Dual-Tier IRS-Assisted Mid-Band 6G Mobile Networks: Robust Beamforming and User Association

The rapid growth of Internet of Things (IoT) applications necessitates robust resource allocation in future sixth-generation (6G) networks, particularly at the upper mid-band (7-15 GHz, FR3). This paper presents a novel intelligent reconfigurable surface (IRS)-assisted framework combining terrestrial IRS (TIRS) and aerial IRS (AIRS) mounted on low-altitude platform stations, to ensure reliable connectivity under severe line-of-sight (LoS) blockages. Distinguishing itself from prior work restricted to terrestrial IRS and mmWave and THz bands, this work targets the FR3 spectrum, the so-called Golden Band for 6G. The joint beamforming and user association (JBUA) problem is formulated as a mixed-integer nonlinear program (MINLP), solved through problem decomposition, zero-forcing beamforming, and a stable matching algorithm. Comprehensive simulations show our method approaches exhaustive search performance with significantly lower complexity, outperforming existing greedy and random baselines. These results provide a scalable blueprint for real-world 6G deployments, supporting massive IoT connectivity in challenging environments.

💡 Research Summary

The paper tackles a pressing challenge for future sixth‑generation (6G) mobile networks: delivering reliable, high‑capacity service in the upper‑mid‑band (FR3, 7–15 GHz) where line‑of‑sight (LoS) links are frequently blocked by dense urban structures. While most existing intelligent reconfigurable surface (IRS) research focuses on terrestrial deployments in millimeter‑wave or terahertz bands, this work pioneers a dual‑tier architecture that combines terrestrial IRSs (TIRS) mounted on buildings with aerial IRSs (AIRS) mounted on low‑altitude platform stations (LAPS). The authors argue that the aerial layer can fill coverage “blind spots” left by ground‑based reflectors, thereby exploiting the relatively favorable propagation characteristics of FR3 while mitigating its blockage vulnerability.

A single multi‑antenna access point (AP) equipped with N antennas serves K single‑antenna users. Direct AP‑to‑user links are assumed unavailable, forcing all communication to travel through one of L IRSs (M = M_y × M_z reflecting elements each). The cascaded channel from AP to a user via IRS ℓ is modeled as h_{ℓ,k}=F_ℓ^H Θ_ℓ f_{ℓ,k}, where F_ℓ and f_{ℓ,k} capture the AP‑to‑IRS and IRS‑to‑user sub‑channels, respectively, and Θ_ℓ is the diagonal phase‑shift matrix of IRS ℓ. Using these channels, the signal‑to‑interference‑plus‑noise ratio (SINR) and achievable rate R_{ℓ,k}=log₂(1+SINR_{ℓ,k}) are derived.

The core optimization problem (P) seeks to maximize the downlink sum‑rate by jointly designing the AP beamforming matrix W and the binary user‑IRS association matrix Υ, subject to per‑user power non‑negativity, a total AP power budget, and strict one‑to‑one matching constraints (each IRS serves at most one user and each user is served by exactly one IRS). The authors prove that (P) is a mixed‑integer nonlinear program (MINLP) and NP‑hard by reduction to the known NP‑complete link‑scheduling problem.

To obtain a tractable solution, the problem is decomposed into two sub‑problems:

1. Beamforming sub‑problem (P1) – With a fixed association, zero‑forcing (ZF) beamforming is applied. The ZF precoder is W = H† (the pseudo‑inverse of the effective channel matrix H), which eliminates inter‑user interference (HW = I_K). Power allocation variables p_k are then chosen to satisfy the AP power constraint. This yields a closed‑form, low‑complexity (≈O(K³)) beamformer that is optimal for the interference‑free case.

2. User‑IRS association sub‑problem (P2) – With the ZF beamformer fixed, the association problem becomes a one‑to‑one matching task. The authors employ a user‑proposing deferred‑acceptance (DA) algorithm. Each user builds a preference list of IRSs ordered by the expected rate (computed from the current beamformer and IRS phase settings). In each round, unmatched users propose to their most‑preferred IRS; each IRS tentatively accepts the proposal with the highest utility and rejects the rest. The process repeats until all users are matched, guaranteeing a stable matching that satisfies the binary constraints. The algorithm runs in O(K·L) time.

Simulation parameters reflect a realistic 6G scenario: N = 64 AP antennas, M = 256 IRS elements per surface, K = 20 users, and L = 5 IRSs (four terrestrial, one aerial). Path loss follows distance‑based models appropriate for FR3, and Rayleigh fading is added. The authors compare their Joint Beamforming and User Association (JBUA) scheme against three baselines: exhaustive search (ES), greedy search (GS), and random search (RS).

Key findings include:

• Performance: JBUA achieves sum‑rate within 2–3 % of the exhaustive‑search optimum, while outperforming GS and RS by 15–25 % across a range of transmit powers.
• Complexity: The exhaustive search’s complexity grows exponentially with K and L, making it infeasible for realistic network sizes. JBUA’s combined ZF + DA approach remains polynomial, with execution times on the order of tens of milliseconds, suitable for real‑time network control.
• AIRS benefit: Introducing a single aerial IRS yields noticeable gains for users whose direct ground paths are heavily blocked, increasing their individual rates by up to 30 % compared to a TIRS‑only deployment.

The paper acknowledges several limitations. First, the assumption of completely blocked direct links may be overly pessimistic; partial LoS could alter the optimal association. Second, ZF ignores noise amplification; alternative precoders such as MMSE or regularized ZF could improve robustness in low‑SNR regimes. Third, the aerial IRS is modeled as static; dynamic altitude control, mobility, and energy consumption are not addressed. Finally, hardware imperfections (phase‑shift quantization, element coupling) are omitted, which could affect real‑world performance.

Despite these caveats, the work makes a substantial contribution by (i) being the first to study dual‑tier IRS operation in the FR3 “golden band,” (ii) formulating a rigorous MINLP that captures both beamforming and matching, (iii) providing a provably stable, low‑complexity solution, and (iv) demonstrating through extensive simulations that the approach is near‑optimal and scalable. The insights are directly relevant to 6G standardization efforts, especially for dense urban deployments where a combination of terrestrial and aerial reconfigurable surfaces can dramatically improve coverage reliability without the cost and power penalties of massive MIMO arrays.