title: Link Budget Analysis for Reconfigurable Smart Surfaces in Aerial Platforms
authors: Safwan Alfattani Wael Jaafar Yassine Hmamouche Halim Yanikomeroglu Abbas Yongaçoglu
text: 
  
  
  
  
  
  
  
  Non-terrestrial networks, including Unmanned Aerial Vehicles (UAVs), High Altitude Platform Station (HAPS) nodes and Low Earth Orbiting (LEO) satellites, are expected to have a pivotal role 
  in sixth-generation wireless networks.
  With 
  inherent features such as flexible placement, wide footprints, and preferred channel conditions, they can tackle several challenges 
  faced by current terrestrial networks.
  However, their successful and widespread adoption relies on 
  energy-efficient on-board communication systems.
      
      
  In this context, the integration of Reconfigurable Smart Surfaces (RSS) into aerial platforms is envisioned as a key enabler of energy-efficient and cost-effective 
  aerial platform deployments.
   RSS consist of low-cost reflectors capable of smartly directing signals in a nearly passive way. 
  
  In this paper, we investigate the link budget of RSS-assisted communications 
  for two RSS reflection paradigms discussed in the literature, namely “specular” and “scattering” paradigms.
   Specifically, we analyze the characteristics of RSS-equipped aerial platforms and compare their communication performance with that of RSS-assisted terrestrial networks using standardized channel models. In addition, we derive the 
   optimal aerial platform placements for both reflection paradigms.
      
  
  Our results provide important insights for the design of RSS-assisted communications. For instance, given that a HAPS has a large 
  area for RSS, it provides superior link budget performance 
  in most studied scenarios. 
  In contrast, the limited RSS area on UAVs and the large propagation loss in LEO satellite communications make them unfavorable candidates for supporting terrestrial users. Finally, the optimal location of an RSS-equipped platform may depend on the platform's altitude, coverage footprint, and type of environment.
      
  
  
  
  
  Reconfigurable Smart Surfaces (RSS), Reconfigurable Intelligent Surfaces (RIS), aerial platform, Unmanned Aerial Vehicle (UAV),  High Altitude Platform Station (HAPS), Low Earth Orbit (LEO) satellite.
  
  
  
  
  Link Budget Analysis for Reconfigurable Smart Surfaces in Aerial Platforms
      Safwan Alfattani, Wael Jaafar, Yassine Hmamouche, Halim Yanikomeroglu, and Abbas Yongaçoglu 
  This work is supported in part by a
  scholarship from King AbdulAziz University, Saudi Arabia, in part by
  the National Sciences and Engineering Research Council of Canada
  (NSERC), and in part by Huawei Canada.
  S. Alfattani is with the Electrical Engineering Department of King Abdulaziz University, Saudi Arabia, and with the
  	School of Electrical Engineering and Computer Science,
  	University of Ottawa, Ottawa, ON, Canada, (e-mail: smalfattani@kau.edu.sa).
  W. Jaafar and H. Yanikomeroglu are with the Department of Systems and
  Computer Engineering, Carleton University, Ottawa, ON, Canada, e-mails:
  (waeljaafar, halim@sce.carleton.ca)
  Y. Hmamouche is with the Mathematical and Electrical Engineering Department, IMT-Atlantique, Brest, France,  (e-mail: yassine.hmamouche@imt-atlantique.fr).
  A. Yongacoglu is with the
   School of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, ON, Canada 
   (e-mail: yongac@uottawa.ca).
      December 30, 2023
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  § INTRODUCTION
  
  As the fifth generation (5G) of wireless systems are being actively deployed, researchers in the wireless community have started investigating new technologies and innovative solutions to tackle the challenges and fulfill the demands of 
  of next-generation (6G) networks.
  One of the main 
  challenges involves supporting ubiquitous connectivity with high data rates in an energy efficient way. 
  With the inherent limitations of terrestrial environments, non-terrestrial networks are 
  envisioned as an enabling technology for ubiquitous connectivity in future wireless communications. 
  
  
  
  
  
  Non-terrestrial networks including such platforms  as  Unmanned Aerial Vehicles (UAVs), High Altitude Platform Stations (HAPS) nodes, and Low Earth Orbit (LEO) satellites are capable of addressing such challenges  as coverage holes, blind spots, sudden increases in throughput demand, and terrestrial network failures. They can address these challenges  due to their  wider coverage footprints, strong line-of-sight (LoS) links, and flexibility of deployment compared to terrestrial
  networks <cit.>. Moreover, the standardization efforts of the  Third Generation Partnership Project (3GPP) aiming to utilize aerial platforms for 5G 
  and beyond have made significant progress, as
  demonstrated by the standardization documents TR 38.811 <cit.>, TR 22.829 <cit.>, and TS 22.125 <cit.>. Furthermore, several commercial projects are either in their initial phases of deployment or under development, which aim to design different types of aerial platforms capable of supporting wireless communications. Such projects include the Starlink LEO constellation by SpaceX <cit.>, the Stratobus HAPS by Thales <cit.>, and the Nokia Drone Networks <cit.>.
  Nevertheless, aerial platforms 
  are not yet a cutting-edge technology,
  and their current size, weight, and power (SWAP) limitations need to be further improved. 
  
  On the other hand, 
  reconfigurable smart surfaces (RSS) 
  
  
  have recently been introduced as an energy-efficient enabling technology
  for next-generation wireless networks <cit.>.[RSS are referred to in the literature by other names, such as software-controlled metasurfaces
  <cit.>, reconfigurable intelligent surfaces (RIS) <cit.>,  intelligent reflecting surfaces (IRS) <cit.> and smart reflect-arrays <cit.>.] An RSS is a thin, lightweight metasurface
  integrated with passive electronic components or switches to provide  unique and controlled manipulation of the wireless signals. It can alter the amplitude of the impinging signal, adjust its phase, and direct it to a target in a nearly passive way <cit.>.
  
  The deployment and utilization of RSS in terrestrial networks has been extensively studied, and 
  
  several research works, prototypes, and industrial experiments, summarized in <cit.>, demonstrated the potential of this technology.
  
  
  
  Given the potential spectral and energy efficiencies of RSS-assisted communications and the stringent energy requirements of communications through  aerial platforms, equipping the latter with RSS 
  presents an attractive solution to the SWAP issue. Indeed, due to the low-cost and negligible energy consumption of RSS reflectors, their use in aerial platforms is expected to support low-cost wireless communications for an extended flight duration. 
  
  
  In our previous work <cit.>, we discussed the feasibility of integrating RSS 
  in aerial platforms of different types.
  We 
  
  proposed a control architecture, detailed potential use cases, and examined associated challenges.
  In the context of UAVs only, 
  the authors of <cit.> showed that using RSS in UAVs enables a panoramic view of the environment, which can provide full-angle 360 signal reflections compared to 180 reflections in RSS-assisted terrestrial networks.
  In <cit.>, the authors presented potential use cases of RSS mounted 
  on UAVs and discussed  related challenges and research opportunities. Similarly, <cit.> investigated the potential of RSS-equipped UAV swarms, where a use case was studied to demonstrate the achievable data rate performance of such systems.
  
  The authors of <cit.> 
  studied the problem of wireless sensor data collection, where sensors were assisted by an RSS mounted on a UAV to reach the collecting sink.
  The objective was to maintain data freshness through accurate optimization of the UAV's location and the RSS phase-shifting configuration. Finally, in the context of LEO satellites,
  the authors of <cit.> investigated the utilization of RSS to support inter-satellite links in the  terahertz (THz) band. The results demonstrated a significant performance improvement in terms of bit error rate compared to non-RSS-assisted communications.
  
  
  Previous works have not thoroughly investigated RSS-enabled communication links, and so a link budget analysis for RSS-assisted non-terrestrial networks remains unexamined.
  
  In contrast, a number of works have studied path-loss models for RSS-assisted terrestrial communications
  <cit.>. While most of these models are  based on mathematical analysis using different approaches, some of them have been experimentally validated <cit.>. 
  These studies revealed the existence of two regimes that 
  govern the performance of RSS-assisted communication systems. The first  is the “specular” reflection paradigm, where the path-loss model is analyzed using geometrical optics and imaging theory. The second is the “scattering” reflection paradigm, which obeys 
  plate scattering theory and radar cross-section analysis. 
  The factors that determine the governing regime of the RSS-assisted systems are the geometrical size of the RSS units, the communication frequency, and the distances separating an RSS from the transmitter and receiver.
  Typically, 
  when an RSS is within a relatively short distance from a transmitter and/or a  
  receiver, or when the RSS units
  are electrically 
  large (e.g., their dimensions are ten times larger than the wavelength denoted by λ), the path loss is governed by the specular reflection paradigm
  <cit.>. 
  Otherwise, the RSS-assisted communication follows the plate scattering reflection paradigm (i.e., when the distances between the RSS units and transmitter or receiver are large or when the RSS unit dimensions are very small)
  <cit.>. 
  It should be noted that
  the scattering paradigm can be designated as “far-field” paradigm, whereas the specular reflection 
  can be referred to as “near-field” paradigm.
  
  
  Due to the specific design and environmental characteristics of aerial platforms compared to terrestrial systems, 
  the former, when equipped with an RSS, are expected to have a different link budget analysis.
  
  Therefore, it is necessary to investigate and assess the benefits of RSS-enabled aerial platforms.
  Three major factors impact the feasibility of RSS-enabled aerial platforms, namely the operating frequency or wavelength, the platform’s surface area reserved for RSS units, and the operating altitude. 
  
  While higher frequency signals are preferable for larger capacity links and enabling the deployment of more RSS reflector units, 
  higher frequency signals
  are more vulnerable to path-loss degradation 
  from the communication distance and atmospheric attenuation. Also, larger platform RSS sizes may lead to a higher reflection gain, which may not be realizable for 
  practical platform sizes.
  Finally, 
  although platforms operating at higher altitudes might be preferable due to their larger coverage footprint, they suffer from excessive propagation losses that may not be compensated for even 
  large area of RSS. 
  
  
  
  
  
  
  In this paper, we aim to provide the link budget analysis for RSS-enabled aerial platform communication systems 
  for specular and scattering reflection
  paradigms. The received power of the system, for different RSS-enabled platforms, is calculated while taking into account the signal strength losses due to the specific characteristics of each platform. To minimize signal loss, we derive the optimal platform location and 
  maximum feasible number
  of RSS reflectors on-board  each platform. Link budget expressions are then derived for realistic communication conditions, as 
  defined by 3GPP standards.
  Finally, numerical results are provided to support the proposed link budget analysis. The contributions of the paper are highlighted as follows: 
  
      
    * To the best of our knowledge, the performance parameters of RSS-enabled communications have been derived only for terrestrial networks and not for non-terrestrial systems, where different signal losses are experienced due to specific characteristics of aerial platforms and atmospheric phenomena. The impact of these factors is taken into account in this work.
      
      
    * 
      We investigate the link budget analysis for RSS-enabled aerial platform communications 
      for different platform types, namely UAVs, HAPS nodes, and LEO satellites. 
      To improve performance, we optimize platform locations and the maximum feasible number of mounted RSS reflectors.
      
      
    * We extend the link budget analysis to more realistic channel conditions, as defined in the 3GPP standards. 
      We also provide numerical results to support the related parameters evaluation and the link budget analysis.
   
  
  
  The rest of the paper is organized as follows. Section <ref> discusses the conditions of the reflection and scattering paradigms, and then analyzes the link budget for RSS-assisted terrestrial networks.  Section <ref> then exposes the characteristics of aerial platforms and derives the optimal platform placement for RSS-assisted aerial 
  communications. This section also investigates the related link budget for both reflection paradigms.
  Numerical results for the terrestrial and non-terrestrial RSS-assisted systems are presented and elaborated in Section <ref>. Finally, Section <ref> 
  concludes the paper.
   
  
   
  
  
  § LINK BUDGET ANALYSIS FOR RSS-ASSISTED TERRESTRIAL NETWORKS
  
  
  
  Here, we present the link budget analysis for RSS-enabled terrestrial communications 
  (e.g., RSS units mounted on a building).
  Given the identified specular and scattering reflection paradigms, we derive the related received power expressions. 
  
  Typically, terrestrial environments are characterized by 
  blockages that result in high path loss, especially in dense-urban and urban environments. 
  Accordingly, terrestrial network planning depends on cellular densification, where multiple base stations (BSs) are deployed in a relatively small area to ensure coverage of all users within the area. 
  But this comes at the expense of additional costs and inter-cell interference.
  To alleviate such inconveniences, the RSS can be deployed on the facades of buildings and used to either extend the cellular coverage or improve the signal quality in poorly served areas. As shown in Fig. <ref>, 
  the signal forwarded by the RSS from the BS to the user equipment (UE) can either
  substitute the direct link when the latter is absent, or it can  be added constructively  to the weak direct link in order to strengthen the received signal.
  
  
  
  
  
  
  
  
  	
  
  
  
  
  
  
  
  
   §.§ The Specular Reflection Paradigm
  
  
  The relation that governs the paradigm
  of the RSS-assisted communications has been defined in <cit.> as follows:
  
      d_ lim = 2 A_tλ,
  
  
  where d_ lim   denotes the maximum distance between
  the RSS and either the transmitter (Tx) or the receiver (Rx)
  in the specular reflection paradigm[An example of (Tx,Rx) in the terrestrial environment is (BS,UE).], and  A_t is the total RSS area.
  
  
  
  	
  When the length and width dimensions of the RSS units are large enough (i.e., above 10 λ), and the distance separating the RSS from the Tx/Rx is less than d_ lim, then the RSS can be considered in the near-field. In this paradigm, the impinging spherical wave forms a circular and divergent phase gradient on the RSS 
  area. Accordingly, the RSS acts as an anomalous mirror and the two-hop link acts as a one-hop path. Hence, the distance path loss is affected by the summation of the traveled distances (i.e., Tx-RSS and RSS-Rx distances), which is known as the specular reflection paradigm <cit.>.
  
  For a Tx-RSS (resp. RSS-Rx) distance D ≤ d_ lim and a large-sized RSS (LRSS), 
  where the reflector unit sizes are 10 λ× 10λ m^2, the minimum required number of reflectors for specular reflection, denoted N_min, can be calculated as
  
      D=2 A_t/λ= 2 N_min( 10 λ)^2/λ= 200 λ N_min⇔ N_min = D200 λ.
  
  The defined N_min will be later used to assess the feasibility of the RSS using the specular reflection paradigm.
  
  
  
  In order to conduct the link budget analysis in this paradigm, we assume the Tx-Rx communication assisted by a building-mounted LRSS. Let x(t) be the transmitted signal by the Tx. 
  Then, the received (noise-free) signal at the Rx, denoted by y(t), can be written as <cit.> 
  
      y(t) = a   x(t),
  
  where a is the wireless channel coefficient, 
  expressed for the sake of simplicity with the log-distance path-loss model. The latter is given by
  
      a = √(P_t G_t G_r)( λ4π d_0) ( (d_0d_l)^γ + ∑_i=1^N d_0^γρ_i e^-j(θ_i + ϕ_i)(d_ti+d_ir)^γ),
    
  where P_t, G_t, and G_r are the transmit power and the transmitter and receiver gains, respectively. Also, d_0 denotes the reference distance, d_l is the distance between Tx and Rx,[We assume here that the direct link Tx-Rx is a weak link <cit.>.
  
  ] 2γ = α is the path-loss exponent, and N is the total number of RSS reflector units. Finally, ρ_i, d_ti, d_ir represent the reflection loss of the i^th RSS reflector, the distance between Tx and RSS i^th reflector, and distance between the RSS i^th reflector and Rx, respectively. Also,  θ_i and ϕ_i are the corresponding incident and reflection angles.  
  Now, the received power at Rx, denoted by P_r, can be written as 
  
      P_r =P_t G_t G_r ( λ  d_0^(γ-1 )4π) ^2  ( 1d_l^γ + ∑_i=1^Nρ_i e^-j(θ_i + ϕ_i)(d_ti+d_ir)^γ)^2.
  
  For the sake of simplicity, we assume here that the LRSS 
  can perfectly adjust the desired phase shifts, and that the reflectors are ideal without any reflection loss, that is,[In practice, RSS reflection loss depends on  the configuration technology and building materials <cit.>. Also, since continuous phase shift implementation is difficult, only a finite discrete set of phase shifts is typically designed. It has been shown  that near-optimal RSS performance can be realized using a small number of phase-shift levels <cit.>. In any case, 
  the loss of a few dB due to the material properties or due to sub-optimal RSS configuration is insignificant compared to the signal propagation loss <cit.>. ]
  
      θ_i + ϕ_i=0 and ρ_i=1,   ∀ i=1,…,N.
  
  Moreover, assuming that the variation of d_ti and d_ir is negligible across the RSS, we have 
  
      d_ti +d_ir≈ 2d, ∀ i=1,…,N,
  
  where d=d_l/2.
  Hence, the received power can be rewritten as 
      P_r = P_t G_t G_r ( λ4π)^2 (d_0^(α-2)/(2d)^α) (1+N)^2.
  
  According to (<ref>), the location of the RSS has no impact on the received power, while the path loss is the dominant factor (e.g., α≥ 3 in urban environments <cit.>). Thus, in typical terrestrial environments, although the received power enhances quadratically with the number of RSS reflectors, it degrades at a much higher rate with 
  the propagation distance.
  
  
  
  
  
  
   §.§ The Scattering Reflection Paradigm
  
  Assuming that the Tx-RSS and RSS-Rx distances are large (i.e., higher than d_ lim), and that tiny RSS reflector units are used (i.e., with dimensions between 0.1λ and 0.2λ), then 
  each reflector capturing the transmitted signal behaves as a new signal source that re-scatters the signal towards the UE. In this 
  paradigm, —the scattering reflection paradigm— the total effect on the transmitted signal is the resultant of the cascaded individual channels Tx-RSS and RSS-Rx <cit.>. 
  
  
  A scattering paradigm for RSS-assisted communication is typically presented as an alternative to the degradation of direct links caused by strong blockages
  <cit.>. Accordingly, the effect of the direct link is ignored, and the effective received signal is only the one scattered by the RSS. Since in this paradigm, the use of tiny RSS reflector units is advocated, we 
  name these small-sized RSS (SRSS).
  
  To accurately assess the SRSS-assisted terrestrial communications, we present next the link budget analysis for two channel models, namely the log-distance and 3GPP based models[
  Several researchers have recently raised practical concerns about the specular reflection paradigm and the use of LRSS <cit.>. Subsequently, we adopt in this paper the practical 3GPP channel model under the scattering reflection paradigm only.] 
  
  
  
  
  
    §.§.§ Log-Distance Channel Model
  
  For the i^th reflector unit of the SRSS, the channel effect of the received signal, denoted a_i, is resulting from two cascaded channels, i.e., Tx-i^th reflector and i^th reflector-Rx  <cit.>. The channel coefficient is given by
  
      a_i = √(P_t G_t G_r) h_tig_irρ_i e^-jϕ_i,  i=1,…,N,
  
  where ϕ_i is the adjusted phase shift of the reflector, while h_ti and g_ir are the complex-valued coefficients representing the links between the i^th reflector and both Tx and Rx. The latter are defined by
  
      h_ti=  ( λ4π d_0) ( d_0d_ti)^γ    e^j θ_ti,   and    g_ir=( λ4π d_0) ( d_0d_ir)^γ  e^j θ_ir,
   
  with θ_ti and θ_ir denoting the transmit and receive channel phases, respectively.
  Following the generalization to the N reflectors, the received power can be expressed by
  
      P_r= P_t G_t G_r( λ4π d_0)^4 d_0^(2 α)( ∑_i=1^Nρ_i e^-j  (ϕ_i - θ_ti-θ_ir) (d_tid_ir)^γ) ^2.
  
  We assume lossless reflectors, i.e., 
  
      ρ_i =1, ∀ i=1,…,N,
  
  and that
  
      d_t ≈ d_ti and  d_r ≈ d_ir, ∀  i=1,…,N,
  
  
  where d_t and d_r are reference distances measured between the center of the SRSS and the Tx and Rx, respectively. Subsequently, the received power can be maximized by coherently combining the received signals through the N reflectors, i.e., ϕ_i = θ_ti + θ_ir. Hence, the received power can be written as
  
      P_r = P_t G_t G_r ( λ4π)^4   ( d_0^(2 α-4)/(d_t d_r)^α)  N^2.
  
  According to (<ref>), P_r degrades faster 
  than in (<ref>), due to the distances multiplication. Also, P_r is maximized when the RSS is the closest to either Tx or Rx.
  
  
  
  
    §.§.§ 3GPP Channel Model
  
  RSS in terrestrial environments can be placed on facades of buildings to smartly reflect signals toward users. Since such smart buildings are expected to be available in modern urbanized environments, we assume in the following the urban scenario of the 3GPP standard model <cit.>
  [Practically speaking, we envision that RSS to be deployed on the facades of high-rise buildings, which are available in urban environments. Also, we expect RSS to be implemented where they would bring profit
  to service providers. Due to the high density of customers in urban areas, it is more likely that RSS will be deployed massively in urban environments and perhaps rarely or never in rural environments.].
  The total path loss for the Tx-SRSS and SRSS-Rx links can be written as
  
      PL=𝒫^LoS PL^LoS + 𝒫^NLoS PL^NLoS + PL_e,
  
  where 𝒫^LoS and 𝒫^NLoS are the LoS and NLoS probabilities, PL^LoS and PL^NLoS are the associated losses in the LoS and NLoS conditions, and PL_e accounts for the extra loss of indoor users. 
  The latter vary greatly in terms of building type,
  location within the building, and movement in the building. For an accurate calculation of PL_e,  we refer the reader to <cit.>. 
  But since the focus in our system is on outdoor users, PL_e is ignored.
  
  The LoS probability in a terrestrial environment between the SRSS and Tx or Rx, assuming that the 
  heights of the RSS-equipped building and Rx are below 13 m,
  can be given by <cit.>
  
      𝒫^LoS=
          
             1    if d_2D≤ 18 m
      18d_2D + exp(-d_2D63) (1-18d_2D)     if d_2D > 18 m,
  
  where d_2D is the 2D separating distance (projected on the ground) between the SRSS and the Tx or Rx, whereas
  the path loss for LoS and NLoS links is given as follows <cit.>: 
      PL^LoS = 28+ 22 log (d_3D) + 20 log(f) + X
  
  and
  
      PL^NLoS = max (PL^LoS, P̅L̅^NLoS)
  
  where
  
      P̅L̅^NLoS   =       13.54 + 39.08 log (d_3D) + 20 log(f)
         -    0.6   (H_x - 1.5)+ X,  x ∈{RSS, Rx},
  
  d_3D is the 3D Tx-SRSS or SRSS-Rx separation distance in meters, f is the carrier frequency in GHz, X is a log-normal random variable denoting the shadow fading, with standard deviation σ = 4 dB and σ = 7.8 dB for LoS and NLoS links, respectively, and H_x denotes the SRSS/Rx height. Specifically, for the Tx-SRSS link, H_x = H_RSS, where H_RSS is the height of the building coated with the RSS, while for the SRSS-Rx link, H_x = H_Rx, with H_Rx is the Rx height.
  
  Accordingly, the received power, in dBm, can be written as
  
      P_r = P_t +  G_t  +G_r - PL_Tx-SRSS - PL_SRSS-Rx + 20 log(N),
  
  where PL_Tx-SRSS and PL_SRSS-Rx 
  represent the path loss for the Tx-SRSS and SRSS-Rx links respectively, calculated using (<ref>).
  
  
  
  
  
  
  
  
  
  
  § LINK BUDGET ANALYSIS FOR RSS-ASSISTED NON-TERRESTRIAL NETWORKS
  
  
  In this section, we start by presenting the aerial platforms characteristics. Then, we derive the link budget analysis of RSS-enabled non-terrestrial 
  communications (i.e., when an RSS is mounted on an aerial platform, such as a UAV, HAPS, or LEO satellite).
  Given the identified specular and scattering reflection paradigms,  we derive the related received power expressions.
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  	
  
  	
  
  
  
  
  
   §.§ Aerial Platforms Characteristics
  
  
  
  Three types of aerial platforms can be used to host RSS technology, namely UAVs, HAPS nodes, and LEO satellites.
  These platforms are usually deployed at different altitudes and target different coverage areas. Specifically, UAVs are deployed around 100 m altitude (and can operate up to 300 m <cit.>), to serve an area below 5 km radius <cit.>.
  
  By contrast, HAPS nodes are quasi-stationary platforms positioned in the stratosphere at an altitude between 17 and 50 km. However, most HAPS projects 
  target an altitude of 20 km due to its preferred 
  atmospheric characteristics for the platform stability and communication quality <cit.>. Thus, HAPS systems have a much wider footprint than UAVs that spans from 40 to 100 km for high throughput <cit.> and can go up to 500 km according to the International Telecommunications Union (ITU) <cit.>. Finally, LEO satellites 
  orbit 
  the earth at an altitude between 400 and 2,000 km, with an orbital period between 88 and 127 minutes <cit.>. Accordingly, LEO satellites have the largest coverage footprint. Nevertheless, the coverage area significantly depends on the satellite's 
  altitude, elevation angle, and coverage scheme (i.e., whether it uses a spot or wide communication beam).
  Consequently, the LEO satellite's footprint has a radius between hundreds and thousands of kilometers <cit.>. To communicate with UAVs and HAPS nodes,  UE can use the same device 
  as it would to communicate with a terrestrial BS.
  However,  different equipment is needed to communicate with LEO satellites, since they require LEO tracking, either mechanically or electronically, in order to compensate for the satellite motion and achieve a reliable communication <cit.>. 
  
  
  In addition to the aforementioned characteristics, the physical size of the aerial platform is crucial to enable hosting the RSS.  
  UAVs have the smallest size, and 
   hence can dedicate only
  a small area for RSS. On the other hand, two types of HAPS are identified, namely the aerostatic HAPS and the aerodynamic HAPS. Aerostatic HAPS nodes, especially airships, are giant platforms whose lengths are typically between 100 and 200 m, whereas aerodynamic HAPS nodes have wingspans between 35 and 80 m <cit.>. Finally, the size of current LEO satellites is less than 10 m <cit.>. Since HAPS nodes and LEO satellites are typically equipped with solar panel arrays, a part of the platform surface can be used to mount  RSS equipment.  
  
  
  
  
   §.§ The Specular Reflection Paradigm
  
  When 
  the Tx and Rx[Notice that Tx and Rx in the non-terrestrial communication context can be different according to the  aerial platform used. For instance, (Tx, Rx) can be (BS, UE) for a UAV, or it can be (Gateway, UE) for a HAPS platform or a LEO satellite. A HAPS UE might be a mobile, vehicular, or fixed cellular user device, whereas a LEO has a fixed UE such as a household receiver <cit.>.] 
  
  are separated by a relatively long distance, an aerial platform equipped with an LRSS can be used to assist the communication. Specifically, the Tx transmits its signal to the LRSS-equipped aerial platform. Then, the LRSS smartly reflects the incident signal towards the Rx, as illustrated in Fig. <ref>. 
  Hence, the received noise-free signal in the specular paradigm is identical to the one in (<ref>), whereas the channel effect is expressed using the free-space path-loss formula as
  
      a = √(P_t G_t G_r)( λ4π) ∑_i=1^Nρ_i e^-j(θ_i + ϕ_i)d_ti+d_ir,
  
  where the LoS wireless link component is predominant, i.e., the path-loss exponent α=2 γ=2.
  By following the same assumptions as in (<ref>)–(<ref>) and adopting a similar phase-shift configuration as in (<ref>), the received power can be given by
  
  
  
  
  
  
      P_r = P_t G_t G_r ( λ4π)^2  N^2(d_t + d_r)^2.
   
  Unlike (<ref>), 
  the parameters λ, N, and (d_t+d_r) have the same scaling law for the received power improvement or degradation.
  
  
  
  
  
  
  
  One of the distinct features of aerial platforms compared to terrestrial networks is 
  their flexibility of placement, which allows to further enhance the system performance.
  
  Given that Tx and Rx are collinearly separated by distance d_l=2 d, and that the aerial platform is located at altitude H_RSS and horizontally separated from the Tx by a distance r, i.e., d_t=√(H_RSS^2+r^2) and d_r=√(H_RSS^2+(2d-r)^2), then the optimal placement of the aerial platform under specular reflection is given by 
  
      r^*=d.
  
  
  That is, the platform is placed
  over the perpendicular bisector of the segment Tx-Rx at altitude H_RSS. 
    
  
  The specular equivalent path-loss distance, denoted d_sp, can be written as 
  
      d_sp = d_t + d_r = 
      √((H_RSS^2 + r^2))  + √(H_RSS^2+(2d-r)^2).
   
  To maximize P_r, we need to minimize d_sp through nulling its first derivative, i.e,
  
      ∂d_sp∂ r =r√(r^2+H_RSS^2)-2d-r√((2d-r)^2+H_RSS^2)=0,
  
  from which we obtain r^*=d. When substituting this solution in the second derivative of d_sp, ∂^2 d_sp/∂ r^2, we get
  
      ∂^2 d_sp/∂ r^2   =   H_RSS^2((r^2+H_RSS^2)^3/2+((2r-r)^2+H_RSS^2)^3/2)((2d-r)^2+H_RSS^2)^3/2(r^2+H_RSS^2)^3/2
         (r=d)=   2H_RSS^2(d^2+H_RSS^2)^ 3/2.
  
  Since ∂^2 d_sp/∂ r^2 > 0, then r^*=d is the optimal value that minimizes d_sp.
  
  Accordingly, the maximal received power can be calculated using (<ref>) for r^*=d as follows:
   
      P_r^* = P_t G_t G_r ( λ4π)^2 N^24 ( H_RSS^2+d^2).
  
   
  
  
  
  
   §.§ The Scattering Reflection Paradigm
  
  Similar to Section II, the scattering reflection paradigm is investigated for two channel models, namely the log-distance and the 3GPP models. 
  
  
  
    §.§.§ Log-Distance Channel Model
  
  Similarly to the SRSS-assisted terrestrial network, the received power at the Rx in the scattering paradigm can be expressed using (<ref>) for α=2, thus:
  
      P_r=P_t G_t G_r ( λ/4 π)^4 (N/d_t d_r)^2.
  
  
  Unlike the specular paradigm, where the optimum aerial platform location is over the perpendicular bisector of segment Tx-Rx, the best platform location under the scattering paradigm is expected to be different due to the cascaded channel effect.
  
  
  Given that Tx and Rx are collineraly separated by distance d_l=2d, and that the aerial platform is located at altitude H_RSS and horizontally separated from Tx by a distance r, then the optimal placement of the aerial platform under scattering reflection is given by
  
      r^*=
      
      d ±√(d^2-H_RSS^2)   if d≥ H_RSS
      
      d     otherwise.
  
  
    
  
  The scattering equivalent path-loss distance, denoted d_sc, can be expressed through
  
      d_sc^2=(d_t d_r)^2=( H_RSS^2+r^2) ( H_RSS^2 + ( 2d-r)^2 ).
  
  To maximize P_r, 
  we must minimize
  d_sc^2 by nulling its first derivative as follows:
  
      ∂d^2_sc∂ r =4r^3-12 d  r^2+(8 d^2+4H_RSS^2)r-4 d H_RSS^2=0.
  
  By solving (<ref>), we obtain the follwing roots:
  
      r^*= 
      d + √(d^2-H_RSS^2)
      
      d - √(d^2-H_RSS^2)
      
      d.
  
  The second derivative is given by
  
      ∂ ^2 d^2_sc∂ r^2 =12r^2-24d r+8d ^2+4H_RSS^2,
  
  in which we substitute the roots of (<ref>). Consequently, we find that (<ref>) is positive only when {r=d and d ≤ H_RSS} or {r=d ±√(d^2-H_RSS^2) and d ≥ H_RSS}. These (r,d) values dictate the best aerial platform locations 
  where received power is maximal.
   
  Physically speaking, Proposition (<ref>) implies that under the scattering reflection paradigm, when the height of a platform is larger than its designed coverage radius, the platform should be placed at the mid-point between the Tx and Rx. However, when the targeted coverage radius is larger than the platform's height, two optimal locations can be used, which are being close to either the Tx or the Rx. 
  
  By substituting the result of (<ref>) in (<ref>) and then (<ref>), the received power at Rx can be written as
  
      P_r^* = P_t G_t G_r ( λ4π) ^4   N^2(d^*_sc)^2.
  
  where d^*_sc is the equivalent path-loss distance for the optimal platform location, given by
  
      d^*_sc=
      
      H_RSS^2+d^2     if d≤ H_RSS
      
      2H_RSSd	        otherwise.
  
    
  Unlike (<ref>), the impact of H, d, and λ, is more important than N in (<ref>) due to the scattering effect.
   
   
  
  
  
  
  
    §.§.§ 3GPP Channel Model
  
  For a fair comparison with RSS-assisted terrestrial communications, we investigate here the link budget analysis for RSS-enabled aerial platforms with realistic 3GPP channel models. In what follows, given that platforms operate at different altitudes and thus may experience different attenuation phenomena, 
  we study the link budget for RSS-assisted UAVs separately from RSS-equipped HAPS nodes and LEO satellites.
  
  
  
  
      
    * The UAV-Based Model:
  
  
   RSS-enabled UAVs are envisioned to cooperate with terrestrial BSs to support terrestrial users. 
   They can tackle coverage gaps or increase the capacity of terrestrial users by reflecting the BSs' signals towards users <cit.>. In such context, it is acceptable to consider the 3GPP channel model between terrestrial BSs and UAVs <cit.>. Due to the relatively low altitude of UAVs, the latter are generally assumed to have full LoS conditions. Consequently, the path loss in rural and urban environments[In contrast to RSS-assisted terrestrial communications, where RSS deployment is expected to be concentrated in urban areas, 
  RSS-equipped aerial platforms 
  have the flexibility needed for both urban and rural areas.] 
  can be given by <cit.> 
  
      PL^ rural   =   max[23.9-1.8 log_10(H_x) , 20] log_10(d_3D)
         +   20log_10(40 π f3) +X, x ∈{UAV, UE}
  
  and
  
      PL^ urban=28+  22log_10(d_3D)+20log_10(f)+X, x ∈{UAV, Rx},
  
  where H_x, d_3D, f, and X are defined as in (<ref>)–(<ref>), except that X has a log-normal distribution with standard deviation given by[Note that variable X may be modified to include the effect of atmospheric turbulence, and thus the value of σ can be adjusted accordingly.]
  
      σ=
          
      4.2  e^(-0.0046   H_x)   in rural environment,
      
       4.64  e^(-0.0066   H_x)   in urban environment.
  
  Subsequently, the received power in dBm can be expressed by
  
      P_r = P_t +  G_t  +G_r - PL_Tx-UAV - PL_UAV-Rx + 20 log(N),
  
  where PL_Tx-UAV and PL_UAV-Rx are the path losses for the Tx-UAV and UAV-Rx links, calculated using either (<ref>) or (<ref>), depending on the considered environment.
  
  
  
  
  
      
    * The HAPS/LEO based Model:
  
  
  
  
  
  The support of future wireless networks through HAPS and LEO satellites is envisioned for both rural and urban areas <cit.>.
  To assess the performance in these different environments,  LoS probabilities are required. Based on the elevation angle of the aerial platform relative to the terrestrial Tx or Rx, denoted by ϑ,  LoS probabilities can be estimated for different environments using <cit.>. For the sake of simplicity, we propose to substitute <cit.> by a LoS probability function, defined as
  
      𝒫^LoS = b_1 ϑ^b_2+b_3,
  
  where b_i, i={1,2,3} are the parameters that depend on the environment,  determined in Table <ref>. 
  The accuracy of (<ref>) is validated in Fig. <ref>, where it is shown to agree with the results of <cit.>.
  Now, the path loss for LoS and NLoS conditions, denoted by PL, can be written as
  
      PL=𝒫^ LoS PL^ LOS + 𝒫^ NLoS PL^ NLOS,
  
  where 𝒫^y and PL^y, y ∈{LoS, NLoS}, are defined as in (<ref>). 
  The signal path between a HAPS/LEO and a terrestrial Tx or Rx undergoes several stages of propagation and attenuation. Specifically, the path losses PL^y, y ∈{LoS, NLoS} are composed as follows <cit.>:
  
      PL^y= PL_b^y + PL_g + PL_s + PL_e, y ∈{LoS, NLoS},
  
  where PL_b^y is the basic path loss, PL_g is the attenuation due to atmospheric gasses, PL_s is the attenuation due to either ionospheric or tropospheric scintillation, and
  PL_e is the building entry loss, expressed in dB. 
  
  
  
  
  
  PL_b^y accounts for the signal's free-space propagation (FSPL), clutter loss (CL^y), and shadow fading (X^y), i.e., 
  
      PL_b^y=FSPL+CL^y+X^y,   y ∈{LoS, NLoS},
  
  where 
  
      FSPL= 32.45+ 20log_10(f) + 20log_10(d_3D),
  
  with d_3D being the 3D distance between the HAPS/LEO and the terrestrial Tx or Rx, expressed as a function of the HAPS/LEO altitude H_z, z ∈{HAPS,LEO} and the platform's elevation angle ϑ as follows: 
  
      d_3D=√(R^2_E sin^2(ϑ)+ H_z^2 +2H_z R_E) - R_E sin (ϑ),
  
  where R_E denotes the earth's radius.
  The clutter loss, CL^y, represents the attenuation caused by buildings and environmental objects. Its value depends on ϑ, f, and the environment type. 
  In LoS conditions, CL^ LoS=0, while for NLoS, the CL^ NLoS values of <cit.> can be used for the typical Ka spectrum band (i.e., between 26.5 and 40 GHz). 
  Finally, X^y  
  is a zero-mean normal distribution with standard deviation σ^y, y ∈{LoS,NLoS}, whose values are determined in <cit.>.    
  For the sake of simplicity, we present the average 
  values of the parameters in Table <ref>[To be noted that variable X^y can be modified to include the effect of external factors, such as the atmospheric turbulence, and platform's drift. Hence, the value of σ^y can be modified accordingly.].
  
  
  
  PL_g is the attenuation caused by absorption due to atmospheric gases. Its value depends mainly on f, ϑ, and d_3D. According to <cit.>, 
  the effect of atmospheric gases is negligible  for f ≤ 10 GHz.
  However, for higher frequency bands 
  suitable for  RSS operations with a large number of reflectors, the selection of frequency windows with minimum atmospheric effect is important.
  In addition to the aforementioned factors, PL_g depends on the dry air pressure p, water-vapor density ξ, and temperature T <cit.>. An illustrative example is shown in Fig. <ref> for different Tx-Rx link lengths, selected for typical distances between a HAPS and Tx or Rx (20 and 100 km) and between a LEO satellite and Tx or Rx (1,000 km). The related parameters (p, ξ and T) are selected on the basis of the mean annual global reference atmosphere, i.e., p= 101300 Pa, ξ = 7.5 g/m^3, and T=15^C <cit.>. The PL_g calculation is carried out using the steps detailed in <cit.>. 
  
  
  
  
  
  
  
  
  Finally, the scintillation loss PL_s is caused by rapid fluctuations of the received signal amplitude and phase. There are two types of scintillation losses, namely the ionospheric scintillation and the tropospheric scintillation. The 
  former only significantly disrupts signals at frequencies below 6 GHz,
  whereas the latter affects only signals in frequencies above 6 GHz.
  The impact of the ionospheric scintillation is only significant for latitudes  in the range [-20, 20] 
  <cit.>. The ionospheric scintillation loss can be calculated as detailed in <cit.>. Specifically, it is derived from the measured peak-to-peak fluctuation as follows: 
  
      PL_s=PF√(2),
  
  where PF is the peak-to-peak fluctuation, equal to 1.1 dB for f=4 GHz, and calculated by the following equation for f ≤ 6 GHz:
  
      PF_(f ≤ 6 GHz)=PF_(f=4 GHz)· (f/4)^-1.5.
  
  
  Since high frequency bands are advocated for the RSS-enabled HAPS/LEO platforms, tropospheric scintillation is taken into account in the path-loss model.
  Specifically, the wireless signal fluctuations are due to sudden changes in the refractive index caused by temperature, water vapor content, and barometric pressure variations. Also, low elevation angles (especially below 5^) are significantly affected by the scintillation loss, due to the longer path of the signal and the wider beam width. 
  The value of the tropospheric scintillation loss is 
  season and region dependent. We refer the reader to <cit.> for the detailed calculation steps.
  
  
  To give an idea of the typical power attenuation level, 
  the  tropospheric attenuation with 99% probability at 20 GHz in Toulouse, France is tabulated in <cit.> for different elevation angles. For the sake of simplicity, we model the related tropospheric scintillation loss by
  
      PL_s = 14.7  ϑ^(-1.136), ϑ∈ [0^∘,90^∘],
  
  which is a valid approximation of <cit.> as shown in Fig. <ref>.
  
  
  Subsequently, the received power in dBm at Rx can be expressed by
  
      P_r    =    P_t +  G_t  +G_r - PL_Tx-H_L -PL_H_L-Rx
         +     20 log(N),   H_L ∈{HAPS, LEO },
  
  where PL_Tx-H_L and PL_H_L-Rx are calculated using (<ref>).
  
  
  
  
  
  The link budget analysis of Section III is summarized in Table <ref>.
  
  
  
  
  
  § RESULTS AND DISCUSSION
  
  In this section, we evaluate the received power for different RSS-mounted platforms, and the impact of several parameters is investigated. Based on the unique features of each platform, as discussed in Sections II and III, we assume typical values of altitude, coverage radius, and RSS area for each platform, as shown in Table <ref>. Moreover, we consider the height of the terrestrial Tx H_ Tx=25 m, while the receiver's height is H_ Rx=1.5 m.
  
  
  
  
  
  
   §.§ Impact of the Number of Reflectors and Environment Type
  
  Given the selected platform, the type of mounted RSS reflectors is of great concern, since different communication paradigms can be 
  followed and these have different costs.
  According to <cit.>, the cost is expected to be approximately proportional to the RSS size and number of RSS reflector units. Consequently, larger reflectors, with dimensions above 10 λ× 10 λ and operating in the specular reflection paradigm, are more expensive than small reflectors (i.e., with dimensions lower than 0.2 λ× 0.2 λ), 
  which operate in the scattering reflection paradigm. 
  Hence, the maximal number of reflectors to install on a platform, denoted N_max, is limited by the reserved area on the platform for the RSS A_t and the reflector's size A_r=c_1 λ× c_2 λ, where c_1 λ>0 and c_2 λ>0 are the length and width of a reflector unit, respectively. Their relation is defined by
  
      N_max= A_tA_r=A_tc_1 c_2 λ^2.
  
  
  In order to  highlight the potential gains of using RSS-equipped platforms, we consider that a communication between a terrestrial Tx and a terrestrial Rx is assisted by an RSS-equipped platform, namely a building facade, a UAV, a HAPS, or a LEO satellite, characterized as in Table <ref>. For the sake of simplicity, we assume that Tx and Rx are located at the edges of the platform's coverage footprint (i.e., within a distance 2d). Moreover, due to the flexibility of aerial platforms, we assume that they are placed at the optimal location according to the considered reflection paradigm, while the terrestrial RSS is assumed 
  to be midway between Tx and Rx[This assumption for the terrestrial RSS is justified by the fact that the latter cannot be 
  moved later to another location given that Tx and Rx locations may change.].
  The operating frequency f=λ/c=30 GHz (Ka-band), where c is the light's velocity in m/s, the receive antenna gain G_r=1 (i.e., 0 dBi), and the path-loss α=4 for the terrestrial communication.
  Finally, the following transmit/receive parameters are set as follows for the log-distance channel model: transmit power P_t=40 dBm and transmit antenna gain G_t=1 (i.e., 0 dBi). For the 3GPP model, P_t and G_t are fixed according to the related standards. Specifically, for the terrestrial and UAV systems, we assume that P_t=35 dBm and G_t=8 dBi <cit.>, while for the HAPS and LEO systems, we set P_t=33 dBm and G_t=43.2 dBi <cit.>. 
  
  
  
  Given the specular reflection paradigm, Fig. <ref> presents the received power as a function of the number of reflectors for different platforms.
  We notice that for UAVs and LEO satellites, the minimum required number of reflectors for specular reflection is greater than the maximum number of reflectors that can be placed on the platform's surface. Therefore, specular reflection cannot be achieved for RSS-equipped UAVs and LEO satellites for the specified coverage areas. This is due to the 
  limited area available for RSS on UAVs
  and to the relatively high operating altitude of LEO satellites.  
  However, specular reflection can be realized using RSS-equipped HAPS systems or terrestrial environments. 
  This is because of the clear LoS links with HAPS nodes and the relatively short
  communication distances in terrestrial environments. 
  As we can also see in Fig. <ref>, N_min=27,000 reflectors for HAPS provides coverage in a 100 km circular area at P_r=-64 dBm. For a smaller coverage footprint, it is expected that a lower number of reflectors would be used.  Although a small number of reflectors is required in  terrestrial environment for  specular reflection, the received power is worse than in the HAPS scenario.
  This is due to degraded terrestrial communication channels, compared to LoS wireless links for the RSS-equipped HAPS.
  Accordingly, a HAPS is the preferred RSS mounting platform in the specular reflection paradigm.
  
  
  
  
  
  
  For the scattering reflection paradigm, we present in Fig. <ref> the received power as a function of the number of reflectors for different platforms. 
  For the sake of simplicity, we show only the results corresponding to the 3GPP channel models where different types of environments are studied, namely dense urban, urban, and rural. Given the same number of reflectors, the RSS-equipped UAV system achieves the best power performance due to short distances and clear LoS wireless links. Moreover, 
  the difference in performance between
  the rural and urban environments 
  is minimal, at about 2 dB.
  For a number of reflectors close or equal to N_max,
  the LEO system has the worst received power performance, 
  which degrades significantly in accordance with the density of the urban environment.
  In contrast, the HAPS system realizes the best P_r values for a number of reflectors near or equal to N_max. 
  This remains the case even in dense urban environments, where a HAPS system may compensate for performance degradation by using a higher number of RSS reflectors or by reducing its coverage footprint (i.e., where the Tx and Rx are closer).
  Consequently, 
  it is worth noting that RSS-equipped LEO systems
  may require further redesigning in order to be feasible, while the HAPS coverage footprint needs to be adjusted according to the environment type of the served area. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
   §.§ Impact of the Carrier Frequency
  
  As shown in Table <ref>, the carrier frequency is a dominant parameter in the link budget analysis. Although using higher frequencies enables high capacity links and addresses the spectrum scarcity issues, 
  such frequencies as millimeter wave and Terahertz may suffer from significant signal attenuation.
  Nevertheless, 
  high frequencies enable the use of small-sized reflectors. And since a large number of these can be used in small areas, this may counterbalance the signal attenuation.
  
  
  
  
  In Fig. <ref>, we evaluate the received power as a function of the carrier frequency, for the same communication model introduced previously. Here, we assume that each platform hosts the maximal number of reflectors N_max, and that the link budget analysis for the scattering reflection paradigm is realized for the log-distance channel model 
  for the sake of comparison.
  The results show that in both specular and scattering reflection paradigms, the HAPS system provides the best performance due to its large surface area that accommodates the highest number of RSS reflectors. On the other hand, the RSS-equipped UAV performs worse than the terrestrial RSS under the specular reflection paradigm because of its small surface area, which accommodates a very small number of reflectors. In particular, when f ≤ 12 GHz, a UAV with dimensions of 0.25 × 0.25 m^2, cannot host a single reflector. Given the scattering reflection paradigm, all platforms demonstrate stable performance for any carrier frequency. Indeed, by combining (<ref>) into (<ref>) and (<ref>) respectively, we obtain the maximal received power, expressed by
  
      P_r^max   =   P_t G_t G_r ( λ4 π)^4 A_t^2(c_1 c_2 λ^2)^2 ( d_t d_r )^α
         =   P_t G_t G_r(4 π)^4(A_tc_1 c_2 )^2 1(d_t d_r )^α,
  
  for the terrestrial environment.  However, for the non-terrestrial one, (if d≤ H_RSS) P_r^max is expressed as
  
      P_r^max   =   P_t G_t G_r ( λ4 π)^4 A_t^2(c_1 c_2 λ^2)^2 ( H_RSS^2+d^2 )^2
         =   P_t G_t G_r(4 π)^4(A_tc_1 c_2 )^2 1(H_RSS^2 +d^2 )^2,
  
  otherwise (i.e., d>H_RSS),
  
      P_r^max = P_t G_t G_r(4 π)^4(A_tc_1 c_2 )^2 1(2H_RSSd)^2.
  
  According to (<ref>)–(<ref>), the received power is no longer dependent on the frequency (or the wavelength), but rather on A_t, c_1 and c_2.
  
  
  
  
  
  
  
  Fig. <ref> shows the received power as a function of the carrier frequency, given different RSS-equipped platforms and environment types. These results were obtained using the 3GPP channel models for the scattering reflection paradigm, i.e.,  (<ref>), (<ref>) and (<ref>). Also, we assume the use of the maximal number of reflectors N_max, dry air atmospheric attenuation, and an average tropospheric scintillation of 0.5 dB for the HAPS and LEO systems. 
  
  We notice that the received power of both terrestrial and UAV systems are insensitive to frequency.
  Indeed, the frequency attenuation is successfully addressed through the deployment of a higher number of reflectors, since N_max increases with f. In contrast, HAPS and LEO systems performance is affected by frequency, and deeply by the atmospheric attenuation at specific frequency ranges. Nevertheless, some spectrum regions present a stable received power behaviour, such as below 40 GHz, and in the 150-350 GHz and 500-700 GHz bands. The latter can be fully exploited for high capacity communications. Finally, depending on the operating frequency band and environment (dense urban, urban, or rural), one  system may be more suitable than another (e.g., the RSS-equipped HAPS is the most interesting one in rural areas for most of the frequency bands).    
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
   §.§ Data Rate Evaluation and Impact of Platform Location
  
  
  For the following simulations, we consider the same assumptions as in Fig. <ref>. 
  Subsequently,  (<ref>), (<ref>) and (<ref>) can be used to evaluate the received power. The related data rate is calculated as 
  
  
      ℛ = B_w log_2(1 + P_r/P_N),
  
  where 
  B_w denotes the bandwidth, F stands for the noise figure, and P_N refers to the noise power, given by
  
      P_N = K T B_w F,
  
  where K= 1.38 × 10^-23J.^∘K^-1 is the Boltzmann constant and T is the temperature in ^∘K. 
  According to <cit.>, when aerial networks operate in frequency bands f ≥ 6 GHz, B_w can be up to 800 MHz in both uplink and downlink, while F=7 dB.
  
  
  
  
  
  
  Assuming that each platform uses N_max reflectors and that B_w=100 MHz, we depict in Fig. <ref> the resulting data rates as a function of the receiver gain G_r. As typical UE has G_r ≤ 5 dBi, 
  both terrestrial and HAPS systems equipped with RSS can
  directly support the downlink communication to users, and this is mainly due to their large RSS areas. However, RSS-equipped UAVs and LEO satellites are unable to match this due to the small RSS areas of UAVs and the high propagation loss of LEO satellites. Alternatively, mounting RSS over UAVs and LEO satellites may support inter-UAV and inter-satellite communications <cit.>. Also, a swarm of RSS-equipped UAVs can be utilized to assist communications cooperatively <cit.>.
  
  The platform placement has an important impact on the data rate performance. Unlike LEO satellites, UAVs and HAPS nodes can be placed at fixed positions above an intended coverage area. However, due to wind and turbulence, these platforms may drift from their initial position, thus degrading communication performance. To assess such an effect, we present in Fig. <ref> the data rate performance as a function of ν=2-r/d, the normalized horizontal Rx-RSS distance. Moreover, we identify the optimal aerial platform location as calculated by (<ref>) and the one provided by the simulations. Here, we assume that G_r=0 dBi, while the remaining parameters are as for Fig. <ref>. 
  
  
  
  
  
  As discussed above, the optimal placement of an RSS-equipped aerial platform depends on the latter's altitude H_RSS and coverage radius d. For the RSS-equiped UAV, the obtained optimal UAV location r^* that achieves the highest data rate (red dot) agrees with that of  (<ref>) (blue circle), for any environment type. For the RSS-equipped HAPS, we distinguish between two cases, namely for d=50 km and d=10 km. In both cases, the optimal simulated HAPS locations and those of  (<ref>) agree in the rural environment, but the latter drift away as the environment becomes urbanized. This is mainly due to the effect of the additional shadowing and NLoS links in the 3GPP model of urban environments, which were ignored in the calculation of  (<ref>). Moreover, this location gap is larger for d=10 km due to a higher shadowing impact. For the terrestrial networks, the best location is either being the closest to Tx or Rx, with a preference for Tx. Indeed, since the BS (at altitude 25 m) has a strong LoS link towards the RSS, the received signal is slightly better than  being the closest to Rx (at altitude 1.5 m). 
  
  
  When an RSS-equipped HAPS operates in a rural environment, drifting from its initial location would have a small impact on communication performance. However, the data rate significantly degrades in an urban environment when the HAPS moves towards the middle of the Tx-Rx segment. A terrestrial RSS achieves the highest performance at optimal locations. However, due to the inflexibility of its deployment and varying Tx and Rx locations, it may not perform at its best. In any case, when designed to assist cellular networks, RSS deployed closest to the BSs would eventually guarantee operating at near-optimal performance.   
  
  
  
  
  
  
  
  
  
  
  
   
   
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
   §.§ Outage Probability Analysis
  
  
  Links between aerial platforms and terrestrial terminals may be subject to random variations due to shadowing and blockages. The  instantaneous received power at a terrestrial terminal can be generally written  as
  
      P_r = P_r + X,
  
  where P_r is the average received power, defined as 
  
      P_r = P_t+G_t+G_r-(PL_Tx-RSS + PL_RSS-Rx) + 20log(N),
  
  
  where  PL_Tx-RSS and  PL_RSS-Rx denote the average path loss of links between the RSS-equipped aerial platform and the transmitter and the receiver, respectively. Also, X represents the resulting shadow fading of both links,
  
  modeled as a zero-mean normal distribution with a standard deviation σ_s = √(σ_Tx-RSS^2+σ_RSS-Rx^2).  
  The  probability density function (pdf) of the received power can be written as
  
      f(P_r) = 1/σ_s √(2π)  exp(- (P_r-P_r)^2/2σ_s^2),  P_r ≥ 0.
  
  Accordingly, the outage probability can be obtained from the cumulative distribution function (cdf) as
  
      𝒫_out=ℙ(P_r ≤ x) =  ∫_0^x f(P_r)  dP_r = 1-1/2 erfc(x-P_r/σ_s √(2)),
  
  where x reflects the receiver sensitivity and erfc(x)= 2/√(π)∫_x^∞ exp(-t^2)  dt is the complementary error function.
  
  
  
  
  
   
  
  
  
  
  
  
  
  
  
  
  
  Using the 3GPP models for the scattering reflection paradigm (Table <ref>) with the characteristics of aerial  platforms (Table <ref>) and same assumptions as in Fig. <ref>, we depict in Fig. <ref> the cdf of the received power at user terminals with 0 dB gain, and assisted by RSS mounted on different aerial platforms in various environments. For any aerial platform, as the receiver's sensitivity degrades (i.e., x becomes larger), the outage probability increases. This performance degradation is more significant in denser urban environments due to higher shadowing loss.
  Nevertheless, the outage performance gap between rural and urban environments is more noticeable for a HAPS-assisted communication than for a UAV-assisted one. 
  
  
  
  
  
  
  
  
  
  The outage probability performance depends on the coverage area of the aerial platform.
  
  To analyze the impact of the coverage area, we illustrate in Fig. <ref> the outage performance as a function of the coverage radius. For these simulations, we assume a receiver power sensitivity of P_r^ th = -115 dBm. From Fig. <ref>, an outage probability lower than 10 % requires a coverage radius below 0.5 km for a terrestrial RSS and below 1 km for a UAV-assisted communication, respectively, whereas a HAPS-assisted communication can support an area of between 40 km and 80 km in radius (≈ 80 times larger than for a terrestrial RSS). This demonstrates the high potential of deploying RSS on HAPS compared to the alternatives.   
  
  
  
  
  
  
  
  
  
  
  
  
  
  § CONCLUSION
  
  In this paper, we conducted a link budget analysis for the envisioned RSS-equipped aerial platforms, namely UAVs, HAPS nodes, and LEO satellites. In a review of the literature, we identified two reflection paradigms: specular and scattering. For each reflection paradigm, we discussed its realization conditions and then derived the associated optimal RSS-equipped platform location that maximizes the received power. Numerical results provided a number of insights into the design conditions of RSS-assisted communications:
  
      
    * The scattering paradigm has gained more interest in the research community than the specular one due to the practical accuracy of the former.
      
    * RSS-equipped HAPS presents superior performance in different types of environments, compared to RSS-based terrestrial and other aerial platforms communications.
      
    * The received power performance is limited by the sizes of the RSS area and number of reflectors.
      
    * When using the maximal number of reflectors for an RSS, the link budget of the scattering reflection paradigm becomes independent from the carrier frequency.
      
    * Supporting ground users with RSS-equipped UAVs and LEO satellites might not be feasible. Nevertheless, RSS can be used to assist inter-UAV or inter-LEO communications. Also, a swarm of RSS-equipped UAVs can support terrestrial users.
      
    * The best RSS-equipped platform location  depends greatly on the operating altitude, coverage footprint, and environment type.
      
    * Finally, 
      unlike other RSS-assisted communications, 
      the ones assisted by an RSS-equipped HAPS sustain the best outage probability/coverage performance in any type of environment.
      
      
      
  
  
    
  
  
  
  
  
  
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