Optimal 3D Deployment and Trajectory Selection of UAVs for Maximum Network Utility and Disaster Management

Advancement in Unmanned Aerial Vehicles (UAV) technology supervised us to use them in many situations like seismic survey of an area, border and restricted area surveillance, disaster rescue, agriculture monitoring, and many others. The deployment of UAVs for expansion and extension of wireless network coverage for surveillance and rescue during and post disaster situations is fenced with promising challenges. The dense user coverage, quality of service (QoS), user data rate requirement, limited short flying time, and optimal trajectory path are some of the pertinent issues that UAVs are encountering. In this work we develop some algorithms for fast deployment of UAVs for application in disaster scenarios and optimal trajectory of each UAV in some specified area. The main aim of the work is to reduce the time complexity for optimal deployment of UAVs in order to optimize diverse parametric constraints. We propose a highly time efficient algorithm for UAV deployment through Lloyd and FCM as the initial localization of position in conjunction with the evolutionary algorithm namely Differential Evolution (DE) and Hybrid Differential Evolution with Learning (HDEL) for finding the optimal location of UAVs. We also develop an algorithm for finding out the optimal trajectory to reach the intended location for effective deployment of UAVs to ensure optimal resource allocation and user coverage. Comprehensive simulation of various performance measuring metrics is obtained and the result shows that the proposed algorithms are well efficient as compared to some of the standard algorithms used in deployment of UAVs.


Introduction
Development and implementation of UAVs for expansion of various wireless services are the recent trends of multidisciplinary research.Due to recent advancements in connected device technology, applications, and some unique inherent advantages, UAV based applications are getting a lot of attention from both academia and industries.To be very specific, UAV promises to be an alternative solution in providing wireless network coverage not only for surveillance but also in public-safety and emergency communications.The application of UAVs as mobile sensor nodes are also a promising area of potential research and development [1], [2].
There are good numbers of work done on the deployment feasibility of UAV in the low altitude platform but still there exist many challenging issues that are yet to be addressed for a fully functional UAV wireless network.In [3], Al-Hourani et.al provided a mathematical model for an optimal altitude of the low-altitude aerial platforms through providing maximum coverage in a considered geo-graphical area.The analysis depicts that the optimal altitude is a function of the maximum allowed path loss and statistical parameters of the urban environment.In [4], the authors elaborated the transport theory for optimal UAV deployment where energy efficiency of UAV is considered as the key constraint for providing long time service in a specific geographical area.In [5], the authors derived a closed-form expression for optimal probability of Line-of-Sight (LoS) connection between a low altitude platform (LAP) and a ground user where the optimal altitude of a drone small cell (DSCs) is also derived in order to maximize the cell coverage.
UAVs are proposed to be used as mobile aerial base stations to provide reliable downlink and uplink communications for ground users, and boost the capacity of wireless networks [6].A comprehensive literature on empirical formulation of air-to-ground channel modeling in UAV communications is deliberated in [7], [8].In [7] the authors deliberated an innovative approach for air to ground channel model in low altitude platforms for UAVs like drones and quadcopters.The alteration of height in optimal UAV planning is an important factor under the constraint of coverage and capacity.However, with the alteration of UAV height two issues occur, i) the coverage radius will vary and hence the user association, ii) the path loss factor will vary and hence the SINR will change which causes data rate fluctuations leading to unsatisfactory QoS [7].In [8] the authors deliberated that due to path loss and shadowing effects of obstacles, the characteristics of the air to ground channel depend on the height of the aerial base stations.By increasing the altitude of a DSC, the path loss increases, however, shadowing effect decreases and the possibility of having LOS connections between ground users and DSCs increases.Therefore, an optimum altitude for which aerial base station provides maximum user coverage and user association need to be investigated.
The deployment of UAV poses a serious challenge and needs careful design strategy in order to maximize the utilization of resources.In UAV planning the energy consumption and service period is highly related to the processing time required in running the optimization algorithm on board of an UAV.In [9] the authors proposed a method to find the positions of drone-BSs in a geographical area using particle swarm optimization (PSO) algorithm.However, the PSO based algorithm is time complex and therefore requires more time in finding the optimal location for deployment of UAV in any geographical area.Also, such algorithm is inefficient to provide optimal number of drone BSs in a specified area for coverage.Hybrid aerial and terrestrial networks have recently emerged for public safety and military communications.Indeed, there is a need to rapidly deploy a network which is able to provide a large coverage of several tens of kilometers and high capacity in respect of serve user at the same time [10].In [11], the authors have discussed about the processing time required in the planning of UAV and proposed algorithm based on K-mean (K-Cov), with K-mean and PSO (K-APSO), Lloyd and mean clustering (X-Cov) to find the optimal location of UAV in a considered area for user coverage.The authors have observed that the execution time required in the X-Cov algorithm is superior as compared to K-APSO.The basic geometric approach in X-Cov provides less execution time in computation of the location of UAV but fails miserably to find the optimal location of UAV in the solution space.However designing of fast and efficient algorithm to address the above issues with reduced time complexity is challenging and an open problem.
The Evolutionary Algorithm (EA) is also proposed to be used in order to find the optimal location of Low Altitude Platform (LAP) in a UAV network [12], [13].However, the model proposed in [13] allowed overlapping of LAPs' coverage by using inter-cell interference coordination (ICIC) where the authors investigated the optimal 3D deployment of multiple UAVs in order to maximize the downlink coverage performance with a minimum transmit power.Given a target geographical area, the authors developed a novel framework to determine the optimal 3D locations of the UAVs with dynamic payload [13].In [14], authors proposed an analytical approach for the optimal location of a ground base station and number of relays needed in the network for maximizing the coverage.However, the authors did not consider UAV deployment issues in order to increase the coverage.In [15], the authors presented a drone assisted public safety broadband network by using DSCs as relay instead of ground based BS.However their proposal lacked practical intuition as it is difficult to deploy such system during emergency situations.In [16], the authors investigated the issue of optimal deployment of UAVs and user association considering user data rate requirement.However, the dynamic characteristics of placement of UAVs in terms of height adjustment and spatial location are not addressed in this paper.Also fast deployment of DSCs in order to satisfy urgent network coverage is also missing in the literature.
For any UAV based wireless communication system, energy consumption of the network plays an important role in order to sustain seamless connection for a longer period of time.In [17], authors proposed an analytical approach through clustering the ground users and provide a UAV for each separate cluster such that the consumption of energy by UAV for uplink communication can be reduced significantly.In [18], authors proposed a model to minimize the deployment time to cover the considered geographic region such that the overall energy consumption of UAV can be reduced.However optimal user association and UAV deployment strategy are not addressed in the paper.
The other serious problem in the public-safety and emergency communications (PSEC) is the sudden increase in network load due to abrupt assembly of users in a specific location at any instant of time.This may be reduced by capacity maximization of the serving network.In [19], the authors worked on the capacity maximization of the heterogeneous network through UAVs.In [20] the authors proposed some methodology for accurate placement of the UAVs by optimizing the UAV assisted delay.In [21], the authors proposed multi-tier drone cell architecture for performance improvement of the heterogeneous network by providing additional resource and coverage on temporary basis.However capacity maximization of the UAV network through proper user association is still missing in the literature.
Failure of connection to backbone network is a common phenomenon in infrastructure based network architecture during disasters which causes serious problem in emergency rescue operations and restoration of normalcy in the zone.In [22], the authors proposed a solution for minimizing the blackout area by introducing Unmanned Aerial BSs (UABSs) and also investigated about the optimal number of UABSs to cover such blackout area under certain constraints.However the authors did not consider random blackout zone with different user density, user coverage, frequency of operation and optimal user association.
Apart from minimizing energy consumption and finding out the optimal location of UAVs in any specified area, optimal trajectory path for deployment of UAVs to any intended location is a serious concern.The trajectory determination of UAV is directly related to the performance of the overall system [23].In [24], author presented a neural network based adaptive tracking control schemes for under actuated systems with matched and mismatched disturbances.Resourcefully manage the trajectory of an un-manned system through converting it to an optimization problem is challenging and recent research trend.UAV route planning for finding a fixed target while using mobile carrier is discussed in [25], where genetic algorithm is used to satisfy the problem constraint and maximizing the visited target.Thereafter in [26], authors presents Dynamic Adaptive Ant Lion Optimizer (DAALO) based route planning for UAV, and demonstrate the efficiency of the algorithm in mountain and city model.
However the chance of getting stuck in the local optimal solution is reduced by estimating probabilistic movement from expert demonstration.The combination of local trajectory optimization and learning from demonstration inherently estimate the optimal trajectory through fine tuning the cost function [27].In [28], authors worked with autonomous robots and have shown swarm movement of the robots without any centralized control.The algorithm demonstrated the centralized control of swarm of autonomous bots which finds application in UAV deployment and trajectory determination.In [29], the authors proposed a time efficient deployment of UAV considering optimal trajectory planning in a 3D urban structure.However the trajectory path planning for swarm of UAVs in the network for maximizing the network utility is missing in the literature.
The optimal deployment of UAV is a complex problem in the present scenario where multiple UAVs have to follow different paths to cover different regions in an area in order to maximize the network utility function.In public safety and emergency communication, fast deployment of UAV confirming user density, data rate and area coverage is a challenging problem which needs to be addressed.The determination of optimal trajectory path for such deployment of UAVs is very essential but is not available in literature.Finding out a viable and time efficient algorithm for optimal deployment of UAVs and trajectory path for maximizing network utility are the primary motivation to carry out this work.
The main contributions of this work are summarized below: i) Formulation of a network utility function based on user density and data rate.ii) Design of hybrid optimization algorithms (L-DE, FCM-HDEL) for efficient and fast UAV deployment.Optimal deployment of UAVs in a specified geographical area is performed based on coverage and capacity constraints, and evaluated their performances based on standard performance measuring metrics.iii) Black out area coverage by maximizing the network utility, and iv) Determination of optimal trajectory path for multiple UAVs for optimal user association and network utility maximization.In Section II, the proposed model is explained.In Section III we establish the objective function and relative constraint of the problem.The algorithm for different proposed scenarios is discussed in Section IV.The results and observations are presented in Section V followed by conclusions in Section VI.

System Model
In this work, we consider a non-uniform distribution of 2000 random static users in a specified area of 5×5 KM 2 [20], [30].Our motivation is to find out the optimal location of UAVs in an efficient way such that each user in the considered geo-graphical area gets the demanded service at the earliest in PSEC scenario.Thus we consider random number of users in the geographical area inspired from [30], and perform the analysis.In our system model, we consider that the UAVs are operating at LTE spectrum of 700MHz, 1800MHz and 2600MHz with a bandwidth of 20 MHz and stationary users provided with maximum download data rate of 512 kbps and the uplink data rate is fixed at 75kbps.
In first phase, we observe the characteristics of two vital component of UAV deployment namely sum capacity and altitude of UAV with the number of UAVs considering 5 km by 5km square area with non-uniform user distribution and find out the suitable UAV development algorithm and then using the best algorithm find out the optimal location of UAV.In second phase, we considered arbitrarily created blackout area that have to be cover the optimal deployment of drone.In the third phase of deployment we proposed an algorithm for finding out the trajectory path in UAV placement.
Through keeping the transmission power of a UAV fixed and the limit of UAV altitude is within the bound of UAV regulation, we assume that each stationary user i∈NU connect with the UAV from where it gets maximum receive power.The interference zone as shown in the Fig. 2 below created when two UAV comes closer to one another, thus our aim is to minimize those interference zone while maximizing the sum utility of the network.For catering each and every user through minimizing the inter UAV interference, user have to establish strong communication link to the UAV and at the same time proper synchronization between the UAVs are also needed such that maximum network utility can be achieved.

Blackout area based UAV Deployment
To cater the user in the blackout area where no communication service is available.Our major concern in this section is how to provide communication service through UAV to the blackout zone which are mainly created after disaster or major power/network failure.We consider the target blackout area as a big polygon and user inside the area as the service target, thus the two major constraint of this problem are coverage area and the total number user to be serve.

Trajectory Path evaluation
After finding out the optimal number of UAV required to cover the area with appropriate fulfillment of user required data rate.Use the trajectory algorithm for finding the optimal path for locating those UAV to their optimal location, such that deployment time is also count in the network utility maximization.

FORMULATION OF OBJECTIVE FUNCTION:
First in the user association phase of the problem, we assume that users are associate with the UAV from which they receive maximum power.For which the distance between the user i and BS j is calculated as 2 2 , ( ) ( ) After this in calculation of path loss associated with the user signal from the associated UAV, we assume the approximated model of LOS probability according to [31] as (2) where α and β are the environmentally dependent constant as [32].
The path loss model for LoS and NLoS links are formulated as [32].
, 4 10log Where γ is the path loss exponent, fc is the operating frequency, c is the velocity of light ηLoS and ηNLoS are the mean additional losses (in dB due to shadowing) for LoS and NLoS connection.Thus the mean path loss model can be approximated as [33].
The positions of user are obtained using GPS and feedback to the BS or central controller, which take the prior decision regarding the height settlement of the ES as furnished by our proposed algorithm.The i th user in the considering area select the BS with maximum receive power.Let ρi be the BS selected by the i th user thus ρi can be written as

P P G G H
The gain of the BS can be calculated as Where θB is the half power beam width (HPBW) of the UAV antenna.Therefore the signal to interference plus noise ratio (SINR) 'г' for each user from the considering UAV can be calculated as  , ,s,  ( , ) 1; arg max 1 Where H is the channel gain of user accessing Resource Block (RB) r while communicating with the nearest serving UAV 'j' in the selected beam 's' and can be calculated as , ,s, 10 , , , Where k is the path loss constant,  ̅ is the path loss exponent, ξi,r,j is the Log-normal shadowing with zero-mean and ,, i r j F is the Rayleigh fading factor.Let ψj be the total number of user connected to UAVj ; Therefore the throughput of the UAV can be formulated as Subject to the constraint C1:

ALGORITHMS
In this section various algorithms for optimal UAV deployment and determination of optimal trajectory are described.The objective function developed in previous section is experimented with meta-heuristic optimization techniques used widely in the literature.Here we present the hybrid optimization algorithms for optimal deployment of UAVs under the described constraints (Eq.( 14a), ( 14b) and ( 14c)).

Optimal UAV Deployment Algorithm
Recalling the benefits of PSO in terms of complexity, ease of implementation and efficiency we have formulated the UAV deployment algorithm based on PSO [34] for the evaluation of optimal number of UAVs.The algorithm is presented below: Evolutionary algorithms are considered computationally superior than the swarm based meta-heuristic optimization techniques and therefore attracts our attention.We develop a hybrid evolutionary algorithm by hybridizing differential evolution (DE) [35] and the Lloyd algorithm [36] for a faster and optimal deployment of UAVs.The Lloyd algorithm is an efficient heuristic method which is better than the k-means clustering [37] as it consider continuous geometric region as input rather than discrete set of points.The proposed algorithm is described below: Change UAV position according to cluster center and calculated height as { 2 , h} 13.
end for 22.
However, Lloyd Algorithm is suffering from global convergence due to consumption of numerous data points in each iteration.Therefore, the quest for faster algorithm continues and a new hybrid model named as Hybrid DE with Learning (HDEL) is developed.The proposed model hybridize the learning behavior of individual agents in the search space in terms of personal best, global bests & global worse and effectively integrate it with the Fuzzy C-Means (FCM) algorithm [38] and is named it as FCM-HDEL.
The Objective function of FCM may be written as: where, D = No. of data points, N = No. of clusters, n = Fuzzy partition matrix exponent for controlling the degree of Fuzzy overlap refers to no. of data points that have significant membership in more than one clusters.m is the fuzziness index determine the level of fuzziness in the clustering.  = i th data point,   = center of the j th cluster ,  = degree of membership of   in the j th cluster.For a given data point   the sum of the membership values for all cluster is one.

RESULTS AND DISCUSSION
In our system model, we consider that the UAVs are operating in LTE-700 spectrum with a bandwidth of 20 MHz [11].We assume that there are 2000 stationary users in the specified geographical area of 5×5 km 2 with a required maximum download data rate of 512 kbps and the uplink data rate is fixed at 75kbps.The simulation of the proposed models are performed in Matlab ® 2015 running on an Intel i7 3.30GHz processor and 4GB of internal RAM.All the presented and proposed algorithms are simulated in the same environment in order to ensure authentic assessment and comparison.5 shows the sum capacity of the network with respect to number of UAVs deployed in the specified area.It is observed that the sum capacity of the network increases with increased number of UAVs deployed in the area which is intuitively satisfied.However, it can also be observed that the sum capacity of the network obtained by the proposed FCM-HDEL is better as compared to K-Cov [11], K-APSO [11], and the proposed L-DE.It can also be observed that the evaluated sum capacity of the network with proposed FCM-HDEL and L-DE is almost similar and better than the previously reported algorithms.
The Sum Log Rate with respect to number of UAVs is presented in Fig. 6.The results in Fig. 5 shows that the sum log rate of the network increases with the deployed UAV in the network.From the results it is observed that the sum log rate achieved with L-DE algorithm for low number of UAVs is greater than all the other algorithms but with the higher number of deployed UAV FCM-HDEL gives better performance.This is because with the higher number of deployed UAVs, FCM-HDEL for its less complexity and high exploration rate can evaluate optimal user association to the deployed UAV efficiently at a faster rate.The HPBW of the antenna used in the drone plays a significant role in determining the number of drones required to cover a geographical area.The impact of varying HPBW on number of UAVs under various optimization techniques is shown Fig. 6.We consider three different HPBW: 120, 140 and 160 for our analysis of the proposed algorithm.The result in Fig. 7 shows that with increasing HPBW lesser number of UAVs are required for effective coverage of the specified area which satisfies our intuitive understanding.

Fig. 7: UAV required versus number of user in the area
In case of deployment of UAV, interrelationship of number of UAVs with their altitudes plays an important role in optimal utilization of resources.Fig. 8 shows the altitude variation of UAVs with number of UAVs considering HPBW=120.We observe that the UAV altitude decreases with the increasing number of UAVs in the deployment area.It can be observed from Fig. 8, that the average height of UAV for any required number of UAVs in case of K-APSO is greater than what is required for L-DE and FCM-HDEL.High altitude UAV require high transmit power and large time to deploy in any area.A low altitude with high accuracy is the desired condition for deployment of UAVs in any circumstances like disaster situations.Fig. 8 is the testimony of the superiority of the proposed model over the existing K-APSO.We also perform the analysis of altitude variation with the number of deployed UAVs considering antenna HPBW of 140 and 160 respectively.Fig. 9: UAV attain altitude versus number of UAV in the considered area considering HPBW of antenna as 140 degree Fig. 10: UAV attain altitude versus number of UAV in the considered area considering HPBW of antenna as 160 degree Fig. 9, shows that the altitude required for the deployment of UAVs with respect to number of UAVs in the deployment area with HPBW =140 degree.Here it can be observed that the altitude of the UAVs with HPBW 120 is higher as compared to HPBW=140 because with higher HPBW UAVs can cover larger area as compared to lower HPBW which also justifies the result.From Fig. 10, it can also be observed that the altitude required with FCM-HDEL is lower than the L-DE and K-APSO which proves the effectiveness of the FCM-HDEL in UAV deployment scenario.
The most important tasks of any public safety and emergency communication network are to cater the user demands and ensure coverage in a blackout area under post disaster situations.Therefore, to carry out a practical UAV planning we consider two scenarios a) user density based UAV deployment and b) blackout area based UAV deployment.In the next section, we perform the UAV planning by using the proposed FCM-HDEL considering the above two scenarios.

User Density based UAV deployment
In this section, we analyze the number of UAVs required and their optimal placements considering user density constraint in multiple operating frequencies with FCM-HDEL algorithm.
Here we consider a 5×5 (KM 2 ) area with a total 2000 number of users, UAVs with an operating frequency of 700MHz, 1800MHz, and 2600MHz, the operating channel bandwidth of 20MHz, and the maximum user data rate at 512Kbps.We analyze the optimal UAV requirement with the popular meta-heuristic and evolutionary algorithm DE, PSO and HDEL The result of the optimal number of UAVs required to cater the requirement of 2000 users in the specified area under the three presented scenarios is tabulated in Table -2 [512:128] kbps, bandwidth of 20MHz and HPBW as 120, the DE, PSO, and HDEL requires 7 numbers of UAVs to cover and cater the user demand.For higher operating frequency respectively for 1800 MHz and 2600MHz 17 and 22 number of UAVs are required, which is justified as because the attenuation and path loss with 700 MHz is comparatively lower than 1800 and 2600 MHz.The corresponding UAV planning for 700MHz operating frequency considering the specified parameters is shown in Fig. 11 with their respective optimal altitudes (in meters).In figure, the green plus sign denotes the static user and the blue square are the optimal location of the UAVs.algorithm [11] has less execution time than our proposed algorithm because it considers only two dimensional space for finding the location and therefore not a convincing method for finding the optimal location of UAVs under the presented scenario.Also, Log-PSO algorithm is quite problematic due to its parametric up-gradation for high mobility cases due to significant change in geographical topology.

Blackout Area based UAV deployment
A blackout zone is the disaster affected area where the mainstay communication is breakdown due to disaster and requires additional support in order to restore communication.In this subsection we analyze optimal UAV deployment in blackout zone with a total 2000 users in an area of 5×5 KM 2 .In order to establish the suitability of the proposed algorithm for deployment of UAV in a disaster affected area we experiment the model with three different geographical topologies.
Considering the practical demography of distribution of population in a geographical region we have created the blackout zone as horizontally stretched (AREA-I), vertically extended (AREA-II) and with physical separation between two affected zones (AREA-III).In a similar manner the proposed algorithm identifies the optimal locations with altitude for other two areas (AREA-II and AREA-III) for three different frequency of operation as shown in Fig. 15 16, it can be observed that the optimal numbers of UAV required to cover users in a blackout zone with 700 MHz operating frequency is 2, whereas with 1800 MHz frequency it is 8 and with 2600 MHz it is 11.It may also be observed that the number of UAVs deployed remains same in all the three different areas for a particular frequency of operation because the areas of the blackout zones are kept as constant in all the cases.It is also important to note that the number of UAVs required is minimum when operating at 700MHz and highest in 2600 MHz for efficient coverage of the disaster affected blackout zone which is intuitively satisfactory.Therefore, deployment of UAVs could be made at any operating frequency for mitigation of disaster situations as per priority and availability.
For fast and effective deployment of UAVs in emergency communication scenario execution time is essential to be obtained for the proposed algorithm.The execution time of the algorithms including the proposed models is obtained for various operating frequencies and is presented in Table 3 and  Table 4.It can be observed that the execution time of FCM-HDEL is comparatively superior to all the other algorithms used in this paper.

Determination of Optimal Trajectory Path of UAVs
The determination of optimal trajectory path for deployment of UAVs is very essential not only for maximizing network utility but to handle emergency situations effectively.In this section, we analyze the trajectory path of the UAVs for easy deployment and maximum utilization of network resources.As described in Algorithm-V of Section-4, nearest UAV is continually following the centroid of the partitioned area.The partition of region is based on continuous granularization of the region of interest and the deployed drones are continuously following the nearest centroid in order to cover the area.The spatio-temporal analysis of the trajectory path for 700 MHz, 1800 MHz, and 2600 MHz operating frequencies are performed and are shown in Fig. 17, Fig. 18 and Fig. 19 respectively.
Considering the velocity of UAV is 200 Kmph, and time required by the control center to update the UAV is 1 Second (assume that each UAV is updated in each iteration from the control center).
Here it was observed that at the initial period of tracking, the distance between the following UAV from the nearest centroid is high and gradually decreases, thus the time required by the UAV at the initial phase of tracking is higher than the later phase.19, shows the location of UAV and the optimal trajectory path at different intervals after launching from the control center in Scenario-III.From result it can be observe that the deployment of UAV from the control center is following one curved line (trajectory path) and all the UAV not follow the same path for deployment.Thus through deployment of UAV the user in the blackout zone of the nearby area also get served equally which increases the network utility.Here the light blue line shows the UAV trajectory path and the black line shows the coverage contour of the UAV, where the red '+' sign shows the centroid of the partitioned zone and blue 'o' sign shows the current position of the UAV.
It has been observed that the time required by 7 number of UAVs of Scenario-I to deploy to the optimal location through following trajectory path need 2.05 Minutes (Considering the control time from the control center is 1 Second ideally) and in case of scenario-II, the time required to get the optimal location is increases due to more number of UAVs.As for higher number of UAVs to deploy, higher number of iteration requires to get the optimal location, here total time of 2.11 Minutes required by the 17 UAV to get the optimal location and in case of Scenario-III, 3.05 Minutes required by 22 number UAV to deploy to the optimal location.

Conclusion
In this paper, we investigated various issues related to optimal deployment of UAVs for maximum network utility considering user density, data rate, and coverage.We establish the network utility function for optimal deployment of UAVs considering user density and data rate.Thereafter we develop time efficient meta-heuristic algorithms for UAV deployment namely L-DE and FCM-HDEL through Lloyd and Fuzzy C-mean clustering algorithm as the initial localization of position in conjunction with the evolutionary algorithms namely Differential Evolution (DE) and Hybrid Differential Evolution with Learning (HDEL) for finding the optimal location of UAVs.The algorithm is then applied into some realistic user density based and blackout region based scenarios for optimal deployment of UAVs.The proposed FCM-HDEL performs better as compared to DE based (L-DE) and widely used PSO based (K-APSO) optimization algorithms in terms of time complexity and optimal deployment.Further the proposed model is applied to UAV deployment under user density constraint for finding out the optimal location of UAVs to cover a specified terrestrial area.It is further extended to address the blackout zone coverage problem of post disaster scenario.The algorithm efficiently able to deploy UAVs in the effected blackout area and determines the number of UAVs required to cover the zone satisfying associated user data rate and optimal resource allocation.Monte Carlo Simulation is performed and the results obtained are compared with PSO based widely used algorithms for optimization.The performance of the proposed FCM-HDEL algorithm is better in comparison to the other algorithms.It is also observe that for efficient coverage, UAV with an operational frequency of 700 MHz is best suitable for deployment.
One of the main contribution of this paper is the analysis of trajectory path determination of UAVs for maximum network utility during deployment.The algorithm for trajectory path determination is developed and the results of deployment is shown at various intervals.The result shows that it took 2.05 minutes, 2.12 minutes, and 3.05 minutes respectively for 7, 17 and 22 numbers of UAV respectively for deployment to the optimal location.
In future, we will investigate the continuous coverage to mobile user through developing dynamic fly management algorithm for UAV applying Markov chain modeling on the required number of UAVs to cover the movable user in the area.
Fig. 1.UAV array antenna radiation in far field 2.1.User density based User density based deployment of UAV deals with the deployment of UAV based on the user traffic generation.Thus through minimizing the inter UAV interference, maximizing the overall network throughput is the prior work.

Fig. 3 :
Fig. 3: Created blackout area coverage with the deployment of drone

Fig. 4 .
Fig. 4. System model to find the trajectory path of UAV

Fig. 5 :
Fig.5: Number of UAV deployed versus Sum capacity of the network Fig.5shows the sum capacity of the network with respect to number of UAVs deployed in the specified area.It is observed that the sum capacity of the network increases with increased number of UAVs deployed in the area which is intuitively satisfied.However, it can also be observed that the sum capacity of the network obtained by the proposed FCM-HDEL is better as compared to K-Cov [11], K-APSO[11], and the proposed L-DE.It can also be observed that the evaluated sum capacity of the network with proposed FCM-HDEL and L-DE is almost similar and better than the previously reported algorithms.The Sum Log Rate with respect to number of UAVs is presented in Fig.6.The results in Fig.5shows that the sum log rate of the network increases with the deployed UAV in the network.From the results it is observed that the sum log rate achieved with L-DE algorithm for low number of UAVs is greater than all the other algorithms but with the higher number of deployed UAV FCM-HDEL gives better performance.This is because with the higher number of deployed UAVs, FCM-HDEL for its less complexity and high exploration rate can evaluate optimal user association to the deployed UAV efficiently at a faster rate.

Fig. 6 :
Fig. 6: Number of UAV deployed versus Sum log rate of the network

Fig. 8 :
Fig. 8: UAV attain altitude versus number of UAV in the considered area considering HPBW of antenna as 120 degree

Fig. 14 (
(a), (b), (c)) shows the UAV placement with their respective altitude for a considered blackout region (AREA-I) due to disaster, with user data rate 512kbps and operating frequency of 700MHz, 1800MHz, and 2600MHz respectively.It may be observed that the number of UAVs are increasing with operating frequency as earlier.Fig. 14: UAV Placement for considered blackout user coverage: User accessing 512kbps data rate in (a) 700MHz (b) 1800MHz and (c) 2600MHz operating frequency in Considered Disaster Area-I : UAV Placement for considered blackout user coverage, User accessing 512kbps data rate in (a) 700MHz (b) 1800MHz and (c) 2600MHz operating frequency in Considered Disaster Area -: UAV Placement for considered blackout user coverage User accessing 512kbps data rate in (a) 700MHz (b) 1800MHz and (c) 2600MHz operating frequency in Considered Disaster Area -III From Fig.14, Fig.15 and Fig.
Fig.17depicts the location of UAV and the optimal trajectory path at different interval after launching from the control center in Scenario-I.Where optimal trajectory path is shown through the blue line, centroid and location of UAVs are shown through the red plus and blue circle respectively.

Figure 19 :
Fig.18shows the final UAV position and the optimal trajectory path for the Scenario-II.
Randomly initialize the cluster membership values   2. Calculate the cluster centers.

Table -
It can be observed from the Fig.11-Fig.13that the average altitude required with 2600 MHz frequency is comparatively lower than the 1800 and 700 MHz, which is justified as because the attenuation and path loss with 700 MHz is comparatively lower than 1800 and 2600 MHz which justify the obtain result.On the other hand, to minimize the inter UAV interference the UAV radius should remain within a certain limit in order to ensure maximum overall network throughput.

Table 3 :
Execution Time needed by algorithms

Table 4 :
Execution Time needed by all the algorithms in topological area wise deployment considering Disaster Area-I