An Optimal Power Allocation and Relay Selection Full-Duplex Store-Carry-Forward Scheme for Intermittently Connected Vehicular Networks

We consider intermittently connected vehicular networks (ICVNs) in which base stations (BSs) are installed along a highway to connect moving vehicles with internet. Due to the deployment cost, it is hard to cover the entire highway with BSs. To minimize the outage time in the uncovered area (UA), several store-carry-forward (SCF) schemes have been proposed in which a vehicle is selected to act as a relay by buffering data to be relayed to a target vehicle in the UA. In this paper, we propose a full-duplex (FD) SCF scheme that exploits the relay’s ability to simultaneously receive and transmit in order to improve the effective communication time (ECT) with the target vehicle and accordingly deliver more data to it in the UA. The optimal power allocation (PA) that maximizes the ergodic capacities of the links is determined and the amount of data that can be buffered inside the BS coverage and can be delivered by each relay candidate to the target vehicle in the UA is found. Since the relay cannot deliver more data in the UA than what can be buffered inside the coverage, the performance of each relay candidate is limited by the minimum of the two amounts and hence is used as a relay selection (RS) criteria. To reduce the computational complexity, an alternative RS scheme that selects the relay candidate that offers the highest ECT is proposed. As compared to half-duplex SCF schemes, simulation results show that the proposed FD schemes are capable of delivering significantly higher amount of data to the target vehicle in the UA.


I. INTRODUCTION
Vehicular communication networks (VCNs) have attracted a lot of attention due to their ability to improve road safety and traffic control as well as support advanced infotainment applications [1]. In certain vehicular environments, such as highways, it maybe hard to provide seamless connectivity due to geographical conditions or deployment cost. VCNs in which the distance between neighboring base stations (BSs) is large such that there are uncovered areas (UAs) between them is known as intermittently connected vehicular networks (ICVNs) [2] or as vehicular delay tolerant networks (VDTNs) [3]. Such lack of connectivity is more common in The associate editor coordinating the review of this manuscript and approving it for publication was Muhammad Awais Javed . developing countries than developed ones due to deployment cost. It is reported in the literature that the average distance between adjacent Internet access points in highways might reach 8-16 km [4]. Therefore, vehicles may fail to fulfill the download requirements of large-size content due to the existence of UAs as well as the short duration inside the coverage area as a result of the high mobility. The problem is even aggravated by the fact that resources in terms of time or bandwidth are shared among vehicles inside the coverage. To overcome this limitation, several cooperative store-carry-forward (SCF) schemes are proposed to convert vehicles from being competitors to cooperators [2].
The time duration in which a vehicle stays in the UA without connectivity is known as the outage time. A moving vehicle may request large amounts of data that cannot be fully VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ transferred within the BS coverage. In such case, this vehicle, referred to as the target vehicle henceforth, suffers from outage in the UA before reaching the coverage of the next BS. If the UA is large, the outage may cause intolerable delay for some applications (e.g., file download or video transmission [2], [3]). To minimize the outage time and provide more persistent services, several SCF relaying schemes have been proposed. In these schemes, based on certain criteria, one or more vehicles are selected to act as relays. While the target vehicle is receiving data from the BS, the selected relay(s) stores part of or the entire remaining data (RD) that cannot be delivered to the target vehicle inside the BS coverage. When the target vehicle enters the UA, the relay stops from storing more data and starts relaying the buffered data to the target vehicle. Consequently, the outage time is reduced by the time duration of the communication between the relay and the target vehicle in the UA. This time duration will be termed as the effective communication time (ECT). Due to the high mobility of the vehicles, the available time for the relay(s) to buffer the target vehicle's data as well as the available time for the relay(s) to stay within the communication range of the target vehicle in the UA are both limited. The ECT between the relay and the target vehicle is clearly equal to the minimum between the available time for buffering and that available for communication in the UA [3]. Therefore, minimizing the outage time in ICVNs remains a real challenge, and this is the main scope of this paper.
In-band full-duplex (FD) communications, where nodes are able to transmit and receive simultaneously over the same band, can achieve high spectral efficiency as opposed to HD communications. Recently, the impressive improvement in self-interference cancellation (SIC) techniques (e.g., in the order of 70−110 dB) has attracted a lot of attention to in-band FD communication as a promising technology for future wireless systems [5]. For VCNs, in particular, there is a great potential for using FD communications where requirements such as the need for space for antenna isolation and for an on-board unit with high computational efficiency as well as energy consumption considerations are less challenging to be satisfied in vehicles than in mobile devices [5]. To the best of our knowledge, with the exception of our previous work in [6], all the existing SCF schemes in the literature that have been proposed for ICVNs are using half-duplex (HD) communication, in which once the selected relay(s) start transmission to the target vehicle, they have to stop from storing more data. On the contrary, FD communication offers the ability of transmitting and receiving simultaneously. Simply put, if the relay is capable of FD communication, the relay can continue in buffering more data as long as it stays within the BS coverage while transmitting to the target vehicle. Therefore, the ECT will be increased, which, in turn, reduces the outage time and allows for delivering larger amounts of information to the target vehicle in the UA.
According to the discussion above, in this paper, we investigate the downlink communication scenario of ICVNs in which a large amount of data may be requested by a target vehicle V o . We propose an FD SCF scheme that exploits the relay's ability of receiving and transmitting simultaneously to improve the ECT between the relay and the target vehicle. Accordingly, more data can be delivered to the target vehicle in the UA. The proposed scheme exploits the spectral efficiency of FD communication to maximize the ergodic capacities of the links. Since the BS can transmit with higher rate to the target vehicle V o , either the relay help will not be required or at least less data must be delivered through the selected relay to V o in the UA. In addition, the relay can buffer more data inside the BS coverage and deliver more data to V o in the UA. Since the proposed scheme depends on ergodic maximization (EM), we refer to it as the EM-SCF scheme hereafter.
The proposed EM-SCF scheme consists of power allocation (PA) and relay selection (RS) steps. Inside the BS coverage, at each time slot, the optimal PA that maximizes the ergodic capacity of the downlink while satisfying the capacity requirements of the uplink is determined for each of the target vehicle and the relay. The capacity requirements of the uplinks are fulfilled by ensuring the outage probabilities of these links are less than an acceptable threshold. At the relaying stage, in which the target vehicle stays in the UA, at each time slot, the optimal PA that maximizes the ergodic capacity of the link between the relay and the target vehicle is found. Clearly, the maximum amount of information that can be buffered by the relay is equal to the sum of ergodic capacities over the time slots in which the relay stays inside the BS coverage, while the maximum amount of information that can be transferred to V o in the UA is equal to the sum of ergodic capacities over the time slots in which the relay can communicate with V o in the UA. Since the relay cannot deliver more information to V o in the UA than what can be buffered inside the coverage, the performance of each relay candidate can be assessed based on the minimum of the two sums of the ergodic capacities. The proposed EM-SCF scheme thus selects the relay candidate that has the maximum minimum.
Finally, to reduce the computational complexity, we propose a hybrid SCF scheme that merges the simple RS of the special case in [6] with the PA of the proposed EM-SCF scheme. Specifically, the hybrid scheme uses the RS of the scheme in [6], i.e., assuming fixed transmission rate (FTR), to select the relay candidate that offers the highest ECT, and thereby can deliver the largest amount of data to the target vehicle V o in the UA. Then, at each time slot, the ergodic capacities of the links are maximized as in the proposed EM-SCF scheme. The rest of the paper is organized as follows: the next section surveys the related works in the literature, Section III presents the system model under consideration along with other assumptions, the problem formulation is then introduced in Section IV followed by the proposed EM-SCF scheme in Section V. Simulation results and discussions are then presented in Section VI before the paper is finally concluded in Section VII.

II. RELATED WORK
Minimizing the outage time is of great interest and it has been previously considered in the literature. The outage time can be significantly reduced if multihop SCF relaying is used such as the schemes in [7]- [9]. However, in addition to the high signaling overhead, the throughput will rapidly diminish as the number of relay hops increases [10]. Accordingly, keeping the number of relay hops as low as possible is preferred [2].
In [11], the outage time is reduced by adjusting the speed of the target vehicle to extend the communication time with the selected relay vehicle. A bivious SCF scheme is proposed in [12], which minimizes the outage time by selecting forward and backward relays. In addition, the speed of the target vehicle is adjusted to extend the communication time. The main drawback of the works in [11] and [12] is that the problem of speed adjusting is solved using the interior-point method that inevitably involves large number of iterations [2]. The SCF scheme proposed in [2], on the other hand, minimizes the outage time by selecting two relays one from each traffic direction. When the first relay loses communication with the target vehicle in the UA, the second relay from the opposite direction starts relaying to the target vehicle. The outage time is minimized by the amount of the sum of the ECT of the two relays. In [13], based on the size of the RD, one or more relays are selected from the opposite traffic direction. While V o receives data directly from the roadside unit (RSU), the selected relays from the opposite traffic direction pre-store part of or the entire RD. When V o enters the UA, the selected relays start relaying the pre-stored data to V o . The work in [13] has been extended in [4], where a cluster-based relay selection is proposed. In this scheme, the target vehicle V o follows the vehicles that have no download requirements and form a cluster together. In addition, one or more relays are selected from the opposite traffic direction in similar criterion as that of [13]. When V o enters the UA, the selected relays and cluster members start relaying the buffered data inside the RSU coverage to V o . In [3], the fact that relay candidates give priority to their data transfer over helping the target vehicle is considered. Based on the size of the RD, relay candidates are selected based on their ECT. The relay candidate that offers the highest ECT is selected first. Since FTR is assumed, the relay candidate with highest ECT is the one capable of delivering the largest amount of data to the target vehicle in the UA.
It is very important to note that all the aforementioned SCF schemes use HD communications, in which once the selected relay starts relaying to the target vehicle, it has to stop from storing more data. The FD SCF scheme we proposed in [6] exploits the relay's ability of receiving and transmitting simultaneously to increase the ECT. More specifically, the selected relay can continue in buffering more data as long as it stays within the BS coverage while transmitting to the target vehicle. The FD SCF in [6] represents a special case of the proposed EM-SCF scheme in this work since, for simplicity, FTR was assumed instead of maximizing the ergodic capacities of the links. In each time slot, the scheme in [6] determines the PA that minimizes the transmission cost (i.e., consumed energy/rate). To achieve that, the optimization problem was formulated as an standard geometric program (GP) and solved using the interior-point method. b) The start of the relaying stage in the HD schemes such as [3]. c) The start of the relaying stage in the proposed FD scheme. d) Relaying stage in the UA.

A. NETWORK MODEL
As mentioned earlier, we consider ICVNs, where BSs are installed linearly (i.e., with equal inter-BS distance d 0 ) along a highway to connect moving vehicles with the Internet. Without loss of generality, we consider the simple one-way highway model used in [3] as shown in Fig. 1. We assume that all vehicles and BSs have equal transmission ranges, denoted by r 0 , i.e., the cell radius is r 0 . Due to the installation cost, it is hard to cover the entire highway with BSs coverage. Thus, we assume that the BSs coverage is not seamless and there are UAs as illustrated in Fig. 1, i.e., d 0 > 2r 0 and the uncovered distance u = d 0 − 2r 0 .
We also assume that BSs and vehicles are capable of FD communications and are equipped with isolated antennas for transmission and reception. Similar to the works in [2]- [4], [11]- [13], we investigate the downlink communication scenario in which a target vehicle V o may request a large amount of data that cannot be received entirely inside the BS coverage. To provide a persistent service, one of the vehicles is selected to act as a relay by buffering part of or the entire remaining data that cannot be delivered to V o inside the BS coverage to be relayed to V o in the UA. Figure 1 illustrates the coverage stage, relaying stage and what differentiates the proposed FD SCF schemes from the existing HD ones. More specifically, Fig. 1(a) shows the coverage stage in which both V o and V k stay inside the BS coverage. In the HD SCF schemes, once V o reaches the UA, the relay V k stops the reception from the BS and starts relaying to V o as shown in Fig. 1(b). On the contrary, in the proposed FD SCF schemes, the relay V k can continue buffering data while relaying already buffered data to V o as demonstrated in Fig. 1(c). Lastly, when both V o and V k are located in the UA, there is one active transmission from V k to V o in all schemes as illustrated in Fig. 1(d).

B. CHANNEL MODEL
Vehicles and BSs are assumed to use in-band FD communications to exchange information. Henceforth, we use c, r and o in the subscript to denote the BS, the relay and the target vehicle V o , respectively. In the downlink from the BS to V o , the signal-to-interference plus noise ratio (SINR) at V o is given by [14] γ where P c,o is the transmission power used by the BS in the downlink, while P o is the transmission power used by V o in the uplink that causes self-interference (SI) to the downlink. The fact that the SI cannot be removed perfectly is captured using the factor β that represents the residual SI, where 0 ≤ β ≤ 1. Also, σ 2 is the variance of the zero-mean additive white Gaussian noise (AWGN). Finally, h c,o is the channel power gain of the link from the BS to V o that is given by [15] where u c,o represents the small-scale fading channel power modelled by an exponentially distributed random variable with unit mean assuming that channels follow Rayleigh fading. Also, g c,o models the large-scale fading power component (i.e., shadowing and pathloss) and h c,c , h r,r and h o,o are the channel power gains of the SI links at the BS, the relay and V o , respectively. All the remaining channels of the network follow the same modelling as h c,o . Similarly, the SINR of the uplink from V o to the BS is equal to For the FD communications between the BS and the relay, the SINR of the downlink and uplink are, respectively, given by where P c,r (P r,c ) is the transmission power used by the BS (the relay) in the downlink (uplink) to the relay (the BS). We assume that the BS is capable of estimating the instantaneous locations of all vehicles inside its coverage as well as their speeds [2], [3]. We also assume that the BS has the large-scale information of all links, which depend on the vehicles' locations and that change with a low rate. As the BS only tracks large-scale information, it avoids the overhead of tracking and transferring instantaneous channel state information (CSI) that is characterized by a fast rate of change due to the vehicles mobility [1].

IV. PROBLEM FORMULATION
The proposed EM-SCF scheme exploits the spectral efficiency of FD communication to maximize the ergodic capacities of the links. Since FD communication is considered, the impact of the uplink transmission on the amounts of data that can be buffered inside the BS coverage and can be delivered to the target vehicle V o in the UA must be taken into account. The optimal PA that maximizes the ergodic capacities of the links inside the BS coverage and in the UA will be determined as explained in the following subsections.

A. COVERAGE STAGE
In each time slot, for each of the target vehicle V o and a relay, say the kth vehicle, V k , the optimal PA that maximizes the ergodic capacity of the downlink while guaranteeing the minimum capacity requirement of the uplink needs to be determined. Since the downlinks are of interest in this work and the usage of the downlinks resources is more intensive as compared to the uplinks [1], the ergodic capacities of the downlinks are maximized while the minimum capacity requirements of the uplinks are fulfilled. For the relay V k , at the i-th slot time slot, assuming that the maximum allowed transmit powers for the BS and the relay vehicle are given by P c max and P r max , respectively, the PA problem can now be formulated as is ergodic capacity of the downlink from the BS to V k while transmission in the uplink is still active, which is given by [ where E[·] returns the expected value, t dt is the exponential integral function of the first order, which is available as a built-in function in software packages such as MATLAB, W is the channel bandwidth, y = . The constraint in (6b) fulfills the minimum capacity requirements of the uplink by ensuring that the outage probability of the link is less than an acceptable threshold O U max where γ U = 2 C − 1 is the SINR threshold and C is the fixed transmission rate, both of the uplink.
The optimization problem in (6) is formulated assuming that transmission in the uplink is active; however, if the relay V k has finished from transmission in the uplink, there will be no interference to the downlink. The ergodic capacity of the downlink in case of no interference from the uplink is given by [17,Eq. (39)] It is worth mentioning that the constraints in (6b) and (6b) are constraining the uplink transmission, and will thus be neglected in this case. The ergodic capacity of the downlink is thus maximized considering the power constraint (6b) only. For the target vehicle V o , the ergodic capacity of the downlink under the existence or the absence of the uplink transmission can be maximized similar to the relay V k by replacing r by o in the superscripts of all the variables used.

B. RELAYING STAGE
As mentioned earlier, when the target vehicle V o enters the UA, the selected relay V k continues buffering more data while transmitting to V o as shown in Fig. 1(c). If the relay V k enters the UA, it stops the reception but continues the transmission to V o as long as it stays within the communication range of V o as shown in Fig. 1(d). First, we will tackle the first scenario in which V k receives from the BS while transmitting to V o . Clearly, there are two active links; the downlink from the BS to V k and the link from V k to V o . Indeed, maximizing both links is the best choice. However, while the capacity of the second link increases as the transmission power P r,o i increases, it causes SI to the downlink. Accordingly, it is difficult to maximize the ergodic capacities of both links concurrently. Alternatively, we choose to maximize the ergodic capacity of the link from V k to V o while setting a minimum capacity requirement, C, for the downlink. We gave more priority for delivering the buffered data to V o over buffering more data from the BS to avoid buffering more data than what can actually be delivered. As will be shown in the sequel, this decision has been tested using simulations and actually resulted in more delivered data to V o in the UA as compared to the choice of maximizing the downlink. Now, the ergodic capacity of the link from V k to V o is given by where q = where γ D r is the SINR of the downlink from the BS to V k that is given by (4) and γ D = 2 C − 1 is the SINR threshold of the same link. The constraint in (10b) ensures that the outage probability of the link is less than an acceptable threshold O D max . Now, if the relay has finished its reception from the BS, which occurs either when it has reached the UA or received all the RD, it will not experience any SI. In that case, the ergodic Finally, the maximum amount of data that can be buffered by the relay V k is equal to the sum of the maximized ergodic capacities of the time slots in which it stays inside the BS coverage, while the maximum amount of data that can be transferred to V o in the UA is equal to the sum of the maximized ergodic capacities of the time slots in which the relay can communicate with V o in the UA. Since the relay cannot deliver more information to V o in the UA than what can be buffered inside the BS coverage, the performance of each relay candidate is limited by the minimum of the two sums of the ergodic capacities. Based on this discussion, the proposed EM-SCF scheme in this work selects the relay candidate that has the maximum minimum as will be discussed in details in the next section.

V. THE PROPOSED EM-SCF SCHEME
In this section, we explain the proposed EM-SCF scheme that exploits the spectral efficiency of FD communication to maximize the ergodic capacities of the links. This scheme enables the BS and vehicles to transmit with higher rates as compared to the special case in [6] and the HD schemes such as those in [2] and [3]. Since the BS transmits with higher rate to the target vehicle V o , either the relay help will not be required or at least less data must be delivered through the selected relay. In addition, the relay will be able to buffer more data inside the BS coverage and deliver more data in the UA.
Since the proposed EM-SCF scheme is not using FTR, it is difficult to find the relay candidate that can help V o the most at the instant of RS. Specifically, it is difficult to determine the amount of data that can be buffered by each relay candidate inside the BS coverage as well as the amount that can be delivered to V o in the UA. Consequently, first, the optimal PA that maximizes the ergodic capacities of the links will be found as formulated in the previous section. Then, we introduce the RS step as well as a proposed hybrid scheme that aims to deliver as large amount of information as possible to V o in the UA. Lastly, we provide a comparison between the RS steps of the proposed schemes and those of previous works in terms of the computational complexity and performance. VOLUME 8, 2020 A. ERGODIC CAPACITY MAXIMIZATION As before, let V k be the selected relay, where the RS will be discussed in Section V-C. The maximization of the ergodic capacities of the links at the BS coverage and the UA is found next.

1) COVERAGE STAGE
The PA problem that maximizes the ergodic capacity of the downlink while guaranteeing the minimum capacity requirement of the uplink is formulated in (6). Using the definition of γ U r in (5), the constraint (6b) can be rewritten as Using the result in [15,Appendix I], which is also restated in Lemma 1 in [1], the constraint in (11) can be expressed as Since large-scale fading parameters are assumed to be fixed within the time slot and small-scale fading is modelled by exponentially distributed random variables with unit mean as mentioned in Section III, (12) reduces to where E P r,c i g r,c i u r,c i = P r,c i g r,c i [15]. Similarly, the other expected values in (12) can be found as expressed in (13). In [18], upper and lower bounds on the outage probability in the left side of (13) were found. This upper bound is given by In the typical area of interest of the outage probability (i.e., in the order of O U max ≤ 5%), the lower and upper bounds are actually so tight and the difference between them almost vanishes [18]. Hence, inspired by [1], the outage probability in the left side of (13) will be replaced by its upper bound in (14) and the problem in (6) can now be expressed as where Since the ergodic capacity E r,u i (V k ) in (7) is monotonically increasing (decreasing) as P c,r i (P r,c i ) increases. The optimal PA problem in (15) necessitates that the outage constraint in (15b) be met with equality. This can be proved by contradiction as follows. Let us assume that at the optimal point, the outage constraint in (15b) does not satisfy the equality, then we have This means, however, that we still can increase P c,r i and/or decrease P r,c i until equality is reached since the objective function in (15) is monotonically increasing (decreasing) with P c,r i (P r,c i ). Therefore, the inequality in the outage constraint contradicts the optimality of the solution. Accordingly, at optimality, the outage constraint in (15b) must be met with equality and P r,c i can be expressed in terms of P c,r i as After substituting P r,c i in the objective function (15) with its value in terms of P c,r i using (17), the objective function becomes monotonically increasing with P c,r i . Meanwhile, P c,r i increases with the increase of P r,c i as can be seen in (17). Accordingly, taking into account the equality of the outage constraint in (17) and the power constraints (15c)-(15d), the optimal PA solution of the problem in (15) can be obtained as and Henceforth, we use E r,u i (V k ) to denote the maximized value of E r,u i (V k ) that is obtained by replacing P c,r i and P r,c i in (7) with their optimal values P c,r * i and P r,c * i , respectively. We next consider the next case as mentioned in Section IV-A; that is if the relay V k has finished transmission in the uplink and there is no interference to the downlink. The ergodic capacity of the downlink in the absence of the SI from the uplink transmission is equal to E r i (V k ) that is given by (8). Since E r i (V k ) is monotonically increasing with P c,r i , the optimal power P c,r * i that maximizes E r i (V k ) is simply equal to P c max . By replacing P c,r i in (8) with its optimal value P c,r * i , we obtain the maximum ergodic capacity E r i (V k ).

2) RELAYING STAGE
First, we tackle the scenario in which the selected relay V k receives from the BS while transmitting to the target vehicle V o that stays in the UA. For this scenario, the PA that maximizes the ergodic capacity of the link from V k to V o while fulfilling the capacity requirement of the downlink from the BS to the relay is formulated as given in (10). Similar to the simplification of the outage constraint from (6b) to (15b), the outage constraint in (10b) can be simplified, and the problem in (10) can be expressed as where As discussed earlier, the optimal PA problem in (20) necessitates that the outage constraint in (20b) be met with equality. Again, this can be proved by contradiction as shown before. Therefore, taking this into consideration along with the power constraints (20c)-(20d), the optimal PA of the problem in (20) can be obtained as and By replacing P r,o i and P c,r i in (9) with their optimal values P r,o * i and P c,r * i , we obtain the maximum ergodic capacity E r,o i . For the last scenario in which the relay V k has finished reception from the BS, there is no SI at the relay. Therefore, the ergodic capacity of the link from V k to V o is equal to E r,o i (V k ) as given by (9). As mentioned in Section IV-B, E r,o i (V k ) is maximized under the power constraint in (20d) only. Like earlier, since E r,o i (V k ) is monotonically increasing with P r,o i , the optimal power P r,o * i is simply equal to P r max . In this case, we denote the maximum ergodic capacity by E r,o i .

B. OVERALL PERFORMANCE OF THE RELAY
As mentioned in Section IV, the performance of each relay candidate is limited by the minimum between the maximum amount of data that can be buffered inside the BS coverage and the maximum amount of data that can be delivered in the UA. In this section, these amounts will be determined based on the optimal PA presented in V-A. We first start with the amount of RD, R d , that must be delivered to the target vehicle V o in the UA through the selected relay is equal to where R q (V o ) is the size of the requested data by V o and E o is the maximum amount of data that V o can receive inside the BS coverage, which is given by with v o and d(V o ) being, respectively, the speed and distance of V o from the reference point O as shown in Fig. 1. Also, t returns the largest integer smaller than or equal to t. The binary variable a i in (24) is indicating whether the uplink transmission is active (a i = 1) or not (a i = 0), viz., where T n (V o ) represents the remaining time for V o to finish transmission in the uplink, which may take the entire coverage time T r (V o ). This is given by with R Tx q (V o ) being the size of the requested data by V o in the uplink.
Similar to [3], among all relay candidates, only candidates that will be within the transmission range r 0 of V o when it reaches the UA will be considered. When V o reaches the UA, the distance between V o and V k is given by where d(V k ) is the location of V k at the instant of relay selection. If |D(V k )| > r 0 , V k will be removed from the candidate list.
On the other hand, the amount of data, E b (V k ), that can be buffered by a relay candidate V k inside the BS coverage is equal to where R q (V k ) is the size of the requested data by the relay candidate V k in the downlink and E r (V k ) is the maximum VOLUME 8, 2020 amount of data that can be received by V k inside the BS coverage. This is given by where t r = T r (V k )/T s and the computation of E r,u i (V k ) and E r i (V k ) is given in Section V-A. The binary variable c i indicates whether the uplink transmission is active (c i = 1) or not (c i = 0) and is given by where t n = T n (V k )/T s . In terms of time, the available time for buffering, T b (V k ), is equal to the time duration in which V k stays inside the BS coverage minus the required time for V k to receive its own data, viz., where t q is the smallest integer in the range [1, t r ] that satisfies . Since the one-way highway model of [3] is adopted as mentioned in Section III, the parameters that only depend on vehicles' locations and speeds can be computed similar to [3]. Specifically, the time duration T m (V k ) in which a relay candidate V k stays within the communication range of the target vehicle V o depends on the locations and speeds of V o and V k (i.e., d(V o ), d(V k ), v o and v k ) and can be found as given in [3, Eqs. (5)- (7)]. However, the relay gives priority to its uplink transmission over helping V o , and thus the relay will not be able to help V o unless the uplink transmission is finished. Therefore, the relay may not be able to use the entire T m (V k ) for relaying. The offered time by a relay candidate V k for delivering data to V o in the UA after finishing transmission in the uplink is consequently equal to where T m (V k ) is the remaining time for V k to finish transmission in the uplink after V o has reached the UA, i.e., where T n (V k ) represents the remaining time for V k to finish transmission in the uplink as given in (27). Based on T m (V k ) and T m (V k ), there are three possible cases for T c (V k ). First, if V k has finished transmission in the uplink before V o reaches the UA (i.e., T n (V k ) < T r (V o )), then T m (V k ) = 0 and the relay can use the entire time T m (V k ) for relaying the buffered data to V o . Second, if V k has finished the uplink transmission after the entire duration T m (V k ) has passed (i.e., T m (V k ) < T m (V k )), the relay will be removed from the candidate list where T c (V k ) = 0. Lastly, if the relay has finished transmission in the uplink after V o has reached the UA but within the duration T m (V k ), the offered time by V k for helping V o in the UA will be equal to the remaining time The maximum amount of data that can be delivered by the relay candidate V k to the target vehicle V o in the UA is equal to where t f and t e are the first and last time slots of the relaying stage, respectively. This stage starts if V o reached the UA and the relay has finished its uplink transmission, and accordingly t f is given by where t returns the smallest integer greater than or equal to t. On the other hand, the relaying stage ends when the time duration T m (V k ) ends. Hence, the last time slot t e of the relaying stage is equal to In (35), the binary variable b i is equal to zero if V k has finished reception and is thus only relaying to the target vehicle V o . It can thus be calculated as The relay reception will stop (i.e., b i = 0) if all data has been received in the previous time slots or the relay has reached the UA. This data comprises both the relay's requested data R q (V k ) in addition to the RD R d that will be relayed to V o in the UA.
Finally, since any relay cannot deliver more information to the target vehicle V o in the UA than what can be buffered inside the BS coverage, a performance metric for each relay candidate can be defined as the minimum of the amounts The relay candidate V k that has the highest metric M k is the one capable of delivering the maximum amount of data to the target vehicle V o in the UA.

C. RELAY SELECTION
At the instant of RS, when the target vehicle V o requests the download of a large file, all the parameters required for the computation of M k of each relay candidate V k are available except for the large-scale fading parameters (i.e., g c,r i , g r,c i , g c,o i , g r,o i , g r,r i ) of the upcoming time slots. As assumed in Section III, these large-scale parameters model both pathloss and shadowing. The pathloss can be determined based on speeds and locations of the vehicles; however, shadowing cannot be computed at the instant of RS. Therefore, the proposed EM-SCF scheme assumes that large-scale fading parameters model the pathloss only at the RS stage (i.e., it excludes the shadowing effect) in order to find M k of each relay candidate V k . It then selects the relay candidate V k that has the highest M k . Indeed, by excluding the shadowing effect, the proposed EM-SCF scheme does not fully guarantee that the selected relay V k will enjoy the highest M k as this relay may suffer from severe shadowing. The impact of that assumption on the ability of the proposed EM-SCF scheme to select the best relay candidate is assessed in Section VI. After the RS step, at each time slot, the proposed EM-SCF scheme computes the optimal PA for transmission as explained in Section V-A. At this stage, both pathloss and shadowing are considered.

Algorithm 1 Proposed EM-SCF Algorithm
Inputs: vehicles speeds v k and locations d(V k ). 1: Find the set K = {V 1 , V 2 , . . . , V K } that encompasses the eligible relay candidates for RS such that |D(V k )| ≤ r 0 , ∀ V k ∈ K, where D(V k ) is given by (28). % RS stage 2: for k = 1 to K do 3: Find M k as given by (39). 4 To make the implementation of the proposed EM-SCF scheme straightforward, Algorithm 1 is presented. Steps (1)-(5) in the algorithm show the RS stage where it is assumed that large-scale fading parameters model the pathloss only as mentioned earlier. The relay candidate that has the highest M k as stated in step (5) will be selected, where M k is given by (39). The remaining steps from (6)-(23) describe the communications based on the location of V o and V k . More specifically, steps (6)-(16) demonstrate communications inside the BS coverage between the BS and each of V o and V k . This stage starts from the RS instant (i.e., i = 1) until the relay V k starts relaying to V o , which marks the start of the relaying stage at the instant i = t f that is given by (36). As mentioned in Section V-A.1, the PA that maximizes the ergodic capacities of the downlinks depends on whether the uplink transmission is active or not. For the target vehicle V o , the uplink transmission is active if a i = 1, where a i is given by (26). For the relay V k , the uplink transmission is active if c i that is given by (31) equals one. The remaining steps (17)-(23) show the communications in the relaying stage between V o and V k in the UA, which starts at the instant i = t f and ends at i = t e , where t e is given by (37). As mentioned in Section V-A.2, the PA that maximizes the ergodic capacity of the link from V k to V o depends on whether V k has finished reception from the BS or not, which is determined by the binary variable b i (38).

D. ALTERNATIVE RELAY SELECTION SCHEME
The proposed EM-SCF scheme consists of RS and PA phases that maximize the ergodic capacities of the links as shown in Algorithm 1. The PA has low complexity as can be seen in (18), (19), (21) and (22). On the other hand, as compared to the RS steps of the FD scheme in [6] and the HD scheme in [3], the RS of the proposed EM-SCF scheme has higher computational complexity. More specifically, the three schemes select the relay candidate that can deliver the largest amount of data to the target vehicle V o in the UA. While this amount is equal to M k in the proposed scheme, it is simply equal to ECT×C in the schemes in [6] and [3]. Clearly, the complexity of computing M k is indeed higher than that of the ECTs of the schemes in [6] and [3] with the latter requiring fewer number of multiplications and additions as illustrated in Table 1. This is because the computation of M k necessitates the computation of E b (V k ) and E d (V k ), which in turn involves exponential operations as well as the evaluation of the exponential integral function E 1 (·). Although the latter might seem complicated, there are very efficient approximations of this function such as in [19] and [20] that offer tradeoff between complexity and accuracy and the complexity of the proposed EM-SCF scheme still remains affordable. In spite of that, in this subsection, we propose a hybrid SCF scheme that merges the RS of the FD scheme in [6] with the PA of the proposed EM-SCF scheme aiming at reducing complexity. First, the proposed hybrid scheme selects the relay candidate V k with the highest ECT as given in [6,Eq. (9)]. Then, at each time slot, the optimal PA of the proposed EM-SCF scheme that maximizes the ergodic capacities of the links is used. Accordingly, the hybrid scheme can be implemented using Algorithm 1 after replacing the RS stage in steps (1)-(5) with selecting the relay candidate that has the highest ECT instead, where the ECT is given in [6,Eq. (9)]. To make the implementation of the proposed hybrid scheme straightforward, Algorithm 2 is presented.

Algorithm 2 Proposed Hybrid Algorithm
Inputs: vehicles speeds v k and locations d(V k ). 1: Find the set K = {V 1 , V 2 , . . . , V K } that encompasses the eligible relay candidates for RS such that |D(V k )| ≤ r 0 , ∀ V k ∈ K, where D(V k ) is given by (28). % RS stage 2: for k = 1 to K do 3: Find the ECT of the relay V k using [6, Eq. (9)]. 4: end for 5: Select the relay candidate V k that has the highest ECT.
% Transmission stage 6: At any time slot i ∈ [1, t e ], the optimal PA that maximizes the ergodic capacities of the links is used exactly as steps (6)-(23) in Algorithm 1.
Since the computation of the ECT in [6, Eq. (9)] depends on the assumption of fixed transmission rate C, the RS step of the hybrid scheme will not be as accurate as that of the EM-SCF scheme. Therefore, the reduction in the computational complexity will be at the expense of the accuracy of selecting the best relay candidate that can deliver the largest amount of data to the target vehicle in the UA. The loss in performance will be quantified in Section VI along with our other results.

E. OPTIMAL HALF-DUPLEX SCF SCHEME
The related HD SCF schemes, e.g., the works in [2]- [4], [11]- [13], are assuming fixed rate for transmission. For fair comparison between the usage of FD and HD transmissions in SCF schemes for ICVNs, the optimal PA that maximizes the ergodic capacities of the downlinks and the link from the relay to the target vehicle are determined in this section.
The ergodic capacity of the downlink from the BS to V k is equal to E r,u i,HD (V k ) = 0.5 We 1 ν E 1 ( 1 ν )/ ln (2), where ν = P c,r i g c,r i /σ 2 [17]. The factor of 0.5 captures the fact that the uplink and downlink in HD transmission use orthogonal channels in time or frequency, while the channel is used simultaneously by both of the uplink and downlink in the proposed FD SCF schemes. Since E r,u i,HD (V k ) is monotonically increasing with P c,r i , the optimal power P c,r * i that maximizes E r i (V k ) is simply equal to P c max . Likewise, the optimal power P c,r * i that maximizes E r,u i,HD (V k ) is equal to P c max . By replacing P c,r i with its optimal value P c max in E r,u i,HD (V k ), we obtain the maximum ergodic capacities E r,u i,HD (V k ).
The performance of each relay candidate can be determined in a similar manner to that of the proposed FD scheme in Section V-B. The amount of data that can be buffered by a relay candidate V k inside the BS coverage is equal to where E r HD (V k ) is the maximum amount of data that can be received by V k inside the BS coverage that is equal to where is given by (25) and the ergodic capacity E r,u i,HD (V k ) is given above. As mentioned in Section II, in the HD SCF schemes, once the target vehicle V o reaches the UA, the relay V k must stop from storing more data and start relaying to V o . On the contrary, in the proposed FD SCF schemes, the relay V k can continue buffering data while relaying buffered data to V o . Hence, t o is used in (41) instead of using t r as in (30).
In terms of time, the available time for buffering is equal to where µ is the smallest integer in the range [1, t o . Again, what differentiates the available time for buffering in (42) from that in (32) is the relay's ability of simultaneous transmission and reception, which allows the relay to store more data while relaying buffered data to V o .
On the other hand, the amount of data that can be delivered by the relay candidate V k to the target vehicle V o in the UA is equal to (2), ζ = P r,o * i g r,o i /σ 2 , t f and t e are given by (36) and (37), respectively. Obviously, the optimal power P r,o * i that maximizes E r,o i,HD (V k ) is equal to P r max . Lastly, similar to the proposed FD SCF scheme in (39), the performance of each relay candidate is limited by the minimum between the amount of data that can be buffered inside the BS coverage and the amount that can be delivered to the target vehicle V o in the UA. i.e., E b HD (V k ) and E d HD (V k ), respectively. The relay candidate V k that has the maximum minimum is the one capable of delivering the highest amount of data in the UA, and accordingly will be selected.

VI. SIMULATION RESULTS
In this section, the performance of the proposed SCF schemes are assessed based on simulations of the system model described in Section III. The performance, in terms of the amount of delivered data to the target vehicle V o in the UA, is compared with that of the special case in [6], the optimal HD SCF scheme in Section V-E and the HD scheme proposed in [3]. All the simulation results presented in this section are obtained from 100,000 realizations, where vehicles are distributed randomly in the highway in each realization. The fixed parameters of the simulations are detailed in Table 2.

FIGURE 2.
A comparison between the available buffering times of the proposed EM-SCF scheme, the special case in [6] the optimal HD SCF scheme in Section V-E and the HD scheme proposed in [3]. Intuitively, when the number of vehicles decreases, the number of relay candidates decreases as well, which decreases the probability of having a relay candidate with a high buffering time. Therefore, the four schemes offer higher buffering time as the number of vehicles increases as seen in the figure.
As mentioned earlier, in the HD scheme in [3] and the optimal HD SCF scheme in Section V-E, once the target vehicle V o reaches the UA, the selected relay stops from buffering more data and starts transmitting the buffered data to V o . On the contrary, in the proposed EM-SCF scheme and the special case in [6], by virtue of the relay's ability of receiving and transmitting simultaneously, the relay can continue buffering data while transmitting to V o . Accordingly, these FD schemes offer significantly higher buffering times. As given in (32) and (42), the available time for buffering is equal to the entire available time for reception inside the BS coverage minus the required time for V k to receive its own data. Since the ergodic capacities of the downlinks are maximized in each of the proposed EM-SCF scheme and the optimal HD SCF scheme in Section V-E, the BS can transmit with higher transmission rates, and consequently, the selected relay can receive its requested data R q (V k ) in a shorter time. Hence, as shown in Fig. 2, the proposed EM-SCF scheme and the optimal HD SCF scheme in Section V-E offer higher buffering time as compared to the special case in [6] and HD scheme in [3], respectively.   Fig. 2 are adopted. For the clarity of the presentation, the performance of the special case in [6] and the HD scheme in [3] and those of the proposed schemes are presented in separate figures. Since the special case in [6] offers higher buffering time as shown in Fig. 2, it consequently offers higher ECT, and accordingly delivers higher amount of data as shown in Fig. 3. In agreement with the discussion on Fig. 2, the performance of both schemes improves as the number of vehicle increases.
As for the proposed schemes and the optimal HD SCF scheme in Section V-E, Fig. 4 shows the impact of the number of vehicles on their performance. Beside having higher buffering time, by virtue of the ergodic capacity maximization of the links, the proposed schemes and the optimal HD SCF scheme in Section V-E can buffer higher amount of data inside the BS coverage as well as deliver more data to V o in the UA. Comparing Figs. 3 and 4, it can be readily noticed that these schemes outperform the special case in [6] and the HD scheme in [3].
In addition to the above, Fig. 4 shows the accuracy of the RS steps of the proposed EM-SCF and hybrid schemes. To achieve that, in each simulation realization, we scanned through all the potential relay candidates and saved the performance metric of the candidate that can deliver the largest amount of data to the target vehicle V o in the UA. By the end of all the realizations, we obtained the performance of the case in which the best relay candidate is selected in each realization. We refer to this performance as the selection bound. As shown in the figure, the proposed EM-SCF scheme offers comparable performance to the selection bound. In agreement with the discussion in Section V-D, the proposed hybrid scheme offers reduction in the computational complexity at the expense of the RS accuracy. Also, to show the importance of the RS step, we show the performance of the case in which one of the relay candidates is randomly selected in each realization. In both the selection bound and random RS, after selecting one of the relay candidates, the ergodic capacities of the links are still optimally maximized as in the proposed EM-SCF scheme. As illustrated in Fig. 4, the performance of the random RS is much lower than that of the proposed schemes, which proves the importance of accuracy of the RS step.
To study the impact of the speed range of the vehicles on the performance, simulations with R q (V k ) ∈ [20, 50] Mbits, R Tx q (V k ) ∈ [20, 50] Mbits, β = −90 dB and a number of vehicles equals 50 are performed. When the speed v k of the relay is close to the speed v o of the target vehicle, the relay stays within the communication range of the target vehicle for a longer time, i.e., higher T m and the amount of data that can be delivered to V o in the UA increases as can be seen in (33), (43), [3,Eq. (8)] and [6,Eq. (12)]. Accordingly, all schemes offer better performance as the speed range of the vehicles decreases as shown in Fig. 5. Due to the same reasons mentioned above about the FD capability of the relay   Figure 6 shows the impact of the size of the requested data by the relay candidates R q (V k ) on the performance of the SCF schemes. When R q (V k ) is increased from [0, 10] to [10,20], [20,30] Since the considered size of the requested data R q (V k ) is too small compared to that of the delivered data by the proposed schemes, it is difficult to notice the reduction and the performance appears as a straight line.
It is worth noting that the HD SCF scheme in [3] may select more than one relay if the RD of the target vehicle V o cannot be delivered by one relay as can be seen in the examples in [3,Fig. 5]. In this work, our goal is to study the potential improvement in the performance of the relay by virtue of using FD instead of HD communications, and accordingly we focused so far on the performance of the best relay only. However, selecting more than one relay allows for delivering even higher amounts of data to V o in UA, which is equal to the sum of the amounts that can be delivered by each of the selected relays. In Fig. 6, we show the performance of the proposed EM-SCF scheme and the HD SCF scheme in [3] in case the best two relays are selected. As can be clearly seen, the proposed scheme significantly outperforms the HD scheme in [3]. The impact of the transmission range r 0 on the performances of the proposed schemes and the optimal HD SCF scheme in Section V-E are assessed in Fig. 7. Simulations with R q (V k ) ∈ [20, 50] Mbits, R Tx q (V k ) ∈ [30, 50] Mbits, β = −90, number of vehicles equals 50 and vehicles speeds randomly assigned in the range [50, 90] km/h are performed. When the transmission range r 0 increases, the relay can stay for longer time within the communication range of the target vehicle V o in the UA, i.e., higher T m (V k ), which in turns increases t e that is given by (37). When t e increases, more data can be delivered through the relay to V o in the UA as given in (35) and (43), and clearly depicted in Fig. 7. As mentioned earlier, by virtue of the spectral efficiency of FD communications as well as having higher buffering time as shown in Fig. 2, the proposed schemes can deliver more data to V o in the UA as presented in Fig. 7.
Finally, Fig. 7 shows the impact of SIC on the performance of the proposed EM-SCF and hybrid schemes. As SIC increases (i.e., less residual SI β), the amount of data that can be delivered to V o in the UA of the two schemes increases as shown in Fig. 7. This is because the relay will be able to buffer more information inside the BS coverage as well as deliver more data in the UA. Inside the BS coverage, the BS can also use higher transmission power P c,r * i in the downlink without violating the capacity requirement of the uplink. As can be seen in (18), P c,r * i increases as β decreases, which in turns increases the ergodic capacity of the downlink E r,u i (V k ) that is given by (7). Similarly, in the UA, the relay can use higher P r,o * i in the transmission to V o without violating the capacity requirement of the downlink. As given in (21), P r,o * i increases as β decreases. The ergodic capacity of the link from the relay to the target vehicle E r,o i (V k ), given by (9), is monotonically increasing with P r,o * i . On the contrary, as SIC decreases (i.e., larger residual SI, e.g., β = −60 dB), the performance of the proposed schemes starts to degrade. When β = −40 dB is used, the optimal HD SCF scheme presented in Section V-E actually outperforms the proposed EM-SCF and hybrid schemes. This result reveals that efficient SIC is required for the proposed EM-SCF and hybrid schemes. Fortunately, as mentioned in Section I, the impressive improvement in SIC techniques (e.g., in the order of 70 − 110 dB reported in [5]) makes the use of the proposed schemes justifiable.

VII. CONCLUSION
We proposed an FD store-carry-forward scheme for ICVNs. The FD capability of the relay has been exploited to extend the ECT with a target vehicle thus minimizing the outage time and delivering more data to it in the UA. Based on information of speeds, locations and data traffic requirements of the vehicles, the optimal PA that maximizes the ergodic capacities of the links is found. Moreover, the proposed scheme selects the relay candidate that can deliver the highest amount of data to the target vehicle in the UA. To reduce the computational complexity, a hybrid scheme is also proposed assuming a fixed transmission rate. This scheme selects the relay candidate that offers the highest ECT. Then, at each time slot, the optimal PA that maximizes the ergodic capacities of the links is determined as in the first scheme. The reduction in the computational complexity comes at the price of delivering less data to the target vehicle in the UA. As compared to the half-duplex SCF schemes, it has been shown that both proposed FD schemes can deliver significantly more data in the UA.