Optimal Transmit Antenna Deployment and Power Allocation for Wireless Power Supply in an Indoor Space

TL;DR

This work addresses reliable indoor wireless power transfer to an arbitrary number of mobile, single-antenna receivers with unknown locations by formulating a max-min optimization over a ceiling-mounted transmit aperture. It proves that the optimal transmit power support is nowhere dense with Lebesgue measure zero, implying a discrete antenna array suffices and that continuous HMIMO apertures are unnecessary for this WPT task. The authors show analytically that, in one dimension, the optimal number of radiating elements is finite, and they validate these findings via discretisation, heatmaps, and performance comparisons to far-field and uniform deployments. The results demonstrate significant gains over benchmarks, with robustness to small-scale fading, and provide practical guidance on how to deploy a finite, often small, number of transmit antennas for reliable indoor power delivery. Applications include powering battery-free IoT wearables and sensors in indoor environments, with implications for the design of future mmWave indoor WPT systems.

Abstract

As Internet of Things (IoT) devices proliferate, sustainable methods for powering them are becoming indispensable. The wireless provision of power enables battery-free operation and is crucial for complying with weight and size restrictions. For the energy harvesting (EH) components of these devices to be small, a high operating frequency is necessary. In conjunction with a large transmit antenna, the receivers may be located in the radiating near-field (Fresnel) region, e.g., in indoor scenarios. In this paper, we propose a wireless power transfer (WPT) system ensuring reliable supply of power to an arbitrary number of mobile, low-power, and single-antenna receivers, whose locations in a three-dimensional cuboid room are unknown. A max-min optimisation problem is formulated to determine the optimal transmit power distribution. We rigorously prove that the optimal transmit power distribution's support has a lower dimensionality than its domain and thus, the employment of a continuous aperture antenna, utilised in Holographic MIMO (HMIMO), is unnecessary in the context of the considered WPT problem. Indeed, deploying a discrete transmit antenna architecture, i.e., a transmit antenna array, is sufficient and our proposed solution provides the optimal transmit antenna deployment and power allocation. Moreover, for a one-dimensional transmit antenna architecture, a finite number of transmit antennas is proven to be optimal. The proposed optimal solution is validated through computer simulations. Our simulation results indicate that the optimal transmit antenna architecture requires a finite number of transmit antennas and depends on the geometry of the environment and the dimensionality of the transmit antenna array.

Figures (5)

• Figure 1: Illustration of a three-dimensional environment with a two-dimensional transmit antenna architecture consisting of a continuum of infinitesimally small radiating elements located in a subsection of the $x$-$z$ plane (orange). The LoS connections of the transmit antenna elements to one receiver (RX) are indicated in orange.
• Figure 2: Absolute value of relative difference between objective values in percent for increasing $N$ for the height-to-width ratios defined in Table \ref{['tab: Considered Environments']}.
• Figure 3: Optimal number of transmit antennas, i.e., number of positions where non-zero powers are allocated by the optimal distribution, for increasing $N$ for the height-to-width ratios given in Table \ref{['tab: Considered Environments']}.
• Figure 4: Heatmaps of optimal power distributions for the height-to-width ratios listed in Table \ref{['tab: Considered Environments']} with $N+1=81$. Each heading indicates the height-to-width ratio from Table \ref{['tab: Considered Environments']}, the dimensionality of the transmit antenna array, and the number of non-zeros of $p^*(a_{ix},a_{iz})$ in brackets, i.e, the optimal number of transmit antennas. The relative amount of power allocated to an antenna is colour-coded according to the colour bar at the bottom. The antennas are partly magnified to aid visualising the solution. The colours of the unmagnified antennas follow from the symmetry of the optimal solution discussed in Section \ref{['section: Methods']}.
• Figure 5: Minimum received power at the worst location in the environment and loss of the benchmark schemes and suboptimal schemes compared to proposed optimal deployment and power allocation. The height is fixed at $2$ m.

Theorems & Definitions (11)

• Lemma 1
• Lemma 2
• Proposition 1
• Corollary 1
• Definition 1: see Dytso2018
• Proposition 2
• Proposition 3
• Proposition 4
• Lemma C.1
• proof