Drone Assisted Network Coded Cooperation With Energy Harvesting: Strengthening the Lifespan of the Wireless Networks

Next generation wireless systems include battery operated devices which demand higher throughput and a better reliability in an energy efficient fashion. To fulfil these requirements, in this paper, we propose a novel scenario where we include a dynamic Wireless Power Splitting (WPS) factor for Energy Harvesting (EH) at nodes in a Drone Assisted Network Coded Cooperation (DA-NCC) system. The dynamic WPS factor used for EH in DA-NCC system is made more realistic by determining through the probability of Line-of-Sight (LoS) occurrence. Analytical framework is developed for residual Analog Network Coding (ANC) noise and variance of ANC-noise in EH scenario. We also derive the average rate and average outage probability expressions for the proposed channel model. Various algorithms are developed for deciding the Air-to-Ground (A2G) channel distributions, harvesting the energy at relay and source nodes and evaluating the performance metrics of our proposed work. Our investigations reveal that the use of EH in DA-NCC improves the lifespan of the network. Our findings play important roles in disaster management scenarios where cellular connections to base stations are disrupted due to natural calamities and battery constrained drones are deployed for assistance.


I. INTRODUCTION
The demand for higher throughput and better reliability is increasing each day among wireless users. To achieve reliability easily, the concept of Cooperative Communication (CC) was introduced where each source-destination pair is aided by a relay and a total of 2N time-slots are required [1]. On the other hand, to achieve a higher throughput, the concept of Network Coding (NC) was introduced [2]. In a typical NC network, intermediate relay nodes combine the received signals and transmit it together thus, saving broadcasting The associate editor coordinating the review of this manuscript and approving it for publication was Yang Tang . time-slots and improving the throughput. To further meet the ever increasing demands, researchers merged NC with CC to form Network Coded Cooperation (NCC) which aims to exploit the advantages of CC and NC at one go [3], [4]. In a typical NCC system, participating sources transmit using a Time Division Multiple Access (TDMA) protocol following which the relay transmits a superposed composite data. Thus, NCC requires a total of N +1 time-slots compared to 2N time-slots in the case of CC only. However, the performance of NCC is limited by the NC-noise that occurs during the extraction of the second copy of the desired signal at the destination node. Authors in [3] discussed the concept of NCC, however, given the static position of VOLUME 10, 2022 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ a ground relay providing reliability in a disaster scenario becomes a tangible task. In order to provide a reliable and faster mode of communication during disaster/post disaster scenario, authors in [5] introduced the usage of drone as a relay in a NCC system. This in turn provides a higher QoS for end users in disaster scenarios as it provides a greater LoS and thus, increased reliability. However, a probability based DA-NCC scenario is still an unmapped area which can provide a better accuracy to evaluate the performance. Another important aspect of state-of-the-art energyconstrained wireless networks is the power consumption of battery operated wireless devices. Thus, conserving/ harvesting energy in such cases must be of great importance not only to users but also to network designers. Extracting energy from the surrounding environment, is called EH. Devices can easily harvest energy from renewable energy sources like solar power, thermal power, wind power etc. which are effective both in terms of power and battery life. However, these kind of uncontrollable natural energy sources do not guarantee a constant source of energy, thus putting systems relying on these sources in jeopardy. To overcome this problem, EH from ambient Radio Frequency (RF) signals have caught the attention of researchers [6], [7]. Such signals not only carry information but also act as a source of energy for users which is referred to as wireless power transfer [8], [9]. This concept has generated considerable interest among researchers in the so-called Simultaneous Wireless Information and Power Transfer (SWIPT) network community. In SWIPT, the energy and information transfer take place at the same time and the relay uses a WPS factor for allocating the power to EH as well as to information. In [10]- [12], the analysis has been carried out by taking fixed WPS factor at relay node. Authors in [13] propose a dynamic scenario, where the relay optimizes the splitting factors based on the local channel condition. In [14], a new time switching protocol is proposed which is an amalgamation of time switching (TS) and adaptive power splitting (APS). To the best of the authors' knowledge, current works do not include a statistical dynamic channel based WPS factor for EH which considers the probability of occurrence of LoS/NLoS between the source and relay. Now, as mentioned before, a drone based network needs appropriate A2G channel modelling for evaluating the accurate network performance. In case of a DA-NCC system, modelling of accurate A2G channels are advantageous because links associated with other nodes also contribute to the performance of the desired node. In the existing works discussed in Section II, A2G links are either modelled as Rayleigh or Rician distributed. However in reality, the A2G links between drone and transmitting nodes and between drone and receiving nodes may differ because of different locations, different obstacles etc. For example, in a multi-user scenario as shown in Fig. 1 distributed while the others as Rayleigh distributed. Thus, the accurate channel assignment among A2G nodes is useful during the allocation of dynamic WPS factors for EH at relay node based on probability of occurrence of LoS and fixed EH at source nodes which has not be designed previously.
Contribution: This work proposes the notion of probability based statistical channel modelling along with EH for DA-NCC system for an accurate channel characterization and strengthening the battery life. Based on the probability of occurrence of LoS/NLoS (P L /P NL ), various A2G links are assigned either Rayleigh (NLoS) or Rician (LoS) distribution and accordingly a dynamic WPS factor is calculated based on probability of occurrence of LoS/NLoS.
The important contributions of this work are as follows: 1) Introduction of the concept of EH in a DA-NCC scenario and provide an analytical model for calculating harvested energy at relay and source nodes. 2) Introduction of a channel dependent WPS factor for EH at relay which varies on the probability of occurrence of LoS/NLoS and it's effects on the system performance. Also, the model considers a fixed WPS factor (ρ = 1) for sources. 3) Evaluating the system performance by considering the drone height and WPS factor as parameters which are based on the probability of occurrence of LoS/NLoS. 4) Derivation of ANC-noise and variance of the ANCnoise in EH scenario for DA-NCC system. The rest of the paper is arranged as follows: Section II includes related work and motivation. Section III elucidates the system model which include probabilistic approach for channel assignment, EH from the RF at R signals and frame format for the availability of CSI at source and relay node. Section IV includes the analytical framework of the considered scenario. Section V includes the formulation of average rate and average outage probability. Results are discussed in the penultimate section, Section VI whereas Section VII concludes the paper.

II. RELATED WORK AND MOTIVATION
Most of the existing works related to UAV/drone assisted scenarios have a static approach for modelling the A2G channels. In [5], the authors derived the closed form expression of the outage probability by considering Rayleigh fading in the disaster scenario where the base station is disrupted. UAV with underlaid Device-to-Device (D2D) communications is considered in [15], in which authors derived the analytical framework for the coverage and rate using A2G links as Rayleigh distributed. Angle dependent Rician fading channel between A2G links is considered in [16], [17]. In [18], authors considered Rayleigh fading among Ground Users (GUs) while a piecewise function is proposed to approximate the probability of LoS for the A2G links. Performance evaluation of UAV assisted cooperative diversity is introduced in [19] by considering A2G links as Rician distributed. Probability-based assignment of A2G links is considered in [20] for drone based CC by considering height independent path loss exponent as well as Rician factor. The above studies considered only fixed A2G channel (Rayleigh or Rician) assignment model between drone and GUs. This leaves a huge unmapped area of dynamic channel modelling of multiple uplink/downlink cases based on probability of occurrence of LoS for drone based networks.
Another major concern for the next generation wireless networks is EH, which is not yet addressed considerably for NCC like multi-source multi-destination scenario in the existing literature. Few literature works are available related to CC that considered EH at relay node. In [21], authors analysed the performance of dual-hop relaying system with EH, considering log-normal channel distribution and Amplify-and-Forward (AF) or Decode-and-Forward (DF) as relaying scheme. In [22], a typical NC network is discussed, in which the relay node harvests energy from wireless transmissions and calculates the probability of successful data exchange and network lifetime gain. EH with incremental relaying in CC is considered in [23] and the expressions of throughput and outage are derived. The overall throughput of self-energized UAV assisted CC is improved in [24] by the use of Full-Duplex (FD) and DF based relaying scheme. In [25], EH in CC is considered in the presence of an eavesdropper where relay node works in FD mode. In [26], EH aided CC is discussed under Rayleigh faded channel conditions and derived the closed form expression of outage probability. Harvest-use-store power splitting with distributed beamforming is considered in [27] for wireless powered multi-relay CC network. Throughput maximization for UAV assisted CC is considered in [28], using time-sharing and power splitting information scheme at UAV. In [29], authors considered power splitting scheme for harvesting the energy at UAV and time switching protocol is used for relaying the information towards the GUs. Authors in [13], [14] derived the closed form expressions of the outage probability of the considered scheme and discuss the effective transmission rate. The model considered by authors in [30] and [31]  aim to maximize the overall SNR of the CC system by proposing an adaptive power splitting protocol. To enhance the harvested energy, authors in [32] have also proposed a dynamic power split receiver and proposed moving the Information Decoding load to a different circuitry. However, the above cited works mostly considers a system with a dynamic WPS. Apart from incorporating a EH model in DA-NCC scenario, in the proposed proposed work, we also aim to determine the energy harvesting factor not just dynamically but also change it statistically with respect to the probability of occurrence of LoS thus making it more malleable for devices like drones.
To this end, we found that the existing literatures deals with the performance of three node configuration (cooperative communication) by considering EH (having dynamic WPS) along with fixed A2G channel (Rayleigh or Rician) model. However, in a practical scenario, such as urban or dense urban environments (high rise urban environment) the A2G channels among sources to drone and drone to destinations are different with different path loss exponent and Rician factor which changes in accordance with the drone height. In such a scenario, the dynamic WPS factor also depends on environments type as well as drone height. This concern motivates us to propose and investigate the channel dependent statistical WPS factor for EH at relay using the probabilitybased approach for assigning the channel between drone and GUs. To the best of our knowledge, this is the first work investigating the performance of drone assisted network comprising of multiple uplinks/downlinks using probability based statistical channel model along with channel dependent statistical WPS factor for EH at drone and fixed WPS factor for EH at source nodes. For developing the analytical framework of DA-NCC, AF relaying scheme is considered at the drone and Maximal Ratio Combining (MRC) is  considered at destination nodes. Table 1 lists the notations and symbols used in this paper.

III. SYSTEM MODEL
We consider a generalized scenario comprising of N source UE-destination UE (UE S i∈{1,2,...N } −UE D i ) pairs in the network as illustrated in Fig. 2(a). The UE S i − UE D i pairs are assisted by a drone which acts as the relay (R) node. Distance between UE S i (UE D i ) and R can be calculated by using d j = h 2 D + r 2 j as shown in Fig. 2 nodes. R performs NC over the signals it received till N th time-slot and sends an amplified composite data to all the UE D i nodes by using AF relaying scheme in (N + 1) th time-slot. Thus, a total of N + 1 time-slots are required to complete one communication cycle (Includes transmission by all UE S i∈{1,2,..,N } and R nodes) of data transmission. The transmission of data from UE S i in orthogonal time-slots followed by the transmission of ACK frame from R is shown in Fig. 3. To achieve diversity, each UE D i tries to extract the 2 nd copy of the desired signal by subtracting the overheard signals received from the UE S j =i and R node. In this work, it is assumed that nodes 1 (UE S i , UE D i , R) are static during one communication cycle of data transmission. However, between two communication cycles, drone (vertical) movement may be significant. Since, UE S i − UE D i nodes are on the ground, the direct link between them may be obstructed by the obstacles for majority of time. As a result, a radio link between them is assumed to have only NLoS components. Although, due to the vertical movement of R, links among UE S i to R and R to UE D i may be dominated by either LoS or NLoS component. Therefore, these links are modelled using probabilistic channel model. To model the effects of LoS and NLoS components, Rician and Rayleigh fading 2 are used, respectively. Energy-related issues for the operation of drone movement have not been considered here. Each transmitting node has the same packet size and transmit the data at a fixed data rate. The processing power required by the relay's transmit/receive circuitry is presumed to be small in comparison to the power required for signal transmission from the relay to the destinations. For the DA-NCC system, in-band RF energy harvesting is being considered. As a result, the relay node can collect RF energy in the same frequency spectrum as data transmission. The friis equation with height dependent path loss exponent can be used to determine the collected RF energy from a transmitter in A2G space. During the development of the analytical framework, nodes working as UE S i and as UE D i are represented by source (S i ) and destination (D i ), respectively.

A. ENERGY HARVESTING FOR DRONE ASSISTED NETWORK CODED COOPERATION
In this subsection, we consider EH for the proposed DA-NCC system at R and S i nodes, as explained below:

1) ENERGY HARVESTING AT RELAY NODE
Block diagram for Power Splitting Relaying (PSR) protocol is illustrated in Fig. 4. In Fig. 4 we see that Y S i R is the received signal at the power splitter PS. Here, PS divides the signal into two parts. The first part is denoted by √ ρ i Y S i R which is used for EH. The extracted energy is stored in battery 3 and later used by R for amplifying the coded signal, while the latter part of signal power is denoted by √ (1 − ρ i )Y S i R which is associated with information signal. In the 1 st N time-slots, R allocates a portion of the received signal power (ρ i P S i ∈{1,2,..,N } ) to EH. The remaining power ((1 − ρ i )P S i ) is used for Information Transmission (IT), where 0 ≤ ρ i ≤ 1 is the power splitting factor. Here, η c denotes signal processing noise. In the (N + 1) th time-slot, R amplifies the coded information signal by using relay power and broadcasts it towards destination nodes.

2) POWER SPLITTING FACTOR
As discussed before, most of the current work consider the WPS factor to be static. On the other hand, in few works (related to CC) authors take a dynamic approach towards setting the WPS factor where they base their calculation on the channel gain. However, the introduction of EH and probability based LoS/NLoS is something which is still unmapped in the field of DA-NCC. This gives us the opportunity to design the WPS factor (ρ) to be statistically dynamic in nature based on probability of occurrence of LoS/NLoS between the source and relay. In this section, we thus propose a statistical dynamic approach for the WPS factor which changes based on LoS/NLoS. By using the proposed channel model (explained further in Section III-B), the average value of power splitting factor at R node may be calculated as where P L and P NL denote the probability of occurrence of LoS and NLoS, respectively. ρ Ric and ρ Ray denote the power splitting factor for Rician and Rayleigh fading, respectively. The value of ρ Ray and ρ Ric can be calculated by using the following proposed formulas The genesis of proposing these formulas is that the dynamic WPS factor may not exceed 1. Therefore, we can formulate the expression of ρ in terms of the Cumulative Distribution Function (CDF). Since the CDF of any distribution lies between 0 and 1. Hence, plotting the CDF gives us a value less than equal to 1 which should be the range of ρ. However, if the channel is too good, there are chances that the value of ρ be tending to 1 thus, providing the entire received signal for RF EH. Thus, putting an upper limit seems suitable which is represented by here.
In (2), denotes the maximum value of ρ that can be allocated for EH at any given time-slot. SNR i and SNR avg denote instantaneous and average SNR, respectively. Q 1 (.,.) denotes the first-order Marcum Q function. As shown above, the value of ρ changes w.r.t the channel conditions. Dynamically setting the ρ factor, extracting more energy from RF signals when the channel conditions are favourable and lesser energy when it's not. Thus, the system is able to maintain a better relationship between EH and IT. However, optimality analysis is not included in the current work.
Algorithm 1 shows the procedure for calculating the harvested energy at R node. Here, we can select any S i∈{1,2,..,N } , and receive the data transmitted by S i in i th timeslot and calculate SNR i and SNR avg from the signal received in that time-slot. Using (2), we calculate the value of ρ and store the harvested energy and power associated with it. Repeat the steps until all S i transmits their data to R. Finally, R uses the harvested power to maintain a fixed relay power. Then R amplifies the combined data and broadcasts it using fixed relay power in (N + 1) th time-slot.
Initialize: Using (2), calculate the value of ρ. 6 Perform EH and IT according to the calculated value of ρ and store energy and data.
Go to Step 2. 9 end 10 In the final time-slot, R uses the harvested power to maintain a fixed P R . Then R performs superposition coding on the stored data, amplifies it and transmits the data with power, P R . Result: EH at R for prolonged life-time and aiding users by providing diversity. On the other hand, a drastic decrease in power extraction from the main battery can be seen with increase in the number of participating S i . This can be explained with the help of (26). As we can see in (26) that with increase in the number of sources, the harvested power increase and thus, decreasing the power extracted from the main battery. Although, as h D increases (above 25 m), the path loss component starts to dominate over LoS component and the amount of power extracted from the main battery of the R increases. On the other hand, if power is not extracted (non EH case), a constant use of power from the main battery of the R is shown in   Here, it may also be noted that the harvested power at R improves the battery life of the R node.

3) ENERGY HARVESTING AT SOURCE NODE
In the system model of NCC in [3], signal from R is destined for D i nodes only. However, it should be noted that due to broadcast nature of wireless channel, S i nodes can also overhear this signal. By utilizing this observation, we propose the reception of signal from R by sources also and use it for the EH purpose. During (N +1) th time-slot, S i∈{1,2,..,N } nodes harvest energy from the signal coming from R. Fig. 6 shows the schematic of the proposed EH at S i nodes. Since, there is no information extraction required at sources, received signal can be utilized completely for EH. Therefore, in this case ρ = 1, which means that the energy associated with signal is completely harvested at S i nodes. During the transmission of the next packet by S i , the harvested power can be utilized. 43060 VOLUME 10, 2022 The power required from the battery is denoted by P S i and defined as where P S i denotes the power transmitted by S i node and HP S denotes the harvested power at S i nodes.  Wakes up at (N + 1) th time-slot and R x data broadcasted by R. 8 Harvest energy using the value of ρ.

9
Go to sleep for i − 1 time-slots. 10 end Result: Successful operation of DA-NCC and EH at S i along with prolonged life-time.
Algorithm 2 shows the procedure for calculating the harvested energy at S i . Here, we assume that each S i has n packets to transmit. Depending on the time-slot assigned during the set-up phase, each S i transmits their data and goes into sleep mode. Within a communication cycle, S i nodes wake-up and receive the signal broadcast by R in (N + 1) th time-slot and harvest the energy by using (29).

B. PROBABILITY BASED STATISTICAL CHANNEL MODEL
In the proposed network, EH factor is a function of channel parameters/distribution. Therefore, it is imperative to model the channel accurately. Since, in a drone assisted networks, channel depends upon the drone height also, it is important to investigate the effect of drone height on channel as well as various system parameters. The P L can be given as [5] where θ = 180 π tan −1 ( h D r j ), is the elevation angle between R and S i (D i ) and a, b are constant values depending upon the environment [5]. P NL may be found by using P L + P NL = 1. In order to make the model more realistic, this work takes the variation of Rician factor 4 by taking height into account using the following model [33] where M ij denotes Rician factor between nodes i and j, A and B is in dB and θ ij is in radian. The maximum value of 4 Height dependent Rician factor is also discussed in [19].
M ij approaches to B, if θ ij → π 2 and minimum value of M ij approaches to A, if θ ij → 0. We also consider h D dependent path loss exponent [33] for modelling large-scale attenuation defined as α = (α L − α NL )P L + α NL (6) where α L and α NL are path loss exponents corresponding to P L and P NL , respectively. By using the proposed channel model, the average received signal power at any node may be defined asP where P L ij and P NL ij denote the average received power corresponding to LoS and NLoS links when signal propagates from i ∈ {S, R} to j ∈ {R, D} node, respectively. Further, P L ij and P NL ij may be found by using the equations given below where P i , d ij , ij , Ric and Ray denote transmitted power by node i, distance between nodes i and j, channel coefficient between i and j nodes, Rician and Rayleigh fading, respectively. Algorithm 3 is used for channel modelling in a DA-NCC scenario as shown in Fig. 2(a). The algorithm needs to be executed throughout one communication cycle for the network under consideration. The first N time-slots are needed at S i∈{1,2,..,N } (Algorithm 3: lines 1-11) and the last (N + 1) th time-slot is required at R (Algorithm 3: lines 12-17) for completing the one communication cycle. For a given h D and environmental parameters, P L i at S i can be calculated by generating a uniformly distributed random number, g i (0< g i <1) and comparing it with P L i . If it is less than P L i , Rayleigh distribution is chosen. If not, Rician distribution is considered for the channel coefficient, S i R . Similarly, distribution of channel coefficient, RD i can be found at R. It may be noted that within a communication cycle, all N + 1 channels being statistically independent, follow two different distributions.

C. FRAME FORMAT FOR EVALUATING CSI AT RELAY AND DESTINATION NODES
It should be emphasized that the knowledge of the channel information/CSI towards undesired sources is also required in order to eliminate the undesired signals from the combined coded signal and extract the 2 nd copy of the desired signal. Depending on the initial network conditions/constraints, the process of delivering CSI to desired as well as other destinations can be obtained in various of ways. During set-up phase, users can transmit pilot signals in appropriate TDMA slots. For example, if a node, say S i∈{1,2,..,N } , wants to communicate, it broadcasts a pilot signal to the entire network. Since all the network nodes are assumed to be at one hop distance, all D i nodes (both desired and undesired) and R node can estimate the CSI between S i and themselves using this pilot signal. During the decoding of signals at VOLUME 10, 2022 Algorithm 3: A2G Channel Allocation Based on P L . 1 Calculate P L and P NL for a given h D and r j at each S i∈{1,...,N } . 4 Generate random number, g i∈{1,...,N } at each S i for i th time-slot.

5
if g i < P L then 6 Allocate S i R → Rician distributed.  12 Generate random number, g N +1 at R for (N + 1) th time-slot. 13 if g N +1 < P L then 14 Allocate RD i → Rician distributed. 15 else 16 Allocate RD i → Rayleigh distributed.

end
Result: Allocation of channel distributions.
any destination, destinations subtract the overheard weighted signals which include all the channel coefficients ( S i R , RD i and S j =i D i ). Thus, the CSI of both S i − R and R − D i are required at the destinations. Now, the knowledge of channel between R − D i can be obtained at the destination by the exchange of pilot symbols between R-D i . However, the knowledge of CSI between S i and R cannot be obtained at destinations using pilot symbols. Hence, to make the CSI of S i and R available at the destinations, we propose two different frame structures for the data and Acknowledgement (ACK) as shown in Fig. 7(a) and Fig. 7(b), respectively. Normally in a multi-casting/broadcasting scenario, messages received are not acknowledged thus, raising questions on the QoS of a broadcasting scenario. To mend this problem, researches have been conducted and various schemes have been proposed. Authors in [34], propose a frame format where the nodes receiving the data only acknowledge it's reception if it is above a particular fixed target data rate. Although unlike [34], we design the data frame such that only the node whose address is succeeded by ACK Flag set to 1 acknowledges the data as shown in Fig. 7(a) where Rel_Add, Dest_Add and Tx_Add represent the relay address, destination address and transmit node address, respectively. Here, Rel_Add and Dest_Add are added in the address list and only ACK is asked from R because it is assumed that the data received at the destination is not reliable enough. Hence, asking for ACK from the respective destinations may supposed to decrease the throughput of the network without gaining much control information. Thus, on receiving data from source (say S i ), R acknowledges the reception by broadcasting an ACK frame. Before broadcasting, R adds the CSI of the channel between S i − R into ACK frame (shown in Fig. 7(b)) which is required at the destinations to decode the 2 nd copy of the desired data. This is received by both the source and destination nodes. The source nodes use this as an acknowledgement for the data sent whereas the destination nodes use it to obtain the CSI which is required while decoding the 2 nd copy of the required data.

IV. DESCRIPTION OF DA-NCC SYSTEM
This section includes the transmission-reception scheme, statistical parameters of ANC-noise and power allocation scheme at S i and R node.

A. TRANSMISSION AND RECEPTION SCHEME FOR DA-NCC
In this subsection, we have developed the analytical framework for DA-NCC system. Consider S i∈{1,2,...,N } − D i pair as the pair of interest. In the 1 st N time-slots, S i transmit their respective signals to D i and R, which is overheard by D j =i,j∈{1,2,...,N } . The signals received by D i , D j and R can be modelled as where l i∈{1,2,..,N } ∈ {Ray, Ric}. The above equations include transmitted power by S i (P S i ), large-scale attenuation (d −α mn ) and small scale ( mn ) fading. It also includes d mn , α and mn which denote distance between m and n nodes, path loss exponent and channel coefficient between nodes m and n, respectively. The Additive White Gaussian Noise (AWGN) between node m and n is denoted by η mn with N ∈ {0, σ 2 }. The signals received at the input of energy-harvester in the 1 st N time-slots are expressed as (10) and IT received at R in the 1 st N time-slots is written as where η R i = √ (1 − ρ i )η S i R + η c having zero mean and variance, σ 2 where l N +1 ∈ {Ray, Ric} and x R denotes ANC signal, given as and Q is known as amplification factor given as [3] Q l 1 ,l 2 ,.., By using (9), (12) and (13), node D i can get the 2 nd copy of desired signal as followŝ where η R j = √ (1 − ρ i )η S j R + η c having mean zero and variance σ 2

B. STATISTICAL PARAMETERS OF ANC-NOISE
In this sub-section, we derive the statistical parameters such as mean and variance of ANC-noise.

1) MEAN
For a given drone height, the mean of (16) is zero because the background noise at node D i and R are statistically independent with zero mean (

2) VARIANCE
The variance of ANC-noise component at node D i for a given h D , is defined as var(N where var denotes variance of N l 1 ,l 2 ,..,l N ,l N +1 i given as Since, η RD i , η R j and η S j D i are assumed to be independent of each other, above equation can be written as Using the property of the variance and the fact that Q l 1 ,l 2 ,..,l N , Ray S j D i are assumed to be constant for a packet duration, above equation can be written as (20) VOLUME 10, 2022 Finally the variance of ANC-noise component at node D i for a given h D , is given as From (21), it is clear that the variance of ANC-noise increases as number of S − D pair increases.

C. DIFFERENT POWER ALLOCATION SCHEMES AT RELAY AND SOURCES
In this sub-section, we discuss the power allocation scheme for different S i and R. The power allocated to S i and R nodes are denoted by P S i and P R , respectively.

1) EH AT RELAY NODE
The EH at R can be written as where 0 < η ≤ 1 is the EH efficiency determined mainly by the circuitry [21]. The harvested energy at R after N time-slots is written as Similarly the harvested power at R after N time-slots can be obtained as where 0 ≤ ρ i ≤ 1. The effective value of P R for statistical channel model is given as ]. (27) During the transmission of the coded packet (formed by combining data sent by different sources) in (N + 1) th timeslot, the power required from the battery to transmit that packet at fixed power (P R ) is defined as

2) EH AT SOURCE NODES
Within a communication cycle, the harvested power at each S i is denoted by HP S and defined as Similarly the effective value of harvested power at each S i is calculated as 5 During the transmission of the i th (i ∈ {2, 3, .., n}) packet, the power required from the battery to transmit the packet at fixed power (P S i ) is defined as Fig. 8 shows the variation of WPS factor (1), Y 1 and power associated with IT (11), Y 2 at drone w.r.t h D . The reason for the curves having different slopes for Y 1 and Y 2 may again be explained as done before for Fig. 5. Here, we observed that for lower values of h D (below h D opt ≈ 12 m), the values of ρ decreases and power associated with IT increases. For higher values of h D (above h D opt ), the values of ρ increases and power associated with IT decreases. Fig. 9 shows the variation of harvested power at S i w.r.t h D . Now, as discussed earlier, as the drone height starts increasing, there is a higher probability of LoS between the sources and relay. Thus, there is an increased probability of Rician fading which helps the sources to harvest more power. This can be observed in the figure as the graph shows an  increasing nature. However, the average harvested power falls after a certain drone height (h D opt ≈ 25 m). This is because after a certain value of h D opt the distance becomes so large that eventually the gain cause due to LoS component takes a back seat and it is overpowered by the path loss component. Here, it may also be noted that the harvested power at S i improves the battery life of the S i nodes.

V. RATE AND OUTAGE ANALYSIS FOR DA-NCC
Here, we formulate the analytical expressions of the rate and outage probability for DA-NCC system using EH at R and S i .

A. RATE ANALYSIS
As shown in Fig. 2(a), the time required to complete the one communication cycle is T and T N +1 is the time-slot assigned to each S i and R. For N S − D pairs, the rate at node D i is defined as where I l 1 ,l 2 ,..,l N ,l N +1 DA-NCC denotes mutual information at node D i . The mutual information at D i is calculated by using MRC technique, where we combine the direct path (S i − D i ) and the relay path (S i − R − D i ) SNRs, which is defined as [3] I l 1 ,l 2 ,..,l N ,l N +1 DA-NCC (33) In (33), the SNR between node a and b is denoted by ab and found by using and symbol l 1 ,l 2 ,..,l N ,l N +1 S i RD i represents SNR at node D i via relay path. Substituting (11) into (15), we can define l 1 ,l 2 ,..,l N ,l N +1 S i RD i as in (35), shown at the top of the next page. After performing few mathematical simplification in (36), shown at the top of the next page we can get (37), shown at the top of the next page. In (37), ab can be found by using (34), where a ∈ {S i,i∈{1,2,..,N } , R} and b ∈ {R, D i,i∈{1,2,...,N } }.

B. OUTAGE ANALYSIS
In this subsection, we investigate the generalized expression of the outage probability for N number of S i∈{1,2...,N } − D i pairs by using MRC scheme at the desired node (D i ). Among all the N number of S i −D i pairs, D i is considered as the node of interest.
For a given spectral efficiency (R), the outage probability is defined as [5] P l 1 ,l 2 ,..,l N ,l N +1 out Using (33) and (38), outage probability for DA-NCC becomes where T N = (2 (N +1)R − 1). Channels among GUs and drone are modelled using the probability based statistical approach. By taking the possible values of l i , l j and l N +1 into account, there are 2 N +1 possible cases of the outage probability for the proposed channel model explained as: The (2 N +1 − 1) th instance occurs when the links S i to R, S j to R are Rician faded and the link R to D i is Rayleigh faded, respectively. Probability of occurrence of this possibility can be calculated by N i=1 [P L ] i P NL . Putting l i = Ric, l j = Ric, Putting the value of Q l 1 ,l 2 ,..,l N from (14) into (35), we can rewrite (35) as P out for cases III, IV,. . . ., 2 N +1 − 2 may be calculated in the same way as discussed above by taking different possible values of l i , l j and l N +1 . By including all the cases depending upon P L and P NL , the average rate and the average outage probability for N number of S−D pairs using the probabilistic channel model can be found in (44) and (45) as written below Final expression for the average C rate and average P out are obtained by weighing each case with corresponding probability of occurrence. The average capacity (44) and outage (45) expressions derived, provide useful insights to the system engineers for evaluating the system performance such as spectral efficiency in Internet of Things (IoT) based smart agriculture scenario where asymmetric object distribution in the environment leads to dissimilar fading among various GUs and hence, justifies the application of the proposed probability based channel assignment model.

VI. SIMULATION RESULTS
In this section, various results are presented to validate the proposed analytical framework. Algorithm 4 is used during the calculation of the average outage probability and average capacity through simulations for N number of S − D pairs. For a given h D and environmental parameters, P L i at S i can be calculated as mentioned in algorithm 4.
For this purpose, generate a uniformly distributed random number g i and compare it with P L i . If g i is less than P L i , choose Rayleigh distribution else Rician distribution for the channel coefficient S i R . Again, using the similar steps at R also, distribution of the channel coefficient RD i can be found. Now calculate I l 1 ,l 2 ,l 3 ,...,l N +1 rate and P l 1 ,l 2 ,l 3 ,...,l N +1 out using (32) and (39) respectively, in each communication cycle. In the last for j = 1 → length (iteration) do 5: Calculate P L and P NL for given h D and r j 6: Generate a random number g i∈{1,2,3,...,N } at S i and g N +1 at R 7: if g 1 < P L , g 2 < P L ,. . . , g N +1 < P L then 8: if g 1 > P L , g 2 > P L ,. . . , g N +1 > P L then 15:   Table 2. A model similar to the system model given in [5] is considered for the comparison purpose with appropriate changes to keep the fairness intact.
We compare the outage probability for different cases as a function of h D in Fig. 10. It can be observed that if R is considered not to be energy constrained, then it does not need to harvest energy thus, providing all the RF energy to the information. Hence, in this case, we get the best results in terms of outage, that can act as an upper bound for reference. That is, we get the best performance when energy is not harvested. On the other hand, if R transmits at the harvested power only (using (14) and (27)), we get the worst performance as the power harvested depends upon the  channel conditions too. Hence, R has less harvested power to transmit, thus, providing the worst performance. Finally, if R transmits with a fixed transmit power but also harvests energy (using only (27)) to maintain this fixed power, then we get relatively better performance. The performance of this scheme depends on the value of set in (2). It's worth noting for all the cases that initially as h D increases, probability of occurrence of LoS also increases. Due to this, the path loss exponent decreases and because of smaller value of h D , large scale attenuation has lesser effect on outage probability. As a result, performance of DA-NCC system improves. After an optimum drone height (≈ 25-28 meters), path loss exponent decreases but due to increase in h D , large scale attenuation increases. Hence, we see an increase in the outage probability. Fig. 11 compares the outage performance of the cases considered in Fig. 10 with respect to rate. Similar logic can be applied as discussed for Fig. 10 in case of Fig. 11. The best outage performance is obtained when full power is conserved for IT (i.e R does not harvest energy). This worsens a bit when R transmits with fixed power and it's the worst when R transmits with variable harvested power as explained above. Fig. 12 shows rate w.r.t h D . The reason for the curves having different slopes for outage probability can again be explained as done before for Fig. 11. It can be observed here that, with an increase in h D , the rate for all the considered  cases shows an increasing nature. However, the worst rate is obtained when R transmits using harvested power only. This is due to variation in the harvested power (based on channel parameters) during different sessions. Whereas, the value of rate is maximum when there is no EH at R because the entire RF power is allocated to IT which is not the case when R harvests energy. Fig. 13 shows average magnitude of ANC-noise w.r.t h D . Here it is noted that average magnitude of ANC-noise decreases as drone height increases for all the three cases. Average magnitude of ANC-noise is low in case when R transmits the coded signal at harvested energy and its value is high when R transmits the coded signal without using EH. This happens because in case of EH the signal power is splitting into two part. The first fraction associated with EH and the 2 nd portion associated with signal.
A plot between outage and power transmitted by source nodes is shown in Fig. 14. It can be observed here that, with an increase in power transmitted by source nodes, the outage probability for all the considered cases shows a decreasing nature. It may be noted from the outcome that the worst performance is obtained when R transmits at harvested power only due to variation in the harvested power (based on channel parameters) during different sessions. Whereas, even though R transmits at a fixed power in the other two schemes, it shows  the best performance when there is no EH at R because the entire RF power is allocated to IT which is not the case when R harvests energy. Fig. 15 depicts the number of packets received successfully at destination w.r.t power transmitted by S i nodes. Here it is observed that as power transmitted by S i increases, the number of packets received successfully at destination increases in both the cases. However, the number of packets received in case of EH is higher as compared to the non EH case due to increase in the harvested power at R with increase in P S i . As a result, the power required from the main battery (P R ) to maintain the fixed P R is lesser in the case of EH. While in case when no EH is considered, a fixed P R is taken from the main battery which reduces the main battery quickly as compared to EH case. It may also be noted here that for a given P S i , the number of communication cycles when considering EH is more as compared the scheme with no EH which improves the lifespan of the proposed network. From the outcomes from Fig. 14 and Fig. 15, we have concluded that even though the performance in terms of outage is relatively worse in case of EH but the higher number of packets received at the destination for EH case compensates it sufficiently.

VII. CONCLUSION
In this paper, we have proposed a dynamic power splitting factor for harvesting the energy at nodes in DA-NCC system. The dynamic nature of EH factor enhances the network lifetime by extracting more energy from RF signals when the channel conditions are favourable and lesser energy when it's not. Thus, the system maintains a better relationship between EH and IT. In order to accurately model the channel for dynamic EH factor at nodes, we have also introduced a generic probability based statistical channel model for modelling A2G links. Results obtained using this proposed model gives a better characterization of links in energy harvesting scenario by taking statistical independence of links into account. Here the harvested energy may not necessarily be sufficient to fulfil the entire energy requirement for the node, but it's contribution increases the lifespan of the node by increasing the number of transmission cycles. Extensive simulations show that our proposal enhances the lifespan of the proposed network. Analytical framework is developed for ANC-noise and variance of ANC-noise for the proposed channel model and EH. We derived the rate equation for the proposed channel model and EH. Algorithm 1 is developed to decide the A2G channels. Algorithms 2 and 3 are developed for harvesting the energy at relay and source nodes. Algorithm 4 evaluates the performance metrics (rate and outage probability) of our proposed work.
The generalized system model is applicable in many real-time scenario such as disaster management, IoT-based application, smart cities etc. in which drone acts as an aerial relay and thus, enhances the reliability of the ground users. Optimization of different parameters (drone altitude and power splitting factor etc.) of the proposed work can be considered as future work which can be beneficial for the next generation wireless systems. Additionally, finding the (approximated) closed form for the definitive expressions presented in this paper may be an insightful future work.