Weihao WANG, Yifan JIANG, Zesong FEI, Jing GUO

School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China

Abstract:To support the ubiquitous connectivity requirement of sixth generation communication, unmanned aerial vehicles (UAVs) play a key role as a major part of the future communication networks. One major issue in UAV communications is the interference resulting from spectrum sharing and line-of-sight links. Recently, the application of the coordinated multipoint(CoMP)technology has been proposed to reduce the interference in the UAV-terrestrial heterogeneous network (HetNet). In this paper, we consider a three-dimensional (3D) multilayer UAV-terrestrial HetNet,where the aerial base stations(ABSs)are deployed at multiple different altitudes. Using stochastic geometry,we develop a tractable mathematical framework to characterize the aggregate interference and evaluate the coverage probability of this HetNet. Our numerical results show that the implementation of the CoMP scheme can effectively reduce the interference in the network, especially when the density of base stations is relatively large. Furthermore,the system parameters of the ABSs deployed at higher altitudes dominantly influence the coverage performance of the considered 3D HetNet.

Key words: Unmanned aerial vehicle; Poisson point process; Coordinated multipoint (CoMP); Statistics of interference; Coverage performance

1 Introduction

Although the worldwide development of fifth generation(5G)communication has facilitated many applications, there is a series of rising use cases that 5G cannot support well; e.g., the future Industry X.0 paradigm requires larger connection density and higher spectral efficiency than the corresponding metrics of 5G (Akyildiz et al., 2020). Therefore, to satisfy these growing demands, both academia and industry around the world have launched research projects on sixth generation (6G) communication(Dang et al.,2020;Giordani et al.,2020). As a solution,the upcoming 6G communication is expected to support 10 times the connectivity density and 5-10 times the spectral efficiency of 5G(Zhang ZQ et al.,2019).

To achieve the target performance of 6G, the integrated network (including the airborne, satellite, cellular, and other constituents) is one of the most important technologies in 6G,where unmanned aerial vehicles(UAVs)play a vital role(Kishk et al.,2020; Saad et al., 2020). As aerial user equipment(UE), UAVs can provide robust navigation service and also exhibit good reliability, security, and thorough performance by connecting to the cellular network (Zeng et al., 2019b). As mobile relays, UAVs can provide short-range line-of-sight (LoS) channels, which are more beneficial for the transmission of signals than the ground-to-ground (G2G) relay nodes (Li B et al., 2018). As aerial base stations(ABSs), UAVs are able to establish communication links quickly and provide coverage for hotspots and emergency situations(Li B et al.,2019;Kishk et al.,2020),which is in line with the development direction of the “intellicise” network (i.e., the network tends to be intelligence-endogenous and primitive-concise)(Zhang P et al., 2022). Specifically, ABSs carrying different types of communication equipment can be deployed in the whole three-dimensional(3D)space,forming the multilayer drone-cell heterogeneous network (HetNet) (Qiu et al., 2019). Owing to the flexibility and high mobility of UAVs, the multilayer drone-cell HetNet is able to serve diversified communication demands (e.g., different qualities of service requirements based on user densities) and support broad connectivity(Bor-Yaliniz and Yanikomeroglu,2016). In addition, compared to the single-layer drone architecture, multilayer drones enable better spectral efficiency performance with stronger adaptability to various types of environments (Sekander et al., 2018).

Despite these advantages, there are some crucial challenges to be solved for the operation of the multilayer drone-cell HetNet. One major challenge to be addressed is the management of interference. In addition to the severe co-channel interference for scenarios in which spectrum sharing is supported (Sekander et al., 2018), LoS links can cause severe aerial-terrestrial interference during both uplink and downlink (Mei and Zhang, 2020). Some interference mitigation techniques for UAV-enabled networks have been investigated in the literature.Specifically, Jacovic et al. (2018) studied the intercarrier and intersymbol interference effects in urban environments and proposed a waveform design on the number of subcarriers to improve the bit error rate performance. To optimize the spectral efficiency,Singh et al. (2018) designed distributed algorithms based on UAV mobility and enhanced the inter-cell interference coordination and cell range expansion techniques. A cooperative non-orthogonal multiple access (NOMA) scheme was proposed by Mei and Zhang (2020) using the backhaul links among base stations(BSs)to mitigate the UAV’s uplink interference with the data rate not greatly decreased.

Among current interference mitigation techniques, the coordinated multipoint (CoMP) technology has been considered an effective technique.The effectiveness of CoMP has been illustrated for terrestrial cellular networks (Irmer et al., 2011) and specified in the current long-term evolution(LTE)-Advanced Releases by the 3rdGeneration Partnership Project (3GPP, 2011). Recently, some works have investigated the applications of CoMP in UAV networks. Li Y et al. (2020) proposed a 3D cellular architecture implementing the CoMP transmission technique on ABSs and aerial UEs based on the binominal point process in stochastic geometry. Liu et al.(2019)studied the optimization of UAV placement and movement for a multi-UAV-enabled multiuser system with CoMP implemented, and derived the bounds of user’s average achievable rates. Using stochastic geometry,Zhang S and Liu(2018)derived the coverage probability and average achievable rate for a multi-UAV network, wherein two UAVs cooperated with each other to provide downlink transmission in postdisaster regions. These aforementioned research works focused only on the performance of UAV networks. Some other works also considered the applications of CoMP in the UAVterrestrial HetNet. To be specific, Sun et al. (2019)proposed a user-centric cooperative scheme for a single UAV to serve ground users in malfunction areas,and derived the coverage probability and the spectral efficiency of the proposed scheme. Wu et al. (2018)proposed a cooperative UAV clustering mechanism for a 3D UAV-assisted terrestrial cellular network to offload ground users to UAVs, wherein energy harvesting and caching were implemented. In Wang XL et al. (2019a), an ABS-assisted cooperative system was considered, in which multiple ABSs relay downlink signals to users from a macro terrestrial BS (TBS) via non-coherent joint transmission, and the closed-form success probability of this system was analyzed. This work was further extended to an NOMA-enabled ABS-assisted cooperative network,and the outage probability was derived (Wang XL et al.,2019b).

However,most of the above works focused on the general design of the CoMP scheme on UAVs, while ignoring the impact of different UAV altitudes on the performance of CoMP in the UAV-terrestrial Het-Net. Since the probability of links to be in LoS conditions is dependent mainly on the height of UAVs(Zeng et al., 2019a), it is necessary to take the deployment of ABSs in the vertical dimension into consideration when designing a CoMP scheme for ABSs.Moreover, most of the above works did not involve the activation mechanism of the cooperative BSs,which can potentially improve the network performance (Tanbourgi et al., 2014a).

In this study,we focus on analyzing the coverage performance of a 3D multilayer UAV-terrestrial Het-Net, in which ABSs are deployed at different altitudes. To reduce the interference in this network, a CoMP scheme based on non-coherent jointtransmission is implemented among TBSs and ABSs(Tanbourgi et al.,2014b),whereby multiple BSs satisfying certain conditions jointly transmit signals to users. In this way,the received signal strength on the user’s side can be improved by combing the received signals non-coherently. The main contributions of this work are summarized below:

1. Based on stochastic geometry, we come up with a tractable mathematical framework to evaluate thenthcumulant of the aggregate interference and the coverage performance of a multilayer UAVterrestrial HetNet with a CoMP scheme. The results validate the accuracy of our proposed model for different numbers of layers.

2. The coverage probability is derived based on an approximation of the interference distribution in the network. The feasibility of the approximation is discussed and the accuracy is validated by our numerical results.

3. The impacts of ABS height and BS density on the coverage performance are investigated. We find that the incorporation of CoMP can reduce the interference effectively under the dense deployment of ABSs. Another important finding is that the system parameters of the higher-altitude ABSs constitute the main factor affecting the coverage performance.

2 System model

2.1 Spatial model

In this work, a multilayer 3D UAV-terrestrial HetNet is considered,which consists of TBSs,ABSs,and terrestrial UEs. The ABSs are assumed to be distributed onKplanes with different heightsHkwithin a 3D space,wherek=1,2,...,K. For analytical tractability,the locations of ABSs in thekthplane are modeled as an independent homogeneous Poisson point process(HPPP), denoted asΦk={yk,j},with densityλA,k, whereyk,jrepresents thejthABS on thekthplane. In addition,we assume that ABSs are hovering with a quasistationary state. The spatial locations of the TBSs are modeled as an independent HPPP with densityλT,which can be represented byΦ0={y0,j}, wherey0,jdenotes thejthTBS. Note that the subscriptkinΦkandyj,kis a non-negative integer in the range of zero toK, wherek= 0 implies the TBS andk ≥1 indicates the ABS.The spatial locations of the terrestrial users can be modeled as an independent HPPP. According to Slivnyak’s theorem in stochastic geometry, the performance of a user located in a certain location can stand for the performance of a user at any location (Haenggi,2012). Without loss of generality, the typical user is assumed at the origin. The universal frequency reuse mechanism is considered, and we further assume that each BS always has at least one UE to serve. Therefore, the typical user will receive interference from non-serving BSs. All the BSs and users are equipped with a signal antenna.

2.2 Channel model

In this study,there exist two types of links. One is the link from the TBS to the user,called the G2G link, and the other one is the link from the ABS to the user,called the air-to-ground(A2G)link. These two types of links are modeled as follows:

1. G2G link

The channel in the G2G link is modeled as the path loss plus block fading. For a specific G2G link,the power received by the user from thejthTBS is

2. A2G link

We adopt the probabilistic transmission model to describe the A2G link (Al-Hourani et al., 2014;Zeng et al., 2019a). For example, the A2G link can be either LoS or non-LoS (NLoS). The probability that an A2G link is an LoS transmission is specified by

whereHkis the height of thekthABS plane, andzk,jis the Euclidean distance between the projection point of thejthABS of thekthplane and the typical user on the horizontal plane. The constantsAandBare environment parameters. Correspondingly, the probability that the A2G link is an NLoS transmission ispN(zk,j,Hk)=1?pL(zk,j,Hk). Consequently,the received power of the typical user from ABSyk,jis a piece-wise function, expressed as

2.3 CoMP transmission scheme

In this 3D UAV-terrestrial HetNet, TBSs and ABSs implement the non-coherent CoMP transmission scheme to provide downlink data transmission for terrestrial users. The network is assumed to work in a distributed manner. Compared with coherent CoMP transmission,synchronization among the cooperating BSs is less restrictive for non-coherent CoMP transmission, which is more practical for the coordination among BSs (Tanbourgi et al., 2014a,2014b; Wang HM et al., 2018). The user-centric CoMP transmission scheme(Tanbourgi et al.,2014a,2014b) is adopted in this work, including the following two steps: BS participation and cooperation activation.

1. At the BS participation step, some BSs are selected as candidate BSs for CoMP transmission.These candidate BSs need to meet the condition;i.e.,the strength of the average received signal transmitted from the BS on thekthplane with the link stateι, denoted asyk,j,ι, has to be larger than the cooperation thresholdΘk,ι. Then, the candidate BSs forming a cooperative cluster can be denoted as

whereBk,ιis the collection of candidate BSs on thekthplane with link stateι,and||yk,j,ι||is the distance between BSyk,j,ιand the typical user.

2. At the cooperation activation step, a part of the BSs from the cooperative cluster are selected to perform coordinated transmission to the typical user.The condition of selection is that the strength of the instantaneous received signal transmitted from the BS on thekthplane with link stateιis larger than the activation threshold ?Θk,ι. The activated cooperative BSs form an activated cooperative cluster, denoted as

whereBa,k,ιis the set of activated cooperation BSs on thekthplane with link stateι.

After the two steps corresponding to Eqs. (4)and(6), the associated BSs for the typical user(i.e.,Ba) can be successfully determined.

3 Coverage probability analysis

3.1 Coverage probability metric

This work adopts the coverage probability as the metric to evaluate the network performance. The definition of this metric is the probability that the signal-to-interference ratio (SIR) at the typical user is larger than a certain thresholdτ, i.e.,

whereSis the instantaneous received signal power from the CoMP BSs andIaggdenotes the instantaneous aggregate interference from non-CoMP BSs.Before quantifying the received desired signal power and the aggregate interference,we first re-categorize the distribution of BSs for analytical convenience.

According to the probabilistic transmission model, the probability that the link between ABS and the typical user is an LoS link is related to the distance between the ABS and the typical user.Therefore,based on the thinning theorem in stochastic geometry (Haenggi, 2012), the spatial distribution of ABSs at each height can be regarded as two independent inhomogeneous Poisson point processes(in-HPPPs). Thus,the spatial location of the BSs in the HetNet can be divided into the following 2K+1 Poisson point processes(PPPs),Ψk,ι:

1.Ψ0,T=Φ0

This point process is composed of all TBSs with constant densityλT,which is the same as that of the original point process for TBSs.

2.Ψk,L={yk,j,L},k=1,2,...,K

This point process is composed of ABSs in thekthlayer whose links with the typical user are LoS links, known as LoS-ABSs. According to the thinning theorem,the density of this point process is

For the considered non-coherent CoMP transmission scheme, the instantaneous received desired signal power is the summation of the signal power from each CoMP BS(the detailed derivation can be found in Tanbourgi et al.(2014b)). Then the instantaneous received desired signal power is

It can be seen from the above formulas that the received desired signal and interference come from the BSs with different link states. For coverage performance analysis without CoMP, the desired signal comes only from an individual BS and we can use the distribution of the fading power gain on the desired link to conduct the analysis. However,this approach is not applicable for the CoMP scenario, where the desired signal comes from multiple BSs. Therefore,similar to previous works (Tanbourgi et al., 2014b;Wu et al., 2018), we first approximate the distribution of the aggregate interference by a well-known distribution(e.g.,having a closed-form formula)and then compute the coverage based on this distribution approximation.

3.2 Interference characterization

Interference is a fusion of many variables.Hence, the exact distribution of the interference is very difficult to obtain. Instead, we decide to find a distribution that fits the interference distribution the best. To implement the distribution fitting, we first characterize the statistics of the aggregate interference and thenthcumulant of aggregate interference as presented in Proposition 1.

Note that the subscriptjingk,j,ιis dropped sincegk,j,ιis independently and identically distributed. This applies toyk,j,ιas well.

By combining Eqs. (16) and (17) with Eq. (15)and substituting Eq.(15)into Eq.(14),we can obtain thenthcumulant ofIaggin Eq. (13).

Next, we need to determine the suitable distribution model that fits the probability distribution ofIagg. According to the literature (Haenggi and Ganti, 2009; Tanbourgi et al., 2014b), Gamma distribution is a good approximation for the interference composed of BSs subject to the PPP. Besides that, Gamma distribution is convenient for deriving mathematical expressions. To see the suitability of Gamma distribution, Fig. 1 shows the probability density function (PDF) approximations for the aggregate interference under different well-known distributions, where the simulation results are generated for comparison purpose. The key parameters of these distributions can be determined from thenthcumulant of the aggregate interference (Guo et al.,2014). It can be seen that, compared to other distributions,the Gamma distribution fits the distribution of the interference the best. In the following coverage probability analysis, we approximate the aggregate interference by the following Gamma distribution with the PDF given by

Fig. 1 Comparison of the probability density function (PDF) of several distributions and the result of simulation of interference

ProofThe first cumulant and the second cumulant correspond to the mean and the variance, respectively. Therefore, according to Eq. (13), we can easily obtain the mean and the variance.

3.3 Formulation of coverage probability

Given that the probability distribution of the interference follows the Gamma distribution,according to Tanbourgi et al. (2014b), the approximated expression of the coverage probability is given in the following lemma:

Lemma 1 By lettingSk,ιdenote the sum of the received signal power of the associated BSs on thekthplane with link stateι, the approximate expression of the coverage probability of the typical user is

For the case of ABSs,Ψk,ιis an in-HPPP and its distribution is described in Section 3.1. Similarly,MSk,ι(s) can be expressed as

After sorting these formulas, we arrive at the results in Eq. (25).

4 Numerical results and discussion

In this section, the derived theoretical expression of the coverage probability of the 3D multilayer UAV-terrestrial HetNet based on the CoMP transmission scheme is verified by Monte-Carlo simulation,and the influence of the key system parameters in the network on the coverage performance is analyzed. The simulation results are generated from the Monte-Carlo simulation in MATLAB. Unless stated otherwise, the system parameters are set as follows:the transmit power of TBSPt,0=40 dBm,the transmit power of ABSPt,k=32 dBm,Kr=1,αL=2.5,αT=αN= 4,ηL= 1,ηT=ηN= 0.2,mL= 3,mT=mN= 1,A= 9.6117, andB= 0.1581 (Hu et al., 2019; Zeng et al., 2019c; Zhou et al., 2019).As for the thresholds related to the formulation of CoMP sets, they are set as

4.1 Analysis validation

Fig. 2 shows the PDF of the simulation results and the analytical results of the aggregate interference. It can be seen that the simulation results ofIaggare generally consistent with the analytical results. Therefore, approximatingIaggas a Gamma random variable is feasible in the 3D HetNet considered in this work. In addition, it can be seen from the figure that when a new layer of the ABS network is added, the expectation and variance of the interference received by the typical user tend to increase.

Fig. 2 Probability density function (PDF) of the interference Iagg

Fig. 3 shows the coverage probability v.s the SIR thresholdτfor different network configurations.The figure shows that the simulation results and the analytical results fit closely, which validates the accuracy of the analytical results. By comparing the results whenK= 3 andK= 2, we can see that when the SIR threshold is low, the coverage probability whenK= 3 is larger than that whenK= 2;while when the SIR threshold is high, the relationship is opposite. After adding a new layer of the ABS network, the number of activated cooperative BSs increases, but at the same time, the number of BSs that cause interference also increases. When the SIR threshold is low,more activated cooperative BSs are beneficial to increase the coverage probability of the typical user; when the SIR threshold is high, the coverage probability of the typical user is more affected by the interference from inactive BSs and non-cooperative BSs. In addition,it can be seen from Fig.3 that under the same conditions and when thresholdτ>?5 dB, using CoMP can increase the coverage probability compared to that in the case not using CoMP. This shows that through the coordinated transmission of multiple BSs, co-channel interference is effectively reduced,which is beneficial to the improvement of coverage performance in the case of dense deployment of BSs.

Fig.3 Coverage probability v.s SIR threshold τ when K =2 and K =3 (H1 =50 m, H2 =100 m)

4.2 Effect of ABS height

For the convenience of discussion, we consider the situation withK= 2. The ABSs deployed at the lower and higher altitudes are named as loweraltitude ABSs with heightH1and higher-altitude ABSs with heightH2, respectively. Fig. 4 shows the coverage probability v.s the lower-altitude ABS heightH1under different lower-altitude ABS densities whenH2=110 m andλA,2=10-5m-2are considered. It can be seen that the coverage probability increases first and then decreases slowly as the height of the lower-altitude ABS increases. This trend can be explained as follows: when the ABS height increases from a lower value, the probability that the link from the activated cooperative BSs to the user is in the LoS transmission condition increases,and the coverage performance improves. As the ABS height continues to increase, the activated cooperative BSs will be farther away from the user and the desired signal power received by the user will be smaller, so the coverage probability decreases.

Fig.5 shows the relationship between the coverage probability and the height of the higher-altitude ABSH2under different densities of the higheraltitude ABS whenH1=10 m andλA,1=10-5m-2are considered. It can be seen that whenH1is fixed,similar to Fig.4,asH2increases,the coverage probability increases at first and then drops a little bit.This implies that there is also an optimal higheraltitude ABS flight height.

By comparing the variation range of the coverage probability with the ABS height in Figs. 4 and 5, it can be seen that the changes in the height of higher-altitude ABSs have a greater impact on the range of coverage probability than the changes in the height of lower-altitude ABSs. This indicates that the height of the higher-altitude ABSs is one of the main factors affecting the coverage probability of this HetNet.

Fig. 4 Coverage probability under different loweraltitude ABS densities v.s lower-altitude ABS height H1 (H2 =110 m, λA,2 =10?5 m?2)

Fig. 5 Coverage probability under different higheraltitude ABS densities v.s higher-altitude ABS height H2 (H1 =10 m, λA,1 =10?5 m?2)

4.3 Effect of BS density

Fig. 6 shows the coverage probability v.s the density of TBSsλTat different heights whenλA,1=λA,2=10-5m-2andH2=50 m are considered. It can be seen that the coverage probability increases as the density of TBSs increases. Fig. 7 shows the coverage probability at different heights v.s the density of ABSsλA,1whenλT=λA,2= 10-5m-2andH2= 50 m. Different from the TBS, it can be seen from Fig. 7 that the coverage probability first decreases and then increases with the increase ofλA,1.This trend can be explained as follows: When the ABS density increases from a small value,due to the limited range of cooperative clusters and the height difference, the number of activated cooperative BSs increases slowly,while the increase in the interference caused by the increase of BS density (especially the interference from LoS-ABSs)has a larger impact on the coverage probability. As the density of ABSs continues to increase,the possibility of the activated cooperative BSs comprising LoS-ABSs increases, so the probability of providing the typical user with coverage under LoS transmission increases,and then the coverage probability increases. In addition, by comparing the variation range of each curve in Fig. 7,we can see that when the height of the ABSs increases, the variation range of the coverage probability with the density of the ABSs is larger, and the coverage probability with higher-altitude ABS is higher than that with lower-altitude ABS. This implies that the density of higher-altitude ABSs is a more important factor affecting the coverage probability of the multilayer UAV-terrestrial HetNet based on the CoMP transmission scheme.

Fig. 6Coverage probability v.s the density of the TBSs λT at different heights (λA,1 = λA,2 =10?5 m?2, H2 =50 m)

Fig. 7 Coverage probability at different heights v.s the density of ABSs λA,1 (λT = λA,2 = 10?5 m?2,H2 =50 m)

By analyzing Figs. 6 and 7, we can find that when the BS density of the terrestrial or ABS network is larger,the coverage performance of the Het-Net that adopts CoMP transmission is better. CoMP transmission can effectively reduce the interference from other BSs in a dense network environment,and a larger BS density is beneficial to the improvement of network coverage performance.

5 Conclusions

In this study, we have investigated the coverage performance of a 3D multilayer UAV-terrestrial HetNet with a CoMP scheme,in which multiple BSs with good channel conditions jointly transmit signals to users non-coherently. Using stochastic geometry,the mathematical framework to characterize the aggregate interference and evaluate the coverage performance of the considered HetNet has been developed. Based on this, the impact of key system parameters on the coverage performance has been studied. The results demonstrated the effectiveness of the CoMP scheme in the considered 3D HetNet under dense environments. It has also shown that the system parameters of the higher-altitude ABS influence mainly the coverage performance. Future work can be done to explore the design or the performance of more complicated cooperative architectures for the 3D UAV-terrestrial HetNet.

Contributors

Yifan JIANG designed the research and processed the data. Weihao WANG drafted the paper. Yifan JIANG helped organize the paper. Zesong FEI and Jing GUO revised and finalized the paper.

Compliance with ethics guidelines

Weihao WANG, Yifan JIANG, Zesong FEI, and Jing GUO declare that they have no conflict of interest.