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Resource-Efficient HAPS-RIS Enabled Beyond-Cell Communications

In the future, urban regions will encounter a massive number of capacity-hungry devices. Relying solely on terrestrial networks for serving all UEs will be a cost-ineffective approach. Consequently, with the anticipated supply and demand mismatch, several UEs will be unsupported. To offer service to the left-out UEs, we employ an energy-efficient and cost-effective beyond-cell communications approach, which uses reconfigurable intelligent surfaces (RIS) on a high-altitude platform station (HAPS). Particularly, unsupported UEs will be connected to a dedicated control station (CS) through RIS-mounted HAPS. A novel resource-efficient optimization problem is formulated that maximizes the number of connected UEs, while minimizing the total power consumed by the CS and RIS. Since the resulting problem is a mixed-integer nonlinear program (MINLP), a low-complexity two-stage algorithm is developed. Numerical results demonstrate that the proposed algorithm outperforms the benchmark approach in terms of the percentage of connected UEs and the resource-efficiency (RE). Also, the results show that the number of connected UEs is more sensitive to transmit power at the CS than the HAPS size.


I. INTRODUCTION
Future wireless networks are expected to face unprecedented demands for continuous and ubiquitous connectivity due to the increasing number of mobile users, the evolving deployment of Internet-of-Things (IoT) networks, and the growing number of novel use cases. Increasing base station (BS) density and using relays may be a straightforward solution to cope with this unforeseen situation, but it comes at the cost of high capital and operational expenditures. Alternatively, a green and an energy-efficient solution that utilizes reconfigurable intelligent surfaces (RIS) in terrestrial networks (TNs) has been introduced [1]. RIS constitutes a large number of low-cost and nearly passive elements, which can be configured to reflect the incident radio frequency (RF) signal to a desired direction [1], [2].
However, the deployment of RIS in terrestrial environments involves several challenges, such as placement flexibility and channel impairments including excessive path loss and shadowing effects. Instead, in [3], we proposed the integration of RIS with non-terrestrial systems and discussed its prospects for wireless systems and services. Since energy consumption is a critical issue in aerial platforms, equipping them with a massive number of active antennas would exaggerate the issue. Alternatively, mounting aerial platforms with RIS can provide an energy-efficient solution [4]- [8]. In addition, due to the favorable wireless channel conditions in non-terrestrial networks (NTN), reconfigurable intelligent surfaces (RIS) can support panoramic full-angle reflection serving wider areas with strong line-of-sight (LoS) links [4], [9]. Further, in [10], we showed that RIS-mounted high-altitude platform station (HAPS) has the potential to outperform other RIS-mounted aerial platforms, due to the large size of HAPS.
To reap the benefits of RIS-mounted HAPS, in [11], we proposed a novel beyond-cell communications approach. This approach offers service to the stranded terrestrial user equipment devices (UEs), whose either channel conditions are below the required quality-of-service (QoS), or are located in a cell with fully loaded BS. In particular, the stranded UEs get service from a dedicated ground control station (CS) through the HAPS-RIS. We showed that HAPS-RIS can work in tandem with legacy TNs to support unserved UEs. We also discussed the optimal power and RIS units allocation design schemes to maximize the system throughput and the worst UE rate.
However, due to practical limitations on system resources, including CS power and HAPS size (equivalently, the number of RIS units), it might be infeasible to serve all unsupported UEs by CS through HAPS-RIS. Accordingly, we formulated a novel optimization problem to maximize the resource-efficiency (RE) of the system.
• A novel resource-efficient optimization problem that maximizes the percentage of connected UEs while minimizing the usage of RIS units and transmit power is formulated.
• Since the resulting problem is a mixed-integer nonlinear program (MINLP) and hard to solve, a low complexity two-stage algorithm is proposed to solve it. • Through numerical results, we study the impact of HAPS size and QoS requirements of UEs on the percentage of connected UEs and demonstrate significant improvements in RE of the system. The rest of the letter is organized as follows. In Section II, the system model is described. Section III presents the problem formulation. The proposed solution and the algorithm for solving the optimization problem are discussed in Section IV. Numerical results and discussion are presented in Section V. Finally, Section VI concludes the letter.

II. SYSTEM MODEL
We consider a typical urban region consists of UEs, terrestrial BSs, a single HAPS-RIS, and one CS, as depicted in Fig. 1. The UEs are assumed to suffer from severe shadowing and blockages, and NLoS paths, which are typical characteristics of propagation media in urban regions. Based on channel conditions between the BSs and the UEs, and the maximum serving capacity of the BSs, a set of K 1 = {1, . . . , 1 } UEs will be supported by direct links from the BSs (referred to as within-cell communications [11]). The set of remaining UEs K 2 = {1, . . . , 2 }, which cannot form direct connection with the terrestrial BS will be served by the CS via HAPS-RIS (referred to as beyond-cell communications [11]). The CS is located somewhere in the HAPS coverage area. Note that K = K 1 ∪ K 2 . We assume that the CS serves the stranded UEs in set K 2 using orthogonal subcarriers, and hence, there will be no inter-UE interference. Further, both within-cell and beyond-cell communications occur in two orthogonal frequency bands, while keeping the subcarrier bandwidth UE same for both types of communications. As a result, the signals from within-cell UEs will not interfere with the signals from beyond-cell UEs and vice versa.
We assume that within-cell UEs are connected optimally with terrestrial BSs, and hence, our focus in this work is on beyond-cell communications. Accordingly, the received signal at UE ∈ K 2 on subcarrier can be expressed as where CS denotes the transmit power of UE and denotes the additive white Gaussian noise (AWGN) ∼ CN (0, 0 UE ), where 0 is the noise power spectral density. ℎ denotes the effective channel gain from the CS to the HAPS-RIS and from the HAPS-RIS to UE , and is given by where CS denotes the antenna gain of the control station, and is the receiver antenna gain of UE . PL CS-HAPS− = PL CS−HAPS PL HAPS− denotes the effective path loss between the CS and UE via HAPS-RIS. Further, Φ k represents the reflection gain of the RIS corresponding to UE , and is expressed as where denotes the reflection loss corresponding to RIS unit . and represent the corresponding phases between RIS unit and both the control station and UE , respectively. represents the adjusted phase shift of RIS unit , and represents the total number of RIS units allocated to UE .
Using (1), the signal-to-noise ratio (SNR) at UE can be written as and the corresponding achievable rate can be expressed as

III. PROBLEM FORMULATION
Using power efficiently at the CS for transmitting signals, and at the HAPS-RIS for activating the RIS units offer greener environment and longer refueling intervals for HAPS. Also, in case of a large UE density or strict QoS requirement, it might infeasible to serve all unserved UEs by the CS via HAPS-RIS. Therefore, we need to select as many UEs that can be supported by the CS, while using as minimum system resources (transmit power and RIS units) as possible. Accordingly, we define a novel performance metric known as resource efficiency as follows: Definition 1: Resource efficiency (RE) of the beyond-cell communication system, , is defined as the ratio between the percentage of served UEs and the average power consumption in dBm by each supported UE, which includes the consumption towards signal transmission and RIS units configuration: where is the indicator variable, if = 1, user will get service by HAPS-RIS, otherwise not if = 0. In the denominator, the tersm 2 =1 CS and 2 =1 RIS represent the total transmit power consumption at the CS and the total power consumed by the RIS units for all supported UEs, respectively. RIS denotes the consumed power by each RIS unit for phase shifting, which is dependent on the RIS configuration technology and its resolution. Finally, |U| denotes the cardinality of the set, which constitutes the UEs supported by the CS via HAPS-RIS.
In the following, we formulate the resource-efficient UEs maximization problem. It can be expressed as where CS max denotes the maximum available transmit power at the CS. ,max and CS ,max denote the maximum number of RIS units and the amount of power allocated to UE , respectively. (7b) limits the number of BSs in the area. Constraint (7c) guarantees that each selected UE satisfies the threshold rate, th , requirement. Constraint (7d) ensures the total number of RIS units allocated to the supported UEs does not exceed the maximum number of available RIS units, max , which is limited by the HAPS size. Constraint (7e) determines the range of the adjustable phase shift for each RIS unit. Constraint (7f) guarantees that the total allocated power by the CS to the selected UEs is less than the maximum available power. Finally, constraints (7g) and (7h) ensure feasible and fair allocation of both RIS units and CS power to each UE.

IV. PROPOSED SOLUTION
Since problem (7) is an MINLP, it is hard to solve optimally with lower complexity. Therefore, we develop a low-complexity algorithm to solve it suboptimally. The main step of the proposed algorithm involves solving (7) in two stages.
In the first stage, we maximize the numerator of (7a) by maximizing the number of UEs, which can establish direct connection with TNs (i.e., by setting = max ), and then finding the set of maximum feasible UEs ∈ K 2 , which can be supported by the CS via HAPS-RIS. To this end, we first sort the channel gains of all UEs. Secondly, under the assumptions of equal power allocation to each UE and perfect reflection of each RIS unit, we allocate the minimum required number of RIS units to each UE as follows: The initial RIS units allocation starts with UEs with the best channel conditions until all RIS units are utilized. As a result, a set U with the largest number of feasible UEs is determined.
In the second stage, the denominator of (7a) is minimized by optimally allocating the CS power and RIS units to each UE belongs to set U. This is accomplished by solving the following optimization problem: Problem (10) is a mixed-integer linear program (MILP) and to solve it efficiently, we relax and to be the continuous variables. The final solution can be obtained as ≈ * and ≈ * . Consequently, the objective and the constraints of (10) become posynomials, and can be solved optimally using geometric programming (GP) technique [12]. The pseudo-code of the proposed two-stage algorithm is described in Algorithm 1.

V. NUMERICAL RESULTS AND DISCUSSION
In this section, we present and discuss the performance of the proposed algorithm. For he purpose of comparison, we employ a benchmark approach, which first allocates equal power to all UEs and then selects the UEs with the highest channel gains to be served first with the minimum number of RIS units until the QoS requirement is satisfied.
In the simulation setup, we consider an urban square area of 10 km by 10 km consisting of = 4 terrestrial BSs serving = 100 uniformly randomly distributed UEs with a minimum separation distance of 100 m among them. We assume that the terrestrial BSs are optimally placed in the considered region. The channel gains between all the UEs and the terrestrial BSs are obtained by following the 3GPP standards [13]. The carrier frequency is set to = 2 GHz with shadowing standard deviation = 8 dB. Unless stated otherwise, the minimum rate for a direct connection between a UE and a BS is th = 2 Mb/s. The Obtain initial from (8). 8: end while 9: end for 10: Stage-1 Output: Selected UEs U. 11: Solve optimally (10) for the set U. 12: Stage-2 Output: CS * and * (∀ = 1, . . . , |U|).  maximum available bandwidth to each BS is BS = 50 MHz, and subcarrier bandwidth for each UE is set to UE = 2 MHz. Accordingly, a UE will be connected to a terrestrial BS that provides the highest data rate, and the collection of such UEs forms the set K 1 . Consequently, the collection of stranded UEs forms the other set K 2 .
On the other hand, the effective channel gains from the CS to all the UEs in set K 2 through HAPS-RIS are obtained using the standardized 3GPP channel model between a HAPS and terrestrial nodes in urban environments [10], [14]. This model considers dry air atmospheric attenuation, and corresponding atmosphere parameters are selected based on the mean annual global reference atmosphere [15]. Further, we assume each UE has 0 dB antenna gain, and noise power spectral density 0 = −174 dBm/Hz. We further set CS max = 33 dBm, and CS = 43.2 dBm [14] in all of the simulations, unless stated otherwise. The values of other parameters are as follow: RIS = 7.8 mW [1], CS ,max = 30 dBm, ,min = 1000 units and ,max = 50, 000 units. Fig. 2 plots the normalized RE obtained using Algorithm 1 (on the left-hand side y-axis) and the percentage of connected UEs ( on the right-hand side y-axis) versus different values of minimum rate requirement min . It also compares the performance of Algorithm 1 with the benchmark approach. The maximum number of RIS units mounted on HAPS is set to max = 220, 000 units. It can be observed that as the QoS (represented by min ) increases, the percentage of connected UEs and the RE drops. However, this performance degradation is more significant in terms of the percentage of connected UEs than the RE. Furthermore, we observed that the RE obtained using Algorithm 1 significantly outperforms the one obtained using the benchmark approach. This is due to the fact that Algorithm 1 optimizes allocation of both power and RIS units to UEs.    In Fig. 3, to study the impact of max , we consider only the second term (i.e., RIS ) of the objective function in (10a). The selected range of max is set between 10,000 and 220,000 units. This range corresponds to a total RIS area between 9 m 2 and 198 m 2 at carrier frequency of 2 GHz 1 . In Fig. 4, only the first term of (10a) (i.e., CS ) is considered to study the effect of CS max on the percentage of connected UEs. The maximum transmit power of CS is set to vary between 30 dBm and 35 dBm, and max is set to 150,000 units. It can be observed from the figures that the percentage of connected UEs increases with the maximum power of the CS CS max , and the maximum number of RIS units max (or the size of HAPS). These behaviours are intuitive as making available more system resources ( CS max and max ) allow more number of stranded users to be served by the CS via HAPS-RIS.

B. Percentage of connected UEs
Figs. 3 and 4 also show that the performance of the proposed approach is 1-3 % higher than the benchmark approach. Moreover, CS max has more significant impact than max on the percentage of connected UEs. By increasing CS max by 2 dB, the percentage of connected UEs increases about 4%, whereas doubling of the RIS size is needed to achieve the same increase in the percentage of connected UEs.
Furthermore, it can be observed from the figures that 76% UEs are served through within-cell communication approach, and the CS supports the remaining UEs via HAPS-RIS. Hence, beyond-cell communications via HAPS-RIS is able to complement TNs.

VI. CONCLUSION
In this letter, we investigated the resources optimization of beyond-cell communications that use HAPS-RIS technology to complement TNs by supporting unserved UEs. In particular, given the limitations of the CS power and HAPS-RIS size, it might not be feasible to support all unserved UEs. Therefore, we formulated a novel resource-efficient optimization problem that simultaneously maximizes the percentage of connected UEs using minimal CS power and RIS units. The results show the capability of the beyond-cell communications approach to support a larger number of UEs. Further, the results show the superiority of the proposed solutions over the benchmark approach and demonstrate the impact of the HAPS size and the QoS requirement on the percentage of connected UEs and the efficiency of the system.