Waveform & Beamforming Optimization

The results highlight fundamental efficiency trends in practical WPT operation: increasing the number of transmit tones consistently reduces power consumption by exploiting the rectifier's nonlinear response more effectively, allowing the transmitter to meet energy harvesting demands with lower RF power. Likewise, enlarging the DMA aperture improves performance by enabling sharper near-field focusing and stronger constructive combining at the rectenna, which translates into lower transmit-side energy expenditure. In contrast, serving more receivers and operating at larger TX–RX distances increases the required transmit power, reflecting the inherent tradeoff between coverage range, user density, and efficiency in multi-user WPT systems.

The above figures show the power consumption as a function of antenna length (left) and user distance (right) with a direct comparison between DMA-assisted and fully-digital transmitter architectures, which provides further system-level insights. The DMA consistently outperforms the fully-digital architecture in terms of power consumption across a wide range of configurations, demonstrating that reconfigurable metasurfaces can inherently deliver higher efficiency for near-field WPT when nonlinear harvesting is taken into account. The relative gain of DMA depends on the saturation power of the HPA, the number of served devices, and link distances, indicating that metasurface-assisted WPT becomes particularly advantageous under energy-constrained amplification and dense receiver deployments. Moreover, the simulations verify that the transmitter can precisely focus electromagnetic energy onto the target devices in the near-field region, whereas only directional beams are obtained in the far-field. This confirms the dual-regime behavior of DMA-based radiators and illustrates the importance of near-field spatial control for maximizing WPT efficiency. 

The findings demonstrate that practical waveform-beamforming co-design, combined with DMA hardware, enables substantial reductions in transmit power while satisfying multi-user energy harvesting requirements, offering a promising pathway toward highly efficient and scalable WPT deployments.

Overall, the findings highlight that BD-RIS can provide tangible WPT efficiency advantages under practical channels featuring NLoS components, and that multi-carrier operation and RIS scaling both contribute meaningfully to improving nonlinear energy harvesting efficiency, establishing BD-RIS as a promising architecture for future WPT deployments beyond conventional RIS designs. 

Moreover, power consumption increases with the number of RF chains for all technologies, except for FD. This trend confirms that adding more RF chains generally increases the PB's power demands as more HPAs are required.  The results for the hybrid architectures do not follow a steady increasing pattern. This behavior arises from a ceiling operation in the losses model for which losses remain unchanged over certain RF chain ranges, leading to reduced power consumption.

The right-hand figure above demonstrates how the geometry of the ITS-equipped PB influences the propagation conditions. In this scenario, a single-RF chain PB is utilized to charge one device. The full illumination strategy results in the central elements of the ITS receiving most of the impinging power, leading to a nonuniform power distribution across the surface. This effect becomes more pronounced as the feeder gets closer to the ITS, significantly reducing the power received by the edge elements. Consequently, the effective aperture of the PB is modified, causing the device to operate in either the near-field (b) or the far-field (d), depending on the feeder's position, even with the same physical aperture of the ITS.

Numerical results demonstrate that the proposed algorithms converge to suboptimal solutions. Moreover, simulation results show that power consumption rises with the number of users and RF chains. Notably, across all these scenarios, PSO outperforms DDPG, requiring lower overall system power consumption.

The above left-hand figure showcases the power consumption Pc as a function of DAC resolution nb for different numbers of tones K. Notably, there is an optimum nb, nb=4. PSO generally achieves lower power consumption across different combinations of DAC resolution and number of tones, owing to its ability to explore the global search space and effectively avoid local minima. In contrast, DDPG explores the solution space sequentially through learned state-action mappings, and relies on past and future experiences to improve its policy over time. While DDPG exhibits stable behavior and smooth trends, it underperforms in minimizing power consumption, likely due to challenges in policy convergence, exploration inefficiencies, and the complexity of high-dimensional action spaces. Moreover, in our simulations, DDPG consistently converged to suboptimal solutions across multiple runs, even with extensive hyperparameter tuning and long training durations. 

The above right-hand figure shows Pc versus the phase shifter resolution B for different number of antennas N. It can be noticed that higher phase shifter resolution for PSs and higher number of antennas enhances performance by offering more control over the transmitted signal's direction and shape, resulting in more harvested power with reduced power consumption. Additionally, it can be observed that the PSO algorithm performs better in terms of power consumption reduction compared to the DDPG algorithm. This indicates that PSO is more effective in optimizing power efficiency while managing the system's scalability.