Hybrid Satellite-UAV-Terrestrial Maritime Networks:Network Selection for Users on A Vessel Optimized with Transmit Power and UAV Position

Xiangling Li,Wenjing Shi

1 School of Information Science and Technology,Beijing University of Chemical Technology,Beijing 100029,China

2 Beijing National Research Center for Information Science and Technology,Tsinghua University,Beijing 100084,China

Abstract: The hybrid satellite-UAV-terrestrial maritime networks have shown great promise for broadband coverage at sea.The existing works focused on vessels collaboratively served by UAV-enabled aerial base station(ABSs)and terrestrial base stations(TBSs)deployed along the coast,and proved that data rate could be improved by optimizing transmit power and ABS’s position.In practice, users on a vessel can be collaboratively served by an ABS and a vesselenabled base station (VBS) in different networks.In this case,how to select the network for users on a vessel is still an open issue.In this paper, a TBS and a satellite respectively provide wireless backhaul for the ABS and the VBS.The network selection is jointly optimized with transmit power of ABS and VBS,and ABS’s position for improving data rate of all users.We solve it by finding candidates for network selection and iteratively solving transmit power and ABS’s position for each candidate.Simulation results demonstrate that data rate can be improved by collaborative coverage for users on a vessel.

Keywords:maritime communications;satellite-UAVterrestrial network; network selection; power allocation;

I.INTRODUCTION

The terrestrial communication networks provide the broadband coverage for densely populated areas, but cannot satisfy the high-speed demand for sparsely populated areas.For the ocean and remote rural areas, the lack of the communication infrastructure is a main factor leading to low-speed communication services.The coming sixth-generation (6G) communication networks aim at realizing the ubiquitous coverage by constructing hybrid satellite-UAV-terrestrial networks.

For maritime communications, hybrid satellite-UAV-terrestrial networks are one of research highlights.The satellite communication networks firstly gained the world-wide attentions due to the ability of the global coverage, but the data rate was inferior to that of terrestrial communication networks.To assist satellite networks in the broadband coverage, the terrestrial communication technologies were extended to the sea area.Then, hybrid satellite-terrestrial maritime networks began.In recent years, to further enhance the broadband coverage, the high-throughput satellites, such as the Shijian-13 and EchoStar-19,were employed instead of narrow-band ones, and the introduced terrestrial communication technologies were developed from fourth-generation (4G) to fifthgeneration (5G) ones[1].However, TBSs have to be deployed along the coast, leading to the limited coverage range of TBSs.To expand the coverage of TBSs,the ship-to-ship/shore communications were employed, such as the TRITON project[2].Specially,the BLUECOM+project used the tethered balloons to provide high-altitude platforms for communication nodes, then the coverage range was further extended[3].In recent years, UAVs gained more and more attentions due to the flexible mobility, and can be employed as movable aerial platforms of base stations.Then,the era of hybrid satellite-UAV-terrestrial networks is coming for maritime communications[4].

For maritime communications, a hybrid satellite-UAV-terrestrial network relays on satellites,TBSs and ABSs.In the existing works,all users on a vessel were only served by a satellite or an ABS[5-8].The data rate of all users on the vessel was limited by that of the satellite-vessel link or the ABS-vessel link.However,if two or more base stations in different networks jointly serve users on the vessel, the date rate can be further improved.Thus, we investigated network selection for users on a vessel in this paper.

The works related with network selection bring benefits to different satellite-UAV-terrestrial networks.Thus, we summarized the related works in different satellite-UAV-terrestrial networks,shown as follows.

1) Maritime communication networks:The complex problems, including wireless spectrum scarcity and large computing latency, which hinders the well cooperation of hybrid networks.To deal with those problems, key technologies, such as spectrum sharing,non-orthogonal multiple access(NOMA) and mobile edge computing (MEC),were employed for maritime communications[5-7].Furthermore, the link scheduling and rate adaptation were optimized by minimizing total energy consumption with quality of service guarantees[8].In the above works,vessels act as users.That is to say,users on the vessel have not been considered.A vessel can only be covered by a base station or a satellite.This paper focuses on users on a vessel and investigates network selection for users on the vessel.

2) Terrestrial communication networks: Key technologies have attracted research attentions, including relay selection and user associations [9-11].In[9], UAVs were employed as aerial platforms of relays between ground users and satellites.In [10], cognitive radio was incorporated into satellite-terrestrial and aerial-terrestrial networks.Users were served by ABSs and TBSs.User association was optimized for maximizing the achievable rate.Different from [10], satellites were considered in[11].ABS-satellite association,user-ABS association and user-TBS association were jointly optimized aiming at balancing fairness and load.Wireless backhaul of TBSs and ABSs was only provided by satellites.The communication performance of wireless backhaul could be coupled with that of satellite communication networks.To make full use of the advantages of hybrid networks, wireless backhaul of a base station can be provided by different networks.Thus, in this paper, wireless backhaul for ABSs and VBSs were provided by TBSs and satellites,respectively.

3) Internet of remote things: Satellite selection,channel selection and gateway selection were optimized, considering uploaded data amount, energy consumption and spectral efficiency[12-14].In[12]and[13],data gathering with the IoT-UAV link and data transmission with the UAV-satellite link were integrated.In [14], parts of UAVenabled relays were selected as gateway, which were used for data transmission between UAVenabled relays and satellites.In [13] and [14],maximum capacity of Low Earth Orbit (LEO)satellites was considered in constraints of optimization problem.The above works mainly worked on hybrid satellite-UAV networks where TBSs were not involved.For maritime communications, TBSs are essential for the broadband coverage.

In this paper,we investigate a hybrid satellite-UAVterrestrial maritime network and focus on users on a vessel.To improve the data rate of users on a vessel,users on the vessel are collaboratively served by ABSs and VBSs in different networks.TBSs and satellites respectively provide wireless backhaul for ABSs and VBSs.Thus, the data rate of access links could approach the total data rate of backhaul links provided by different networks.To select the best network for each user and improve the data rate of access and backhaul links,network selection for users on the vessel is jointly optimized with transmit power of the ABS and the VBS,and ABS’s position.The main contributions are summarized as follows.

· A hybrid satellite-UAV-terrestrial maritime network was considered,consisting of TBSs,ABSs,VBSs,satellites and users on vessels.Users on a vessel are collaboratively served by an ABS and a VBS,different from the existing works for maritime communications[5-8].TBSs and satellites respectively provide wireless backhaul for ABSs and VBSs, different from the existing works for terrestrial communications[9-11].

· Network selection for users on a vessel was jointly optimized with transmit power of the ABS and the VBS, and ABS’s position, aiming at improving data rate of all users on the vessel.

· The optimization problem is non-convex.We solve it by finding candidates of the solution for network selection,and iteratively solving transmit power and ABS’s position by using each candidate.Simulation results demonstrate that the performance gain can be achieved by collaborative coverage for users on a vessel.

The rest of this paper is organized as follows.In Section II,the system model is introduced.The problem for network selection for users on a vessel is formulated and solved in Section III.In Section IV,simulation results are presented.Section V concludes the paper.

II.SYSTEM MODEL

We consider a hybrid satellite-UAV-terrestrial maritime network, as shown in Figure 1.Satellite networks cover the whole sea which ranges from the coastal waters to the distant sea waters.Users on a vessel communicate with satellites via a VBS.TBSs are deployed along the coast and serve users on vessels in the coastal waters.TBSs can reduce the communication burden of satellite networks.UAV-enabled ABSs cover the blind zones of terrestrial networks and satellite networks.TBSs provide wireless backhaul for ABSs.For the satellite-VBS link and the TBS-ABS link, the data rate is limited, which hinders the communication performance of users on vessels.In this paper, to improve the data rate of users on a vessel,users on a vessel are jointly covered by an ABS and a VBS.

Figure 1.System model of a hybrid satellite-UAV-terrestrial maritime network.

Figure 2.The positions of the related communication nodes in the x-y plane, including a TBS,an ABS,a VBS,a vessel and users on the vessel.

We assume that theg-th TBS provides wireless backhaul for theu-th ABS.Let cg,tand cu,tdenote the position of theg-th TBS and theu-th ABS at timetin the x-y plane, where cg,t= [xg,t,yg,t]Tand cu,t= [xu,t,yu,t]T.Letdg,u,tdenotes the distance between theg-th TBS and theu-th ABS at timetin the xy plane, expressed asdg,u,t=‖cg,t-cu,t‖2.Letzg,tandzu,tdenote the altitude of theg-th TBS and theuth ABS at timet.Both TBSs and ABSs are equipped with a single antenna.The two-ray model is used for the TBS-ABS link[15-17].The channel gain from theg-th TBS and theu-th ABS can be expressed as

Similarly, the two-ray model is also used for the ABS-user link.We assume that users on thes-th vessel are jointly covered by theu-th ABS and thes-th VBS.We also assume that there areNusers on thesth vessel.Let cn,tdenote the position of then-th user at timetin the x-y plane, where cn,t= [xn,t,yn,t]T.Letdu,n,tdenotes the distance between theu-th ABS and thes-th VBS at timetin the x-y plane,expressed asdu,n,t=‖cu,t-cn,t‖2.Letzn,tdenote the altitude of then-th user on thes-th vessel at timet.Based on the assumption thatzu,t,zn,t ≪du,n,t,the channel gain fromu-th ABS andn-th user can be expressed as

Letzs,tdenote the altitude of thes-th VBS at timet.Let cs,tdenote the position of thes-th VBS at timetin the x-y plane, where cs,t= [xs,t,ys,t]T.The freespace path loss model is used for the VBS-user link.The channel gain from thes-th VBS to then-th user at timetcan be given by

whereds,n,tdenotes the distance between thes-th VBS and then-th user at timet,expressed asds,n,t=

III.NETWORK SELECTION FOR USERS ON BOARD

In this section, to realize collaborative coverage for users on board, we formulate the optimization problem of network selection, transmit power and ABS’s position,and iteratively solve it to achieve the optimal solutions.

3.1 Problem Formulation

Let as,tand au,tdenote network selection for users on thes-th vessel.as,n,tandau,n,tare then-th element in as,tand au,trespectively.If then-th user selects thes-th VBS at timet,as,n,t=1,otherwiseas,n,t=0.If then-th user selects theu-th ABS at timet,au,n,t=1, otherwiseau,n,t= 0.Moreover, each user is only served by one base station so that we have

Let Ps,tand Pu,tdenote transmit power of thes-th VBS and theu-th ABS.Ps,n,tandPu,n,tare thenth element in Ps,tand Pu,trespectively.Considering maximum transmit power of base stations,we have

wherePs,maxandPu,maxdenote maximum transmit power of thes-th VBS and theu-th ABS respectively.

LetPgdenote transmit power of theg-th TBS.LetGgandGudenote the antenna gain of theg-th TBS and theu-th ABS.Our works focus on the performance gain achieved by network selection for users on a vessel,so we ignore the effect of the small-scale channel fading on the performance.To mitigate the interference, we assume that orthogonal resources have been used in the hybrid satellite-UAV-terrestrial maritime network.The achievable rate of theu-th ABS at timetis expressed as

whereσ2denotes noise power.LetGsandGndenote the antenna gain of thes-th VBS and then-th user.The achievable rate for then-th user served by thesth VBS at timetis expressed as

The achievable rate for then-th user served by theu-th ABS at timetis expressed as

The total achievable rate of users on thes-th vessel at timetcan be expressed as

The achievable rate of the access side cannot exceed that of the backhaul side so that we have

whereR0denotes the data rate provided by satellites.Due to the large distance between satellites and VBSs,we assume thatR0is a constant.To satisfy minimum requirement of the data rateRminfor each user, we have

In this paper, the hybrid maritime network has dynamic topology because of mobile communication nodes,such as vessels and ABSs.The dynamic properties of the hybrid maritime network can decrease the communication performance.To guarantee the data rate for users on thes-th vessel,theu-th ABS changes its position according to the position of thes-th vessel.In this paper,we consider that the altitude of UAVs is fixed.Considering the limited velocity of UAVs, we have

wheredmaxdenotes the maximum flight distance during the time interval Δt.In addition to ABS’s position,network selection and transmit power of theu-th ABS and thes-th VBS are adjusted to improve the data rate for users on thes-th vessel.We assume that the positions of users,theu-th ABS and thes-th VBS at timet-1 have been obtained.Based on the above analysis, we jointly optimize network selection, transmit power and ABS’s position at timetto maximize the total achievable rate of users on thes-th vessel at timet.The optimization problem can be expressed as

The optimization can be conducted at the central processor, then the optimal results can be transmitted to the selected base station.Complex calculation and long transmission distance could cause the undesired latency.We notice that most of vessels sail along the fixed routes on the ocean.The historical or premeasured data of positions of vessels and users on vessels can be obtained.At timet-T0, we can use the obtained data to predict positions of vessels and users on vessels at time t,then use the predicted data to optimize network selection, transmit power and ABS’s position.The time periodT0can be approximatively determined according to the time occupied by complex calculation and transmission.Thus,the effect of complex calculation and large transmission latency could be avoided.

3.2 An Iterative Solution

The optimization problem (17) cannot be directly solved because of the coupling relationships among the variables including network selection, transmit power and ABS’s positions.To solve the optimization problem (17), we find candidates of the solution for network selection, and then solve transmit power and ABS’s positions for each candidate.Finally,we obtain the optimal solutions by comparing the total achievable rate of candidates,as shown in Algorithm 1.

3.2.1 Candidates for Network Selection

For givenPu,n,t,Ps,n,tand cu,t,network selection can be achieved by solving the following problem.

We consider that network selection can be determined by the number of the served users and users’positions.To obtain candidates for network selection,we have the following lemma.

Lemma 1.Users are sorted in ascending order of the distance ds,n,t,1≤n ≤N.For given|as,t|=i and|au,t|=N -i,

are the optimal solutions of optimization problem

Proof.The achievable rate, such asRs,n,tandRu,n,t,is in reverse proportion to the horizontal distance between a transmitter and a receiver.Due to the long distance between theu-the ABS and thes-th vessel,the effect of different positions of users on the achievable rateRu,n,tcan be ignored.To maximize the total achievable rateRs,t, the users served by thes-th VBS should be carefully selected.According to (4)and(10), for given|as,t|=i, wheniusers served by thes-th VBS are close to the position of thes-th VBS,Rs,tin optimization problem (21) can be maximized.Then, the optimal solutions of optimization problem(21)can be achieved.

According to Lemma 1, for given|as,t|=iand|au,t|=N - i, a solution of network selection can be achieved, which could not satisfy constraints in(13), (14) and (15).As described in Lemma 1, the solution of network selection is determined according to the distanceds,n,t.By using the achieved solution of network selection,transmit power and ABS’s position can be optimized so that only solutions satisfying constraints in (13), (14) and (15) can be obtained.Thus,according to Lemma 1,we select candidates of the solutions of network selection by setting|as,t|=i,0≤i ≤N.Then, for thei-th candidate,we optimize transmit power and ABS’s positions by solving the following problem.

We decouple the optimization problem in(22)into two subproblems and solve them iteratively.For thej-th iteration,two subproblems are described as follow.

3.2.2 Optimization of Transmit Power

By using the obtained ABS’s positionsobtained in the(j-1)-th iteration,we optimize transmit powerby solving the following problem.

According to (7) and (15), the lower bound ofcan be expressed as

We assume that each user communicates with thes-th VBS with the same data.According to (7) and (14),the upper bound ofcan be expressed as

The achievable rateis in proportion to transmit power.If,the optimal solution ofis denoted as

Similarly, we assume that each user communicates with theu-th ABS with the same data.If,the optimal solution ofis denoted as

where the lower and upper bounds ofare expressed as

3.2.3 Optimization of ABS’s Positions

To solve the optimization problem (30), by introducing a variableη, the objective function and the constraint(15)is rewritten so that the optimization problem is given as follows.

To make the problem in(31)more tractable, the Taylor expansion is employed to approximateRu,n,tandRg,u,tas the linear functions.Then,the constrains(32)and(13)can be approximated by

where

Then,the optimization problem(31)is rewritten as

Algorithm 1.Solve the optimization problem of network selection,transmit power and ABS’s position.Require: c1u,t,N,M,Q Ensure: as,t,au,t,Pu,t,Ps,t,cu,t 1: for i=1:N +1 do 2:■■ais,t■■=i-1■■=N -i+1 4: Set ais,t and aiu,t according to Lemma 1 5: for j =1:M do 6: Obtain Pj 3:■■aiu,t u,t and Pj s,t according to (26) and(27)7: for q =1:Q do 8: cru,t =cq u,t 9: Solve the problem in (42) and then obtain the solution cq u,t 10: end for 11: cju,t =cq u,t 12: end for 13: Piu,t =Pj u,t 14: Pis,t =Pj s,t 15: ciu,t =cj u,t 16: end for 17: Compute Ris,t by using ais,t,aiu,t,Piu,t,Pis,t,ciu,t 18: Find the maximum of Ris,t, expressed as Rs,t =Rks,t,1 ≤k ≤N +1 19: as,t =aks,t 20: au,t =aku,t 21: Pu,t =Pku,t 22: Ps,t =Pks,t 23: cu,t =cku,t

The problem in (42) can be iteratively solved with CVX[18].

IV.SIMULATION RESULTS

In this section, simulation is performed to validate the performance of our proposed algorithm.Theg-th TBS is located at (0,0,100) m.The users are randomly distributed on thes-th vessel with width of 50 m and length of 360 m[19].The ABS-based network and VBS-based network are operated at 5.8 GHz and 2.0 GHz carrier frequency and the bandwidth is set to be 20 MHz.The main parameters are given in Table 1.

Table 1.Simulation parameters.

4.1 Performance Analysis of the Backhaul Link of the ABS

Thes-th vessel is located at (0,80000,10) m at time(t-1)and moving to the next location with speed vector(10,0,0)m/s during the time interval Δt.To serve the users on thes-th vessel,theu-th ABS moves from the location (0,yu,t-1,300) to cu,t, whereyu,t-1∈{20,30,40,50}km.Figure 2 shows the positions of the related communication nodes in the x-y plane,whereyu,t-1= 40 km.We set that the initial value c1=(0,yu,t-1).The maximum transmit power of the ABS varies in the range[8,24]dBm.

The simulation result is shown in Figure 3.When the distance between the TBS and the ABS at timet-1 is given, the total achievable rate increases with ABS transmit power before the maximum total achievable rate reaches.This increase caused by ABS transmit power is because the data rate of the TBS-ABS link is larger than sum rate of the ABS-user links.When the distance between the TBS and the ABS at timet-1 decreases,the maximum total achievable rate is improved.But before the maximum total achievable rate reaches, the total achievable rate increases with the distance between the TBS and the ABS at timet-1.Thus,the total achievable rate is closely related with the position of the ABS at timet-1.

Figure 3.Total achievable rate with different locations yu,t-1 and transmit power of the ABS.

4.2 Performance Analysis of the Backhaul Link of the VBS

To illustrate the performance gain achieved by network selection, the comparison is performed among a ABS based coverage,a VBS based coverage and our proposed hybrid coverage.In the ABS based coverage, users on the vessel is only served by ABSs and wireless backhaul of ABSs is provided by TBSs.In the VBS based coverage, users on the vessel is only served by VBSs and satellites serve VBSs.In our proposed hybrid coverage, users on the vessel is cooperatively served by ABSs and VBSs.The data rate of the satellite-VBS link varies in the rangeR0∈{10,30}bits/s/Hz.The maximum transmit power of the ABS varies in the range[8,24]dBm.

The simulation results are shown in Figure 4 and Figure 5.Obviously, the best performance reaches with our proposed hybrid coverage.Besides, when TBS transmit powerPgand the data rate of the satellite-VBS linkR0increase, the maximum total achievable rate can be improved.

Figure 4.Total achievable rate with different transmit power of the TBS and the ABS.

Figure 5.Total achievable rate with the data rate of the satellite-VBS link.

V.CONCLUSION

We proposed a hybrid satellite-UAV-terrestrial maritime network where users on a vessel were collaboratively served by a UAV-enabled ABS and a VBS.A TBS and a satellite provided wireless backhaul for the ABS and the VBS respectively.The network selection, transmit power and ABS’s position were jointly optimized aiming at maximizing the total achievable rate of users on the vessel, subject to constraints on backhaul.We solve it by finding candidates for network selection,and iteratively solving transmit power and ABS’s position for each candidate.Simulation results demonstrated that the total achievable rate could be improved by collaborative coverage for users on a vessel.

ACKNOWLEDGEMENT

This work was supported in part by the National Natural Science Foundation of China (Grant No.62001265) and the Fundamental Research Funds for the Central Universities(Grant No.buctrc202124).