Bufferaided distributed spacetime coding schemes and algorithms for cooperative DSCDMA systems
 Jiaqi Gu^{1}Email authorView ORCID ID profile and
 Rodrigo C. de Lamare^{1, 2}
https://doi.org/10.1186/s1363801607528
© The Author(s) 2016
Received: 24 May 2016
Accepted: 7 October 2016
Published: 26 October 2016
Abstract
In this work, we propose bufferaided distributed spacetime coding (DSTC) schemes and relay selection algorithms for cooperative directsequence codedivision multiple access (DSCDMA) systems. We first devise a relay pair selection algorithm that can exploit all possible relay pairs and then select the optimum set of relays among both the sourcerelay phase and the relaydestination phase according to the signaltointerferenceplusnoise ratio (SINR) criterion. Multiple relays equipped with dynamic buffers are then introduced in the network, which allows the relays to store data received from the sources and wait until the most appropriate time for transmission. A greedy relay pair selection algorithm is then developed to reduce the high cost brought by the exhaustive search that is required when a large number of relays are involved in the transmission. The proposed techniques effectively improve the quality of the transmission with an acceptable delay as the buffer size is adjustable. An analysis of the computational complexity of the proposed algorithms and the delay and a study of the greedy algorithm are then carried out. Simulation results show that the proposed dynamic bufferaided DSTC schemes and algorithms outperform prior art.
Keywords
DSCDMA networks Cooperative systems Relay selection Greedy algorithms Space time coding Dynamic buffer1 Introduction
The everincreasing demand for performance and reliability in wireless communications has encouraged the development of numerous innovative techniques. Among them, cooperative diversity is one of the key techniques that has been considered in recent years [1–4] as an effective tool to improving transmission performance and system reliability. Several cooperative schemes have been proposed [5–7], and among the most effective ones are amplifyandforward (AF), decodeandforward (DF) [7–9] and various distributed spacetime coding (DSTC) technique [10–14]. For an AF protocol, relays cooperate and amplify the received signals with a given transmit power. With the DF protocol, relays decode the received signals and then forward the reencoded message to the destination. DSTC schemes exploit spatial and temporal transmit diversity by using a set of distributed antennas. With DSTC, multiple redundant copies of data are sent to the receiver to improve the quality and reliability of data transmission. Applying DSTC at the relays provides multiple processed signal copies to compensate for the fading and noise, helping to achieve the attainable diversity and coding gains so that the interference can be more effectively mitigated. As a result, better performance can be achieved when appropriate signal processing and relay selection strategies are applied.
1.1 Prior and related work
In cooperative relaying systems, different strategies that employ multiple relays have been recently introduced in [15–20]. The aim of relay selection is to find the optimum relay so that the signal can be transmitted and received with increased reliability. Recently, a new cooperative scheme with relays equipped with buffers has been introduced and analyzed in [21–24]. The main purpose is to select the best link according to a given criterion. In [21], a brief introduction to bufferaided relaying protocols for different networks is described and some practical challenges are discussed. A further study of the throughput and diversity gain of the bufferaided system has been subsequently introduced in [22]. In [23], a new selection technique that is able to achieve the full diversity gain by selecting the strongest available link in every time slot is detailed. In [24], a maxmax relay selection (MMRS) scheme for halfduplex relays with buffers is proposed. In particular, relays with the optimum sourcerelay links and relaydestination links are chosen and controlled for transmission and reception, respectively.
1.2 Contributions
In this work, we propose bufferaided DSTC schemes and relay pair algorithms for cooperative directsequence codedivision multiple access (DSCDMA) systems. Specifically, in the proposed cooperative DSCDMA systems, a relay pair selection algorithm (exhaustive/greedy) that selects the optimum set of relays automatically according to the signaltointerferenceplusnoise ratio (SINR) criterion is performed at the initial stage. In particular, for the exhaustive search, all possible relay pairs are examined and compared, while for the proposed greedy relay pair selection, a reduced number of relay pairs are evaluated. Therefore, a link combination associated with the optimum relay group is then selected, which determines if the corresponding buffers are ready for either transmission or reception. After that, the transmission for the cooperative DSCDMA system begins. In particular, the direct transmission for the first phase takes place between the source and the selected relay combination when the buffers are in the reception mode. On the other hand, when the corresponding buffers are switched to the transmission mode, the DSTC is performed for each user from the selected relay combination to the destination during the second phase. With dynamic buffers equipped at each of the relays, the proposed bufferaided schemes take advantage of the high storage capacity where multiple blocks of data can be stored so that the most appropriate ones can be selected at a suitable time instant. The key advantage of introducing the dynamic buffers in the system is their ability to store multiple blocks of data according to a chosen criterion so that the most appropriate ones can be selected at a suitable time instant with the highest efficiency. Furthermore, when referring to cooperative DSCDMA systems, the problem of multiple access interference (MAI) that arises from nonorthogonal received waveforms in DSCDMA systems needs to be faced. However, the use of buffers and the application of relay selections can effectively help in the interference mitigation by allowing transmissions performed over better conditioned channels.

We propose a bufferaided DSTC scheme that is able to store enough data packets in the corresponding buffer entries according to different criteria so that more appropriate symbols can be selected in a suitable time instant.

We propose a relay selection algorithm that chooses a relay pair rather than a single relay as the DSTC transmission needs the cooperation of a pair of antennas. The proposed algorithm selects the target relay pair in order to forward the data, which effectively helps with the interference cancelation in the cooperative DSCDMA systems as better transmission conditions are adopted through the proposed selections.

A greedy relay pair selection technique is then introduced to reduce the high cost brought by the exhaustive search that is required when a large number of relays are involved in the transmission.

We propose a dynamic approach so that the buffer size is adjustable according to different situations.

An analysis of the computational complexity, the average delay, and the greedy algorithm are also presented.
The rest of this paper is organized as follows. In Section 2, the system model is described. In Section 3, the dynamic bufferaided cooperative DSTC schemes are explained. In Section 4, the greedy relay pair selection strategy is proposed. In Section 5, the dynamic buffer design is given and explained. The computational complexity is studied, and the analysis of the delay and the greedy algorithm are then developed in Section 6. In Section 7, simulation results are presented and discussed. Finally, conclusions are drawn in Section 8.
2 DSTC cooperative DSCDMA system model
the 2×1 vector \(\mathbf {b}_{r_{m,n}d,k}=\left [\hat {b}_{r_{m}d,k}(2i1), \hat {b}_{r_{n}d,k}(2i)\right ]^{T}\) is the processed vector when the DF protocol is employed at relays m and n at the corresponding time instant, and \(\mathbf {n}_{r_{m,n}d}=\left [ \mathbf {n}(2i1)^{T}, (\mathbf {n}^{*}(2i))^{T} \right ]^{T}\) is the noise vector that contains samples of zero mean complex Gaussian noise with variance σ ^{2}.
where \(\mathbf {w}^{k}_{r_{m,n}d}\) is the receive filter for user k at the destination.
Consequently, after testing all possible symbols for ML detection, the most likely symbols are selected. This scheme groups the relays into different pairs, and a more reliable transmission can be achieved if proper relay pair selection is performed.
3 Proposed bufferaided cooperative DSTC scheme
where SINR _{ p,q } denotes the highest SINR associated with the relay p and relay q. After the highest SINR corresponding to the combined paths is selected, two different situations need to be considered as follows.
3.1 Sourcerelay link
where SINR _{ u,v } denotes the second highest SINR associated with the updated relay pair Ω _{ u,v }. \(\{ \mathrm {SINR_{sr_{m,n}}}, \mathrm {SINR_{r_{m,n}d}}\} \setminus \mathrm { SINR^{pre}_{p,q}}\) denotes a complementary set where we drop the \(\mathrm {SINR^{pre}_{p,q}}\) from the link SINR set \(\{ \mathrm {SINR_{sr_{m,n}}}, \mathrm { SINR_{r_{m,n}d}}\}\). Consequently, the above process repeats in the following time instants.
3.2 Relaydestination link
The received signal is then processed by the detectors at the destination. Clearly, the above operation is conducted under the condition that the corresponding buffer entries are not empty; otherwise, the second highest SINR is chosen according to Eqs. (20) and (21) and the above process is repeated.
The proposed bufferaided cooperative DSTC scheme
% List all possible relay pairs 
% Select the combination with the highest SINR 
\(\phantom {\dot {i}\!}\mathrm {SINR_{p,q}=max \{ \text {SINR}_{sr_{m,n}},\text {SINR}_{r_{m,n}d} \}}\) 
%Sourcerelay link 
if \(\phantom {\dot {i}\!}\mathrm {SINR_{p,q}} \in [\mathrm {SINR_{sr_{m,n}}}], m,n \in [1,L]\) 
if the buffers entries are not full 
\(\phantom {\dot {i}\!}\mathbf {y}_{sr_{l}}(2i1)=\sum \limits _{k=1}^{K} \mathbf {h}_{s_{k}r_{l}} b_{k}(2i1)+\mathbf {n}_{sr_{l}}(2i1),l\in [p,q],\) 
\(\phantom {\dot {i}\!}\mathbf {y}_{sr_{l}}(2i)=\sum \limits _{k=1}^{K} \mathbf {h}_{s_{k}r_{l}} b_{k}(2i)+\mathbf {n}_{sr_{l}}(2i),l\in [p,q].\) 
%Apply the detectors at relay n and relay q to obtain 
\(\phantom {\dot {i}\!}\hat {b}_{r_{l}d,k}(2i1)\) and \(\hat {b}_{r_{l}d,k}(2i)\) and store them 
in the corresponding buffer entries (l∈[p,q]) 
break 
else %choose the second highest SINR 
\(\phantom {\dot {i}\!}\mathrm {SINR^{pre}_{p,q}}=\mathrm {SINR_{p,q}}\) 
\(\phantom {\dot {i}\!}\mathrm {SINR_{p,q}} \in \text {max} \{\mathrm {SINR_{sr_{m,n}}}, \text {SINR}_{\mathrm {r_{m,n}d}} \} \setminus \mathrm {SINR^{pre}_{p,q}}\) 
end 
else %Relaydestination link 
\(\phantom {\dot {i}\!}\mathrm {SINR_{p,q}} \in [\mathrm {SINR_{r_{m,n}d}}], m,n \in [1,L]\) 
if the buffers entries are not empty 
\(\phantom {\dot {i}\!}\mathbf {y}_{r_{p,q}d,k}(2i1)= \mathbf {h}_{r_{p}d}^{k} \hat {b}_{r_{p}d,k}(2i1)+\mathbf {h}_{r_{q}d}^{k} \hat {b}_{r_{q}d,k}(2i)+\mathbf {n}(2i1),\) 
\(\phantom {\dot {i}\!}\mathbf {y}_{r_{p,q}d,k}(2i)=\mathbf {h}_{r_{q}d}^{k} \hat {b}^{*}_{r_{p}d,k}(2i1)\mathbf {h}_{r_{p}d}^{k} \hat {b}^{*}_{r_{q}d,k}(2i)+\mathbf {n}(2i).\) 
%Apply the detectors/ML at the destination for detection 
break 
else%choose the second highest SINR 
\(\mathrm {SINR^{pre}_{p,q}}=\mathrm {SINR_{p,q}}\) 
\(\phantom {\dot {i}\!}\mathrm {SINR_{p,q}} \in \text {max} \{ \mathrm {SINR_{sr_{m,n}}}, \mathrm {SINR_{r_{m,n}d}}\} \setminus \mathrm { SINR^{pre}_{p,q}}\) 
end 
end 
%Recalculated the SINR for different link combinations and 
repeat the above process 
4 Greedy relay pair selection technique
In this section, a greedy relay pair selection algorithm is introduced. For this relay selection problem, the exhaustive search of all possible relay pairs is the optimum way to obtain the best performance. However, the major problem that prevents us from applying this method when a large number of relays involved in the transmission is its considerable computational complexity. When L relays (L/2 relay pairs if L is an even number) participate in the transmission, a cost of L(L−1) link combinations is required as both sourcerelay links and relaydestination links need to be considered. Consequently, this fact motivates us to seek alternative approaches that can achieve a good balance between performance and complexity.
Consequently, all possible relay pairs involved with base relay q are listed as Ω _{ p,q }, where p∈[1,L],p≠q. The SINR for these (L−1) relay pairs are then calculated as in Eqs. (9) and (10). After that, the optimum relay pair Ω _{ n,q } is chosen according to Eq. (15) and the algorithm begins if the corresponding buffers are available for either transmission or reception.
4.1 Transmission mode
where \(\left \{\mathrm {SINR_{sr_{p}}}, \mathrm {SINR_{r_{p}d}} \right \} \setminus \mathrm {SINR^{pre}_{q}}\) denotes a complementary set where we drop the \(\mathrm {SINR^{pre}_{q}}\) from the link SINR set \(\left \{\mathrm {SINR_{sr_{p}}}, \mathrm {SINR_{r_{p}d}} \right \}\). After this selection process, a new relay pair is chosen and the transmission procedure repeats as above according to the buffer status.
4.2 Reception mode
where U represents a full buffer set. In this case, if the buffers are not full, then, the sources send the data to the selected relay pair Ω _{ n,q } over two time instants according to Eqs. (16) and (17). Otherwise, the algorithm reselects a new relay pair as in Eqs. (29), (30), and (31).
In summary, the relay pair selection algorithm solves a combinatorial problem using exhaustive searches by comparing the SINR of all links and combinations. Alternatively, a lowcomplexity algorithm (for example, the proposed greedy algorithm) could be used to reduce the computational complexity of the pair selection task.
The proposed greedy relay pair selection algorithm
%Choose a single relay with the highest SINR that 
corresponds to a specific base relay q 
\(\mathrm {SINR^{base}_{q}}=\text {max} \{\mathrm {SINR_{sr_{p}}}, \mathrm {SINR_{r_{p}d}}\}, p\in [1,L]\) 
For p=1:L % all relay pairs associated with relay q 
if p≠q 
Ω _{relaypair}=[p,q] 
% when the links belong to the sourcerelay phase 
\(\text {SINR}_{sr_{p,q}}=\frac {\sum \limits _{k=1}^{K} \mathbf {w}_{s_{k}r_{p}}^{H} \rho _{s_{k}r_{p}} \mathbf {w}_{s_{k}r_{p}}+\mathbf {w}_{s_{k}r_{q}}^{H} \rho _{s_{k}r_{q}} \mathbf {w}_{s_{k}r_{q}} }{\sum \limits _{k=1}^{K} \sum \limits _{\substack {l=1\\l\neq p,q}}^{L} \mathbf {w}_{s_{k}r_{l}}^{H} \rho _{s_{k}r_{l}} \mathbf {w}_{s_{k}r_{l}} + \sigma ^{2}\mathbf {w}_{s_{k}r_{p}}^{H} \mathbf {w}_{s_{k}r_{p}}+ \sigma ^{2}\mathbf {w}_{s_{k}r_{q}}^{H} \mathbf {w}_{s_{k}r_{q}}},\) 
% when the links belong to the relaydestination phase 
\(\text {SINR}_{r_{p,q}d}=\frac {\sum \limits _{k=1}^{K} (\mathbf {w}_{r_{p}d}^{k})^{H} \rho _{r_{p}d}^{k} \mathbf {w}_{r_{p}d}^{k}+(\mathbf {w}_{r_{q}d}^{k})^{H} \rho _{r_{q}d}^{k} \mathbf {w}_{r_{q}d}^{k}}{\sum \limits _{k=1}^{K} \sum \limits _{\substack {l=1\\l\neq p,q}}^{L} (\mathbf {w}_{r_{l}d}^{k})^{H} \rho _{r_{l}d}^{k} \mathbf {w}_{r_{l}d}^{k} + \sigma ^{2}(\mathbf {w}_{r_{p}d}^{k})^{H} \mathbf {w}_{r_{p}d}^{k}+ \sigma ^{2}(\mathbf {w}_{r_{q}d}^{k})^{H} \mathbf {w}_{r_{q}d}^{k}},\) 
% record each calculated relay pair SINR 
end 
end 
\(\phantom {\dot {i}\!}\mathrm {SINR_{n,q}}= \text {max} \{ \text {SINR}_{sr_{p,q}} \, \ \text {SINR}_{r_{p,q}d} \}\) 
if%Reception mode 
if the buffers entries are not full 
\(\phantom {\dot {i}\!}\mathbf {y}_{sr_{n,q}}(2i1)=\sum \limits _{k=1}^{K} \mathbf {h}_{s_{k}r_{n,q}} b_{k}(2i1)+\mathbf {n}(2i1),\) 
\(\mathbf {y}_{sr_{n,q}}(2i)=\sum \limits _{k=1}^{K} \mathbf {h}_{s_{k}r_{n,q}}b_{k}(2i)+\mathbf {n}(2i).\) 
%Apply the detectors at relay n and relay q to obtain 
\(\phantom {\dot {i}\!}\hat {b}_{r_{n,q}d,k}(2i1)\) and \(\hat {b}_{r_{n,q}d,k}(2i)\) and store them 
in the corresponding buffer entries 
else %choose another link with the second highest SINR 
\(\phantom {\dot {i}\!}\mathrm {SINR^{pre}_{q}}=\mathrm {SINR^{base}_{q}}\) 
\(\phantom {\dot {i}\!}\mathrm {SINR^{base}_{q}} \in \text {max} \{\mathrm {SINR_{sr_{p}}}, \mathrm {SINR_{r_{p}d}} \} \setminus \mathrm { SINR^{pre}_{q}}\) 
%Repeat the above greedy relay pair selection process 
end 
else%Transmission mode 
if the buffers entries are not empty 
\(\phantom {\dot {i}\!}\mathbf {y}_{r_{n,q}d,k}(2i1)= \mathbf {h}_{r_{n}d}^{k} \hat {b}_{r_{n}d,k}(2i1)+\mathbf {h}_{r_{q}d}^{k} \hat {b}_{r_{q}d,k}(2i)+\mathbf {n}(2i1),\) 
\(\phantom {\dot {i}\!}\mathbf {y}_{r_{n,q}d,k}(2i)= \mathbf {h}_{r_{q}d}^{k} \hat {b}^{*}_{r_{n}d,k}(2i1)\mathbf {h}_{r_{n}d}^{k} \hat {b}^{*}_{r_{q}d,k}(2i)+\mathbf {n}(2i).\) 
%Apply the detectors/ML at the destination for detection 
else%choose another link with the second highest SINR 
\(\phantom {\dot {i}\!}\mathrm {SINR^{pre}_{q}}=\mathrm {SINR^{base}_{q}}\) 
\(\phantom {\dot {i}\!}\mathrm {SINR^{base}_{q}} \in \text {max} \{\mathrm {SINR_{sr_{p}}}, \mathrm {SINR_{r_{p}d}} \} \setminus \mathrm { SINR^{pre}_{q}}\) 
%Repeat the above greedy relay pair selection process 
end 
end 
%Repeat the above greedy relay pair selection process 
5 Proposed dynamic buffer scheme
The algorithm to calculate the buffer size J
If SNR _{ cur }=SNR _{ pre }+d _{1} 
then J _{cur}=J _{pre}−d _{2}, 
where SNR _{ cur } and SNR _{ pre } represent the input SNR after and before 
increasing its value, 
J _{cur} and J _{pre} denote the corresponding buffer size before and after 
decreasing its value, 
d _{1} and d _{2} are the step sizes for the SNR and the buffer size, respectively. 
The algorithm for calculate buffer size J based on the channel power
If \(\min \ h_{s_{k}r_{l}}\^{2} \leq \gamma \) or \(\min \ h_{r_{l}d}\^{2} \leq \gamma, \ \ l\in [1,L]\) 
J _{cur}=J _{pre}+d _{3} 
else 
J _{cur}=J _{pre}−d _{3} 
end 
where d _{3} represents the step size when adjusting the buffer size. 
6 Analysis of the proposed algorithms
In this section, we analyze the computational complexity required by the proposed relay pair selection algorithm, the problem of the average delay brought by the proposed schemes and algorithms, followed by the discussion of the proposed greedy algorithm.
6.1 Computational complexity
Computational complexity
Processing  Algorithm  Multiplications  Additions 

Relay pair selection  Exhaustive search  7K N L ^{3}  (2K N+K)L ^{3}+2L 
−7K N L ^{2}  −(2K N+K+2)L ^{2}  
Relay pair selection  Greedy search  21K N L ^{2}  6K N L ^{2}+3K L ^{2} 
−7K N L  −3K L−L+1  
Channel estimation  Exhaustive search  (2N+1)K L  (2N−1)K L 
Greedy search  
Receive filter computation (RAKE)  Exhaustive search  4N J  (4N−2)J 
Greedy search 
6.2 Average delay analysis
The improvement of the performance brought by the bufferaided relays comes at the expense of the transmission delay. Hence, it is of great importance to investigate the performancedelay tradeoff of the proposed bufferaided DSTC schemes [30]. In this subsection, we analyze the average delay of the proposed schemes and algorithms.
We assume that the source always has data to transmit and the delay is mostly caused by the buffers that equip the relays. Let T(i) and Q(i) denote the delay of packets of M symbols transmitted by the source and the queue length at time instant i for DSTC schemes, respectively.
where Q=E[Q(i)] represents the average queue length at the relay buffer and R _{ a } (in packets/slot) is the average arrival rate into the queue.
Clearly, the above results demonstrate that the transmission delay is linear with the buffer size.
Apart from that, the DSTC scheme will introduce further delay. For the DSTC scheme, the relay pair needs to wait an extra time slot for the second packet to arrive. Then, the relay pair can transmit the packets to the destination using DSTC scheme. In other words, the DSTC scheme takes two time slots to transmit two packets, and as a result, it brings extra delay obviously [32–34]. Meanwhile, the relay pair selection processing also brings delay. For both exhaustive and greedy selections, they need to calculate the best relay pair from the candidates pool. This processing need extra computation time until the best relay pair is selected.
6.3 Greedy relay selection analysis
Because the number of relay pairs that we have to consider for the greedy algorithm is less than exhaustive search, the proposed greedy algorithm provides a much lower cost in terms of flops and running time when compared with the exhaustive search. In fact, the idea behind the proposed algorithm is to choose relay pairs in a greedy fashion. At each stage, we select the set of relays with the highest SINR. Then we consider the availability of the buffers, if the corresponding buffer entries do not satisfy the system mode, we reselect the relay pair in the following stages. After several stages, the algorithm is able to identify the optimum (or a near optimum) relay set that can satisfy the current transmission. To this end, we state the following proposition.
Proposition 1
Proof
where \(\Omega _{\mathrm {exhaustive(i)}}^{1}\) represents the ith relay pair selected at the 1st stage of the exhaustive relay selection method.
7 Simulations
In this section, a simulation study of the proposed bufferaided DSTC techniques for cooperative systems is carried out. The DSCDMA network uses randomly generated spreading codes of length N=16. The corresponding channel coefficients are modeled as uniformly random variables and are normalized to ensure the mean signal value over all transmissions is unity for all analyzed techniques. We assume perfectly known channels at the receivers and we also present an example with channel estimation. Equal power allocation is employed. We consider packets with 1000 BPSK symbols and step size d=2 when evaluating the dynamic schemes. We consider fixed bufferaided exhaustive/greedy (FBAE/FBAG) relay pair selection strategies (RPS) and dynamic bufferaided exhaustive/greedy (DBAE/DBAG) RPS.
Another example depicted in Fig. 3 b compares the proposed bufferaided DSTC transmission with different RPS and nonbufferaided DSTC transmission with different RPS. In this scenario, we apply the linear MMSE receiver at each of the relay and the RAKE at the destination in an uplink cooperative scenario with three users, six relays, and buffer size J=6. Similarly, the system gain brought by the use of the ML detector at the destination and the performance bounds for a singleuser bufferaided exhaustive RPS DSTC are presented for comparison purposes. The results also indicate that the proposed bufferaided DSTC strategies (J=6) have higher diversity gain when compared with the ones without employed DSTC schemes during the relaydestination phase. Furthermore, the BER performance curves of our greedy RPS algorithm approaches the exhaustive RPS, while keeping the complexity reasonably low for practical use.
8 Conclusions
In this work, we have presented a dynamic bufferaided DSTC scheme for cooperative DSCDMA systems with different relay pair selection techniques. With the help of the dynamic buffers, this approach effectively improves the transmission performance and help to achieve a good balance between bit error rate (BER) and delay. We have developed algorithms for relaypair selection based on an exhaustive search and on a greedy approach. A dynamic buffer design has also been devised to improve the performance of bufferaided schemes. Simulation results show that the performance of the proposed scheme and algorithms can offer good gains as compared to previously reported techniques.
Declarations
Acknowledgements
This work is funded by the ESII consortium under task 26 for lowcost wireless ad hoc and sensor networks.
Competing interests
The authors declare that they have no competing interests.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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