simulation results, the
4-PSK modulation is used in all figures. Moreover, we consider a wireless network with L+2 nodes, one
source node {S}, one destination node {D} and L relay nodes, which are randomly and independently
distributed as explained in section 2.1 and shown in Figure 1. The source node, destination node, and all relay
nodes are equipped with single antennas. In addition to that, it is assumed that the CSI is unknown all nodes
in the whole network. In the simulation results, the simulated SER curves for both techniques using the DF
protocol and using two, three, and four relays are generated. It is observed that the performance of the
proposed technique is better than the conventional DUSTC one with much less complexity.
In Figures 4 to 6, the performance analysis of the cooperative networks depends on the error term
occurred due to decoding errors made in the relays as shown in (3). Therefore, if we assign more SNR, i.e.,
40 dB more, at source-relays links, 𝑆𝑁𝑅𝑠−𝑟, than relays-destination links 𝑆𝑁𝑅𝑟−𝑑, the diversity and coding
grain can be improved as shown in Figures 7 to 9. The SNR at the source- relays links is 𝑆𝑁𝑅′
𝑠−𝑟 =
𝑆𝑁𝑅𝑠−𝑟 + 40 𝑑𝐵, however in Figures 4 to 6, it is assumed that the total SNR is SNRtotal=SNRs-r + SNRr-d
where SNRs-r = SNRr-d. The complexity of the proposed system is low at source node, relay nodes and
destination node where the proposed system of L relay nodes operating at a data rate r bps/Hz requires a
decoding search space of 2r
search for each symbol at each relay node and at the destination node while
cooperative networks of L relay nodes employing DUSTC and operating at the same data rate requires a
decoding search space of 2rL
for L symbols at each relay node and at the destination node.
Figure 4. SER performance vs. SNR for different
DSTBC techniques using four relays and 4-PSK
modulation
DSTBC techniques using three relays and 4-PSK
modulation
DSTBC techniques using two relays and 4-PSK
modulation
DSTBC techniques using two relays and 4-PSK
modulation when 𝑆𝑁𝑅′
𝑠−𝑟 = 𝑆𝑁𝑅𝑠−𝑟 + 40 𝑑𝐵

 ISSN: 2088-8708
1186
Figure 8. ER performance vs. SNR for different
DSTBC techniques using three relays and 4-PSK
Figure 9. ER performance vs. SNR for different
DSTBC techniques using four relays and 4-PSK
4. CONCLUSION
In this paper, we have proposed a differential space-time coding technique. The proposed technique
enjoys high error performance with full data-rate and low encoding and decoding complexity as compared
with the traditional DUSTC technique. The bit error performance of the proposed system is analyzed by
computer simulation. The performance of the proposed technique outperforms the reference techniques for
two, three, and four relay systems.
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BIOGRAPHIES OF AUTHORS
Samer Alabed is currently an Associate Professor and the Head of Biomedical
Engineering Department at the German Jordanian University, Jordan. He was an associate
professor of Electrical Engineering at the college of engineering and technology in the
American University of the Middle East (AUM), Kuwait, from 2015 to 2022. He also worked
in Darmstadt University of Technology, Darmstadt, Germany, from 2008 to 2015. He received
his Ph.D. degree in electrical engineering and information technology from Darmstadt
University of Technology, Germany. During the last 18 years, he has worked as an associate
professor, assistant professor, researcher, and lecturer in several German and Middle East
universities and supervised tens of master students and several Ph.D. students. He received
several awards and grants from IEE, IEEE, DAAD, DFG, ERC, EU, AUM. He was invited to
many conferences and workshops in Europe, United States, and North Africa. He can be
contacted at email: samer.alabed@gju.edu. Further information is available on his homepage:
http://drsameralabed.wixsite.com/samer.
Nour Mostafa received the Ph.D. degree from the Queen's University Belfast
School of Electronics, Electrical Engineering and Computer Science, UK, in 2013. He was a
Software Developer with Liberty Information Technology, UK. He is currently an Associate
Professor of computer science with the College of Engineering and Technology, American
University of the Middle East. His current research interests include cloud, fog and IoT
computing, grid computing, large database management, artificial intelligence, and distributed
computing. He can be contacted at email: Nour.Moustafa@aum.edu.kw.

 ISSN: 2088-8708
1188
Wael Hosny Fouad Aly has received his Ph.D. degree at the University of
Western Ontario in Canada in 2006. Dr. Aly is a Professional Engineer of Ontario P.Eng.
(Canada). Dr. Aly is currently working as an Associate Professor of Computer Engineering at
the College of Engineering and technology at the American University of the Middle East in
Kuwait since 2016. Dr. Aly's research interests include SDN networking, distributed systems,
optical burst switching (OBS), wireless sensor networks (WSN), differentiated services, and
multi-agent systems. He can be contacted at email: Wael.Aly@aum.edu.kw.
Mohammad Al-Rabayah holds a PhD in electrical engineering from the
University of New South Wales (UNSW) since the year 2011. He is currently an assistant
professor at the American University of Middle East (AUM) – Kuwait, since 9/2018. He is
teaching various courses for the undergraduate students, an academic advisor for electrical
engineering students, and a member of many committees at the department level responsible
for maintaining high level of education and research at the department. Al-Rabayah also
worked as an assistant professor at Prince Sultan University (PSU), Riyadh-KSA, for the
period between 8/2015 and 8/2018. During his time, he taught many courses at the
communications and networks department and participated in many training workshops to
develop his professional career, and to support the university efforts toward gaining the
international engineering accreditation ABET. He worked as an assistant professor at Prince
Sattam bin Abdulaziz University (PSAU), Kharj- KSA, in the period between 10/2014 and
6/2015. His current research is in the fields of wireless networks, and cooperative wireless
communications. He can be contacted at email: Mohammad.alrabayah@aum.edu.kw.

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