DMA-Aided MU-MISO Systems for Power Splitting SWIPT via Lorentzian-Constrained Holography

Technical Summary: DMA-Assisted MU-MISO Systems for Power-Splitting SWIPT via Lorentzian-Constrained Holography

Problem Statement
This contribution addresses the design of a co-located system for simultaneous wireless information and power transfer (SWIPT) within a downlink architecture for Multi-User Multiple-Input Single-Output (MISO). The system employs Dynamic Metasurface Antennas (DMAs), a class of holographic MIMO systems, to serve multiple users who simultaneously require a Signal-to-Interference-plus-Noise Ratio (SINR) for information decoding (ID) and a minimum amount of harvested energy (EH).

The central challenge lies in the joint optimization of three coupled variables: digital precoding vectors, DMA weight matrices, and Power-Splitting (PS) ratios. In contrast to traditional beamforming, DMA weights are subject to Lorentzian-constrained conditions, where the amplitude and phase of each metasurface element are intrinsically coupled (corresponding to a specific sinusoidal relationship). This constraint, combined with the non-convex nature of the PS-SWIPT problem and the inclusion of practical nonlinear energy harvesting models, makes the transmit power minimization problem difficult to solve directly.

Methodology
The authors propose a unified optimization framework based on Alternating Optimization and Semidefinite Programming (SDP). The solution is executed in two main phases within an iterative algorithm:

1. Optimization of the Digital Precoder and PS Ratio: With fixed DMA weights, the problem is reformulated as a convex SDP. By relaxing the rank-one condition for the beamforming matrices, the optimal digital precoders and power-splitting ratios are efficiently determined using standard solvers (e.g., CVX).
2. Optimization of the DMA Weights: With fixed precoders and PS ratios, the problem is transformed into a tractable SDP to find ideal, unconstrained beamforming weights. These ideal weights are subsequently projected onto the feasible Lorentzian-constrained set.
   • The contribution integrates several Lorentzian-Constrained Holographic (LCH) mapping schemes to handle the projection, including Phase Holography (LCPH), Unitary Shift Holography (LCUSH), and Amplitude-Only Holography (AOH).
   • Crucially, the integration of the recently proposed Adaptive-Radius LCH (ARLCH) scheme is highlighted. Unlike traditional methods that map solutions onto a fixed unitary Lorentzian circle, ARLCH dynamically optimizes the projection diameter. This enables a better amplitude-phase trade-off and minimizes the discrepancy between the ideal unconstrained weights and the physically realizable Lorentzian weights.

The algorithm alternates between these two steps until convergence is achieved, ensuring monotonically non-increasing transmit power. The framework also integrates both linear and nonlinear (logistic) energy harvesting models to evaluate the impact of rectifier saturation and noise.

Main Contributions

• Unified Framework: The contribution formulates a transmit power minimization problem for DMA-assisted PS-SWIPT under simultaneous SINR and EH constraints and provides a tractable, SDP-based benchmark.
• First Joint Optimization: To the authors' knowledge, this is the first work addressing the joint realization of DMA weights, digital precoding, and power-splitting design specifically for co-located SWIPT users (where each user performs both ID and EH), a scenario distinct from prior works focusing on separated users.
• Integration of ARLCH: The study systematically evaluates multiple LCH mapping strategies in the SWIPT context and integrates the ARLCH scheme to improve the amplitude-phase trade-off and reduce projection losses.
• Practical Modeling: In contrast to existing studies, the formulation explicitly includes practical nonlinear energy harvesting models and investigates their impact on beamforming performance and energy efficiency.

Numerical Results
Simulation results conducted under near-field line-of-sight conditions with spherical wavefront modeling demonstrate the following:

• Energy Efficiency: The proposed ARLCH-based approach achieves significant transmit power reductions compared to baseline LCH schemes (LCPH, LCUSH, AOH) and fixed power-splitting methods.
• Nonlinear Impact: The results underscore that nonlinear EH models significantly influence the required transmit power. Specifically, higher charging rates in the nonlinear model lead to lower power requirements, and the proposed method accurately captures this saturation behavior.
• Optimal Power-Splitting: Optimal Power-Splitting (OPS) proves critical; fixed or equal power-splitting strategies lead to degraded performance, particularly under varying channel conditions and hardware noise levels.
• LCH Comparison: Among the mapping schemes, ARLCH outperforms the others through adaptive balancing of amplitude-phase relationships, while AOH fails due to poor phase alignment, and LCPH suffers from too many elements being deactivated.

Significance and Claims
The contribution claims that the proposed framework effectively bridges the gap between the hardware simplicity of DMAs and the complex requirements of future SWIPT systems. By leveraging the ARLCH scheme within a unified SDP framework, the system can overcome the intrinsic limitations of Lorentzian constraints (amplitude-phase coupling) without requiring the high number of RF chains found in fully digital architectures.

The authors emphasize that while the SDP-based approach entails higher computational complexity than manifold-based or ADMM methods, it provides a necessary unified benchmark for fair comparison of various LCH strategies and enables the evaluation of practical nonlinear constraints. The work positions DMA-assisted SWIPT as a viable, energy-efficient architecture for low-power wireless networks and 6G use cases, provided that the specific challenges of Lorentzian mapping and the optimization of co-located users are addressed via the proposed alternating optimization strategy.