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Performance analysis of cognitive AF relay networks with multiuser switched diversity in Rayleigh fading channels
 Anas M. Salhab^{1}Email authorView ORCID ID profile and
 Salam A. Zummo^{1}
https://doi.org/10.1186/s1363801709152
© The Author(s) 2017
 Received: 2 October 2015
 Accepted: 9 July 2017
 Published: 28 July 2017
Abstract
The multiuser switched diversity (MUSwiD) selection schemes are useful in reducing the required channel estimation load in wireless networks. In this paper, we propose and evaluate the performance of cognitive amplifyandforward (AF) MUSwiD relay networks where a cognitive user is selected among a set of users for data reception. The selection process is performed such that the endtoend (e2e) signaltonoise ratio (SNR) of the selected user satisfies a predetermined switching threshold. Such a user that satisfies this threshold is scheduled instead of the best user to receive its message from the secondary source. In the proposed system, we consider a cognitive source, a cognitive relay, a set of cognitive users, and a primary user. In this paper, an upper bound on the e2e SNR of a user is used in deriving of closedform approximations for the outage probability and average symbol error probability (ASEP) of the studied system in addition to deriving the ergodic channel capacity. To get more about system insights, the performance is studied at the high SNR regime where approximate expressions for the outage probability, SEP, diversity order, and coding gain are derived. The derived analytical and asymptotic expressions are verified by MonteCarlo simulations, and some numerical examples are provided to illustrate the effect of some parameters such as number of users and switching threshold on the system performance. Findings illustrate that the diversity order of the studied cognitive AF multiuser switched diversity relaying network is the same as its noncognitive counterpart. Also, results show that the asymptotic results tightly converge to the exact ones, and the analytical bounds are indeed very tight, validating the accuracy of our approach of analysis. Furthermore, findings illustrate that the proposed MUSwiD user selection schemes are efficient in the range of low SNR values, which makes them attractive options for practical implementation in emerging mobile broadband communication systems. In contrast, these selection schemes are shown to be inefficient in the range of high SNR values where the multiuser diversity gain is noticeably degraded when they are implemented.
Keywords
 Amplifyandforward
 Cognitive relay network
 Multiuser switched diversity
 Switching threshold
1 Introduction
Allowing secondary (unlicensed) users to simultaneously share the spectrum of primary (licensed) users is known as cognitive radio. Cognitive radio has been proposed to improve the spectrum resource utilization efficiency in wireless networks [1]. Several cognitive radio paradigms have been proposed in [2], among, which is the underlay scenario. This paradigm allows users in a secondary cell (secondary users) to utilize the frequency bands of users in a primary cell (primary users) only if the interference is below a certain threshold. Another important technique, which is used to provide diversity and to enhance the quality of wireless channels is the cooperative or relay network [3]. In such network, a relay or a set of relays are employed to help the source node transmitting its message to destination. Currently, a lot of research is being conducted on what is called cognitive relay networks (CRNs), which are also known as spectrumsharing relay networks. In designing spectrumsharing underlay systems, a major challenge is to fulfill the two conflicting objectives; protecting the primary user from interference, and satisfying the quality of service (QoS) requirement of secondary users. Between these objectives, the former is of higher priority, making strict regulation of secondary transmit powers necessary [4].
The outage performance of decodeandforward (DF) CRNs was evaluated in [5–10]. In these studies, the secondary cell was assumed to include a source, a set of relays, and a destination in addition to a primary user in the neighboring primary cell. Closedform expressions for the outage probability were derived assuming Rayleigh fading and bestrelay or opportunistic relaying scheme. Recently, the outage performance of DF CRNs with the N ^{th}best relay selection scheme was presented in [11] and [12], respectively. Such scheme is efficient in conditions where the best relay is unavailable for relaying and is busy in some scheduling and load balancing duties in other parts of the network. Particularly, in [12], Zhang et al. evaluated a closedform expression for the outage probability where the relay with the N ^{th} best second hop power metric is selected to forward the secondary source message to destination. This metric is conditioned on the maximum transmit power at the relay and the maximum tolerated interference power level at the primary user. In [13], three relay selection scenarios were proposed, the relay with the best second hop, the relay with worst second hop, and the relay satisfying the minimum level of interference with the primary user. Closedform expressions for the outage and error probabilities were derived assuming Rayleigh fading channels.
In [14], the outage performance of amplifyandforward (AF) CRNs was studied with two relay selection criteria, full channel estimation where channelstateinformation (CSI) of all links are assumed to be available at the source and partial channel estimation where CSI of relays first hops are required at the source for relay selection. The opportunistic and partialrelay selection schemes were also recently studied in [15] where the outage and symbol error probabilities in addition to ergodic capacity were evaluated for AF CRNs. The outage and error rate performances of an underlay fixedgain AF CRN with reactive relay selection were evaluated in [16]. Among the relays, which satisfy the interference constraint, the relay with the best endtoend (e2e) channel is selected to forward the source message to destination. In [17], the error rate performance of an AF CRN was studied using the partialrelay selection scheme in which the relay with the strongest first hop channel was selected as the best relay. As an extension to the previous works on AF CRNs, the outage performance of an AF CRN with multiple primary users was recently presented in [18]. A study that proposes three relaying strategies was presented in [19]. These strategies are: selective AF, selective DF, and partial relay selection AF relaying. Asymptotic expressions for the outage probability and coding gain were provided in addition to studying the effect of imperfect channel estimation on the system performance.
Recently, in addition to deriving the ergodic channel capacity, Bao et al. evaluated in [20] the outage probability and error probability performances of AF CRNs assuming Rayleigh fading channels. An upper bound on the e2e SNR was used in the analysis where the dependence between channels from the source and relays in the secondary cell and primary user in the primary cell were taken into account in all derivations. A study that combines between the overlay and underlay CRNs was presented in [21]. While the primary system is idle, secondary users utilize licensed spectrum with overlay mode, and secondary transmitters are with transmit power limits. While primary system is active, secondary users utilize licensed spectrum with underlay mode, and secondary transmitters are with transmit power limits and peak interference power constraints. Upper bound for outage probability was derived assuming Rayleigh fading channels with the existence of direct link in the secondary cell. The effect of interference caused by a primary user on all receiving nodes in a secondary cell was studied in [22]. Closedform and asymptotic expressions for the outage probability were derived over Rayleigh and Nakagamim fading channels and with the DF bestrelay selection scheme being used.
Currently, the performance of CRNs with multiple secondary users is attracting a lot of researchers to work on such important topic. In [23], da Costa et al. evaluated the outage performance of DF spectrumsharing relay networks with multiple primary and secondary users over Nakagamim fading channels. Opportunistic scheduling was used where the secondary destination of the best channel is allowed to receive the secondary source message. In [24], the secondary user was selected in multiuser CRNs to achieve the largest secondary rate while satisfying primary rate target. The authors showed that the diversity order of the primary system equals number of secondary users and for the secondary system equals number of secondary users plus 1. Closedform expressions for the outage probability were derived in [25] for multiuser multirelay CRNs with DF and AF relaying schemes over Rayleigh fading channels. The secondary user with best direct link with the secondary source was scheduled to receive from secondary source. The same system studied in [25] was also studied in [26] but with one primary user. Most recently, the outage performance of CRNs with one secondary source, one secondary relay, multiple secondary users, and one primary user was evaluated in [27]. Unlike previous studies, the interference between primary user and the secondary relay and users is considered in this work. Opportunistic scheduling was used to select the secondary user with the best second hop SNR. Most recently, the opportunistic scheduling was used in [28] and [29] to select among secondary users in DF and AF multipleinput multipleoutput cognitive relay networks, respectively.
As can be seen, the mostly used user selection scheme in multiuser CRNs is the opportunistic scheduling. A drawback of this scheme is the heavy load of channel estimations it requires to select the best user among the available users where the channels of all users need to be estimated each transmission time. Usually, in systems using this scheme, the SU relay is assumed to possess perfect CSI of the relaydestinations links each transmission time, which necessitates that each SU destination or user to estimate its channel and feed it back to the relay each scheduling period. As the number of users in the system increases, the opportunistic scheduling becomes much complicated, and hence, it is often a practical interest to come up with a low complexity scheduling algorithm with a reasonable system performance. An efficient candidate, which can reduce the number of feedback signals between the SU relay and users and hence reducing the system complexity is the lowcomplexity MUSwiD selection scheme. In this scheme, each user can trigger a feedback only when the channel quality is greater than a predetermined threshold. The idea behind the thresholdbased feedback scheme is that only the users with good enough channel quality are worth being considered to be scheduled [30, 31]. This idea was first used in space diversity systems where the switchandexamine diversity combining (SEC) selection scheme was used to select among antennas [32]. In contrast to the opportunistic scheduling, which requires a heavy load of channel estimations or a heavy feedback each transmission time, in the MUSwiD scheme, once a checked user satisfies a predetermined switching threshold, it is scheduled for data reception. In this scheme, the e2e SNR of a secondary user is compared with a certain switching threshold. If it is larger, this user is selected to receive the secondary source message, if not, other user is examined. This process continues till a suitable user is found or the last user is reached. Later, if the last user is found unacceptable, the scheme sticks to it. The MUSwiD user selection schemes proved their effectiveness in reducing the required number of channel estimations, and hence, in reducing the system complexity when compared with the opportunistic user selection scheme [33]. More details on how the MUSwiD selection scheme works are provided in Section 2. Another motivation to this research work is the conduction of comprehensive performance analysis to the considered system model with the use of the MUSwiD lowcomplexity user selection scheme. The derivations and performance measures are being presented for the first time in this paper.
To the best of our knowledge, the performance of cognitive AF relay networks with multiuser switched diversity over Rayleigh fading channels has not been presented yet. The contributions of our paper over the existing studies are as follows: we propose the MUSwiD user selection scheme for cognitive AF multiuser relay networks in addition to analyzing its performance. In contrast to the opportunistic scheduling, in MUSwiD scheme, the first checked secondary user whose e2e SNR exceeds a predetermined switching threshold is selected to receive the secondary source message. Once a user is selected, no need for communicating further feedback signals between the users and the scheduling unit, which is the SU relay in our study. This results in a noticeable reduction in the required number of channel estimations, saves the power of users, and hence, reduces the system complexity. The proposed user selection scheme becomes mainly efficient as the number of users in the system increases. In such condition, the opportunistic scheduling and other scheduling schemes, which require all users channels to be estimated each transmission time become much complicated. In this paper, we derive closedform approximations for the outage probability and ASEP for the independent nonidentically distributed (i.n.i.d.) and independent identically distributed (i.i.d.) cases of users channels. We also derive the ergodic channel capacity for the case of i.i.d. users channels. First, an upper bound on the e2e SNR of a user is introduced. Then, this bound is used to derive a conditional cumulative distribution function (CDF) of the SNR at the output of the MUSwiD selection scheme combiner, which is then used to evaluate the e2e outage probability, ASEP, and ergodic channel capacity of the system. In order to get more insights about the system performance, we study the performance at the high SNR regime where approximate expressions for the outage probability, ASEP, diversity order, and coding gain are derived and analyzed. Furthermore, the MUSwiD with postexamine selection (MUSwiDps) which is an improved version of the conventional MUSwiD user, selection scheme is introduced and analyzed. The main difference between the MUSwiDps and the MUSwiD schemes is in the case where the last user is reached and found unacceptable. In such condition, the MUSwiDps scheme chooses the best user among all checked users to receive the source message.
This paper is organized as follows: Section 2 presents the system and channel models. The performance evaluation is conducted in Section 3. Section 4 provides the asymptotic performance analysis. Some simulation and numerical results are discussed in Section 5. Finally, Section 6 concludes the paper.
2 System and channel models
where \(X=\frac {\mathcal {I}_{\mathsf {p}}}{N_{0}}h_{\mathsf {s,r}}^{2}\), Y=h _{ s , p }^{2}, \(X_{k}=\frac {\frac {\mathcal {I}_{\mathsf {p}}}{N_{0}}h_{{\mathsf {r}},k}^{2}}{h_{\mathsf {r,p}}^{2}}\). The MUSwiD user scheduling is achieved by selecting the user with the e2e SNR \(\gamma _{k}^{\mathsf {up}}\) satisfies a predetermined switching threshold.
The used symbols and their description
Symbol  Description  Symbol  Description 

S  Secondary source  G  Gain of R 
D _{ k }  k ^{th} secondary destination  h _{ s , p }  Channel coefficient between S and P 
R  Secondary relay  h _{ s , r }  Channel coefficient between S and R 
P  Primary user  h _{ r , p }  Channel coefficient between R and P 
\(\mathcal {I}_{\mathsf {p}}\)  Interference threshold  h _{ r,k }  Channel coefficient between R and D _{ k } 
P _{ s }  Transmit power at S  n _{ s , r }  Noise at R 
x  Source symbol  n _{ r,k }  Noise at D _{ k } 
P _{ R }  Transmit power at R  N _{0}  Noise power 

Fairness. Achieving fairness among users or achieving maximum sum capacity is a tradeoff issue. Also, maximizing the sum capacity is not always an appropriate optimization criterion for realistic network scenarios since users usually have asymmetric channel statistics. To guarantee fairness among users in the selection process, the time division feedback access can rearrange the user sequence every scheduling opportunity so that every user can have the same chance of taking the first place in user sequence over an extended period of time. Also, it is worthwhile to mention here that the sum capacity of such systems can be enhanced by assigning different switching thresholds for the different users as discussed in [33]. This issue is beyond the scope of our paper.

Centralized scheduling. In order to avoid any collusion, which may happen when multiple users send feedbacks, a centralized feedback collection method can be used. This method organizes the users to be orthogonal when they send feedbacks, such as time division multiplexing (TDM) where users are separated over time.
The multiuser switched diversity selection schemes proved themselves as a less complicated user selection schemes compared to the opportunistic scheduling from the number of channel estimationswise. This happens on the expense of the system sum rate, which was shown in [35] to be compensated by significant savings in the CSI feedback load. The authors showed that the MUSwiD user selection schemes provide significant reduction of CSI feedback load at the cost of slight reduction in the achievable multiuser diversity gains, especially, at the low SNR values. This makes the MUSwiD selection schemes an attractive option for practical implementation in emerging mobile broadband communication systems.
3 Performance analysis
In this section, we evaluate closedform approximations for the outage probability and average symbol error probability of the studied system. The channel capacity if also derived and numerically calculated in this section. The outage probability is a measure for the system performance and the possibility of the system to fall in outage. This is clear from the definition of the outage probability, which says that the system could get in outage once the SNR at the destination goes below a predetermined outage threshold γ _{ out } or, equivalently the system is unable to achieve adequate reception. The possibility of the destination SNR to fall under a certain threshold exists in any communication system. In regard to deriving the ergodic capacity, as we are considering slowly varying fading channel model, this means that the coherence time of the channel is much larger than the data rate, and hence, the fading status remains constant over a large number of transmitted bits. This means that the average (i.e., ergodic) capacity of the channel could be a suitable measure for the best achievable capacity of the considered system links. In summary, the ergodic capacity we derived in this paper is valid under the assumption that the information symbol is long enough to ensure the longterm ergodic properties of the links.
3.1 Outage probability
In this section, we evaluate closedform approximations for the outage probability for the i.n.i.d. and i.i.d. cases of users channels. The outage probability is defined as the probability that the SNR at the scheduled destination γ _{ up } goes below a predetermined outage threshold γ _{ out }, i.e., P _{ out }=Pr[γ _{ up }≤γ _{ out }], where Pr[.] denotes the probability operation. Our results on the outage probability of the studied system are summarized in the following lemma and corollary.
Lemma 1
where Δ _{1}=λ _{1} γ _{ T }+λ _{ s , p }, \(\Delta _{2}=\sum _{u=0}^{p}\lambda _{2_{((lw+v_{u}))_{K}}}+\lambda _{1}\gamma _{\mathsf {T}}+\lambda _{\mathsf {s,p}}\phantom {\dot {i}\!}\), \(\Delta _{3}=1+\lambda _{2_{((lw+v_{g}))_{K}}}\gamma _{\mathsf {T}}\phantom {\dot {i}\!}\), and \(\Delta _{4}=\sum _{u=0}^{p}\lambda _{2_{((lw+v_{u}))_{K}}}+\lambda _{1}\gamma _{\mathsf {out}}+\lambda _{\mathsf {s,p}}\).
Proof
Please, see Appendix. □
Corollary 1
Proof
where λ _{1} is as defined in the Appendix and \(\lambda _{2}=\Omega _{{\mathsf {r,p}}}\Big /\left (\Omega _{{\mathsf {r,d}}}\frac {\mathcal {I}_{\mathsf {p}}}{N_{0}}\right)\). Upon substituting (5) in (4) and following the same procedure as in the Appendix, we get the result in (3). □
3.2 Average symbol error probability
where a and b are modulationspecific constants. Our results on the SEP of the studied system are summarized in the following lemma and corollary.
Lemma 2
where Γ(.,.)is the incomplete gamma function defined in ([ 37 ], Eq. (8.350.2)), 𝜗 _{1} =λ _{1} γ _{ T }+λ _{ s , p } and 𝜗 _{3}=2λ _{1} γ _{ T }+λ _{ s , p }.
By replacing γ _{ out } with γ in (2) and using the partial fraction expansion and the integration in (8) and with the help of ([37], Eq. (3.361.2)) and ([37], Eq. (3.383.10)), we get the result in (9).
Corollary 2
By replacing γ _{ out } with γ in (3) and using the partial fraction expansion and the integration in (8) and with the help of ([37], Eq. (3.361.2)) and ([37], Eq. (3.383.10)), we get the result in (10).
3.3 Ergodic channel capacity
Our result on the ergodic capacity of the studied system is provided in the following lemma.
Lemma 3
where α, β, α ^{′}, and β ^{′} are as given in the proof below. According to authors knowledge, the integrations in (12) have no closedform solution. Hence, the ergodic channel capacity of the system is numerically evaluated.
Proof
Upon substituting (14) in (11) and after some mathematical arrangements and with the help of ([37], Eq. (4.291.15)), we get the result in (12). □
4 Asymptotic performance analysis
Due to complexity of the achieved expressions in previous sections, it is hard to get more insights about system performance. Therefore, we see that it is important to derive simple expressions for the outage probability and ASEP at the high SNR values where more insights about the system behavior can be achieved. In this section, we evaluate the asymptotic outage performance of the studied system with the MUSwiD and MUSwiDps user selection schemes. At high SNR values, the outage probability can be expressed as \(\phantom {\dot {i}\!}P_{\mathsf {out}}\approx (G_{\mathsf {c}}\text {SNR})^{G_{\mathsf {d}}}\), where G _{ c } denotes the coding gain of the system and G _{ d } is the diversity order of the system [36]. The parameters on which the diversity order depends will affect the slope of the outage probability curves, and the parameters on which the coding gain depends will affect the position of the curves. In the upcoming analysis, the users are assumed to have identical channels.
where γ(.,.) is the incomplete Gamma function defined in ([37], Eq. (8.350.1)).
It is clear from (17) that the system with the MUSwiD selection scheme has a diversity order of 1 and a coding gain that is function of Ω _{ s , r }, λ _{ s , p }, γ _{ out }, and γ _{ T }.
It is clear that the asymptotic outage probability of the MUSwiDps user selection scheme is exactly the same as that of the MUSwiD scheme. Accordingly, the asymptotic SEP of the MUSwiDps scheme will be equal to that of the MUSwiD scheme as obtained in (19).
As can be seen from the results in (17) and (22), the coding gain of the system with the MUSwiD and MUSwiDps user selection schemes is affected by several parameters as Ω _{ s , r }, λ _{ s , p }, γ _{ out }, and γ _{ T }; while the diversity order is constant at 1. This is clear in the numerical examples where all curves of different K asymptotically converge to the same behavior and result in a diversity order of 1. It is expected from the way the MUSwiD and MUSwiDps selection schemes operate that the gain achieved in system performance due to having more SU destinations to happen at the SNR values that are comparable to γ _{ T }. As in this case, the switching rate will increase and the probability of having better users increases also. At the same time, as the asymptotic analysis is done at high SNR values, it is expected to have most of the users being acceptable the whole time and thus, the first checked user is being selected in the two selection schemes. This means all curves of different K asymptotically converge to same behavior, and this explains why the system with the two selection schemes has the same diversity order and the same coding gain as will be shown in numerical examples. In addition, it can be noticed from (17) and (22) that the diversity order of cognitive CSIassisted AF MUSwiD relay network is the same as that of its noncognitive counterpart. Specifically, it is equal to 1 and is independent of the primary network. It is worthwhile to mention here again that the importance of the proposed MUSwiD and MUSwiDps user selection schemes is in the reduced number of channel estimations and feedback load they require each transmission time compared to the opportunistic scheduling. Furthermore, from the asymptotic results, we conclude that the MUSwiD user selection schemes are inefficient at the range of high SNR values where the diversity order of the system becomes fixed and equal 1 when they are implemented. Accordingly, it is preferable to apply such lowcomplexity user scheduling schemes in systems that operate at the low range of SNR values as in the emerging mobile broadband communication systems. This fact about the applicability of the MUSwiD selection schemes was also proved and mentioned in [35].
The optimum switching threshold can be numerically calculated to minimize the e2e outage probability or symbol error probability. Due to complexity of the achieved expressions, any further manipulation with them to find the optimum threshold will increase the system complexity. Alternatively, we present here a simple method that can be used to get approximate but accurate values of the optimum switching threshold. In general, a good choice of the switching threshold is to have it near the average value of the e2e SNR, which can be upper bounded by the minimum of its two hops. Therefore, the optimum switching threshold can be calculated using \(\text {min}\left (\frac {\frac {\mathcal {I}_{\mathsf {p}}}{N_{0}}h_{\mathsf {s,r}}^{2}} {h_{{\mathsf {s,p}}}^{2}},\frac {\frac {\mathcal {I}_{\mathsf {p}}}{N_{0}}h_{{\mathsf {r}},k}^{2}}{h_{\mathsf {r,p}}^{2}}\right)\). This method give excellent results as will be seen in the coming section.
5 Simulation and numerical results
In this section, we illustrate the validity of the achieved analytical and asymptotic expressions via a comparison with MonteCarlo simulations. We also provide some numerical examples to show the effect of some system parameters such as number of users, switching threshold, and outage threshold on the system performance.
6 Conclusions
In this paper, we evaluated the performance of a cognitive CSIassisted AF relay network with the MUSwiD user selection scheme. Closedform approximations for the outage probability and average symbol error probability were derived for the i.n.i.d. and i.i.d. cases of users channels. The ergodic channel capacity was also numerically evaluated. Furthermore, the system outage and error probability performances were evaluated at high SNR values where simple expressions for the outage probability, symbol error probability, diversity order, and coding gain were derived and analyzed for the MUSwiD and MUSwiDps user selection schemes. MonteCarlo simulations proved the accuracy of the achieved analytical and asymptotic results. Findings illustrated that the proposed MUSwiD user selection schemes are efficient in the range of low SNR values, which makes them attractive options for practical implementation in emerging mobile broadband communication systems. In contrast, these selection schemes are inefficient in the range of high SNR values where the multiuser diversity gain is noticeably degraded when they are implemented. Furthermore, results illustrated that the gain achieved in performance due to having more users happens in the range of SNR values that are comparable to the switching threshold.
7 Endnotes
^{1} Secondary users can know the channel information of the primary user by either a direct reception of pilot signals from a primary user [39], or by exchange of channel information between primary and secondary users through a band manager [40].
^{2} This assumption is possible if the primary transmitter is located far from the secondary user [41], or the interference is represented in terms of noise when the primary transmitter’s signal is generated by random Gaussian codebooks [42].
^{3} In this paper, the switching threshold is numerically calculated to optimize the e2e outage probability. Also, a simple method is proposed in Section 4 to obtain approximate but accurate values of the optimum switching threshold.
^{4} The time duration of the feedback channel is not long, and hence, the MUSwiD scheduling scheme does not cause additional delay to the scheduling process [35].
8 Appendix
8.1 Proof of Lemma 1
where \(\lambda _{1}=1\Big /\left (\Omega _{\mathsf {s,r}}\frac {\mathcal {I}_{\mathsf {p}}}{N_{0}}\right)\) and \(\lambda _{2_{k}}=\Omega _{\mathsf {r,p}}/\left (\Omega _{{\mathsf {r}},k}\frac {\mathcal {I}_{\mathsf {p}}}{N_{0}}\right)\).
where \(\sum _{v_{0}<\ldots <v_{p}}^{w1}\) is a shorthand notation for \(\sum _{v_{0}=0}^{wp1}\sum _{v_{1}=v_{0}+1}^{wp}\ldots \sum _{v_{p}=v_{p1}+1}^{w1}\).
Upon substituting (30), (31), and (32) in (29) and using (33), the outage probability can be evaluated in a closedform approximation as in (2).
Declarations
Acknowledgements
This work is supported by Deanship of Scientific Research (DSR) at King Fahd University of Petroleum & Minerals (KFUPM) through project #: RG14081,2.
Competing interests
The authors’ declare that they have no competing interests.
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Authors’ Affiliations
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