Drone assisted device to device cooperative communication for critical environments

This paper proposes drone assisted device-to-device cooperative communication (DA-DDCC) for critical situations during post-disaster management. The proposed network utilizes the autonomous mode of D2D communication for setting up the link in the absence of a central node. This network incorporates cooperative communication using drone in D2D session for improving reliability of the overall system. A probability-based statistical channel model for such networks is proposed by taking the statistical independence of links into consideration. Unlike the existing air-to-ground (A2G) channel models that use either Rayleigh or Rician distribution for uplink (UL) and downlink (DL) channel modelling, our approach takes the probability of occurrence of line of sight (LoS) into account while predicting the appropriate channel distribution for UL and DL separately. For performance evaluation of the proposed network, average outage probability and average capacity are derived using the proposed channel model. Monte Carlo simulations are conducted to verify our analysis. Moreover, a multi-cluster DA-DDCC scenario is also being analyzed through simulations from an interference perspective to justify the usefulness of the proposed channel model. Results obtained through this investigation can be utilized in selecting various crucial system parameters judiciously for enhanced performance during post-disaster scenario.


INTRODUCTION
In recent years, fifth-generation (5G) and beyond 5G (B5G) technologies are being developed to increase the data rates and network capacity for conventional cellular networks. Multiple input multiple output (MIMO) and network traffic offloading techniques are used for achieving such objectives [1][2][3]. Equipping multiple antennas needs more hardware, cost, and size. Consequently, these methods are not preferred for most of the battery operated tiny devices. To enhance the cellular network performance, traffic offloading techniques are also used in literature. Traffic offloading may be achieved mainly by two methods, one is through small cell (micro/pico/femto) deployment in macro-cells and the other is using device-to-device (D2D) communications [4]. However, the first method may be inconvenient due to a lack of dynamism that occurs because of can be harnessed to set-up communication links among various nearby users. For example, this kind of ad-hoc link set-up can be very useful in search and rescue missions during postdisaster management operations. Rescue groups and victims can easily communicate, and the recovery process can speed up. Various works related to the D2D communication can be found in [6][7][8]. However, existing literature does not harness the autonomous mode of the D2D communication technique thoroughly.
Inherent limitations of the D2D communication technique (such as device size, limited range, battery constraint) call for an association of suitable method to take care of random nature of channel effects. Therefore, use of unmanned aerial vehicle (UAV) or drone in D2D links is proposed to incorporate cooperative communication (CC) for increased reliability by combating the effect of deep fades. This provides an additional path (diversity) between devices for improving the performance of the network along with accuracy in crucial decisions. To the best of our knowledge, this is the first attempt to integrate CC with D2D links in autonomous mode. UAVs/drones are an emerging use cases for next-generation wireless networks. By adjusting the position of drone, the probability of LoS can be increased. Facebook [9] and Google [10] have been deploying a large number of drones for providing better services to rural areas. Amazon [11] is making use of small drones for service delivery purposes. On the one hand, drones can be used as temporary aerial base stations in a cellular network [12], on the other hand, drones can also be used as aerial relays [13] for establishing cooperation between remote sensors and the base station. Further, the introduction of a drone in D2D set-up brings cooperation which provides robust and reliable communication in critical operations like rescue missions. Drone-based CC has been discussed in [14] with fixed channel distributions and without using D2D communication. UAV-assisted D2D network in underlay mode is discussed in [15] and authors derived outage probability using Rayleigh fading for A2G links. UAV-assisted D2D network in underlay mode using large scale fading is discussed in [16]. Cellular based D2D network in semi-autonomous mode using Rayleigh fading is discussed in [17]. In [18] an autonomous mode selection scheme for underlay D2D communication using Rayleigh fading is discussed. However, none of the existing works address the use of drone assisted D2D links in autonomous mode for critical situations.
In existing drone-related works, while modelling the channel between user and drone (relay) or vice-versa, either Rayleigh or Rician distribution is assumed for both the links, based on the non-line-of-sight (NLoS) or LoS conditions [19][20][21]. Authors in [22] used the Nakagami-m fading channel for modelling A2G links to derive coverage probability. In [23], Nakagami-m faded channel is used for two-hop energy harvesting UAV relay assisted communication. Secrecy outage probability and secrecy diversity gains of the UAV assisted relay cognitive network under Nakagami-m channel are discussed in [24]. In [25], the authors considered unmanned aircraft as a relay node between ground stations without taking the direct link between ground stations and derived outage probability by assuming A2G links as Rician distributed. In [26], communication between ground users (GUs) are considered via UAV, without considering the direct link between them. The authors analyze the outage probability by considering Nakagami-m fading between A2G links. All these works assume the same 'm' parameter for UL and DL. UAV assisted underlay mode of D2D communication is discussed in [27], and the authors analyzed coverage and rate by considering A2G links as Rayleigh fading channel. UAV based relaying, scheduling, and trajectory optimization are discussed in [28] without considering the direct link between GUs. Authors in [29] analyzed the secrecy rate by adopting free space path loss model for both uplink and downlink.
However, it should be noted that in practical scenario source to drone and drone to destination channels are statistically independent as the obstacles present may vary in both the channels. Therefore, both these channels may not belong to the same LoS (NLoS) condition. It may happen that within a cycle of cooperative communication, one of these links may encounter strong LoS while other link may see only NLoS components. One such possible scenario is shown in Figure 2. It may be noted that with the present (or lower) height of drone, the direct path between drone and UE S is obstructed while a direct path exists between drone and UE D . Therefore, the use of a single distribution for modelling the channel in both the links may not be appropriate. Additionally, in order to obtain better link conditions, if the height of drone increases, channel statistics may further change. In general probability of getting LoS increases with the height of drone. Therefore, the system model must be adaptive enough to take such a dynamic nature of links statistics into account. This observation may be justified analytically with the help of the following argument: For a given height of drone, there exists a probability of occurrence of LoS. Using total probability rule, the probability of occurrence of NLoS can also be found. This implies that a link (source to drone or drone to destination) may confront LoS conditions with a corresponding probability of occurrence of LoS but at the same time, it may suffer from NLoS conditions also with the probability of occurrence FIGURE 2 Illustration of DA-DDCC scenario where dissimilar obstacles in UE S -R and R-UE D channels lead to different channel conditions. In particular, UE S -R link is dominated by NLoS components (may be modelled by Rayleigh distribution) and R-UE D link is dominated by LoS components (may be modelled by Rician distribution) of NLoS. Therefore, calculations of any performance metric must be averaged over all the possible channel conditions. As per our knowledge, existing literature assumes the same distribution for both the links and thus does not take link independency into account.

Motivation
Autonomous mode of D2D communication is the prime motivation for this work. D2D communication can be exploited in networks in two ways. Under normal environment when the base station is functioning properly, D2D communication (in underlay, overlay, and controlled modes) may be utilized for improving spectrum utilization, data rate, energy efficiency etc. Whereas, during critical situations such as earthquakes, floods, various communication infrastructures like base station which plays an important role in setting up the communication links are disrupted, an autonomous mode can be useful. This mode does not require a base station to set-up the D2D communication link. Thus, disaster management can be executed smoothly. D2D communication is highly sensitive to channel conditions [30]. MIMO or other complex signal processing techniques cannot be practiced to cope with deleterious effects of bad channel conditions due to power constraint at batteryoperated devices. This prompts us to propose the use of cooperative communication in a D2D set-up. Use of cooperative communication increases the reliability of the D2D setup as an appropriate simpler combining technique may be used at the receiver. With many practical applications (public safety, big smart cities etc.) and challenges (drone deployment, device to relay channel modelling etc.), drone-based D2D communications also stimulate many non-trivial issues. One such critical challenge is the accurate channel modelling between a drone and on-ground devices, which still lacks indepth study. This motivates us to investigate the probability-based statistical approach for finding suitable distributions for UL and DL individually. For such harsh environmental conditions, the proposed DA-DDCC network gives an on-demand, cost-effective, energy efficient, and reliable solution required for speeding up the recovery process. Moreover, given the recent advancements in drone technologies, using drones as a relay (or full-fledged base station) in rescue operations may be a game-changer.

Contributions
Main contributions of this work can be summarized as follows: (i) Integration of drone in the autonomous mode of D2D communication for enhancing the reliability and accuracy of various services. Introduction of the drone as relay serves the purpose of establishing cooperative communication among devices. (ii) A generic statistical channel model for better characterization of links between nodes in a DA-DDCC network. Unlike previous works, where A2G (uplink as well as downlink) links were modelled as either Rayleigh or Rician distributed for NLoS or LoS links respectively, this model takes a probability-based statistical approach to decide the link distribution between user equipment (UE) and relay node. The pseudocode of proposed model for simulation purpose is further elaborated in Section 6. (iii) In contrast to the existing works on cooperation [31][32][33], where relay remains in the same plane as source and destination, this work proposes and analyses vertical adjustment of the position of drone to get a better LoS link. Hence, drone as relay gives us additional degree of freedom to ameliorate the network performance. (iv) A model of rescue operation for fire detection is proposed using two clusters DA-DDCC approach. Two clusters DA-DDCC scenario is analyzed taking inter-cluster interference into account. Outage and rate expressions are derived in series form for getting valuable insights into the system.
The rest of this paper is organized as follows. In Section 2, we describe the DA-DDCC system model. Sections 3 and 4 present the outage and capacity analysis, respectively, followed by DA-DDCC multi-cluster scenario in Section 5. Section 6 provides the simulation results, and finally, Section 7 concludes the paper. Notations and symbols used in the paper are shown in Table 1.   of source-destination pairs. It is assumed that only NLoS link exists between UE working as a transmitter and UE working as a receiver. However, an additional path is introduced between UEs via drone. Nodes working as sources (transmitters) and as destinations (receivers) are represented by UE S and UE D , respectively. The drone acts as a relay (R). For the discussion ahead, cluster representing our proposed DA-DDCC scenario (Figure 1(b)), consists of a pair of devices is considered for description purpose similar to Figure 3. Distance between a source (S ) (or destination (D)) and R can be calculated by using d = √ h 2 D + r 2 as shown in Figure 3. The elevation angle of drone from ground is denoted by theta ( ). Channel between S and R or R and D is either Rayleigh or Rician distributed depending on the probability of occurrence of LoS (ℙ L ) (or NLoS (ℙ NL )) component to be decided by the proposed statistical channel model. The system operates over the principle similar to TDMA scheme. Total of two time-slots are required to complete one session of data transmission. Different timeslots are assigned to UE S and R for transmitting the data. Transmission of a source is received by destination as well as overheard by drone. Drone forwards it to the destination node in successive time-slot by using suitable forwarding schemes such as amplify and forward (AF) or decode and forward (DF). Due to limitations of drone, we are considering AF relaying scheme which requires comparatively less complex circuitry. For achieving diversity, selection combining (SC) is used at destination node keeping battery constraint of devices into account.

DA-DDCC SYSTEM MODEL
In this work, it is assumed that UE nodes (S, D) are quasistatic. Vertical movement of the quasi-static drone may be significant between two consecutive communication phases. For better LoS, height of the relay (drone) node may be harmonized from the horizon plane during subsequent communication phases, if required. Since UEs are at ground, the direct link between them may remain obstructed by obstacles most of the time. Hence, a radio link between them is assumed to have NLoS component only. Due to the vertical movement of drone, links among UE S to R and R to UE D may change significantly. Therefore, these links are modelled individually using the proposed channel model (based on ℙ L (ℙ NL )), following the procedure illustrated in Section 6. To model the effect of LoS and NLoS components, Rician and Rayleigh fading are used, respectively. System parameter for Rayleigh faded channel is = Rician fading parameter is defined as M = s 2 2 2 , where s 2 and 2 2 denote the average power related to LoS and NLoS link, respectively [34]. Since statistically UE S -R and R-UE D links are independent, S and R may have different channel state even after having the same value of ℙ L . This is primarily due to the difference in the presence of various obstacles like buildings, trees, hills etc. between UE S to R and R to UE D nodes. Energy-related issues for the device/drone are not considered here. We assume that all UEs and drone have a single antenna and operate in half-duplex mode. Channel state information (CSI) is known by the receiver nodes (UE D and R) only. Each transmitting node having the same packet size. It is assumed that coherence time is long enough to complete a packet transmission. However, channels may change independently between two consecutive transmissions. The altitude of UEs, antenna heights of both the users and drone are neglected during the study. Generalized power allocation scheme used in our model is as follows where Ψ 1 , Ψ 2 ∈ (0, 1], denote power allocation factors. P S and P R denote power transmitted by source and relay node, respectively. Symbol  t denotes the available power in the network given as

Effect of drone height over A2G channel model
In order to develop the analytical framework for the proposed network model, it is imperative to investigate the effect of drone height on various system statistics. In this subsection, we describe the effect of drone height on the probability of occurrence of LoS (NLoS). The probability of occurrence 1 of LoS (ℙ L ) is given as [38] , and a, b are constant values depending upon the environment type given in Table 2.
The probability of occurrence of NLoS (ℙ NL ) can be calculated by using ℙ L + ℙ NL = 1. Figure 4(a) shows the variation of ℙ L w.r.t drone height and horizontal distance for different environments. From Figure 4(a), it may be observed that ℙ L is high in an urban environment as compared to a high-rise urban environment for any combination of (r, h D ). In an urban environment, increasing the distance between low altitude drone and UEs, increases the probability of having more and more obstacles between drone and UEs. Therefore, for low values of h D , ℙ L decreases with an increase in r. However, at very high altitudes, obstacles do not affect the LoS significantly. So, for high values of h D , ℙ L remains almost constant with r. For high-rise urban environments, even moderate heights of drone (≈ 40m) are unlikely to clear obstructions among drone and UEs. Therefore, increment in r decreases the ℙ L . 1 Few more approaches to model ℙ L may be found in [35,36] and [37].
The average received signal power () at node can be written by cramming the effects of both LoS and NLoS components as where  L i j ,  NL i j denote average received power corresponding to LoS and NLoS links when signal propagates from i to j node (i, j ) ∈ {(S, R), (R, D)}, respectively. Further, parameters  L i j and  NL i j may be found by using the equations given below where  i , d i j , ℏ i j , Rice, and Ray denote transmitted power by node i, distance between i and j node, channel coefficient between i and j node, Rician and Rayleigh fading, respectively. It may be noted that  i j includes the effect of both large scale as well as small scale fading. Figure 4(b) shows average received power at drone (calculated using (3)) w.r.t drone height (h D ) and Rician factor (M ). From Figure 4(b), it may be observed that for given h D the average received power at drone increases with M and for given M it increases up to an optimum drone height due to increase in ℙ L , then decreases due to an increase in path loss.

Description of DA-DDCC
For description purpose, the model shown in Figure 3 is considered. In 1 st time-slot, S transmits the signal to D which is overheard by R also. Signal received at D and R can be modelled as where i j denotes AWGN noise with  ∈ (0, 2 i j ), l 1 is either Ray (with ℙ NL ) or Rice (with ℙ L ), the method for deciding l 1 is explained in Section 6. Relay uses AF scheme to forward the signal towards destination node in 2 nd time-slot which can be written as where both l 1 and l 2 ∈ {Ray, Rice}. It may be noted that during a particular transmission cycle, l 1 and l 2 may belong to different distributions also depending upon the obstacles present in the S -R and R-D channels. Effect of various combinations of l 1 , l 2 on system performance is discussed in Section 3. ℚ l 1 is known as amplification factor given by [31] Another copy of the desired signal at destination node can be found by using (6) and (7) as followŝ where  l 1 ,l 2 denotes AF-noise component at D, given by Assuming average channel gain remains constant for the duration of a packet (for a given drone height) and average noise power at D and R are same ( 2 = 2 RD = 2 SR ). Mean of the AF-noise is zero and the variance of AF-noise component at node D becomes [40] 2 . (11)

AF-noise for Statistical Channel Model
Effective values of  l 1 ,l 2 and 2  l 1 ,l 2 in case of statistical channel model can be found by averaging (10) and (11) over all the four possible cases (as discussed in Section 3) of various combinations of l 1 , l 2 as: where (m 1 , m 2 ) ∈ (L, NL) and j ∈ (Ray, Rice). Here L corresponds to Rice and NL corresponds to Ray channel. Figure 5 shows the average magnitude of AF-noise w.r.t drone height. It may be observed from Figure 5 that average magnitude of AF-noise is different for all four models. The average magnitude of AF-noise for Rayleigh (l 1 =l 2 =Ray) and Rician (l 1 =l 2 =Rice) models 2 are calculated using (10) and for the proposed probabilistic channel model by using (12). For the hybrid model, ℏ SR and ℏ RD are assumed Rayleigh distributed below an optimum drone height (h D 0 ≈18-22m as shown in Figure 4(a)) and Rician distributed above h D 0 .
2 Rayleigh (Rician) model represents the system where UE S -R and R-UE D both the links are modelled using Rayleigh (Rician) distribution.

OUTAGE ANALYSIS USING PROPOSED STATISTICAL CHANNEL MODEL
As stated earlier, due to statistical independence, S to R and R to D channels may witness different obstacles hence, must be modelled individually using appropriate distributions. Taking all the possibilities into account, there are four combinations for channel distributions of ℏ SR and ℏ RD possible. Therefore, in order to get the average outage probability of the DA-DDCC network, all cases must be accounted. This section analyses all four cases. Due to the mathematical complexity, SC technique is used at the destination node in all the cases. Signal to Noise Ratio (SNR) at the destination node for SC scheme can be defined as [20] .
SNR at node n when node m serves as transmitter is denoted by ⋎ l mn and found by using For ⋎ Ray SD , m = S , n = D and l = Ray. Symbol ⋎ l 1 ,l 2 SRD represents SNR at node D via relay path. It can be calculated as SNR used in (16) can be calculated by putting, m ∈ {S, R}, n ∈ {R, D} and l ∈ {Ray, Rice} in (15). Outage probability is defined as [31] ℙ l 1 ,l 2 where T denotes pre-decided threshold value. Using (14) and (17), we can write We need to calculate the 1 st and 2 nd terms separately for obtaining the outage probability. Solution of the 1 st term can be obtained as [40] ℙ To the best of our knowledge, solution of the 2 nd term is not available in the literature with the present form of (16). Therefore to solve further, an upper bound [41] is considered as follows where is a system dependent multiplicative factor proposed for better matching between the analytical and simulation model. Using (20), solution of the 2 nd term of (18) can be written as where⋎ Solution of (22) requires the consideration of all four cases as discussed below.

Case 1
Out of four cases, one possible instance occurs when S to R and R to D links are Rayleigh faded as shown in Figure 6. Assuming links are independent, the probability of occurrence of this case can be given by ℙ NL ℙ NL . Putting l 1 = l 2 = Ray in (22) and solving further results into (19) and (23) in (18), outage probability for case 1 can be obtained as

Case 2
Another possible instance may occur when S to R and R to D links are Rayleigh and Rician faded, respectively as shown in Figure 7. Assuming independent links, the probability of occurrence of this case can be calculated by ℙ NL ℙ L . Putting l 1 = Ray and l 2 = Rice in (22), solution of the 3 rd term can be written as and the 4 th term can be rewritten as Further simplification of (26) leads to [32] ℙ where Q 1 (., .) is the first-order Marcum Q function, and = Putting (27) and (25) in (22), we can obtain Putting (19) and (28) in (18), we can obtain the outage probability for case 2 as ℙ Ray,Rice out

Case 3
Third instance occurs when S to R and R to D links are Rician and Rayleigh faded, respectively as shown in Figure 8. Assuming independent links, the probability of occurrence of this case can be calculated by ℙ L ℙ NL . Putting l 1 = Rice and l 2 = Ray in (22). Solution of the 3 rd term can be written as Putting (30) and (31) in (22), we can obtain Putting (19) and (32) in (18), we can obtain the outage probability for the case 3 as written below ℙ Rice,Ray out

Case 4
The last possible case occurs when both S to R and R to D links are Rician faded as shown in Figure 9. Again the probability of occurrence of this case is defined by ℙ L ℙ L taking link independence into account. Putting l 1 = l 2 = Rice in (22). Solution of the 3 rd term can be written as and 4 th term can be rewritten as putting (34) and (35) in (22), we can obtain Putting (19) and (36) in (18), we can obtain the outage probability for case 4 as written in (37).
Taking all the four cases into account, average outage probability for the DA-DDCC can be found as Final expression for the outage probability in (38) is obtained by weighting each case with the corresponding probability of occurrence.

CAPACITY ANALYSIS FOR DA-DDCC
In this set-up, let the bandwidth assigned to each time-slot is  2 , where  denotes the bandwidth available in the system. Taking direct (S -D) and relay path (S -R-D) into account, rate at D using SC, can be defined as where  l 1 ,l 2 DA−DDCC , mutual information between the direct path (S -D) and the relay path (S -R-D), can be defined as The average capacity also can be found by weighting each case with appropriate probabilities as

INTERFERENCE LIMITED MULTI-CLUSTER DA-DDCC SCENARIO
As a practical use case of our proposed model, a scenario is considered where two non-overlapping clusters are operating adjacent to each other. In real-time, clusters may represent two areas served by two different drones in a post-disaster scenario. Since due to practical constraints, a complete disaster scene cannot be covered by a single drone, therefore multiple drones are required to serve various small areas. However, the optimal number of drones required and coordination among drones are not being considered here. Due to the broadcast nature of the wireless channel, links of one cluster may interfere with other. While improving the performance of the overall network, it becomes imperative to take the interference into account to set various network parameters optimally. This asks for the proper modelling of interference in the network. To the best of our knowledge, drone assisted D2D communication in a cooperative environment has not been analyzed in literature in an interferencelimited scenario.
Received interference power is a function of link distribution between nodes also. Interference power may be high if the link consists of LoS component, as compared to the case when only NLoS component is present. As we discussed in the previous section that ℙ L is a function of drone height also, this implies that changing the drone height affects ℙ L which in turn affects the amount of interference power received at the destination node. Increasing the drone height affects the system in two ways. Firstly it increases the ℙ L for UE S 1 (desired transmitter) hence, quality of the desired signal at drone improves. Secondly, it improves the link quality between drone and UE S 3 (interferer) also, therefore, the amount of interference power also increases. Moreover, there are two interfering links affected by the drone height. Since interfering links are also statistically independent, they may be Rician distributed with ℙ L or Rayleigh distributed with ℙ NL . This justifies the need for a probability-based statistical channel model for modelling such an interference-limited scenario.

Multi-cluster DA-DDCC system model
The network model consists of two neighbouring clusters 3 (C 1 , C 2 ) as shown in Figure 10. Without loss of generality C 1 is assumed as the desired cluster. Each cluster consists of a pair of devices (UE S 1 -UE D 2 and UE S 3 -UE D 4 ) and a drone (R 1 , R 2 ). Similar to our previous framework, communication within a cluster is divided into two time-slots. The direct links among device pairs (UE S 1 -UE D 2 , UE S 3 -UE D 4 ) are assumed to be Rayleigh distributed due to absence of the LoS component. Rest of the links (UE S i∈{1,3} -R 1 , R j ∈{1,2} -UE D 2 ) associated with either the cluster of interest or interfering cluster are assumed to be either Rayleigh or Rician distributed determined by the statistical FIGURE 10 Fire disaster management scenario using DA-DDCC showing interference between D2D clusters channel model (as explained in Section 6). For modelling purpose, it is assumed that both the clusters are operating in synchronization. Effect of interference from C 2 is observed on C 1 . It is assumed that UE is being served by the drone having best possible radio links towards the UE. For better understanding, drone heights of R 1 and R 2 are now represented by h D 1 and h D 2 , respectively.

Description of inter-cluster interference in DA-DDCC
For the ease of description, nodes UE S i and UE D i are now represented by S i and D i , respectively for this section. Without loss of generality D 1 is considered as node of interest. In 1 st time-slot, S 1 and S 2 transmit the signal x 1 and x 2 to D 1 and D 2 , which are overheard by drone R 1 and R 2 , respectively. At the same time, due to inter-cluster synchronization, R 1 and D 1 receive interfering signal x 2 from S 2 . Channel distributions associated with links S 1 -R 1 and S 2 -R 1 depend on ℙ L (ℙ NL ) 4 . Based on ℙ L (ℙ NL ), 4 (2 2 ) possible cases may occur for the scenarios shown in Figure 11. For example, in 1 st time-slot of a particular transmission cycle, one such case may be {ℏ S 1 R 1 , ℏ S 2 R 1 }={Ray, Rice}. The signals received at node R 1 and D 1 in 1 st time-slot  1 can be written, respectively as where l 1 and l 2 are either Ray (with ℙ NL ) or Rice (with ℙ L ) as decided by the proposed statistical channel model explained in Section 6. The upper subscript  1 in (42) represents the timeslot. Relay R 1 and R 2 amplify the signals received from S 1 and S 2 and forward them towards destination nodes D 1 and D 2 , respectively in 2 nd time-slot. Again in this synchronized scenario, D 1 receives interference signal (x 3 ) from R 2 . Channel distributions associated with links R 1 -D 1 and R 2 -D 1 depend on ℙ L (ℙ NL ). Based on ℙ L , 4 (2 2 ) possible cases may occur for the scenarios shown in Figure 11. For example, in 2 nd time-slot of a particular transmission cycle, one such case may be {ℏ R 1 D 1 , ℏ R 2 D 1 }={Rice, Ray}. Signal received at D 1 in 2 nd time-slot  2 can be written as where x 3 is sent by R 2 , l i∈{3,4} ∈ {Ray, Rice} and ℚ l 1 ,l 2 is known as amplification factor given as [31] Destination node can get another copy of desired signal given in (46) by using (43) in (44). Taking the direct (S 1 -D 1 ) and relay path (S 1 -R 1 -D 1 ) into account, rate at D 1 using SC in the interference-limited scenario for D2D pair (S 1 -D 1 ) can be defined as where  l 1 ,l 2 ,l 3 ,l 4 DA−DDCC , the mutual information between direct path (S 1 -D 1 ) and the relay path (S 1 -R 1 -D 1 ), can be defined as where ⋎ Ray D 1 denotes the Signal to Interference plus Noise Ratio (SINR) at D 1 , given as =S denotes SINR of relay path at D 1 , given as where ⋎ l mn can be calculated using (15) with updated range of variables as l ∈ {l 1 , l 2 , l 3 , l 4 }, m ∈ {S 1 , S 2 , R 1 , R 2 } and n ∈ {R 1 , D 1 }.
Average Outage Probability and Capacity:All possible combinations of l , ∈{1,2,3,4} result in total 2 4 cases. Taking all the cases, as a function of ℙ L and ℙ NL into account, the average outage probability at desired node can be found as where ℙ l 1 ,l 2 ,l 3 ,l 4 out Similarly the average capacity can be found as where m 1 , m 2 , m 3 , m 4 ∈ {L, NL} and l 1 , l 2 , l 3 , l 4 ∈ {Rice, Ray}.
Here, L corresponds to Rice and NL corresponds to Ray chan-  can be evaluated using method outlined in the flow chart shown in Section 6. Then averaging it out over all possible cases leads to the numerical values of (51) and (52). The average outage (51) and capacity (52) expressions derived provide useful insights to the system designer for evaluating the system performance such as throughput in interference-limited scenario where asymmetric object distribution in the environment leads to dissimilar fading among various nodes and hence, justifies the application of the proposed probability based channel assignment model.

SIMULATION RESULTS
In this section, simulations are carried out to verify the analytical framework developed in this study. Results for a single cluster are presented first and after that, results for the interference-limited scenario are discussed. Analytical results are compared with simulation results for some representative cases. Parameters used in the simulation are given in Table 3. For simplicity, Ψ 1 = Ψ 2 = 0.5 is considered for simulation purpose. However, the framework is equally applicable for other values also. The flow chart of our proposed approach for channel modelling for drone assisted scenario is shown in Figure 12. The same method is being used during simulations for assigning (probability) distribution to a particular channel. The algorithm needs to be executed twice in one cooperative cycle for the network under consideration, first at UE S and then at drone. Thus, two channels being statistically independent may follow two different distributions 5 . Matrices such as the outage probability, rate and required transmitted power are chosen to validate the proposed model. Outage probability (ℙ out ) is defined as the probability that received SNR (SINR) is below some pre-decided threshold Intuitively, it is the height where loses due to continuously increasing path loss are exactly balanced by gain due to improving values of probability of LoS. Before this optimum point, due to short distances, losses due to path loss are dominated by probability of LoS that results in a decrement of ℙ out . After the optimum point, however, path loss increases at a higher rate than probability of LoS that gives rise to high values of ℙ out . Figure 14 shows the ℙ out w.r.t rate for different channel models. It may be noted that for different values of rates, outcome corresponding to the probabilistic model lies between the two extremes of Rayleigh and Rician models. Degradation in the outage performance with increment in the required rate for all the three models is due to the fact that channel support continuously degrades for the large values of required rate. Figure 15 shows the required values of drone height (Y 1 ) and rate (Y 2 ) for achieving certain ℙ out . Simulation and analytical results are in a good match. Expressions in (38) and (41) are used to find an optimum value of drone height and rate for a given required ℙ out .  Figure 17 shows that increasing the drone height for a fixed value of rate parameter, results in higher values of outage. Increasing the drone height results in better LoS as well as higher path loss. After a certain height of drone, path loss dominates that leads to high values of ℙ out . Simulation and analytical results predict almost similar values. Figure 18 shows variation of the ℙ out w.r.t drone height and Rician factor for Rician and probabilistic channel models. It may be observed here that optimum point for small values of M is lower as compared to large values of M . It may also be noted that at low value of h D , the probabilistic channel model predicts higher values of the outage probability as compared to Rician channel while at a high value of h D , performances are almost the same for both the models. Figure 19 shows variation of ℙ out w.r.t drone height and Rician factor in different environments namely urban and high rise urban. It may be observed that the outage probability is low in the urban environment as compared to the high-rise urban environment for most combinations of (M , h D ). In urban environments, for given M outage decreases upto an optimum value of h D (which is different for low and high values of M ) due to

FIGURE 19
Outage probability for different environments the dominance of increment in ℙ L . After an optimum value of h D , path loss starts dominating and results in a higher outage. However, the impact of M on ℙ out values is more for the urban environment as compared to the high rise urban. Figure 20 predicts the required transmitted power w.r.t drone height for fixed ℙ out using different channel models. Behaviour of different slopes may again be explained with the similar arguments presented earlier for Figure 13. The results obtained in Figure 20 provides very useful insight for minimization of the transmitted power, which is one of the main issues related to D2D or drone-based networks. Here, we also note that upto an optimum height (≈20-22m) drone saves the energy by transmitting at less power. Figure 21(a) predicts the suitable horizontal position of drone for different values of transmitted power for the fixed ℙ out using different channel models. It is observed from Figure 21(a) that centre position of drone needs less transmission power as compared to other horizontal position of drone. Behaviour of different slope may be explained with the help of Figure 20. Figure 21(b) gives the required height of drone to achieve a fixed ℙ out as a function of horizontal position of drone. It may also be noted here that for a given ℙ out , central position of drone requires the maximum height.

Effect of interference on system performance
In this subsection, we present results for an interference-limited multi-cluster scenario. Figure 22 shows ℙ out at UE D 2 w.r.t drone height (h D 1 ) and rate. It is interesting to note that unlike Figure 13 and Figure 14 of a single cluster scenario, most of the values predicted by our proposed model lies no more in between the other two models. After a certain drone height (h D 1 ≈ 7m) the proposed channel model predicts less outage as compared to other two existing channel models. Primary reason behind this behaviour is the fact that for this node configuration, interference link S 2 -R 1 comes out to be mostly Rayleigh distributed by following the method explained in Section 6. This results in less interference power and hence, low outage probability. Figure 23 gives the required value of h D 1 for various combinations of the ℙ out and drone height (h D 2 ) of the interfering cluster. Expression found in (51) can be used to achieve an optimum drone height (h D 1 ) for a given required ℙ out and interfering drone height (h D 2 ). It may be noted that required values of h D 1 are less affected by variation in h D 2 for most values of ℙ out , since . After that rate of change of increment of LoS does not increase much. Figure 24 gives variation of the ℙ out w.r.t transmitted power for our proposed approach along with two other existing approaches. It may be noted here, the ℙ out decreases as transmitted power increases for proposed (a) as well as existing models (b). However, the values predicted by our model are lesser than the values predicted by two other models. The requirement of reduced transmitted power results in high life time of devices (drone).

CONCLUSION
We have introduced drone assisted device to device cooperative communication. A probability based generic statistical channel model has been proposed to model links individually in such networks where the height of drone may change in order to enhance the network performance. Results obtained using this proposed model have been compared with two other commonly used channel models namely Rayleigh model and Rician model. It has been observed that the proposed probabilitybased model gives a better characterization of links in such a dynamic network by taking statistical independence of links into account. Analytical closed-form expression of the outage probability along with capacity using the proposed channel model have been derived and verified with simulation results. Moreover, few more performance metrics have been investigated to get more insight into the system behaviour.
As an application scenario, a multi-cluster network has been discussed from an interference perspective. It has been demonstrated using simulations that use of models other than the probability-based statistical model, may result in non-optimal values of network parameters which may affect system perfor-mance and energy consumption drastically. The results show that for a given horizontal node configuration, a specific range of height of drone would result in the better performance. This helps the network designer to choose the optimum height of drone along with other crucial system parameters in various application scenarios and thus to minimize the energy consumption of drone and battery-operated devices. The proposed drone based network provides a cost-effective, temporary recovery solution for setting up a quick communication set-up where an existing cellular base station becomes non-functional. Optimization of drone altitude and field-test of our system model is considered for future work. Integration of Internet of Things (IoT) with this drone-based D2D network to make the system more robust in critical situations may be an exciting research direction. Development of framework for proposed channel model using Nakagami-m distribution may also be an insightful work in future.