Joint Resource Allocation and UAV Scheduling With Ground Radio Station Sleeping

Applications of Unmanned aerial vehicles (UAVs) have advanced rapidly in recent years. The UAVs are used for a variety of applications, including surveillance, disaster management, precision agriculture, weather forecasting, etc. In near future, the growing number of UAV applications would necessitate densification of UAV infrastructure (ground radio station (GRS) and ground control station (GCS)) at the expense of increased energy consumption for UAV communications. Maximizing the energy efficiency of this UAV infrastructure is important. Motivated by this, we propose joint resource allocation and UAV scheduling with GRS sleeping (GRSS). Further, we propose the use of coordinated multi-point (CoMP) with joint transmission (JT) and non-orthogonal multiple access (NOMA) along with GRSS to increase the coverage and data rates, respectively. Through exhaustive simulation results, we show that the proposed CoMP along with GRSS results in up to 10% higher energy savings and 24% increase in coverage. Further, NOMA along with GRSS results in up to 9% enhancement in throughput of the system.


I. INTRODUCTION
Now-a-days, Drones are being used in a wide variety of applications like surveillance, disaster management, communication, weather forecast, wildlife monitoring, aerial photography, shipping and delivery, 3D mapping [1]. With an increasing number of applications, unmanned aerial vehicles (UAVs), also known as Drones, will soon be densely populating the low-altitude air space. These UAV deployments are expected to provide highly reliable communication in various scenarios [2]. To ensure autonomous UAV operations, one of the key requirements is reliable communication links with ground infrastructure. Communication with UAV is broadly divided into two components [3]. One of them is the Control and Non-payload communication (CNPC) link and the other is the Payload data link. The CNPC link plays a key role in The associate editor coordinating the review of this manuscript and approving it for publication was Ghufran Ahmed . delivering telecommand and telemetry information such as flight control, status monitoring, location, etc. The Payload data link delivers the data to both the parties, i.e., from the GRS to the UAV and vice versa. A reliable CNPC link is essential to ensure the secure integration of UAVs into national air space (NAS). Hence, this paper deals with the CNPC links.
In recent years, a considerable amount of work has been done in the area of CNPC channel modelling. In [5]- [7], the authors have published a series of works related to CNPC channel modelling for different environments. In [5], the channel model has been developed for over-water settings. In [6] and [7], the authors have analysed channel in hilly and mountainous settings, and suburban and nearurban environments, respectively, in the frequency bands allotted by World radio conference-12 (WRC-12) [3] for CNPC operation. In [8], the authors have presented UWB channel modelling for air-to-ground propagation channels. In [9], UAV air-to-ground channel model has been developed for mmWave systems. In [10], [11], the authors have analysed the Doppler effect on the air-to-ground channel and the methods to mitigate the same. Several works like [12]- [19] have considered UAV deployment as the aerial base station and considered coverage analysis, optimal altitude deployment, user association etc. However, resource allocation and energy efficiency for UAV communications have not been considered.
The secure integration of UAVs into NAS is not possible without analysing the GRS network. The GRS is an important part of the network which aids in establishing communication with the UAV and allocates resources to the UAVs accordingly. GRS is the most energy consuming unit in the UAV communications like Base station (BS) in cellular network. Base station sleeping (BSS) is a known technique for energy efficient operation in cellular network [20]. In general, every network is designed for a nominal number of users (here UAVs). Like any other network [20], we expect in a UAV network also the UAV density would vary with time and falls below certain threshold at multiple instants. In such scenarios, we investigate whether some GRSs can be moved into sleep mode to conserve energy while still maintaining QoS. Motivated by it, this is the first work that explores GRSS for energy efficient UAV communication network.
Coverage and throughput issues with BSS have been addressed in [20] and [21] using CoMP with JT and NOMA, respectively. Motivated by this, we consider CoMP with JT and NOMA with GRSS in this paper. We use CoMP with JT interchangeably with CoMP throughout the text. The trade-off between energy, coverage, throughput for GRSS, joint GRSS and CoMP, and joint GRSS and NOMA considering the mobility of the UAV has not been much discussed in the literature. This is the motivation of our work. The major contributions of this paper are as follows: • We formulate the GRS sleeping optimization problem which ensures quality of service (QoS) to each UAV when GRS is in sleep mode.
• We design a dynamic GRS sleeping algorithm that ensures QoS to each UAV when GRS is in sleep mode.
• We propose a joint GRSS and CoMP algorithm to compensate for the coverage loss due to GRSS.
• We propose a joint GRSS and NOMA algorithm to compensate for the throughput drop due to GRSS.
• We present extensive simulation results of the proposed algorithms and provide a comparative study of these results with the benchmark system, benchmark with CoMP, and benchmark with NOMA. The rest of the paper is organized as follows. Section II describes the System model. Section III includes the problem formulation. Section IV and Section V, respectively, give the details of CoMP and NOMA considered in this paper. The proposed algorithms are presented in Section VI. Extensive numerical results are presented in Section VII. Section VIII gives the concluding remarks.

II. SYSTEM MODEL
We consider a randomly deployed homogeneous OFDMA based GRS network in which the set of GRSs and UAVs in the network are denoted using G = {1, 2, 3, . . . , G} and U = {1, 2, 3, . . . , U }, respectively. We consider that the UAVs and GRSs are deployed randomly with density λ u per km 2 and λ g per km 2 , respectively. In Fig. 1, we present the system model considered in this work [22]. In this paper, we focus on the downlink, however, similar results can also be obtained for uplink. Without loss of generality, here we assume that the GRSs are divided into clusters of size n. However, this framework can be extended to varying cluster sizes. We consider a clustering based on distance among the GRSs. Alternatively, any other clustering mechanism can also be considered. There are various other ways of clustering like K-means clustering [23] etc. Let M = {1, 2, 3, . . . , M } denote the set of sub-channels available in the network. All important mathematical notations used in this paper are summarized in Table 1. Next, we discuss the spectrum allocation for UAV communication considered in this paper.

A. SPECTRUM ALLOCATION FOR UAV COMMUNICATIONS
Since CNPC carries telecommand and telemetry information, the International Civil Aviation Authority (ICAO) has decided to operate these links in secure bands designated by International Telecommunications Union (ITU). The designations [3] are as follows: • Aeronautical mobile (route) service (AM(R)S) for terrestrial CNPC.
• Aeronautical mobile-satellite (route) service (AMS(R)S) for satellite CNPC for Beyond line of sight BLOS) CNPC. The spectrum requirements for the Unmanned aircraft systems CNPC (UAS CNPC) are officially defined by the ITU radio-communications sector (ITU-R) considering the data requirements and UAV density estimated for the year 2030. The bandwidth allocation [3] is as follows: • 34 MHz for the terrestrial-based LOS CNPC. • 56 MHz for satellite-based BLOS CNPC. World radiocommunication conference in 2012 recommended a new spectrum for AM(R)S for UAS CNPC. The spectrum assigned is as follows [3]: • 5030 MHz -5091 MHz (C-band).
• 960 MHz -1164 MHz (L-band). In this paper, we consider L-band for numerical analysis. However, the algorithms which we propose further are equally valid for other bands. Next, we present the power allocation and UAV association considered in this work.

B. POWER ALLOCATION AND PHYSICAL CHANNEL MODEL
Let P g denote the total power transmitted by a GRS. We consider the power allocated per subchannel m by the GRS g as follows.
The signal-to-interference-plus-noise ratio (SINR) of a UAV u from a GRS g, denoted by γ m u,g , on a subchannel m is given as where, P m g is the power allocated to the subchannel m by the GRS g as in (1), m ĝ =ĝ g∈G P m g h m u,ĝ is the interference on the subchannel m, and σ 2 is the noise power. h m u,g denotes the channel gain between the UAV u and the GRS g and it is given as follows.
where, G u is the antenna gain, υ is the penetration loss, ρ is the loss due to small scale fading as in [24], G g (φ) is the directivity gain, and PL(u, g) is the path loss for the distance d between u and g. The pathloss between UAV and GRS as in [7] is written as follows.
where, n is the path loss exponent, d is the propagation distance, d min is the minimum distance of a UAV from the GRS, and X is the shadowing variable. F u,g is the free space path loss term with center frequency f c and is as follows [7]. We consider Line of sight (LOS) probability, P LOS as in [22] and it is expressed as    where, θ d 0 is the elevation angle which is expressed as θ = tan −1 (h 0 /d 0 ), h 0 is the altitude of UAV, and d 0 is the horizontal distance between UAV u and GRS g. B and C are environment-dependent constants. Similarly, the NLOS probability can be expressed from (4) as P NLOS (θ d 0 ) = 1 − P LOS (θ d 0 ). Next, we discuss the UAV association considered in this paper.

C. UAV ASSOCIATION
Given P m g as the power allocated by the GRS g to the UAV u on the subchannel m, we consider the UAV association with the GRS based on the maximum received power. Let x m u,g denote the binary association of UAV u with GRS g on the subchannel m and is given as where, h m u,g is the channel gain between UAV u and GRS g on the subchannel m as in (3). The binary variable x m u,g is 1 when the UAV u associates with GRS g and is 0 otherwise. Next, we discuss link rate of the UAV considered in this paper.

D. RATE COMPUTATION
We consider adaptive modulation and coding scheme (MCS) which is summarized in Table 2 for mapping SINR to spectral  efficiency as in [25]. Let, η(γ m u,g ) denote the spectral efficiency of a UAV u on a subchannel m in bits/symbol from GRS g. The link rate of UAV u from the GRS g with the spectral efficiency η(γ m u,g ) is where, SC OFDM , SY OFDM , and T sc represent the number of subcarriers per channel, number of symbols used per subcarrier, and time duration of a subframe, respectively. M represents the number of subchannels. We consider an α-fair time-based scheduler at each GRS which allocates all the M subchannels for a downlink UAV scheduling time fraction denoted by β u,g to a UAV u associated with it. We have considered the maximum received power based association of UAVs with the GRSs as in 5. Thus, for a UAV u, β u,g is non-zero for only one GRS g. The resultant downlink rate for any UAV u is given as Next, we present the UAV distribution considered in this work.

E. UAV DISTRIBUTION
We denote the area under consideration as . The UAVs are assumed to be distributed randomly using PPP in the considered area with an average UAV density of λ u per km 2 . The set of UAVs associated with GRS cluster k at time t is represented by U k and the number of UAVs associated with this cluster be denoted by . As already mentioned, CNPC links carry critical information pertaining to UAV navigation. Compromising with QoS in such scenarios can be disastrous. So, GCS should keep track of the SINR of UAVs and update the sleeping patterns accordingly. The GCS would update the sleeping patterns periodically using the recently updated SINR estimates. Next, we present the GRS distribution and sleeping patterns considered in this work.

F. GRS DISTRIBUTION AND SLEEPING PATTERNS
The GRSs are deployed randomly using Poisson point process (PPP) in the area with an average density of λ g per km 2 . The set of GRSs in a cluster k is represented by G k . As shown in Fig. 1, a GCS which consists of an air traffic controller (ATC) and other necessary equipment would control all the GRSs currently being operated in its jurisdiction. However, to focus on GRS sleeping we do not represent GCS in the figures after Fig.1 in this paper. Whenever a UAV enters into the coverage area of a cluster, the trajectory information of that particular UAV will be shared with the GCS handling that cluster. With the trajectory information and log files of all UAVs currently operating in that cluster, a dynamic energysaving procedure can be initiated by the GCS. The GRS can estimate the SINR and rate of any UAV in its coverage. The GRS shares this information with the GCS which can then decide based on the UAV load in the network which GRS to be in sleep mode. These parameters will be updated at regular intervals as well as whenever a new UAV enters the coverage area. While estimating whether a GRS goes to sleep mode or not, QoS constraints such as coverage and rate of UAV should be taken care of. Maintaining these QoS constraints, at any given point of time, following sleeping patterns are possible within a cluster of size n: A n−1/n , A n−2/n , A n−3/n ,. . . ,A (n−(n−1))/n which in general can be represented as A n−i/n , where, i = 1, 2, 3, . . . , n−1. A n−i/n means n−i out of n GRSs operating in the cluster are in sleep mode. Let A 0 denote the nominal system where no GRS is in sleep mode.

G. UTILITY FUNCTION
The utility function for an α-Fair UAV scheduler with the variable x is expressed as [25] Next, we present the performance metrics used to characterize the QoS in this work.

H. PERFORMANCE METRICS
There are three key performance metrics, namely, coverage probability, throughput, and energy efficiency considered in this work. The coverage probability is defined as the probability that a UAV u receives SINR γ m u,g greater than the minimum SINR threshold S as specified in MCS [25] from at least one GRS g. We consider α-fair throughput over the set of UAVs and is expressed as follows [20].
where, α is the fairness parameter, R u as in (7), and V g is the set of UAVs associated with the GRS g. We denote energy efficiency by ES a1/a2 (%) and it is defined as the percentage of energy saved via GRS sleeping. Each value of ES a1/a2 (%) corresponds to a particular GRSS pattern A a1/a2 . Let the energy consumed per unit time by a GRS be denoted by E. Then, nE is the energy consumed by the nominal system, A 0 , since all n GRSs are on. The energy consumed E would be approximately constant irrespective of the number of UAVs associated with the GRS. Thus, a suitable measure of energy efficiency for a GRSS pattern A a1/a2 in percentage when compared to the nominal system is given by [20].
where, a1 is the number of GRS sleeping and a2 is the total number of GRS considered. The joint optimization problem for resource allocation and energy efficiency is presented in the following section.

III. JOINT RESOURCE ALLOCATION AND ENERGY EFFICIENCY OPTIMIZATION
We consider A a1/a2 , the sleeping pattern as in Section II-F where, a1 is the number of GRSs sleeping and a2 is the total number of GRSs considered in the cluster. Similarly, the binary variable y g denotes whether the GRS g is sleeping (y g = 0) or active (y g = 1). Let ξ a and ξ s denote the active and sleeping mode power consumption by GRS, respectively. Since we consider homogeneous GRSs, the power consumed ξ a and ξ s GRS are equal for all GRSs in the respective mode.
The ξ s is significantly smaller as compared to ξ a . Further, we consider the data rate of every UAV u in the system should be greater than the operator fixed rate threshold τ k . Given the binary association of UAV u with GRS g on the subchannel m, y m u,g as in (5), SINR as in (2) at a time instant t, the joint resource allocation and energy efficiency problem for a cluster k (U k , G k ) is formulated and presented as follows.
u∈U k where, (11) is the overall objective function for maximizing throughput and energy efficiency of the system with respect to the operator threshold τ k and the UAV scheduling time constraint. (11) increases with increase in the utility function of the UAVs which in turn increases the throughput. Thus, (11) increases with increase in the throughput of the cluster. Since ξ s ≤ ξ a , as more number of GRSs go into sleep mode, the denominator of (11) decreases, and thus, increasing the energy saved. Given the set of GRSs in cluster G k , the constraint on (12) specifies that at least one GRS should be active in the cluster k. The data rate of the particular UAV u is computed in (13) and the minimum rate constraint on the UAV's data rate R u is specified in (14). Every cluster k can have its own rate threshold τ k . If each UAV in the system has the data rate R u greater than its corresponding τ k , then GRS sleeping in a particular pattern is feasible. Otherwise, all GRS are active over the cluster to maintain the QoS of UAVs. The overall time fraction allocated to associated UAVs with the GRS g should not exceed one and it is shown in constraint (15). The UAV association is subject to change with every GRS sleeping pattern. Therefore, the constraint on UAV's association with only active GRS is given in (16). The constraint in (17) specifies that the SINR of UAV γ m u,g should be greater than certain threshold S, i.e., no UAV should lose coverage after GRSS. The SINR and the positive time constraint are specified in (2) and (18), respectively. The overall system problem can be solved for a cluster. However, the same optimization problem formulated is applicable for all the clusters with varying cluster size. The given Problem P1 in (11) is mixed-integer nonlinear programming (MINLP) problem and is hard to solve in real-time for the binary variable y g , discrete rate threshold τ k , and the UAV scheduling time fraction β u,g . Therefore, the problem is decomposed into UAV scheduling problem and joint UAV scheduling with GRS sleeping problem. Given the GRS sleeping pattern A a1/a2 , i.e., y g , the decomposed UAV scheduling problem formulated for a cluster k with QoS threshold τ k is as follows.
The KKT conditions necessary to find the optimal solution for the aforementioned problem are as follows.
where, (22) is the first-order necessary condition for optimal β u,g . The complementary-slackness conditions are specified in (23) and (24). Applying (21) in (22), we get The optimal β u,g should satisfy the condition β u,g > 0 as in (18) and the complementary-slackness condition as in (24). Therefore, we consider D u,g = 0 in (26) and on further simplification, Substituting (27) in (15), we get, On substituting (28) in (27), the optimal β u,g is β * u,g = x u,g y g r The similar UAV scheduler for α = 1 is computed by maximizing u∈U log(R u ) in the objective function as in (8).
The proportionally fair UAV scheduling time fraction with α = 1 is written as follows.
Given this UAV scheduling time fraction, the joint UAV scheduling with GRS sleeping problem is presented as follows.
P3 min s.t. (12), (16), (17), (30), where, the objective function in (31) is minimizing the number of active GRS. This is equivalent to maximizing the number of GRSs sleeping. (33) computes the data rate of the UAV u over the active GRS using the (30). The data rate of the UAV u should be greater than the threshold τ k . We use the optimal β * u,g computed in (30) for our GRS sleeping problem. Since y g is binary, in order to find the GRSS pattern with maximum energy savings, we need to check for all possible combinations of y g in the set G k . UAVs are subjected to varying mobility conditions. This varying mobility leads to varying QoS due to GRS sleeping. Thus, we next evaluate CoMP and NOMA for enhanced coverage and throughput, respectively, during GRSS.

IV. COORDINATED MULTI-POINT
Coordinated multi-point with the joint transmission which hereafter is referred to as CoMP is a proven technology to enhance coverage and provide better QoS in cellular scenario [20]. This is the motivation to consider CoMP along with the GRSS. We consider that the GRSs in a cluster can cooperate and perform CoMP [20]. Let each cluster formed while clustering the GRS be CoMP clusters as well. Without loss of generality, we focus on cluster k. The set of UAVs and GRSs in cluster k is U k and G k , respectively.
We consider that the CoMP based system allocates a fraction of resources to CoMP UAVs in which all the GRSs within the CoMP cluster transmit jointly on the downlink to the CoMP UAVs. Whenever a UAV u in the CoMP cluster k receives the SINR less than a predetermined threshold denoted by χ then that UAV is served as a CoMP UAV. Let the time fraction in which all the GRSs within the CoMP cluster k transmit jointly on the downlink be denoted by θ k . Then (1 − θ k ) will be the time fraction in which the GRSs serve their corresponding non-CoMP UAVs individually. Note that each CoMP cluster k can have its own θ k .
Let U k,c and U k,nc denote the set of CoMP and non-CoMP UAVs in the cluster k. The SINR received by the CoMP UAV u, where, u ∈ U k,c in the downlink time fraction θ k from the  (2).
The link rate for the CoMP UAV is computed as follows.
Similarly, the link rate of non-CoMP UAVs is computed as in (6). The resultant data rates of the CoMP UAV u in cluster k based on [20] is given as where, θ k is the total CoMP time fraction available for all CoMP UAVs in the cluster k, β u,k is the UAV scheduling time fraction allocated for a CoMP UAV u by the cluster k, and r u,k is the link rate as in (35). The optimal UAV scheduling time fraction β u,k allocated to a CoMP UAV u by the cluster k as in [20] is given as follows.
Similarly, the optimal CoMP time fraction for a cluster k, θ k based on [20] is The resultant rate of non-CoMP UAV u from GRS g is given as follows.
Next, we present the other key technology, Non-orthogonal multiple access (NOMA) considered in this work. VOLUME 9, 2021

V. NON-ORTHOGONAL MULTIPLE ACCESS
High throughput and spectral efficiency are two key aspects that motivated us to look into Non-orthogonal multiple access (NOMA). When a GRS is in sleep mode there will be some loss in the coverage and throughput. The coverage is compensated by CoMP while the throughput can be compensated by adopting NOMA. We consider a NOMA system [21] for all GRSs where superposition coding (SC) is used to multiplex the signals of UAVs associated with a GRS and assume successive interference cancellation (SIC) is implemented at the receivers to separate the signals. Without loss of generality, we consider the k th cluster. For each GRS g in the k th cluster, let N g be the number of UAVs associated with it. For NOMA, all the UAVs are sorted with respect to their channel gains as |h m u 1 ,g | 2 > |h m u 2 ,g | 2 > |h m u 3 ,g | 2 > . . . > |h m u Ng ,g | 2 . Given this arrangement, the UAVs are divided into two groups. Let U k,g be the set of UAVs associated with GRS g in cluster k. U 1 k,g be the first group of UAVs and U 2 k,g be the second group of UAVs. If N g is even, then U 1 k,g = {1, 2, 3, . . . , N g /2} and U 2 k,g = {N g /2 + 1, N g /2 + 2, N g /2 + 3, . . . , N g /2 + N g /2}. The pairing is such that UAV 1 from U 1 k,g is paired with lowest channel gain UAV which is nothing but (N g /2) th UAV in the set U 2 k,g , UAV 2 from U 1 k,g is paired with (N g /2 − 1) th UAV in the set U 2 k,g and so on. In this way, all UAVs from U 1 k,g are paired with the UAVs in the U 2 k,g . Thus, all UAVs associated with the GRS g are paired when N g is even. Similarly, when N g is odd U 1 k,g = {1, 2, 3, . . . , N g /2 }, U 2 k,g = { N g /2 + 1, N g /2 + 2, N g /2 + 3, . . . , N g /2 + N g /2 }, where UAV pairing is the same as before. The only difference is that, the (N g /2) th UAV is left unpaired. This will be served as OMA UAV.
Let a NOMA pair be denoted by the ordered pair (p, q) where, p ∈ U 1 k,g and q ∈ U 2 k,g . Let N g denote the set of all NOMA ordered pairs associated with GRS g. When N g is odd, the unpaired UAV is not included in the set N g and such UAV be denoted by N 0,g . Hence, N g = {(p1, q1), (p2, q2), . . . , (p N g /2 , q N g /2 )}. Let B denote the number of pairs formed for the GRS g in cluster k.
Here, we consider P-NOMA, where GRS allocates power to each NOMA pair based on their channel gains. In a pair, the UAV with a larger channel gain is allocated lesser power in comparison to the UAV with a small channel gain. Thus, both UAVs receive the superimposed signal from the GRS g. The SINR of the strong UAV p in the b th NOMA pair over sub-channel m is given as where, the power from the GRS g over a sub-channel m, P m g is given in (1), the channel gain h m p,g is given in (3), is the aggregate interference received by the UAV p on the sub-channel m from all other GRSs, and ζ b is the fraction of total power allocated to higher channel gain UAV by the GRS g in NOMA pair b. We need to note that UAVs in a b th NOMA pair share same resources in time domain and successive interference cancellation is done at strong UAV, i.e., p th UAV. Similarly, the SINR for weak UAV q in the same NOMA pair b is given as follows.
where, h m q,g is the channel gain of the weak UAV in the b th noma pair, σ 2 is the noise power, ĝ∈G\g P m g h m q,ĝ is the interference received by the weak UAV from all other GRSs, and (1 − ζ b ) is the total power fraction assigned to the weak UAV in the b th NOMA pair. Given the SINR of strong UAV p and weak UAV q, the link rate, r b u,g of the respective UAVs are computed based on (6). The resultant data rate of UAV u with NOMA based on [21] is given as follows.
where, β b u,g is the time fraction allocated to the b th NOMA pair by GRS g and r b u,g is the link rate of the UAV u in b th NOMA pair by GRS g. The optimal UAV scheduling time fraction β b u,g allocated to the b th NOMA pair by GRS g for α = 1 based on [21] is given as follows.
where, U g,b is the set of UAVs associated with GRS g present in b th NOMA pair, b =0,b∈N g u∈U g,b x b u,g is the total number of UAVs in the NOMA pair b, and x 0 u,g is binary variable represents the association of unpaired UAV u in GRS g. The optimal power allocation scheme for ζ b has been discussed in [27] for cellular scenario and the same can be applied here.
In the following section, we propose three algorithms to dynamically solve the problem mentioned in (31).

VI. DYNAMIC GRS SLEEPING ALGORITHM WITH UAV MOBILITY
We propose a Dynamic GRS sleeping algorithm for the UAV network which simultaneously ensures energy efficiency and coverage. The presented optimization problems in (11), (19), and (31) are for a time instant t, whereas, UAV's position varies with every time instant t. The decision of GRS sleeping is taken based on QoS constraint as in (14) and (17). The proposed dynamic sleeping algorithm is hereby illustrated for the cluster k. However, the same can be applied to all the clusters. This algorithm searches for the sleeping pattern A t, * a1/a2 which maximizes the energy savings at time instant t while ensuring that the QoS constraints in (14) and (17) are satisfied.
Each GRS in the cluster estimates the SINR of UAVs associated with it at discretized (with step size δ) time intervals and shares this information with the GCS. The step size δ can be varied up to the desired accuracy level. Let the SINR  (2) 8: (7) 9: vector of UAVs associated with cluster k at time t be ×1 . With this SINR vector, rates of UAVs are calculated using (6) and (7). Let that rate vector be ×1 . The GRS computes an estimate of SINR vector a1/a2 and the corresponding rate vector a1/a2 using (2) and (7), respectively, for different sleeping patterns at each time instant t. The proposed algorithm searches for a GRS sleeping pattern in the descending order of their energy saving. Hence, initially, these vectors are calculated for A n−1/n configuration as this configuration results in the maximum energy savings. If no UAV loses coverage, i.e., no element of the SINR vector a1/a2 should be less than S dB, then the corresponding rate vector a1/a2 is calculated. In case the rate of no UAV doesn't drop below the threshold τ k , i.e., no element of the vector a1/a2 should be less than τ k , then this sleeping configuration is optimal for the time instant t, i.e., A t, * a1/a2 = A n−1/n . If either of the aforementioned conditions (QoS constraints) fail, then the a1/a2 and a1/a2 are updated for the next maximum energy savings configuration, i.e., A n−2/n . In case A n−2/n configuration also doesn't satisfy the above conditions, then the algorithm checks for A n−3/n configuration. In this way, the algorithm checks until the configuration, A 1/n if the configurations A n−1/n to A n−(n−2)/n fail to satisfy the QoS constraints. If the configuration A 1/n also fails to satisfy the QoS constraints, then the algorithm gives the output as A 0 , i.e., no sleeping is possible and all GRS in the cluster should be active. Whenever a new UAV enters or leaves the coverage area of the GCS, gets updated and at the same time all other parameters mentioned in the algorithm are recomputed. The proposed algorithm is presented in Algorithm 1. Next, we present Dynamic GRS algorithm with CoMP considered in this paper.  (2) 8: if ∃ γ u,g < S ∈ a1/a2 & j < J then 9: Calculate γ u,g = f ({P m g h m u,g }) as in (34) and (2) denoted asˆ a1/a2 10: Calculate R u = f ({η(γ u,g )M}) as in (36) ∀u ∈ U k , denoted asˆ a1/a2 11: if ∃ u s.tˆ a1/a2 < S orˆ a1/a2 < τ k then 12: j = j + 1 13: else ifˆ a1/a2 ≥ S &ˆ a1/a2 ≥ τ k then 14:  (7) 20: if ∀ u s.t R u ≥ τ k then 21: The GRS sleeping can result in energy saving at the cost of coverage and UAV's data rate. Given any GRSS pattern A a1/a2 , UAVs SINR and data rate are computed as in (2) and (7), respectively. If any of the UAV's SINR falls below the threshold S, then we perform CoMP for cluster k. The updated SINR vectorˆ a1/a2 is computed as in (34) and (2). In case SINR of any UAV in theˆ a1/a2 is below the threshold S, then the heuristic presented in Algorithm 2 increments the value of j (index of the GRSS pattern after sorting the patterns in the descending order of their energy savings as shown in Algorithm 1 and Algorithm 2) and check for the next GRSS pattern. If the SINR of all UAVs is above the threshold S, then the updated rate vectorˆ a1/a2 is computed with CoMP as in [20]. Thus, the heuristic now considers the updated rate vectorˆ a1/a2 for the selection of configuration A a1/a2 . Please note that CoMP is performed only if at least two GRSs are active. For example, CoMP is not applicable for the VOLUME 9, 2021 (2) 8: (7) 9: Calculate˜ ∀u ∈ U k , as in (40) 18: else 19: j = j + 1 20: end if 21: end while configuration in Fig. 3. The detailed algorithm for dynamic GRS sleeping with CoMP is presented in Algorithm 2. In the following subsection, we present dynamic GRS sleeping with NOMA.

B. DYNAMIC GRS SLEEPING WITH NOMA
After sleeping configuration is determined using either Algorithm 1 (without CoMP) or Algorithm 2 (with CoMP), i.e., given the GRSS pattern A t, * a1/a2 , the UAVs in the cluster k are paired based on Section V using NOMA. In this work, NOMA pairing is done without considering CoMP while determining the appropriate sleeping configuration. Please note that the UAVs that are associated only with the GRSs in cluster k are paired using NOMA. Given the NOMA UAV pairing, the SINR and data rate of UAVs for NOMA are computed as in (38), (39), and (40), respectively. The throughput of the system with NOMA is now computed using this updated SINR vector˜ a1/a2 and rate vector˜ a1/a2 . The detailed algorithm is presented in Algorithm 3. Given the GRSS pattern, the inclusion of CoMP and NOMA increases coverage and the throughput of the system, respectively. The detailed numerical results for the three algorithms are presented next.

VII. NUMERICAL RESULTS
In this section, we present numerical results to validate our analysis. We first verify the average throughput of the benchmark system for various λ u and λ g . We then show that considering CoMP along with the benchmark system results  in an increase of coverage at the expense of the decreased throughput. We also present the results for NOMA along with the benchmark system and show that the average throughput of the system increases by considering NOMA. Further, we present the numerical results of the discussed algorithm for GRS sleeping. The energy saved when GRS sleeping is performed with and without CoMP, and the corresponding throughput results are also presented. The increase in the throughput by adding NOMA for GRS sleeping is also presented.
In this section, we do not directly compare the performance of the proposed algorithms with those of the existing works on UAV communications. This is because the existing works on UAV communications [3]- [24] focused on channel modelling for CNPC links and did not study the infrastructure and energy consumption related issues. We present the advantages of the proposed framework in energy savings and the gain in throughput using Monte Carlo simulations performed using MATLAB_R2021a. We consider a system where, GRSs are deployed randomly using Poisson point process (PPP) [20]. Results are plotted for multiple GRS densities, namely, {6, 8, 10, 12, 14} per km 2 and for multiple UAV densities, {10, 20, 30, . . . , 100} per km 2 .The parameters used in the simulation are summarized in Table 3. The UAV densities and GRS densities are varied to study the impact of sleeping, NOMA, and CoMP on low, average, and high densities. An area of 10 km 2 is considered for the simulation. However, results presented focus on the center area of 1 km 2 . The simulation for each GRS density and for each UAV density is averaged over 10 3 location realizations as well as fading and shadowing realizations. Simulation results are presented for the center cluster and the cluster size in the simulation is considered to be 4. Clustering of GRS is done based on the distance among the GRSs. Euclidean Distance from one GRS to the other GRSs is calculated and 3 GRSs which are close to the GRS from which distance has been calculated are grouped under one cluster [28]. We have ensured that a GRS doesn't belong to two or more clusters simultaneously.
The trajectory of all UAVs is calculated using the Random waypoint mobility model. Random waypoint mobility model [29] is defined as follows: In the Random waypoint mobility model, the nodes change their velocity and direction at each time interval. Here nodes represent UAVs and minimum velocity is not zero. Here velocity ranges from 32 m/s to 120 m/s. It is assumed that each UAV moves with a uniform velocity which is chosen uniformly randomly from the range mentioned. At each time interval, t UAV chooses an angle from the set (0, 2π] and moves in that direction with already chosen uniform velocity ν. So, during this time interval, UAV moves with a velocity vector (νcosθ(t), νsinθ(t)). Following these rules, if any UAV moves out of the boundary then it is bounced back into the simulation field with an angle of π − θ(t). The random waypoint mobility model is a memoryless model. Hence, the current angle of the traverse is independent of the previous one. Fig. 6 shows a part of the trajectory of a UAV generated using a random mobility model. The variation of throughput for different λ g and λ u are presented in Fig. 7. It is observed that for a particular λ g by increasing λ u throughput of the cluster is gradually decreasing. The increase in λ u makes the α-fair scheduler allocate less fraction of time to each UAV and this attributes to the reduction in overall throughput of the cluster. However, by increasing the λ g , the throughput curve is moving up which indicates the increase in the throughput of the system. Increasing the λ g increases the overall time fraction allocated to each UAV due to which there is a rise in throughput of the system.
The throughput of the system is also calculated by considering NOMA and CoMP individually with GRSS. It is observed that the system performance in terms of throughput improves after using NOMA. On the other hand, CoMP improves coverage at an expense of decreased throughput. For a given λ g and λ u system with NOMA has more throughput than benchmark while the system with CoMP has less throughput than the benchmark. Fig. 8 shows the throughput variation of NOMA and CoMP comparing it with the benchmark system for λ g = 6/ km 2 . The throughput of the system when NOMA is considered is the highest because of the pairing between UAVs. Due to this pairing, more time fraction  is available to each UAV to transmit its data than that of the benchmark system. When CoMP is considered, there is a system level requirement of CoMP and non-CoMP time fraction. This decreases the amount of time fraction available to each UAV when compared with that of benchmark system. Hence, the throughput of the system with CoMP is less than that of the benchmark system. As mentioned that CoMP increases the coverage, the result validating this observation is presented in Fig. 9. We can see that the coverage with CoMP in both cases is better than without CoMP. The coverage of the system with GRSS is less than that of the benchmark system because in the benchmark system, all the GRSs in the cluster are in active mode but when GRSS is considered, few GRSs in the cluster are in sleep mode. However, when CoMP is considered in both the systems, all active GRSs in the cluster jointly transmit the signal to UAVs whose SINR is below a certain threshold. Thus, more UAVs come into the coverage.  This is the reason for increased coverage of the CoMP based system in Fig. 9. Fig. 10 shows the trends of throughput when GRSS alone is performed, GRSS with NOMA, and GRSS with CoMP is performed. From the trends, it is observed that the throughput drop due to GRS sleeping can be compensated using NOMA. However, at lower UAV densities, it can be seen that there is no significant difference among the three curves in Fig. 10. with the increase in the UAV density NOMA gives better throughput. Fig. 11 shows the energy savings. The advantage of CoMP during GRSS is seen in energy savings. It can be observed from the plot that average energy saved is decreasing with an increase in the UAV density for a constant GRS density. There are two energy saving bars shown against each UAV density. One bar is without CoMP and the other is with CoMP. Using CoMP while deciding GRS sleeping pattern, significantly increased the average energy savings but at a cost of slight reduction in the average throughput. For a given GRS density, at lower UAV density, energy-saving with and without CoMP doesn't show much difference. However, there is an approximate difference of 10% seen as UAV densities reach 40 per km 2 . At higher UAV densities GRSS with CoMP is shown to be more energy efficient. Hence, performing GRSS along with CoMP significantly increases energy savings. However, from the throughput perspective, NOMA is seen performing better even in GRSS. Fig. 12 shows a detailed comparison of the average throughput of the benchmark system with NOMA, CoMP, with GRSS, with GRSS and NOMA, with GRSS and CoMP. From the bar graph in Fig. 12, it is observed that when GRSS is performed, the throughput of the system is dropped and thereby applying NOMA has compensated a part of the throughput drop. The order of the throughput seen is Benchmark with NOMA ≥ Benchmark ≥ GRSS with NOMA ≥ GRSS ≥ GRSS with CoMP ≥ Benchmark with CoMP. The throughput of the Benchmark system with CoMP is less than the throughput of the system with GRSS and CoMP because after GRS sleeping some UAVs are offloaded to the other clusters. Hence, the scheduling time fraction is increased for the remaining UAVs resulting in a higher throughput. The throughput of the benchmark system with CoMP is the least among all scenarios. However, CoMP significantly increases the coverage as seen in Fig. 9. On the other hand, the throughput of the benchmark system with NOMA is higher in all other scenarios. Motivated by this in future we plan to investigate a joint CoMP-NOMA system for UAV communications.

VIII. CONCLUSION
In this paper, we have proposed algorithms for maximizing the energy efficiency of the UAV infrastructure through a dynamic GRS sleeping subject to coverage and rate constraints. To the best of our knowledge, this is the first study of energy efficiency done in the area of CNPC links for UAV communication. We have formulated the GRS sleeping as an optimization problem. Then, we have proposed a dynamic GRS sleeping algorithm with UAV mobility to solve the optimization. We have demonstrated that the proposed algorithm achieves significant energy efficiency through numerical results. Further, we have shown that CoMP with GRSS achieves significant energy savings and NOMA compensates for the throughput loss due to GRSS.