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Hierarchical RIS Association for FR3 Space-Air-Ground Integrated Networks
Muddasir Rahim, Irfan Azam, Soumaya Cherkaoui
TL;DR
FR3 space-air-ground networks must associate users across terrestrial and satellite-assisted links as connectivity conditions and limited RIS resources vary. The paper proposes a hierarchical matching framework and reports higher network sum rate than greedy and random association schemes.
Problem
FR3 networks can offer several viable communication modes, making user association challenging when UEs compete for limited RIS resources.
Source: §I · p. 2, §III · p. 4Method
Results
The proposed scheme consistently achieves higher network sum rate than greedy and random association schemes across the evaluated settings.
Source: §IV · pp. 5–6, §V · p. 6Takeaways & Limitations
The framework is designed to support seamless connectivity and efficient network-resource utilization while satisfying RIS capacity constraints.
Source: §V · p. 6
Abstract
from arXiv · showhide
The growing demand for diverse sixth-generation (6G) applications requires efficient connectivity, seamless service continuity, and extended network coverage. Although terrestrial infrastructures can effectively serve most wireless user equipment (UE), communication reliability may be significantly degraded in remote or blocked environments. To address this challenge, this paper proposes a reconfigurable intelligent surface (RIS)-assisted space-air-ground integrated network (SAGIN) operating in the upper mid-band (FR3) spectrum. The considered network consists of a terrestrial base station (BS), a low Earth orbit (LEO) satellite, multiple terrestrial RISs (TRISs), and unmanned aerial vehicle-mounted RISs (ARISs), where the BS serves as the primary access node, while the LEO satellite provides complementary connectivity when terrestrial links are unavailable or cannot satisfy the required quality-of-service (QoS) requirements. Within this framework, we formulate a hierarchical RIS association problem to maximize the achievable network sum rate under RIS capacity constraints. The resulting optimization problem is a mixed-integer nonconvex problem due to the binary association variables and the coupling among UEs competing for limited RIS resources. To efficiently solve the problem, we develop a hierarchical many-to-one matching-based RIS association framework. Specifically, UEs with satisfactory terrestrial connectivity are first associated with TRISs, whereas UEs that cannot be reliably served by the terrestrial network are subsequently associated with ARISs through the non-terrestrial network. Simulation results demonstrate that the proposed hierarchical association framework significantly outperforms greedy and random association schemes in terms of the achievable network sum rate.
I. INTRODUCTION
FR3 offers a 7–15 GHz capacity-and-coverage tradeoff, but its propagation and blockage challenges leave hierarchical UE–RIS association in FR3 SAGINs underexplored. The paper proposes prioritizing terrestrial service and using LEO-assisted aerial RISs when terrestrial connectivity is inadequate.
I. INTRODUCTION
- 7–15 GHz FR3 offers a tradeoff between sub-6 GHz bandwidth limitations and the severe propagation losses of millimeter-wave and terahertz bands.The passage presents FR3 as a promising spectrum candidate for 6G services requiring enhanced capacity and wide-area coverage.Source: §I · p. 1
- Hierarchical UE–RIS association for FR3 SAGINs remains an open problem, as most RIS work focuses on terrestrial networks.The introduction also notes that earlier hierarchical studies often assume direct terrestrial links are unavailable, unlike the range of viable FR3 links.Source: §I · pp. 1–2
- FR3 reliability is challenged by path loss, penetration loss, and sensitivity to line-of-sight blockage; RISs can reconfigure propagation through passive beamforming.The passage frames RISs as a way to enhance coverage without active relaying.Source: §I · p. 1
- The proposed hierarchy uses TRISs for satisfactory terrestrial links and LEO-assisted ARISs when terrestrial service is unavailable or fails QoS requirements.The BS is the primary access node, while the satellite provides complementary connectivity.Source: §I · pp. 1–2
A. Contributions
The paper proposes an FR3 RIS-assisted SAGIN and a hierarchical many-to-one association framework to maximize network sum rate under RIS-capacity constraints. Simulations report higher sum rate than greedy and random association schemes.
A. Contributions
- The proposed FR3 SAGIN comprises a terrestrial BS, a LEO satellite, multiple TRISs, and ARISs, with the satellite providing complementary connectivity when terrestrial service is inadequate.Source: A. Contributions · p. 2
- The framework maximizes network sum rate under user-association and RIS-capacity constraints, first associating UEs with satisfactory terrestrial connectivity to TRISs and then associating remaining UEs with ARISs via NTN.Source: A. Contributions · p. 2
- The proposed hierarchical association framework significantly outperforms greedy search and random search in achievable network sum rate.The contribution statement gives no numerical gain.Source: A. Contributions · p. 2
II. SYSTEM MODEL AND PROBLEM FORMULATION
The system model combines terrestrial and non-terrestrial access, with a BS and multiple TRISs serving UEs when terrestrial links are suitable and a LEO-assisted ARIS path otherwise. The RISs are modeled as planar arrays, and the passage specifies the network nodes’ Cartesian locations.
II. SYSTEM MODEL AND PROBLEM FORMULATION
- The illustrated SAGIN includes a terrestrial BS, a LEO satellite, ARIS, multiple TRISs, and K UEs.The BS is the primary access node in the described system model.Source: §II · p. 2, Figure 1 · p. 2
- UEs use the terrestrial BS, aided by multiple TRISs, when terrestrial links are suitable; otherwise, the LEO-assisted link uses an ARIS.The BS is described as the primary access node because of its low latency and cost-effective deployment.Source: §II · p. 2
- Each RIS is modeled as a uniform planar array with M = Mx × My passive reflecting elements, and the model specifies Cartesian locations for the BS, UEs, TRISs, ARIS, and satellite.Source: §II · p. 2
A. Channel Modeling of the Proposed SAGIN
The channel model represents BS- and LEO-based service through terrestrial and aerial RIS paths. It also specifies how terrestrial QoS selects the transmission mode and how the effective channel supports SINR and rate calculations.
A. Channel Modeling of the Proposed SAGIN
- The BS is the primary access node, with LEO service used when terrestrial links are unavailable or fail QoS; TRISs assist the TN and an ARIS assists the NTN.The considered service paths include direct BS-to-UE or TRIS-assisted terrestrial service and LEO-assisted service.Source: A. Channel Modeling of the Proposed… · p. 2
- The modeled terrestrial paths include the direct BS-to-UE channel, the BS-to-TRIS channel, and the TRIS-to-UE channel.The passages identify the corresponding direct channel vector, BS–TRIS channel matrix, and TRIS–UE channel vector.Source: A. Channel Modeling of the Proposed… · p. 3
- The aerial path is modeled through the LEO-satellite-to-ARIS channel and the ARIS-to-UE channel.The passages identify the satellite–ARIS channel matrix and the ARIS–UE channel vector.Source: A. Channel Modeling of the Proposed… · p. 3
- The transmission mode is selected by comparing the BS-assisted rate with Rmin: αk = 1 selects BS service, and αk = 0 selects LEO service.The choice prioritizes terrestrial communication and uses LEO-assisted service otherwise.Source: A. Channel Modeling of the Proposed… · p. 3
- The RIS reflection matrix is assumed to use ideal phase shifts and unit reflection amplitude; the effective channel then supports SINR and achievable-rate calculations.The SINR expression uses transmit-power scaling, beamforming, and AWGN variance as described in the passages.Source: A. Channel Modeling of the Proposed… · p. 3
B. Optimization Problem Formulation
The formulation chooses UE–RIS associations to maximize network sum rate, subject to binary assignment and RIS-capacity constraints. TRIS and ARIS assignments are restricted to the corresponding BS-aided and LEO-aided modes.
B. Optimization Problem Formulation
- The objective is to maximize network sum rate by selecting UE–TRIS and UE–ARIS associations.UEs with satisfactory terrestrial connectivity use the BS through TRISs; remaining UEs use the LEO satellite through ARISs.Source: B. Optimization Problem Formulation · p. 3
- The association decisions are binary, and each RIS is limited to supporting at most ζ UEs.The formulation applies binary assignment constraints and a maximum-capacity constraint to both TRISs and ARISs.Source: B. Optimization Problem Formulation · p. 3
- Only BS-aided UEs can be assigned to a TRIS, while only LEO-aided UEs can be assigned to an ARIS.These mode-specific restrictions are imposed alongside the capacity constraints.Source: B. Optimization Problem Formulation · p. 3
III. PROPOSED DEFERRED ACCEPTANCE FRAMEWORK
The paper addresses the coupled, mixed-integer nonconvex UE-association problem with a three-phase hierarchical deferred-acceptance framework. It selects transmission modes, matches terrestrial users to TRISs, then assigns remaining users to the ARIS.
III. PROPOSED DEFERRED ACCEPTANCE FRAMEWORK
- The association problem is mixed-integer and nonconvex, with coupled UE pairing decisions competing for limited RIS resources.The framework is presented as a deferred-acceptance many-to-one matching approach to solve this problem.Source: §III · pp. 3–4
- The framework has three sequential phases: transmission-mode selection, UE–TRIS association, and UE–ARIS association.Fig. 2 depicts the proposed hierarchical deferred-acceptance many-to-one matching framework.Source: §III · p. 4, Figure 2 · p. 4
- In the TRIS phase, UEs rank TRISs by achievable rate and propose in preference order; each TRIS keeps its preferred requests up to capacity and rejects the rest.Rejected UEs continue proposing to their next-preferred TRIS until matched or all TRISs have been explored.Source: §III · p. 4
- In the ARIS phase, initially non-terrestrial UEs and UEs rejected by all TRISs enter the aerial set, where the ARIS admits requests up to capacity by priority.The algorithm outputs the final UE–TRIS and UE–ARIS association matrices.Source: §III · p. 4
IV. SIMULATION RESULTS AND DISCUSSION
The proposed hierarchical association achieves the highest network sum rate against greedy and random schemes across the evaluated settings. Results also show how sum rate varies with transmit power, RIS size, UE count, and ARIS altitude.
IV. SIMULATION RESULTS AND DISCUSSION
- Across the transmit-power range, the proposed scheme achieves the highest network sum rate, ahead of GS and RS.The comparison is shown in Fig. 3.Source: §IV · p. 5, Figure 3 · p. 5
- More RIS reflecting elements improve network sum rate for all schemes, while the proposed framework consistently outperforms GS and RS.The comparison is shown in Fig. 4.Source: §IV · p. 5, Figure 4 · p. 5
- As UE count rises, network sum rate initially increases, then gradually decreases beyond a point as RIS-resource competition and interference grow.The larger network area achieves a higher sum rate; the proposed scheme outperforms GS and RS in both deployment scenarios.Source: §IV · p. 5, Figure 5 · p. 6
- Increasing ARIS altitude gradually decreases network sum rate across all schemes, while the proposed method remains highest across the considered altitudes.The decrease is attributed to greater propagation distance and resulting path loss.Source: §IV · p. 6, Figure 6 · p. 6
V. CONCLUSIONS
The paper proposes hierarchical many-to-one RIS association for FR3 SAGINs, routing users according to terrestrial connectivity and maximizing sum rate under RIS capacity constraints. Simulations show consistent sum-rate gains over greedy and random association schemes.
V. CONCLUSIONS
- The proposed hierarchical many-to-one matching framework maximizes network sum rate while satisfying RIS capacity constraints.The paper studies RIS-assisted SAGINs operating in the FR3 spectrum.Source: §V · p. 6
- Users with satisfactory terrestrial connectivity are associated with TRISs, while remaining users are served through ARISs via the NTN.The conclusion describes this routing as supporting seamless connectivity and efficient network-resource utilization.Source: §V · p. 6
- Simulations show that the framework consistently outperforms greedy and random schemes in achievable network sum rate.Future work will jointly optimize RIS association and resource allocation and examine robust designs under imperfect channel state information and dynamic network conditions.Source: §V · p. 6