Stacked Intelligent Metasurfaces Assisted UAV Communications

Technical Summary: Stacked Intelligent Metasurfaces Assisted UAV Communications

Problem Statement
Unmanned Aerial Vehicles (UAVs) offer flexible deployment and strong line-of-sight connectivity for next-generation wireless networks. However, implementing multi-user communications with large antenna arrays on UAVs is constrained by energy and payload limitations. Conventional fully digital beamforming requires numerous radio frequency (RF) chains, leading to prohibitive power consumption and hardware complexity. While Single-Layer Reconfigurable Intelligent Surfaces (RIS) have been proposed to reduce complexity, they offer limited degrees of freedom for wavefront shaping. Furthermore, existing literature on Stacked Intelligent Metasurfaces (SIMs) for UAVs is sparse; prior works either focus on uplink scenarios, omit digital precoding in hybrid architectures, or rely on data-driven solutions lacking analytical tractability for joint optimization of beamforming and UAV positioning.

Methodology
The paper proposes a unified framework for a downlink SIM-assisted multi-user UAV system. The architecture employs hybrid beamforming, where low-dimensional digital precoding is performed at the baseband, and analog wave-domain processing is handled by a SIM consisting of $L$ cascaded metasurface layers. The system aims to maximize the multi-user sum rate by jointly optimizing three coupled variables:

1. Digital Beamformer ($\mathbf{V}$): The precoding matrix at the base station.
2. SIM Phase Configuration ($\{\mathbf{\Phi}_l\}$): The transmission coefficients of the $L$ metasurface layers.
3. UAV 3D Position ($\mathbf{q}$): The spatial coordinates of the UAV.

To solve the resulting non-convex optimization problem, the authors develop an Alternating Optimization (AO) framework that guarantees monotonic improvement of the objective function:

• Digital Beamformer: For fixed SIM coefficients and UAV position, the digital beamformer is derived in closed form using Zero-Forcing (ZF) precoding based on the Moore–Penrose pseudoinverse of the effective channel.
• SIM Optimization: The authors utilize a Block Coordinate Descent (BCD) approach, optimizing one metasurface layer at a time. Within each layer, individual phase shifts are updated element-wise. By constructing a quadratic minorizing surrogate function based on Wirtinger calculus, the authors derive a closed-form update rule (Minorization-Maximization) that ensures the sum rate does not decrease with each iteration.
• UAV Positioning: For fixed beamforming and SIM configurations, the UAV position is refined using Projected Gradient Ascent (PGA). The authors analytically derive the gradients of the sum rate with respect to the UAV coordinates, accounting for the distance-dependent path loss and phase shifts in the LoS channel model.

Key Contributions

• System Model: The paper establishes a comprehensive system model for a hybrid SIM-assisted UAV downlink, incorporating Rayleigh-Sommerfeld diffraction theory to model signal propagation between cascaded metasurface layers and from the SIM to ground users.
• Algorithmic Framework: It introduces a tractable joint optimization algorithm that couples digital precoding, multi-layer SIM phase shifts, and 3D UAV placement. Unlike prior works, this framework analytically treats the hybrid multi-layer design without relying on black-box machine learning.
• Closed-Form Updates: The proposed algorithm provides closed-form solutions for the digital beamformer and SIM phase updates, reducing computational complexity compared to generic non-convex solvers.
• Convergence Analysis: The paper proves that the proposed algorithm generates a non-decreasing sequence of objective values that converges to a finite limit, with limit points satisfying blockwise first-order optimality conditions.

Numerical Results
Simulations demonstrate that the proposed SIM-assisted architecture significantly outperforms conventional single-layer RIS-based hybrid beamforming schemes. Key findings include:

• Power Efficiency: The performance gap between the proposed multi-layer SIM and the single-layer benchmark widens as transmit power ($P_{max}$) increases. The multi-layer SIM creates a better-conditioned effective channel, reducing the power penalty associated with ZF inversion.
• Layer Depth vs. Aperture Size: Increasing the number of metasurface layers ($L$) improves sum rate due to richer wave-domain processing, though gains eventually saturate. Conversely, increasing the number of meta-atoms per layer ($M$) yields continuous performance improvements due to enhanced array gain and spatial resolution.
• Design Trade-off: The results suggest that under a fixed budget of total meta-atoms, a design with a moderate number of layers combined with a sufficiently large aperture per layer is more effective than deep stacking with small apertures.

Significance and Claims
The paper claims to fill a critical gap in the literature by providing an analytically tractable framework for SIM-assisted hybrid UAV systems. It highlights that shifting beamforming functionality from the RF domain to the electromagnetic (wave) domain via stacked layers enables energy-efficient architectures suitable for aerial platforms. The authors assert that their proposed joint optimization of digital precoding, SIM configuration, and UAV positioning offers a practical pathway to realizing high-spectral-efficiency, low-complexity UAV communications for future networks. The work validates that multi-layer wave-domain processing offers tangible spectral efficiency gains over single-layer designs, particularly in scenarios requiring flexible 3D deployment.