Virus outbreaks seriously affect all aspects of life and lead to increasing infection and toll rates. COVID-19 has a very high infection rate, and it has spread to almost all the territories of the world [1–3]. Unfortunately, this virus is genetically variant and may last for a few years. Governments and health organizations recommend quarantine and increased social distance to reduce the infection rate and mitigate the other consequences. The quarantine means that we should rely mainly on online services and that these should be provided to as many people as possible worldwide. Many services such as e-commerce and e-learning services are used extensively and require a supporting communication network infrastructure as many employees, trainees, and students work from home [4,5].

Despite the high demand on the Internet during this pandemic, some regions in some countries suffer from weak or even a lack of communication network infrastructure, and this affects the countries’ capability to support their population with e-services such as e-learning. Deploying terrestrial networks for these regions within a short period of time is impossible or requires very costly infrastructure. Therefore, governments can utilize satellite systems to provide extensive coverage instead [6]. However, the considerable distance from which satellites operate and the special terrestrial transceivers and installation requirements are barriers to the use of such systems. Besides, satellite systems provide low data rates, which may not suit the current package of Internet services that is used to meet people’s requirements [7].

Another difficulty in Internet provision through satellites is the high rates of service provision, which is not suitable for the current economic situation. Therefore, a new communication system infrastructure should provide compatible, high-speed Internet at a low cost. Alternatively, high-altitude platforms (HAPs) can be employed to provide superior, comprehensive coverage and high-quality communication performance [8]. HAPs are airborne balloons, airships, or unmanned aircraft that operate in the stratosphere; these can provide coverage to an area of up to 1000 km in diameter and have a communication channel performance like that of satellite systems but at very low relative altitudes.

Students in remote rural areas that suffer from a lack of communication services or inadequate cellular coverage and minimal Internet rates are unable to continue their distance or e-learning. Flying airborne systems and moving them to such inaccessible areas will provide instant wireless communication infrastructure, thereby relieving students [9]. In this paper, we consider a HAP to provide an efficient solution for the rapid establishment of the communication network to help students access e-learning services remotely [10]. The development of efficient antenna techniques at the HAP will improve data rate provision to support Internet services and the number of users.

The main objective of this paper is to solve the problem of Internet service provision in remote areas with undeveloped communication infrastructure and those where such infrastructure is impossible to develop. Therefore, we propose and analyze a new end-to-end model for the emergency and fast deployment of a communication system using a novel cross-layer between the adaptive antenna, MAC layer, and application layer; the system’s mathematical and geometrical models are also investigated along with the practical applicability and feasibility of the system.

The paper is arranged as follows: Section 2 discusses the related cross-layer optimization techniques for the current systems and HAPs. It also details the current e-learning systems and their requirements, while Section 3 introduces the proposed HAP e-learning system model. In Section 4, we demonstrate the adaptive cellular e-learning HAP system using adaptive antenna arrays onboard HAP. Section 5 explores the role of adaptive antenna arrays in coverage cells’ formation and adaptation. Section 6 presents the communication performance evaluation, and finally, Section 7 concludes the paper.

Fig. 1a shows e-learning services provision from HAP by adaptive antenna arrays system onboard HAP fed by the coverage information from the university site’s ground station. The beamforming information is defined according to the registered report of the students on the university e-learning database—such as home locations, academic schedule, the number of students in a common remote region, the minimum services bit rate, etc. This information is extracted at the HAP beamformer input to direct suitable beams for students’ locations. The HAP acts as a repeater in this case and can be considered as a fixed “stratospheric satellite” [32].

The beamforming can be done through many suitable planner antenna structures, such as two-dimensional or concentric arrays. This paper focuses on concentric arrays due to their performance superiority and azimuth-independent beam-generation property. The taper profile function feeds the array to improve the sidelobe performance and reduce the co-channel interference if frequency reuse is applied.

Fig. 1b shows the distribution for HAP coverage cells. The system splits the coverage into area coverage (residential area) and antenna spot beams within the residential area. We assume that we have N residential areas, M spot beams, and P applications and services within each beam. The proposed model for managing applications is based on socket and port numbers, and the network administrator identifies the privilege for each application. The beam data rate is Cm, while the network operation center (NOC) data rate is CT. The beams and the associated data rates are distributed based on users’ activities and application priorities.

The system starts by allocating the total data rate (CT) at NOC, applying policies and limitations, and calculates the antenna array feeding currents required to form a coverage beam. Then, it receives the requester’s order and verifies that the beam covers it. If the requester is out of beam coverage, the system forms a new beam and allocates resources to the MAC. Then, it calculates the data rate in the formed beam to allocate more resources to it. Once the beam array is created with the corresponding data rate and the resources are assigned, the system checks whether the requested application is open. If the application is open, the system applies for limitation roles, receives more applications, and checks their types. It gives the best allowed resources to the application within the schedule, and then it is ready to welcome new requests. But if the application is not in the plan, it verifies if the application is permitted to give the best-effort resources. If it is not, it should be blocked. If the application is originally not open, the program calls the application layer for data rate adaptation. The flowchart of this plan is shown in Fig. 2.

This section demonstrates and discusses the system adaptation parameters for HAP e-learning services. These parameters include the operation on both the application and physical layers to control the data rates of different e-learning applications and the overall cell data rate. Eq. (1) shows the total NOC link capacity:

(1) CT=∑n=1N⁡∑m=1M⁡∑p=0P⁡Cm(n,p)

where Cm is calculated based on the cross-layer model for the physical and application layers’ data rates for each beam in a specific area. Simply, Cm can be controlled as follows:

(2) Cm(n,p)=∅(Rm,Am)

where Rm and Am are the rate adaptation parameters of the physical and application layers, respectively. In an e-learning communication system, students need to access a limited number of applications; these can be classified into three main categories: e-learning platforms such as Blackboard, video streams, and general web access. The data rate for each type depends on the number of students in each area, and the one with a large student population is expected to get a fair share from the total data rate, CT . To equitably distribute CT , we use the same-level source utilization approach for managing resources proportionately in relation to the student population in each coverage area.

Proportional utilization coefficient, Ku , is the result of the division of the student population in each area, Si , by the total number of students included by coverage, Stotal , i.e.,

(3) Ku=SiStotal

Then, the total data rate designated for the i area with multiple beams, Bi , is given as follows:

(4) Bi=∑m=1M⁡∑p=1P⁡Cm(i,p)

which can also be expressed as

(5) Bi=KuCT

The NOC can dedicate η of the data rate in the i^th area to the e-learning platform, EL_i, because of students’ need to attend classes, upload assignments, and take exams. On the other hand, students might need to watch some supplementary tutorials via different video streaming platforms, VS_i, which is ζ of the data rate and may be smaller than η to avoid the abuse of data consumption. Finally, δ of data rate in a specific area is devoted to web browsing, WB_i, to help students search or find written tutorials. Eqs. (6) to (8) depict these distributions mathematically:

(6) ELi=ηBi

(7) VSi=ζBi

(8) WBi=δBi

To find the data rate for each student in the same area for a specific service such as e-learning, we divide ELi by the number of students in the area, as follows:

(9) ELSi=ELiSi

Eventually, we express the application layer data rate adaptation parameter for the i^th beam, Am , as follows:

(10) Am=ELi+VSi+WBiM

This scheme is compared with some typical e-learning services in terms of data rates in Tab. 1.

The other physical-layer adaptation factor for Cm and Rm represents the capability to control the m^th cell’s gross data rate, which should be balanced according to the number of students in each cell. Therefore, we can consider Rm as the cell radius that should be controlled to accommodate a suitable number of students in the cell, which effectively controls the required gross data rate for that cell, i.e., Cm . The next section presents the implementation of this adaptation through the harnessing of adaptive antenna arrays onboard HAP.

We can address the problem of delivering local e-learning services by incorporating the e-learning management system into the communication facility to bridge the information gap in distant or isolated regions. Consider a HAP station located at an altitude of h km in the stratosphere, as shown in Fig. 3. The maximum coverage diameter can be obtained by the following equation:

(11) ρo=rcos−1(rr+h)

where r is the earth radius. The maximum diameter of HAP coverage can extend to about 1000 km for a HAP located at the height of 20 km. However, due to shadowing effects, the coverage diameter is lowered to a few hundreds of kilometers. The coverage zone may be much less wide for local regions corresponding to the main university campus and could extend to 300 kilometers based on the district distribution. Therefore, such a system delivers interactive e-learning services to students in remote locations that suffer from low or limited connectivity. The controlling parameters for the system design can be defined as student density in remote areas, minimum bit rate requirements for each student, communication channel capacity ( Cm ), HAP altitude ( h ).

Some beaming techniques, such as directional spot-beam antennas or antenna arrays, provide service beam from HAP. The spot-beam directional antennas are more suitable for fixed service applications in which the coverage area per beam is constant. On the other hand, adaptive antenna arrays adapt to varying system conditions such as university schedule, student density, services bit rates, etc. The beam shape and gain vary with these parameters. The system can harness several antenna array structures such as two-dimensional arrays and concentric circular arrays (CCA), which are used in this work for HAP communications.

Fig. 4 shows concentric arrays with uniform element separation at the half-wavelength distance point between elements in the same ring and between concentric rings. The taper profile is applied centrically on the rings, and the highest feeding amplitude feeds the innermost ring elements. The phase responses of the elements are adjusted to direct the main lobe toward the desired region. Also, the beam width can be adjusted by controlling either the taper profile or the number of utilized rings in the array [33].

Therefore, the array power gain can be demonstrated as follows:

(12) Gt(θ,∅)=|W(θo,∅o)HSCA(θ,∅)|2

where, W(θo,∅o) is the weighting vector of the array, SCA(θ,∅) is the array steering vector, and H is the Hermitian operator. If the number of elements in the k^th ring in the concentric array is L_k and K rings form the array, the weighting vector is given as follows:

(13) W(θo,∅o)=Γ⊙SCA(θo,∅o)

Where Γ is the subarrays weighting coefficients, ⨀ is the Hadamard product, and SCA(θo,∅o) is the array steering vector that corresponds to the main-lobe direction. Finally, Γ is expressed as follows:

(14) ΓT=[α1α2…αm…αM]

where αk is a colon sub-vector of Lk elements of the same amplitude coefficient value αm .

The k^th subarray amplitude coefficient αk is proposed to be as follows:

(15) αk=(cos⁡((k−1)π2K))2.3,k=1,2,…,K

Generally, as shown in Fig. 5, the m^th service beam from HAP can cover an area, am , which is given by:

(16) am=πRm2cos⁡(θm)

where, Rm is the footprint half-major axis in θm direction and is given by

(17) Rm=h(tan⁡(θm)−tan⁡(θm−0.5Bθ))

and Bθ is the beamwidth in the θm direction. Therefore, the cell area can be related directly to the beamwidth and direction as follows:

(18) am=πh2(tan⁡(θm)−tan⁡(θm−0.5Bθ))2cos⁡(θm)

Fig. 6 displays the cell area’s variation with the beam direction at different beamwidth values. As shown in this figure, for beam directions up to 40°, especially for small beamwidths, the beamwidth mainly controls the cell area where the effect of the beam direction is negligible. Increasing the beam direction beyond this limit results in a rapid increase in the cell area due to projection on the earth’s surface, where the cells become more elliptical.

The system links the total number of students located in a cell with the cell area from the following relation:

(19) Sm=Dsam

where Ds is the student density in the remote or isolated area. On the other hand, we can design the coverage beam from the following relation:

(20) am=SmDs

Therefore, we can design the required coverage beam for a specific number of students and density for this area.

The signal level and probability of error at the student premises should be acceptable to achieve a specific communication link performance. The received signal power level at the student e-learning receiver input, Ps , can be written as follows:

(21) Ps=PtGsGt(θ,∅)(λ4πds)21ξ

where, Pt is the HAP transmitted power; Gs is the receiver antenna power gain; Gt(θ,∅) is the HAP transmitting antenna gain; λ is the signal wavelength; ds is the slant distance between the HAP and the student receiver; ξ is an excess attenuation due to atmospheric losses, shadowing, fading, and extra margin for the communication link. Assuming the QPSK modulation scheme, the probability of error at the student receiver is given by [34]

(22) pe=12erfc(PsNoBs)

where, No is the noise power spectral density, erfc is the complementary error function, and Bs is the student accessible bit rate. Therefore, the signal strength and the communication link’s quality depend mainly on the received signal power from HAP and the required bit rate. Larger bit rates require more substantial received power to maintain the probability of error within an acceptable range. Therefore, the antenna gain at HAP plays an essential role in the achievement of the required e-learning service quality for students in remote areas. We can manage the beam downlink capacity from HAP toward a specific area by adapting students’ schedules to deliver the highest possible data rate for them.

For example, suppose that the maximum beam downlink speed of the overall e-learning channel is 1 Gbps, and each student can be assigned 2 Mbps. In this case, the total number of simultaneously served students is less than or equal to 500. The service beam from HAP can be split into multibeam when the number of simultaneously served students is less than the beam capacity, and the coverage footprint can be extended to cover other remote regions. In the next section, we demonstrate the adaptive array structure at HAP that achieves the objective of adapting both the beam power gain and coverage area according to the remote area’s location and the number of students.

In this scenario, the concentric rings are weighted using Eq. (15), in which the maximum weight is assigned to the innermost ring, while the outermost ring has the lowest weight value. This tapered profile is proposed mainly for sidelobe reduction, which is essential for reducing the unwanted radiation toward other co-channel beams. We examined the radio coverage from HAP for a single beam generated toward an arbitrary direction of ( 50∘,45∘ ). The center of the cell is located approximately 35 km from the sub-HAP point, while the end-of-coverage extends to about 56 km. The footprint shown in Fig. 7a represents the array power gain for a concentric array of 10 rings with 5 antenna elements in the innermost ring. The antenna elements are considered isotropic radiators, and the peak power gain of the array is 40 dB as per the weighting profile in Eq. (15).

Fig. 7b shows the free-space path loss investigation; here, it ranges from −132.5 at the sub-HAP point to −142 dB at the end of coverage, and the maximum line-of-sight distance at the end of coverage is 60 km. In this case, the coverage area is considered a square of 80 km side length, which is suitable for local university coverage. The free-space loss affects the student premises’ received signal level and should be considered in the link budget calculations. Also, for remote regions that are far from the university campus, coverage can be secured by locating the HAP at a suitable location that can be directly seen from the university site. Consequently, higher-gain directional backhaul antennas are required at the university site to boost signals to/from the HAP.

If we consider 30 Watts of transmitted HAP beam power with a 10-dB extra attenuation margin, the resulting received power in dBm over the beam coverage region is as shown in Fig. 8a; the main-lobe spot is shown in dark red and has power levels of more than −50 dBm. For a channel bandwidth of 20 MHz, the probability of error for QPSK-modulated digital signals for the coverage region is as shown in Fig. 8b, in which the brown ellipse represents the area that has an error of less than 10−13 , which fits the required link quality and assures stable transmission for most communication services.

In this scenario, the antenna array beamforming system is examined for the formation of multibeams using the same elements and weighting function for feeding these elements as listed in Tab. 2. The weights in this figure are very similar to those in the single-beam scenario. They can be considered the sum of three individual weighting vectors corresponding to the individual beams in the multibeam structure. Generally, for M spot beams, the array weighting function can be written as follows:

(23) WM=∑m=1M⁡W(θom,∅om)

For example, as shown in Fig. 9a, three arbitrary beams directed at ( 50∘,45∘ ), (45 ∘,135∘ ), and ( 45∘,300∘ ) can be formed using Eq. (23). The system can control the HAP transmitted power to provide higher values of received signal powers at the student premises, especially at the end-of-coverage regions. The red-colored parts represent the regions with acceptable levels of received power, which are almost higher than −70 dBm. If the student receiver is equipped with directional antennas, the received power can be improved further.

The received signal quality for the described multibeam scenario is depicted in Fig. 9b, in which the brown regions with a probability of error less than 10−13 meet the required service quality. A 20-MHz channel capacity at 5 GHz is approximately 380 Mbps, which can roughly serve about 190 students simultaneously over the covered spot areas, with 2 Mbps delivered to each student. Several channels or wider channel bandwidths, along with suitable multiple access schemes, can be utilized by using the 5G spectrum at higher frequencies such as 6 GHz with bandwidths more than 100 MHz to provide data rates of more than 1 Gbps, which can accommodate a larger number of students in the remote areas.