Floating meta-bubbles: aerial gateway and routing on the sky

Reflecting intelligent surface technology (RIS) is regarded as a key enabler of the sixth-generation (6G) communication system. It provides the ability to reshape radio channels through passively reflecting beams in a reconstructive manner. Furthermore, aerial RIS (ARIS) introduces more flexibility in providing line-of-sight (LOS) links. Unfortunately, most of the related research efforts supposed the system as a planar RIS mounted on a satellite, unmanned aerial vehicle (UAV), or balloon despite reported limitations of planar RISs. The essential problem in designing any planar RIS network resides in mutual orientation and alignment difficulty, especially under random fluctuation of position/orientation due to wind conditions or UAV wobbling in the hover state. So, this paper highlights spherical RIS (bubble) as the optimal choice for aerial beam routing where the orientation/rotation can be completely relaxed. It outperforms planar RIS in terms of RIS networking flexibility, dead zone relaxation, and coverage extension. Consequently, due to the added degrees of freedom, many new deployment scenarios/use cases are recommended such as introducing meta-bubbles as intermediate gateways between satellite and ground nodes and extending network infrastructure installation down to the client level to enhance its visibility and throughput. Simulations demonstrate the superiority of meta-bubbles in minimizing channel loss over successive multi-hop routing.


Introduction
As usual, successive generations of mobile communication are imposing higher restrictions on key performance indicators (KPIs) and enabling new services and applications.As soon as the standardization of the fifth-generation (5G) mobile communication was released, academic research efforts turned to reshaping the sixth-generation (6G) paradigm for resolving highly challenging conditions [1][2][3][4][5][6][7].Consequently, a combination of many enabling technologies is suggested for realizing it such as terahertz (THz) communications, visible Light Communications (VLC), cell-free massive MIMO, reflecting intelligent surfaces (RIS), non-terrestrial networking, and 3D networking.However, fixing RISs on building walls and facades imposes many geometric limitations.It fails to support LOS connections with a proper few RIS nodes.
Page 2 of 17 Salah J Wireless Com Network (2024) 2024 :61 In this paper, aerial intelligent reflecting surface (ARIS) [8,9] is studied where the transmitted beams can be reflected and routed in the sky over wide regions and different heights.Unfortunately, most of the related research efforts supposed the system as a planar RIS mounted on a satellite, unmanned aerial vehicle (UAV), or a balloon [8,[10][11][12][13][14][15][16][17] despite the reported limitations of planar RISs [18].Furthermore, the planar reflecting RIS is not the optimal choice for sky reflections compared to spherical RIS.Planar RIS has many limitations on mutual relative orientation and exhibits higher sensitivity to small vibrations.However, there is limited interest in spherical RISs [19].So, this paper sheds light on the spherical RIS and how it better matches aerial routing on semi-spherical balloons (meta-bubbles) where the reflected signal strength can be maintained constant irrespective of its orientation.The same spherically shaped balloon is used for simultaneously lifting and wave manipulation through its outer surface.Two main independent functions are defined namely, 1) Routing: The received beam is focused in a certain direction, 2) Gateway: The received beam from one direction is distributed for covering a certain area.Furthermore, these meta-bubbles can be employed as aerial gateways for dead zones or ruler regions where their operation can be streamlined to user-level installation as shown in Fig. 1.Communication clients can independently enhance its accessibility by installing a tethered balloon as a local gateway.This configuration enables network independent RIS control similar to user-controlled RIS [20].Our simulations demonstrate the superiority of spherical RIS over planar RIS in aerial routing.Finally, some recommended use cases of meta-bubbles are provided.

Overview
Future cellular networks aim to provide continuous connectivity anywhere even under low expected profit [21].So, rather than traditional cellular systems, new cost-effective solutions should be introduced.For that, it assumes employing non-terrestrial networks for covering scenarios that cannot be covered by terrestrial networks [22,23] or under disaster conditions [24].So, floating base stations are introduced from Google [25].Also, UAVs are introduced to assist in coverage enhancement [26][27][28].Furthermore, tethered UAVs enjoy higher stability by wired powering and backhauling [29][30][31].It increases the probability of a line-of-sight (LOS) channel and reduces fading impact.However, interference impact should be considered under large-scale deployment scenarios [32].

Fig. 1 Floating meta-bubbles
However, it is predicted that networked tethered flying platforms (NTFPs) will have an essential role in complementing the limitations of traditional cellular networking [33].
Further flexibility in beam routing can be attained through aerial RIS by mounting the RIS on a UAV or balloon [11,13].It locates RIS at a higher height that provides better visibility and wider accessibility.Also, ARIS is employed for relaying satellite signals toward ground stations [12].

Motivations for spherical RIS
There are many reasons for preferring spherically shaped RIS over planer RIS.These reasons arise from geometric restrictions related to planar RIS and/or degrees of freedom available in the spherical shape.Other motivations arise from some dedicated scenarios that match spherical shapes rather than planar shapes.In this subsection, some of these essential reasons are discussed.

Position/orientation inaccuracy problem
Practically, UAVs undergo: 1) mechanical vibration/wobbling due to rotating rotors [57] and 2) position shift/disorientation due to wind disturbance [58,59] in the hover state.Hence, it exhibits random movement or fluctuations in both position and orientation that cause disorientation and misalignment under UAV-based directional communication [60][61][62][63][64][65][66][67].Consequently, the same problem is extended to the planar RIS-assisted UAV scenarios [18] where any small movement may lead to severe misalignment.While the signaling should be adapted continuously for beam steering and tracking moving clients w.r.t fixed RIS nodes [68][69][70], ARIS movement in aerial scenarios adds more complexity to the control issue.Disorientation may lead to a complete RIS outage between nearby RIS nodes.
However, the situation gets worse under the following conditions: • Higher frequencies: Working at a higher frequency band is combined with more directional transmission (in pencil beams) to compensate for severe path loss.So, beam alignment/tracking becomes more challenging under RIS wobbling.• Aerial routing: For multiple cascaded aerial RIS nodes as a network, the misalignment impact is accumulated.It is too difficult to maintain optimum mutual orientation between multiple planar RISs carried on UAVs/balloons under position fluctuations, vibrations, and wind disturbance.

Varying effective aperture
Even under an ideal scenario (without wobbling), the received power by the ARIS varies along the orientation angle between the ground base station and the ARIS surface.The same ARIS appears in different effective areas for different ground positions.The orientation sensitivity of planar RIS is discussed in the system model section in detail.Practically, the effect of mutual TX/RX positions with respect to the ARIS, wind effect, and/or wobbling (in the drone case) jointly impacts the overall affective ARIS area and, hence, the net channel gain.

Entire-space limitations
Conventional RIS is built on a metallic substrate layer that limits its wave-manipulation capabilities across the half-space.Some solutions are provided for manipulating the waves over the entire space without limits.For example, RISs may be aided by a small number of relays as in [71] where the successive RIS nodes do have not proper orientations.Advanced manufacturing solutions are introduced for providing full space simultaneous transmitting and reflection RIS (STAR-RIS) [72][73][74][75].Furthermore, beyond diagonal RIS (BDRIS) [76,77] is introduced for providing full space coverage without limits.BDRIS strikes a trade-off between performance and circuit complexity [78].It incurs higher complexity and mutual coupling issues [76,79].Anyway, the ability of beam focusing and hop length varies with the target direction [48].Also, mounting planar RIS on UAVs or balloons masks some directions due to the body of the UAV or the balloon itself.Even under BDRIS mounting on a UAV [80], it still exhibits high sensitivity to hovering, wind disturbance, and varying effective aperture.

Complicated network planning under large-scale networking
Usually, RIS networking is assumed in different topologies, parallel [81,82], cascade [48,50,52,53,83], or hybrid manner [49].In all topologies, the optimization is performed based on channel gains or path loss between RIS nodes, base stations, and intended users.Joint beamforming optimization is applied where the active beamforming is carried on the BS side, while the passive beamforming is carried on RIS [84][85][86].It is well known that channel gains depend on the seen aperture (affective area) and LOS availability.Hence, orientation plays an essential role in enlarging RIS aperture and determining channel gain.For fully exploiting RIS networking in wireless communications, a careful design of RIS locations and orientations should be jointly assured.Regarding large-scale network planning [87], the problem does not involve only the positions of RIS nodes but also their orientations.Hence, imposing orientation as an additional optimization parameter severely complicates the problem.

Planar RIS mounting
Mounting a planar RIS on a UAV or balloon requires fixing the RIS surface on a special supporting board that can stand against environmental conditions.However, it imposes an increased weight overhead.Also, it increases the exposed surface to the wind and exerts higher resistance against wind direction.So, it magnifies wind impact.On the other hand, under the spherical RIS case, rather than lifting independent planar RIS, the metasurface is reshaped in such a way as to enclose the floating bubble without additional weight overhead.

Available degrees of freedom in the spherical shape
Arising from isotropic attributes of the spherical shape shown in Fig. 3, it relaxes all concerns related to planar RIS as follows: • Orientation/rotation invariance.

System model
To show the main difference between the planar and spherical RIS, the received power will be investigated in the two cases by introducing channel gains of single-hop reflection.Suppose a receiving aerial RIS surface located at distance L at a line-ofsight angle, α with the direction of a pencil beam radiation from BS as shown in Fig. 4.
Starting from basic principles, it is well-known that for a transmitted power P Tx , the received power P RX can be approximated by the percentage of intercepted waves by the receiving aperture A eff (effective area).
It is worth mentioning that the mutual orientation has a critical impact on the apparent effective aperture area where the amount of the intercepted power depends on the orientation angle, α .More specifically, for the isotropic radiation case, the received power can be expressed as the ratio of the receiving aperture area to a spherical area at the receiver position that is located at a distance L from the transmitting position [88].
By assuming, high gain (pencil beam) transmission with an extremely small beam width, BW φ , BW θ in the azimuth and elevation as shown in Fig. 4, instead of dis- tributing the transmitting power equally on the spherical area ( 4πL 2 ) , the power is focused on a smaller beam waist.Hence, the denominator in Eq. 1 is replaced by the beam area at the receiving aperture, A Beam .Consequently, the received power can be expressed as the ratio of the effective area of the receiving RIS aperture to the beam front area (beam waist).It represents the amount of intercepted beam by the RIS surface.Also, assume that the aerial RISs are standing at a far enough distance such that the whole RIS surface is completely enclosed by beam radiation.Also, the following points should be stated: (1) Fig. 4 System model • The receiving effective area and consequently the received power by the planar RIS are too sensitive to the orientation, while the spherical RIS is orientation/rotation invariant.• The received power by spherical RIS is fixed and proportional to the half-spherical area (maximum effective area of the spherical shape).• By approximating the radiated beam pattern by a cone with equal beam widths (φ = θ ≡ BW θ ) , the beam area at length L can be determined as • As assumed in [19], the area of the planar (disk shape) RIS is assumed equal to the maximum effective area of the spherical RIS which equals half of the spherical area.
The radius of the planar disk R Disk = √ 2R sphere , where R sphere represents the sphere radius.
• Hence, the physical area of planar RIS is half of the spherical area.
• The effective receiving area in the planar case is governed by the orientation/angle ( α) between the BS and RIS or between RIS nodes in intermediate hops [48].• For planar RIS Hence, the channel gain (η) can be expressed by the following term:

For spherical RIS
By inspecting the channel gains for both planar and spherical RISs, we note that: • In both cases, channel gain depends on RIS surface area, separating distance between RIS and BS and beam width, BW θ .• For a fair comparison, rather than defining the RIS in terms of the number of elements, the size of the RIS area is expressed in terms of the spherical RIS area.• The impact of orientation on the effective area and received power appears in the dependence on the orientation angle, α. (2) R sphere cos(α) (5)

Routing methods
We are interested in comparing the aerial routing under the spherical RIS network against the planer RIS network.The superiority of spherical aerial routing appears in extending coverage over multiple hops.Thus, single-hop channel gain is extended to multiple-hop end-to-end channels.The base station is assumed at a proper height that enables LOS access toward some of these floating RISs through highly directed beams.The RIS nodes are employed in a focusing function where the reflected beams are focused toward the next RIS node.In the considered scenario, there is a single BS assisted by the planer/spherical aerial RISs over a 5 km area.BS is equipped with multiple antennas for enabling high-gain beamed radiation.
In terms of graph theory, the RIS surfaces (nodes) and the links that connect any two surfaces are regarded as vertices and edges, respectively.RIS network is composed of a set of N nearby RIS vertices J {1, 2, . . . . . ., N } .Some of these successive nodes can be aligned: ϒ = {n 1 , n 2 , • • • , n K } through K + 1 hops for delivering (routing) the radiated beams from the BS (source vertex) to a certain user location (without any direct LOS path) where n k ∈ J represents the index of a selected node.
For efficient aerial beam routing, graph theory can be exploited for selecting the optimal path (through the distributed RIS nodes) according to cost function along the path such as the overall signal power transfer.So, it seems as a combinatorial optimization problem.Hence, any hop (link) between any RIS node can be represented by its channel gain η hop,i→j that represents power transfer efficiency related to a specific link ( RIS i → RIS j ).
For K successive hops between K + 1 RISs, the net (end-to-end) channel gain along the path ϒ is expressed as multiplication of these successive gains as follows: It is worth observing that the beamforming gain is already imposed by introducing the beamwidth θ k .
Similarly, the net channel gain along the path ϒ after K aerial hops on the spherical RIS network can be expressed as: So, the optimal path provides the maximum channel again by optimal selection of links (hops).
The problem is like a single-source shortest path (SSSP) problem [89].However, the cost or weight function of each link should be represented in terms of the reciprocal of the power transfer efficiency.Hence, this cost function represents a loss function.Correspondingly, the overall path cost has to be minimized under the optimal path.(6) η Net,planner (ϒ) The link cost and the total path cost can be defined as follows, respectively: Simpler calculations can be carried out by taking the logarithm for converting multiplications into additions as follows.
where C ϒ represents the total cost of the path.Selecting the optimal path is converted into finding the minimum total path weight (minimum loss), The weights of the N RIS nodes graph will be formulated in N × N symmetric adja- cency matrix (C cos t) where the element (i, j) is a link weight (loss) in both directions, while the diagonal ele- ments C i,i are weighted by extremely high values.Also, node availability can be regarded similarly by assigning these links to extremely high values C i,j = C j,i = ∞ to be excluded from the current routing problem.At that end, our problem formulation matches the SSSP problem with positive weights.Hence, Dijkstra's algorithm [89] can be applied to the generated cost matrix that represents our network.

Results and discussion
In this section, numerical simulations are introduced to demonstrate the superiority of the aerial spherical RIS network over the aerial planar RIS network.

Simulation parameters and environment
The simulation parameters are stated as follows.We consider the outdoor environment over.Ten randomly distributed aerial RISs are assumed with different heights over a 5 km area.A single BS is equipped with a reconfigurable holographic surface (RHS) [90] for providing directed radiation.The BS provides equal beam widths (φ = θ = 10 • ) .
It injects pencil beam radiation into the RIS network.However, in the successive routing hops, the directed beam exhibits different beamwidth (θ k ) according to the focus- ing ability of the reflecting RIS.The user equipment (UE) has a single omnidirectional antenna.The carrier frequency is set as 5 GHz.As assumed in [19], a disk-shaped planar RIS is assumed with equivalent area to the spherical RIS maximum effective area.The radius of the planar disk R Disk = √ 2R sphere , where R sphere represents the sphere radius.

Results and discussion
First, by considering the orientation impact on a single hop between BS and RIS node(BS → RIS i ) or between intermediate RIS hops ( RIS i → RIS j ), the channel gain is evaluated on different orientation angles between the transmitting point and the receiving RIS as shown in Fig. 5.
As indicated by Eq. 6 and Eq. 7, for both planar/spherical RIS network, the channel gains depend on RIS area, hop separating distance, and beamwidth.For planar RIS only, orientation angle is regarded as an additional factor affecting channel gain.The channel gain of the planar RIS is severely degraded under imposing different orientations/angles ( α k ) between the BS and RIS or between RIS nodes.This stems from the corresponding variation of the effective area of the surface intercepted by the directed beam.
Second, by considering beam routing over multiple hops, end-to-end channel gain is provided for different number of routing hops {1, 2, . . ., k, . . ., N } .As shown in Fig. 6, it is clear that multiple hops by spherical RISs exhibit less significant loss of channel power gain as compared to those by planar RISs.It can be justified by regarding the critical impact of mutual orientation on planer RIS.Hence, there is a successive channel gain attenuation after n hop of the planer network by cos(α k ) 2n compared to a spherical RIS network that exhibits orientation independency.By applying optimal routing through Dijkstra's algorithm for routing on different positions over the target area, it is observed that a spherical network tends to prefer routing on more hops than a planar network.
• This may be justified based on excessive channel loss in successive hops in planar scenarios due to orientation constraints.On the other hand, successive spherical routing enables higher power focusing along shorter distances.On average, the end-to-end channel gain of the two networks over multiple hops can be demonstrated in Fig. 6. • It is worth mentioning that the orientation parameter α k negatively impacts the channel gain twice, first, through reducing the planar effective area, second, through reducing focusing surface ability as indicated in [48].Hence, successive beamwidths θ k are increased.

Recommended use cases
The intended floating bubble should be simple and cheap.So, it is recommended to be implemented through a lighter-than-air (LTA) balloon type where the bubble is filled by low-density LTA gas like helium [33].The tethered balloon is covered by the RIS surface.The same spherically shaped balloon is used for simultaneously lifting and wave manipulation through its outer surface.As shown in Figs.7 and 8, there are two main independent functions that can be performed by the spherical RIS: 1) Routing: The received beam is focused in a certain direction, 2) Gateway: The received beam from one direction is distributed for covering a certain area.Usually, beam routing is performed through intermediate stages, while the gateway is found in the last stage at the interested serving area.Based on these two functions, some recommended use cases of meta-bubbles are introduced below.

Client-level bubble (self-gatewaying)
While reconfigurability enables multi-functioning, dynamic, and passive beam steering/scanning [68][69][70]91], it necessitates continuous sensing and heavy computations/ signaling [92].Hence, it represents one of the operator solutions that may not be simply extended for employment from the client side independently where it is just required to enhance coverage of some dead zones or increase the visibility of some areas.
Regarding simple scenarios, the client is interested in enhancing its communication conditions without being involved in complicated infrastructure and resource dedication from the network operator.So, the floating bubble meets the client's need by relaxing multi-functionality and supporting a gatewaying function only.It is intended to have small bubbles to the level that enables client-launched bubbles.This slightly changes the traditional absolute dependency on network operators for enhancing coverage.By inspecting the city view from the sky, buildings have different heights where some buildings mask others.Users become free to increase their visibility to operating BSs by launching their dedicated gateways on building roofs.Hence, the buildings' heights may be virtually equalized w.r.t BS visibility.
Hence, as shown in Fig. 9, it can be used in urban areas for clearing dead zones by installing small balloons in the center of that area.Also, it enhances the service in rural areas by operating it as a gateway.
It is worth mentioning that the essential concept of the gateway is inspired by the solar concentrator [93] where it is required to collect solar radiation from all directions to be forwarded to a specific direction.This holds the same functional meaning as a gateway.Furthermore, on-demand coverage can be made in uninhabited areas through a flying gateway.
Fig. 9 Floating meta-bubbles on different scenarios

Coverage extension
It is well-known that each macrobase station has a certain coverage region.Around the BS, the signal strength is high enough to provide high data rates, while users at the cell edge have lower data rates (just connected).Similar to traditional scenarios where small cells were installed for locally enhancing service at certain regions or for increasing overall network capacity, a network of meta-bubbles can be installed for extending the coverage of the BS or enhancing coverage for users at the cell edge as shown in Fig. 10.As shown, routing the beam through successive near bubbles maintains high signal strength and high data rates at specific target areas.For example, short-distance beam routing from the BS through "A-B" nodes, preserves high channel gain.On the other hand, beam routing over long distances may provide lowerspeed connections outside the traditional coverage zone of that BS.For example, direct beam routing from BS toward the "H" node extends coverage region but with low capacity.

Aerial routing
On the level of network operators, cooperative routing requires multiple aligned ARIS.Employing aerial routing based on meta-bubble overcomes orientation limitations related to building facades along planar RISs [48].

Hybrid FSO/RF gateway
Among different wireless access technologies, radio frequency (RF) still is the optimal access way from the user's perspective because some part of the signal likely may find its way toward the user even under non-line-of-sight (NLOS) scenarios.However, it leads to some critical concerns represented in security, energy, and interference (limited frequency reuse rate) issues.Moreover, RF-based RIS needs a large form factor to capture waves with effective power levels.On the other hand, optical wireless communication (OWC) enjoys a very wide spectrum along neglected interference compared to the RF band.Also, the RIS form factor is very small under the optical band.Hence, it is clear that hybrid free-space optical (FSO) communication complements RF systems by enabling RF access to users while allowing optical backhauling as shown in Fig. 11.Other than relaying involving [94], direct hybrid RIS designs [12,95] are already available.It needs to be extended to spherically shaped RIS.

Conclusion
This paper highlights the opportunities of spherical RIS balloons over planar RIS in non-terrestrial networking.Instead of lifting independent planar RIS, the same balloon can be covered by spherically shaped RIS.It relaxes the orientation sensitivity due to wind disturbance.Also, it simplifies network planning/routing without imposing additional orientation parameters.Furthermore, the routing and gateway functions of spherical RIS are emphasized.Some interesting use cases are recommended where small balloons can be installed independently to provide a cost-effective solution that enhances client visibility by creating a direct aerial path between the base station and the intended area.So, it can be used in urban areas to resolve dead zones.Rural areas and uninhabited areas can be connected by introducing meta-bubbles as a beam gateway.A small bubble can be launched independently to provide a communication entry point for a specific region.This paper aims to motivate research efforts on that point as an effective and practical solution for extending network coverage based on customer-level infrastructure.

Figure 2
Figure 2 demonstrates wind disturbance impact on the orientation of planar RIS mounted on a balloon.

Fig. 2
Fig. 2 Impact of wind on planar RIS (vertically/ horizontally) mounted on balloon

Fig. 5
Fig. 5 Impact of orientation on the effective aperture/channel gain (single hop)

Fig. 10
Fig. 10 Coverage extension by network of meta-bubbles