Due to the rapid development of UAV in reducing their costs, sizes, weights and consumptions, they have attracted a significant attention for many civilian and commercial applications. Deployed as aerial BS , UAV can quickly provide wireless connections e.g. in the damaged areas after disasters for rescue purposes. By leveraging the nearly LoS radio propagation channels, UAV can also be utilized as relays to enable energy-efficient sensing and internet-of-things [9121255, 9115248]. Moreover, other applications such as network network optimization, smart agriculture, forest monitoring, goods delivery, etc. [hayat2016survey, kumar2018unmanned] are becoming autonomous and convenient with the help of UAV. Meanwhile, UAV as new aerial UE connected to the existing cellular networks, i.e. cellular-connected UAV [8470897, 8918497], have been identified as an important paradigm shift. The current almost everywhere cellular networks are expected to provide reliable C2 communications to e.g. enable visual LoS flight tasks and high-throughput payload communications such as high-definition videos from UAV-UE. However, although the nearly LoS channels are advantageous to receive higher powers, UAV can in turn cause sever interference to other UAV-UE and terrestrial UE. This becomes more critical with the rapid growth of the number of UAV put in operation in cellular networks, significantly and negatively affecting the connectivity of both aerial and terrestrial UE.
Different techniques have been investigated to provide reasonable services to UAV and terrestrial UE. In [8528463, 8869706, 8470897], the authors proposed to exploit massive MIMO available at BS side to point beams towards intended UE and more sophistically place spatial nulls to UE in other cells that are vulnerable to the interference. In such a way, beamforming gain and spatial multiplexing gains can be harvested to improve the wireless connectivity. Although massive MIMO at BS is promising, it requires large invests and takes time to upgrade the infrastructure. As a cheaper and fast alternative, implementing a beamformimng system or directional antennas on board the UAV was proposed in [8301389, 9082692]. The authors have shown its effectiveness to increase the uplink performance of UAV communications. It is worth noting that R. Zhang et al. have conducted considerable investigations on UAV communications. For example in , by jointly optimizing the UAV’s uplink cell associations and power allocations, the weighted sum rate of the UAV and terrestrial UE was optimized. In , idle BS without serving any other UE in the UAV’s communication channel were exploited to help co-channel BS mitigate the interference. In , more different interference coordination schemes were summarized and discussed.
Although the above mentioned approaches have demonstrated potentials in improving the performance of serving flying UAV and protecting terrestrial UE, they do not well consider the case where the UAV density could be, at least locally, very high, which is probable in the near future. The basic assumption in these investigations, e.g.[9324909, 9099899, 8811738, 9082692], is that only a few (maybe only one) UAV exist in a large area. However, as predicted by Federal Aviation Administration (FAA), the number of commercial UAV fleets can reach up to 1.6 millions by 2024 [6guav, FAA]. In [aerialporfilev1], a typical use case of cellular-connected UAV is recognized as the package delivery, e.g. the Amazon Prime Air project in early stage, with a medium to high UAV density. It is estimated that several UAV can exist per square mile near to the warehouse or operations center around 2022, which means that probably each cell (at least in the hotspot areas) can have several active UAV-UE. Developing robust interference mitigation techniques for massive UAV-UE deployment scenarios is also considered as a key open problem in . Therefore, identified as an important communication scenario that has seldomly been addressed in the literature, we in this work focus on the uplink communication for UAV-UE of high densities. Due to the nearly-LoS channels, these UAV-UE can cause severe interferences to terrestrial UE in a rather large area. As demonstrated in , the connectivity probability of terrestrial UE can be lowered significantly, e.g. from 0.95 to 0.7 with the number of UAV increasing. To avoid the many UAV negatively affecting the performance of terrestrial UE, we assume, similarly as discussed in [8758988, 8869706], that UAV-UE and terrestrial UE use orthogonal RB in each transmission interval as illustrated in Fig. 1. This spectrum sharing has been suggested in  as the most suitable strategy for maintaining a minimum guaranteed rate for UAV and a high performance of terrestrial UE if the number of UAV is large. The investigation in  also shows its effectiveness. Therefore, the crux we aim to solve in this work is to optimize the uplink performance of UAV coping with the inter-cell interferences among them. The main contribution and novelties of this paper are summarized as follows:
By exploiting the special characteristics of the nearly LoS UAV propagation channels, different schemes applied in the frequency domain and/or the time domain are proposed to optimize the sum SE or the minimum SE of UAV. It is worth noting that an important and practical constraint, i.e. uplink SC constraint, is also considered. The formulated problems are solved via the GP principle and the SCA technique.
Extensive simulations considering both full buffer transmission mode and bursty traffic mode are performed to evaluate the performances of the proposed schemes. The numerical results show the effectiveness of these algorithms and provide important insights into the practical system design.
The rest of this paper is structured as follows. In Sect. II, low altitude A2G channel characteristics and preliminarily analysis of scheduling, power control and interference are discussed to provide understanding for the uplink UAV communications. In Sect. III, different power control and scheduling schemes are proposed and elaborated. Sect. IV presents the extensive simulations in full buffer mode and bursty traffic mode for evaluating the proposed schemes. Detailed discussions are also included. Finally, conclusive remarks are given in Sect. V.
Ii Understanding the uplink communications of cellular-connected UAVs
In this section, we discuss the characteristics of the propagation channels among UAV and terrestrial BS, and preliminary analysis of scheduling, power control and interference is also included.
Ii-a Low altitude A2G propagation channels
Many measurement-based investigations such as [3gppenhance, 7936620, 8807190, 9170768, xuesongjsac] have demonstrated that the A2G propagation channels at higher heights are nearly LoS. For example, 3GPP [3gppenhance] suggests a LoS probability of 1 for rural area and moderately high UAV altitude larger than 40 m, which is also verified by the measurements in [xuesongjsac] for even lower heights. In , PLE were found to be almost free-space values as 2.1 and 2 at 60 m and 120 m, respectively. In [8807190, 9170768], the Rician K-factors of the A2G channels were found to be large for most cases at higher heights with mean value around 15 dB. Although in few cases, the K-factor could be smaller due to, e.g., the reflections from buildings [9170768, xuesongjsac] in urban or industrial areas, spatial analysis in [xuesongjsac] for the A2G channels has shown that the additional cluster(s) are usually separable to the LoS cluster in the azimuth domain with angle differences larger than 60. This means that if a UAV is equipped with directional antennas, even the channel with several clusters can probably be simplified as a single-cluster channel with a high K-factor. This is a reasonable expectation, since as shown in Fig. 3 in Sect. II-C, using omnidirectional antennas onboard UAV can cause rather severe interferences. The authors in  exploited an array consisting of six directional antennas each with a HPBW of 60 to cover the whole 360 azimuth, and the best antenna was triggered for the communication. This relatively simple and low-cost switching strategy of directional antennas was able to significantly improve the performance. Given the above reasoning, in this work we assume the nearly-LoS A2G channels are flat in the frequency domain. Moreover, for the same reasons and relatively low speeds of low-altitude UAV, we also assume the A2G channels have relatively large coherent time, e.g. tens of ms or even longer [ZeyuTWC], in which the channel gains remain almost unchanged.
Ii-B Packet scheduling for Uav-Ue
We use both time-domain and frequency-domain packet scheduling for UAV-UE. Conventionally in cellular networks, e.g. LTE, packet scheduling is achieved via the so-called FDPS [5671623, 5062197] (note that time-domain is inherently considered in FDPS). The instantaneous channel conditions of UE at all RB in a cell are the inputs of FDPS, according to which different bandwidth portions are dynamically allocated to different UE to better exploit the available frequency and user diversity, meanwhile fulfilling the uplink SC constraint. A well-known and commonly used approach is the PF-FDPS that maximizes the long-term sum logarithmic utility of the system [5062197, 4786509]. Specifically, consider a cell with a set of UE and a set of RB, the th RB at time is allocated to the UE with index such that
where indicates the data rate potentially achievable by the th user on RB at time , and is the historical average rate of the th UE.
In the focused communication scenario where all UAV-UE are with frequency-flat channels, ’s of the th UE tend to be similar across all the RB.111They are not exactly the same because the interference may change at different RB. With SC constraint further considered e.g. as shown in , the PF-FDPS tends to allocate almost all RB to the same UAV-UE. In other words, much less frequency diversity gain can be harvested for UAV-UE compared to that of terrestrial UE with frequency selective channels. Thus, in this work, we exploit time-domain PF to decide which UAV-UE or UAV-UE to be active for transmission, e.g., in the bursty traffic mode in later Sect. IV-B. After that, resource allocation and power control are jointly optimized via sophisticated methods, which will be proposed and discussed later in Sect. III.
Ii-C Inter-cell interferences
We in this subsection show the inter-cell interferences among UAV-UE via a simulation. The detailed configuration of the simulation is included in Table I. Briefly, 48 sectored cells, as illustrated in Fig. 2, were considered. The BS heights were 35 m, the downtilts of the sector antennas were 8.5, and the ISD was 2 km. In each realization, 48 UAV-UE were randomly generated in the 48 cells at the height of 60 m. The channel model was consistent with that empirically obtained in . The power control scheme applied in the simulation was OLPC. Specifically, the transmitted power in dBm is obtained as [maggi2020bayesian]
where is the configured maximum output power (which was 23 dBm), is path loss, is the number of RB allocated for this UE, is the fractional power control compensated parameter, and is the power received at one RB if path loss is fully compensated. Note that and were optimized by exhaustive searching in the simulation scenario as illustrated in Fig. 2. Five hundred realizations were performed to obtain a distribution of the SINR of individual UAV. Fig. 3 illustrates the CDF of SINR with UAV equipped with omni-directional antennas, direction antennas of 60 HPBW and directional antennas of 30 HPBW, respectively. It can be observed from Fig. 3 that omni-directional antennas onboard UAV can usually cause severe interferences to each other. Using directional antennas with HPBW of 60 can improve the SINR significantly, due to the directional radiation pattern suppressing interferences. However, the improvement from 60-HPBW antennas to 30-HPBW antennas is much less than that from omni-directional to 60-HPBW antennas. This means that using 60-HPBW antennas could be a suitable choice considering the performance improvement and complexing increasing. Nevertheless, interference can still be sometimes high for some UAV-UE. Therefore, further improvement/optimization is still needed. In the sequel, we propose different schemes based on the GP-principle for this purpose.
Iii GP-based schemes
In this section, we elaborate different schemes proposed in the frequency domain and time domain based on the GP-principle to enhance the uplink UAV communications. Note that these schemes are not isolated to each other and can be applied together. However, to not complicate the mathematical expressions and discussions while still keeping the essence, we discuss them separately. For example, when discussing frequency-domain approaches, we do not consider time-domain.
Iii-a Frequency-domain maximization of the minimum SE of Uav-Ue
As discussed in Sect. II-B, let us first consider that in a cell at most one UE is scheduled. That is, at a TTI a set of cells are active each with one UAV-UE scheduled. In each cell, all the reserved bandwidth is allocated to the scheduled UAV-UE. We denote the channel gain from the UAV-UE in the th cell to the th cell as , and all the channel gains are contained in . Intuitively, is the gain of the serving link, whereas are that of interfering links. Note that is attributed to the path loss, shadow fading, radiation patterns of antennas. Moreover, due to the assumption of frequency-flat channels, we assume is independent on the RB index. The power density of thermal noise is indicated by . We proposed to divide the frequency resource into segments, and the transmitted power of the th UAV-UE on the th bandwidth segment is denoted by . Then the serving SINR of the th UAV-UE on the th bandwidth segment can be calculated as
where is the compact notation of the power allocation for all the UAV-UE. The achieved SE (bit/s/Hz) of the th UAV-UE is then calculated according to Shannon formula as
The problem of maximizing the minimum SE of all UAV-UE can be formulated as
where is the total output power of the th UAV-UE usually confined in a range from (e.g., 0) to (e.g., 23 dBm), and the objective is to find the optimal solving the problem. Note that of the th UE can be dependent on . The underlying reasoning is that this allows competing UAV-UE transmitting on different bandwidth resources with different power densities to avoid severe interferences so that the minimum SE can be increased. An intuitive case is that two neighboring edge-UE are allowed to transmit on the first half and the second half , separately. Nevertheless, problem (6) omits the uplink SC constraint, i.e., the same power density must be applied for continuous RB. We discuss firstly how to solve (6) and consider the SC constraint later. Problem (6) can be equivalently rewritten by introducing auxiliary variables ’s and ’s as
which is equivalently
This is a non-convex problem. If holds for all and meaning that can be well approximated by , problem (8) is almost a GP-problem where a posynomial is minimized with upper bounded posynomial and/or equality monomial constraints [4275017, cai2020centralized]. However, interferences in the UAV communications are generally significant. It is also possible that a UAV-UE may not transmit power at some bandwidth segments to avoid interference. Therefore, we resort to solve the problem via a series of GP using the single condensation principle [4275017, cai2020centralized]. In our case, the term is replaced by a monomial , where matrix contains all , i.e. , and and ’s are constants to be properly set. Problem (8) can then be solved according to Algorithm 1. It is essential that the meets three requirements  to achieve convergence and feasibility of finally resulted power allocation, which include i) for all . This is to guarantee the resulted power allocation always meets the original constraints. ii) at the condensation point . This guarantees the monotonicity of optimal values obtained in successive iterations. iii) at the condensation point. This is to make sure that after convergence, KTT conditions for the original problem is also met. Specifically, a condensation satisfying these requirements with linear complexity can be applied to calculating ’s and ’s as [cai2020centralized]
It is worth noting that the solution obtained using Algorithm 1 is not necessarily globally optimal.
Considering the uplink SC constraint: The power allocation of the same UE at different bandwidth segments obtained by Algorithm 1 can be arbitrarily different. This is applicable whenever the uplink SC constraint is no longer needed. Considering the SC constraint to maximize the minimum SE is NP-hard 
. Thus we proposed a heuristic Algorithm2 for this purpose based on Algorithm 1. The proposed algorithm mainly includes three steps. i) Obtain the first power allocation using Algorithm 1 without SC constraint. ii) Allocate continuous frequency resources for UAV-UE according to the result obtained in i). iii) Perform Algorithm 1 again considering the SC constraint obtained in step ii). That is, for each UAV, the power density on allocated continuous segments is kept the same, and the power density of non-allocated segments is set to zero.
The heuristic part (step ii)) of Algorithm 2 is described as Algorithm 3. The purpose is to find continuous bandwidth segments of each UE with powers that change as little as possible. Notice that due to the frequency-flat channels, we can reorder the columns of obtained in step i) while keeping the same performance. Intuitively, if there exist two or more UAV-UE causing significant interferences to each other on the same frequency resource, they probably will use different resources, and their SINR on some segments could be very low. To increase the minimum SE as possible, it is necessary to identify and put emphasis on this kind of UE. We thus exploit the SINR matrix to reorder columns. The first step in Algorithm 3 is to find the UE with index that has the minimum in the SINR matrix . Then the SINR matrix and power matrix are updated by rearranging the columns according to descending/ascending order of the SINR of the th UAV-UE on the bandwidth segments. This is trying to smooth the SINR change (and power change) at neighboring bandwidth segments. Finally, for each UE, expanding continuous frequency resources starting with the bandwidth segment having the largest SINR till the summed rate on these bandwidth segments is larger than a pre-defined threshold of the original overall summed rate on all segments. Fig. 4 illustrates an example application of Algorithm 2. In this example, 24 cells are active each with a UAV-UE. Bandwidth is divided into segments. It can be clearly observed from Fig. 4(c) or (d) that UE 2 and 10 are using interleaved bandwidth segments, which means that they cause severe interferences to each other if transmitting on the same frequency resource, e.g. when . The finally maximized minimum equivalent SINR (i.e., ) obtained using Algorithm 2 in this case is 3.2 dB. As a comparison, the maximized minimum equivalent SINR obtained using Algorithm 1 without considering SC constraint, as shown in Fig. 4(b), is 4.9 dB due to more freedom in power allocation. Whereas when using the whole bandwidth, i.e. , for SC transmission, the maximized minimum equivalent SINR is only -3.6 dB.
Iii-B Time-domain maximization of the minimum SE of Uav-Ue
This is a scheme assuming that the scheduled UAV-UE are allowed to transmit for a certain time period, e.g. a set of TTI, which is still within the coherent time of the channels. As mentioned, in each TTI, we assume a UAV-UE is using the whole with the same power density to not complicate the expression without losing essence. The problem can then be formulated as
where with indicating the output power of the th UAV-UE at the th TTI. Moreover, is also modified as
This problem can be solved essentially almost the same as described in Algorithm 1. Moreover, we do not need to consider the SC constraint as it has been met in each TTI.
Iii-C Frequency-domain maximization the sum SE of Uav-Ue
Based on the notations as described in Sect. III-A, we directly write out the problem as
where the last line in (13) is a QoS constraint. We show Algorithm 4, which is proposed to solve (13) with SC constraint also considered, as the most complicated example. The key is to find an initially feasible SC power allocation (may not exist) that meets the QoS constraint, which must be based on the scheme proposed in Sect. III-A. We do not redundantly write algorithms for other easier cases. For example, without SC constraint, the step 1 in Algorithm 4 can be modified as to exploit Algorithm 1 to find an initially feasible power allocation, and the SC constraint is also removed from step 3.
Iii-D Time-domain maximization of the sum SE of Uav-Ue
Iii-E Scheduling and power control for multiple Uav-Ue
Multiple UAV-UE in a cell, e.g. a set of UE with the highest time-domain PF priorities in the th cell, may be allowed to transmit simultaneously. The methodology is essentially similarly to what we have discussed for single-UE cases. For example, to maximize the minimum SE of all UAV-UE in the network, the problem can be formatted similarly to (6) as
with the SE of the th UE in the th cell modified as
because of totally UAV-UE sharing the frequency resources in the th cell. With the SC constraint further considered, one can exploit Algorithm 2 to conduct packet scheduling and power control for individual UE. An additional consideration is that UE in the same cell have to use orthogonal bandwidth segments unless NOMA technique is applied. Basically, the flavors are the same, although the multi-UE scenario is slightly different from (more complicated than) the single-UE scenario.
Iv Simulation and discussions
In this section, we demonstrate the performances of the different schemes proposed in Sect. III via extensive simulations. Full buffer mode and bursty traffic mode are considered in Sect. IV-A and Sect. IV-B, respectively.
Iv-a Full buffer mode
1) Single UE per cell case:
In this subsection, we focus on the full buffer uplink transmission mode, where UAV-UE are assumed to constantly transmit uplink data. In the simulation, a network with 48 sectored cells as illustrated in Fig. 2 is applied. Important simulation parameters are the same as included in Table I in Sect. II-C. We assume that an array consisting of six antennas with 60 HPBW is onboard the UAV , and the best directional antenna is switched on for the uplink communication. The percentage of active cells ranges from 0.5 to 1. That is, in each realization, a random portion of the 48 cells are active with a UAV-UE in full buffer mode transmission. Totally 300 realizations, each with random locations of UAV, are performed to obtain the performances of different schemes.
FD: Frequency domain; TD: Time domain; Max-Sum: Maximization of the sum SE; Max-Min: Maximization of the minimum SE; QoS: QoS constraint; SC: Single carrier; : Segment number in frequency domain; : TTI number.
Fig. 5 illustrates the CDF of SE obtained using the proposed schemes as summarized in Table II.222To ease the description, we use e.g. “FD SC Max-Min” to denote frequency domain maximization of the minimum SE considering SC constraint. The abbreviation style is also similarly applied for other schemes. Specifically, Fig. 5(a) illustrates the CDF of the minimum SE achieved in individual realizations, Fig. 5(b) illustrates the CDF of the mean SE obtained in individual realizations, and in Fig. 5(c) the CDF of SE of all UAV-UE in all realizations are presented. In the OLPC scheme, UAV-UE are transmitting on the whole reserved bandwidth according to (2) with the optimized and as shown in Table I. As another scheme, Max-Sum is conducted without QoS constraint. In the frequency domain, three different Max-Min schemes are performed which include FD Max-Min (), FD Max-Min () and FD SC Max-Min (). Moreover, FD SC Max-Sum () is also applied with QoS constraint set as 0.8 bit/s/Hz for all UAV-UE. Similarly in the time domain, TD Max-Min () and TD Max-Sum () with QoS constraint as 0.8 bit/s/Hz are conducted. Table III summarizes the performance gains of these schemes applied in the full buffer mode for different groups of UAV-UE compared to that of OLPC. According to the three subfigures of Fig. 5 and Table III, we have the following observations and findings.
The Max-Min schemes can achieve better minimum SE compared to that of OLPC and Max-Sum without QoS constraint. Specially, the minimum SE of Max-Sum without QoS constraint is almost always zero, which means that in the interference dominant scenario, there are always UE(s) being sacrificed to maximize the sum SE. Moreover, it can be observed that with a larger or no SC constraint, FD Max-Min can achieve a larger minimum SE. This is reasonable since a larger and/or no SC constraint can provide more freedom for UAV-UE to avoid severe interferences by transmitting on interleaved bandwidth segments. Furthermore, we can observe that the performance of TD Max-Min () is close to that of FD Max-Min () regarding the achieved minimum SE. This is understandable because the SC constraint is not a concern in time domain while still keeping the similar freedom of avoiding severe interference by transmitting at interleaved times. Thus, TD Max-Min is considered as a good option. Nevertheless, the power density in FD Max-Min can be higher which is advantageous for edge UE, so that the performance of TD Max-Min is slightly lower than that of FD Max-Min
Although the various TD/FD Max-Min schemes can achieve better minimum SE, they have less mean SE compared to that of OLPC. The reason is that in the Max-Min schemes, all the UAV-UE in a realization are with the same SE, as we can observe that the curves of Max-Min schemes in Figs. 5(a)-(c) are the same. This is also easy to be verified by contradiction as follow. Assume that there are one or several UE with higher SE, then their transmitting powers can be decreased to increase the minimum SE until all UAV-UE have the same SE. Therefore, the SE of UE in good conditions are limited leading to smaller mean SE. In addition, it is straightforward that the Max-Sum without QoS constraint can achive the best mean SE.
Compared to OLPC, Max-Min schemes are favorable to UE in bad conditions however limit the SE of UE in good conditions; whereas the Max-Sum without QoS constraint sacrifices the UE in bad conditions. By introducing QoS constraints into Max-Sum, the compromise can be tuned. For example, it can be observed from Fig. 5(a) that the minimum SE of FD SC Max-Sum with QoS constraint and TD Max-Sum with QoS constraint are realized as 0.8 bit/s/Hz if there exist feasible solutions, otherwise the original Max-Min SE are kept. It can be observed from Fig. 5(b) that the mean SE are increased compared to that of the corresponding Max-Min schemes. Moreover in Fig. 5(c), it can be observed that the SE of UE in bad conditions (e.g., UE with SE below the 20th percentile) are guaranteed, and the SE of other UE in better conditions are not limited too much either. It is worth noting that the TD Max-Sum with QoS constraint herein can achieve overall better performance for both types of UE compared to the OLPC scheme.
2) Multi UE per cell case:
As discussed in Sect. III-E, it is possible that multiple UAV-UE can be scheduled in each cell. We consider herein a simple case, i.e. scheduling two UE per cell in the full buffer mode. All the 48 cells are active, and the FD Max-Min scheme with is utilized. Fig. 6 illustrates the SE of two-UE scheduling and the SE of single-UE scheduling. It can be observed that the performance of two-UE scheduling is better than that of the single-UE scheduling. This is due to that by scheduling more UAV, each UAV tends to use less bandwidth compared to that of single-UE scheduling. With the same allowed maximum transmit power, a higher maximum power density tends to be achieved in multiple-UE scheduling. For those UAV with large path loss, i.e. power limited UAV, higher power density is favorable for them to increase their SE. This shows the potential of multiple-UE scheduling. In the bursty traffic mode in the sequel, we still focus on the single UE scheduling.
Iv-B Bursty traffic mode
In this subsection, we focus on the bursty traffic mode, where a UAV-UE is assumed to transmit a packet of certain size. The same network topology as described in Table I
for the full buffer mode is still applied herein for the bursty traffic mode. Differently, UAV-UE in the bursty traffic mode are assumed to enter the network according to a Poisson distribution with an arrival rateas 2.5 UE/s/cell. All active UAV-UE transmit 4 Mb data and leave the network once the transmission is finished. Additional parameters configured for the bursty traffic mode are included in Table IV. Furthermore, in the full-buffer simulation as discussed before, it is clear that we assume the algorithm or the computing center knows the information of the channel gains among all UAV-BS pairs, i.e. , so that the all the UAV-UEs can be optimized jointly. We denote it as “centralized application of algorithms”, which may require considerable resources for UAV-UE to perform channel estimation and feedback the estimated channel information to the computing center. It is also possible to “de-centralize” the algorithm, e.g., that the optimizations are done for individual groups of UAV-UEs. For the bursty traffic mode, we will discuss both centralized and de-centralized application of algorithms in the sequel.
1) Centralized application of schemes:
Fig. 8 illustrates the CDF of SE of UAV-UE for different schemes applied.333It can be seen in Table III that Max-Min (=1/=1) has worse performances for all groups of UAV-UE. Also considering that the uplink SC constraint is practically required, we thus omit Max-Min (=1/=1) and FD Max-Min (=20) in the simulation of bursty traffic mode. Specifically, the SE of a UAV-UE in the bursty traffic mode is calculated as
where and are the time instants when the UE enters into and leaves the system, respectively, and [bit] is the total amount of data transmitted by the UAV in the period from to . Moreover, the first 1.6 s of the system is not considered to exclude the “warming-up” stage. Fig. 8 provides the following insights.
It is interesting to observe from Fig. 8 that in the bursty traffic mode FD SC Max-Min and FD SC Max-Sum with QoS have smaller performances, i.e. in (16), for all UAV-UE than that of OLPC, although in the full buffer mode they can achieve larger minimum SE compared to that of OLPC. This is because the SE of UAV-UE in better channel conditions are limited to maximize the minimum SE or to meet the QoS constraint in each updating time interval. In other words, the mean (or sum) SE of UAV-UEs is decreased in a updating interval, as indicated in Fig. 5(b). Consequently, UAV-UE in relatively good channel conditions stay in the system for a longer time compared to the case, e.g., in the Max-Sum without QoS constraint, where they can transmit with much higher rates. Moreover, since these UAV-UEs in relatively good conditions tend to be scheduled with higher priorities compared to those UAV-UEs in relatively bad channel conditions, the average SE of UAV-UEs in bad channel conditions are also decreased due to longer inactive period, although when they are active they indeed have higher minimum SE, finally leading to smaller averaged SE of all UAV-UE in the bursty mode. This is similarly true for observing that TD based schemes have better performance than that of their corresponding FD methods, e.g. from FD SC Max-Min to TD Max-Min, and for that TD/FD Max-Sum with QoS have better performances than TD/FD Max-Min in the simulation case herein.
However, it is not necessarily that the larger the sum (or mean) SE in individual updating time intervals are, the better the overall performance is. For example, comparing the curves of TD Max-Sum with QoS and Max-Sum without QoS, it can be observed that TD Max-Sum with QoS has better performance for UAV-UE at lower percentiles, although Max-Sum without QoS indeed can achieve largest sum SE at each updating time interval. This is because in each updating time interval of Max-Sum without QoS constant, a certain number of UE are almost muted with zero rates, as indicated in Fig. 5
(c). This means that a SE balance between UAV-UE in bad and good channel conditions in each updating time interval must be properly tuned to achieve a good system performance in the bursty traffic mode, especially when the QoS or SE of UE at lower percentiles are key evaluation metrics.
Table V summarizes the performance gains of the schemes applied in the bursty traffic mode for different groups of UAV-UEs compared to that of OLPC. It can be seen that TD Max-Sum with QoS is a good scheme with best edge UE performance and still not-bad overall performance. By tuning the QoS constraints, it is possible to achieve an optimized balance between UAV-UE in bad and good channel conditions for a pre-defined key evaluation metrics.
2) Decentralized (locally centralized) application of schemes:
We also evaluate the performances of the schemes when applying them separately to clusters of cells in the network. That is, the whole network is divided into several clusters of cells, and the schemes are applied for each of these cells without considering the existence of other clusters in each updating time interval. After optimizing resource and power allocation of each cluster, the performance of the whole network is evaluated by combining all clusters. The main reasons to do so include that i) The centralized way requires channel state information among all UE and all sector cells, which is probably practically challenging and consumes additional resources for signaling; ii) Giving too much fairness among all UAV-UE may finally degrade the overall performance since the UE with relatively good channel conditions may be also limited; iii) Although a UAV-UE may cause interference to many cells, it is still true that the badly affected ones are cells relatively close to this UAV-UE in terms of distance and beam direction. In the simulation considered herein where individual UAV-UE are assumed to use the best beam with a 60 of HPBW, each three co-site sectored cells are grouped as a cluster as illustrated in Fig. 2, i.e., the whole network with 48 sector cells is divided into 16 clusters.
Fig. 8 illustrates the CDFs of the SE of all UAV-UE for different schemes applied cluster-wise. It is interesting to find that all the proposed schemes have better performances compared to that of OLPC. Specially, FD SC Max-Min, FD SC Max-Sum with QoS and TD Max-Min are improved significantly compared to that as illustrated in Fig. 8. This is because fairness in each updating time interval is decreased which leads to a larger sum SE hence improves the final bursty performance. However, the performances of TD Max-Sum with QoS and Max-Sum without QoS decrease slightly compared to their centralized versions as shown in Fig. 8. The reason is that the centralized TD Max-Sum with QoS and Max-Sum without QoS can already achieve relatively good performances for both cell-edge and cell-center UAV-UE, i.e., fairness problem is not that severe as in, e.g., FD SC Max-Min, and decentralized applications of them instead decreases the performance since the UAV-UEs were not jointly optimized.
Based on the extensive simulations in both full buffer mode and bursty traffic mode conducted for the proposed schemes, we would like to summarize several points as follows.
The proposed schemes in frequency domain and/or time domain can obtain optimal or suboptimal resource and power allocations for UAV-UE subject to certain constraints. Generally, time domain methods can achieve better performances, since SC constraint has to be considered when applying frequency domain methods. However, whenever the SC constraint is no longer required, frequency domain methods are better choices than the time domain methods, since higher power densities can be achieved.
In the full buffer mode which emulates high traffic load, methods that maximize the minimum SE can have the best minimum SE, whereas the SE of UAV-UE in good conditions, e.g. cell-center UAV-UE, may be limited significantly. Maximizing the sum SE without considering QoS constraints can achieve the best sum SE. However, the SE of some UAV-UE can be always close to zero. Nevertheless, maximizing the sum SE considering QoS constraints is a compromise for both cell-edge and cell-center UAV-UE. Moreover, it is possible to achieve an optimized value for the target key performance indicator by properly tuning the QoS constraint for difference service scenarios.
The performance of UAV-UE in the bursty traffic mode are different from that in the full buffer mode. For example, it is not necessarily that the method that maximizing the minimum SE in each updating time interval can achieve better averaged SE for lower-percentile UAV-UE. Overall, performances of all UAV-UE depend on both the minimum SE and sum SE achieved in each updating time interval. The method that maximized the sum SE in TD with a certain QoS constraint can be considered the best option for bursty traffic mode transmission. Besides centralized algorithms, decentralized application of algorithms can decrease the signaling and computation load. Moreover, the performance of decentralized frequency domain methods can also be increased, although they are still lower than that of the centralized TD maximization of sum SE with QoS constraints. Nevertheless, if the time domain method cannot be done, e.g. due to short updating time interval of the system, decentralized frequency domain methods can be good options.
In this contribution, different scheduling and power control algorithms have been proposed for the uplink communications of cellular-connected UAV. Generally speaking, the time-domain maximization of sum SE with a QoS constraint properly tuned works satisfactorily for UAV in both high and medium/low traffic conditions. Other methods may emphasize different groups of UAV-UE. Moreover, scheduling multiple UAV are favorable for power-limited UAV as the maximum power density can be increased. Cluster-wise application, with lower computation and signalling loads, can also increase the performances of frequency domain methods. Future work will try to solve the joint multi-cell multi-UAV scheduling, resource allocation and power control problems for the case where massive MIMO is used at BS and/or UAV and terrestrial UE may use non-orthogonal RB.