Power Transfer between Two Antenna Arrays in the Near Field

TL;DR

This work analyzes power transfer between an active multi-antenna feeder (AMAF) and a reflective intelligent surface (RIS) in the near-field, focusing on the $F/D<1$ regime for array-fed arrays. The coupling is modeled by a complex matrix ${\mathbf{T}}$ with entries $T_{n,m} = \dfrac{\sqrt{E_A(\theta_{n,m})E_R(\phi_{n,m})}\;\exp(j\pi r_{n,m})}{2\pi r_{n,m}}$, and the system is analyzed via singular value decomposition ${\mathbf{T}}={\mathbf{U}}{\mathbf{S}}{\mathbf{V}}^{\sf H}$ to compare center-feed (${\mathbf{v}}_1$) and end-feed configurations. Key findings are: (i) in $F/D<1$, AMAF-RIS power transfer deviates from the inverse-square law due to taper, with $\sigma_1^2$ increasing by about 3 dB when $F$ halves; (ii) end-feed yields better beam shapes with non-eigenmodes than eigenmodes but center-feed still provides higher gain; (iii) the center-feed configuration achieves greater power transfer than end-feed, and the dominant dependence is on $F/D$ rather than RIS size, with the condition number of ${\mathbf{T}}$ remaining roughly constant for fixed $F/D$. These results guide design of near-field, array-fed reflectarrays/transmitarrays and illustrate a practical, SVD-based beamforming interpretation of the AMAF-RIS coupling.

Abstract

We present numerical results with a focus on power transfer between two standard linear antenna arrays placed in the near field, where a much smaller active multi-antenna feeder (AMAF) space feeds a far larger passive array referred to as a reflective intelligent surface (RIS). The interest is in the regime of focal length to diameter ratio ($F/D$) less than unity. We address the question of center feed vs. end feed for array fed array antenna architectures and present the following novel findings and contributions: 1. In the regime of $F/D$ ratio less than one, the AMAF-RIS power transfer deviates from the classical inverse square law. Furthermore, the behavior of the power transmission coefficient is more sensitive to the $F/D$ ratio than to a particular RIS size. 2. For an end feed, non-eigenmodes provide better beam shapes than the eigenmodes, which are still inferior to beam shapes from the center feed eigenmodes. 3. The center feed provides more power gain than an end feed. This clearly illustrates that the center feed configuration should be used for array fed arrays, in contrast to the classical parabolic geometry.

Figures (6)

• Figure 1: An Active Multi-Antenna Feeder (AMAF) center feeding a RISICC2023, in the $F/D<1$ regime. AMAF and RIS are $N_a$ and $N_p$ elements respectively, standard linear arraystrees in a 2D geometry for simplicity and better intuition.
• Figure 2: $\sigma_1^2/\sigma_4^2$ (dB) for different $F/D$ ratios and RIS sizes $N_p$.
• Figure 3: A tilted AMAF end feeding a RIS.
• Figure 4: AMAF Patterns. PEM refers to the principal eigenmode, i.e., when the AMAF is configured along ${\bf v}_1$. Non-PEM refers to AMAF configuration along $|{\bf v}_1|$.
• Figure 5: Magnitude profiles across RIS at $F=110$. PEM and Non-PEM refer to AMAF configurations ${\bf v}_1$ and $|{\bf v}_1|$, respectively.