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Implicit Neural Representation of Beamforming for Continuous Aperture Array Systems

Shiyong Chen, Jia Guo, Shengqian Han

Abstract

In this paper, a learning-based approach is proposed for optimizing downlink beamforming in multiple-input multiple-output (MIMO) systems that employ continuous aperture arrays (CAPAs) at both the base station (BS) and the user. Beamforming in such systems is a spatially continuous function that maps a coordinate on the CAPA to a corresponding beamforming weight. We first propose an implicit neural representation (INR), termed BeaINR, to parameterize this function directly. Further, noting that the optimal beamforming function can be expressed as a weighted integral of the channel response function, we propose a second INR, CoefINR, to represent the weighting coefficient function, which indirectly optimizes the beamforming function. Simulation results show that the proposed INR-based methods achieve comparable or higher spectral efficiency (SE) than the considered baselines, while requiring substantially lower inference latency. Moreover, CoefINR reduces training complexity and improves frequency generalizability relative to BeaINR by leveraging the optimal beamforming structure.

Implicit Neural Representation of Beamforming for Continuous Aperture Array Systems

Abstract

In this paper, a learning-based approach is proposed for optimizing downlink beamforming in multiple-input multiple-output (MIMO) systems that employ continuous aperture arrays (CAPAs) at both the base station (BS) and the user. Beamforming in such systems is a spatially continuous function that maps a coordinate on the CAPA to a corresponding beamforming weight. We first propose an implicit neural representation (INR), termed BeaINR, to parameterize this function directly. Further, noting that the optimal beamforming function can be expressed as a weighted integral of the channel response function, we propose a second INR, CoefINR, to represent the weighting coefficient function, which indirectly optimizes the beamforming function. Simulation results show that the proposed INR-based methods achieve comparable or higher spectral efficiency (SE) than the considered baselines, while requiring substantially lower inference latency. Moreover, CoefINR reduces training complexity and improves frequency generalizability relative to BeaINR by leveraging the optimal beamforming structure.

Paper Structure

This paper contains 11 sections, 1 theorem, 18 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. INR of Beamforming Function
  4. INR of Weighting Coefficient Function
  5. Simulation Results
  6. Simulation Setup
  7. Learning Performance
  8. Generalizability
  9. Inference and Training Complexity
  10. Quantization Effects
  11. Conclusions

Key Result

Proposition 1

The optimal beamforming function $\mathbf{w}(\mathbf{s})$ lies in the functional subspace spanned by the channel response function $\{ h(\mathbf{r}, \mathbf{s}) \}_{\mathbf{r}\in\mathcal{S}_\mathrm{U}}$. That is, $\mathbf{w}(\mathbf{s})$ can be represented as where $\mathbf{c}(\mathbf{r}) = [c_1(\mathbf{r}), \cdots, c_N(\mathbf{r})] \in \mathbb{C}^{1\times N}$ denotes a set of weighting coefficie

Figures (4)

  • Figure 1: Illustration of the downlink CAPA system.
  • Figure 2: Performance comparison under different constraints
  • Figure 3: SE versus user CAPA size.
  • Figure 4: SE versus quantization bits.

Theorems & Definitions (1)

  • Proposition 1