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SPARK: Sparse Parametric Antenna Representation using Kernels

William Bjorndahl, Mark O'Hair, Ben Zoghi, Joseph Camp

TL;DR

SPARK introduces a training-free, hybrid representation for antenna and RIS radiation patterns that decomposes a pattern into a low-order global base and a handful of sparse localized lobes. By using a spherical-harmonic (or Fourier) base plus anisotropic Gaussian kernels, SPARK achieves large reductions in reconstruction error with far fewer parameters than dense pattern grids, enabling fast pattern evaluation and interpretable control. The method employs a robust four-stage fitting procedure with prominence-based center selection and joint alternating refinement to balance global and local components, and it demonstrates up to 2.8× (AERPAW) and 10.4× (RIS) MSE reductions, along with a 12.65% mean uplink goodput gain under a fixed budget. These results highlight SPARK’s potential to reduce CSI overhead while maintaining high-fidelity, hardware-aware beam management, and its applicability to open RAN ecosystems via compact, reusable pattern primitives.

Abstract

Channel state information (CSI) acquisition and feedback overhead grows with the number of antennas, users, and reported subbands. This growth becomes a bottleneck for many antenna and reconfigurable intelligent surface (RIS) systems as arrays and user densities scale. Practical CSI feedback and beam management rely on codebooks, where beams are selected via indices rather than explicitly transmitting radiation patterns. Hardware-aware operation requires an explicit representation of the measured antenna/RIS response, yet high-fidelity measured patterns are high-dimensional and costly to handle. We present SPARK (Sparse Parametric Antenna Representation using Kernels), a training-free compression model that decomposes patterns into a smooth global base and sparse localized lobes. For 3D patterns, SPARK uses low-order spherical harmonics for global directivity and anisotropic Gaussian kernels for localized features. For RIS 1D azimuth cuts, it uses a Fourier-series base with 1D Gaussians. On patterns from the AERPAW testbed and a public RIS dataset, SPARK achieves up to 2.8$\times$ and 10.4$\times$ reductions in reconstruction MSE over baselines, respectively. Simulation shows that amortizing a compact pattern description and reporting sparse path descriptors can produce 12.65% mean uplink goodput gain under a fixed uplink budget. Overall, SPARK turns dense patterns into compact, parametric models for scalable, hardware-aware beam management.

SPARK: Sparse Parametric Antenna Representation using Kernels

TL;DR

SPARK introduces a training-free, hybrid representation for antenna and RIS radiation patterns that decomposes a pattern into a low-order global base and a handful of sparse localized lobes. By using a spherical-harmonic (or Fourier) base plus anisotropic Gaussian kernels, SPARK achieves large reductions in reconstruction error with far fewer parameters than dense pattern grids, enabling fast pattern evaluation and interpretable control. The method employs a robust four-stage fitting procedure with prominence-based center selection and joint alternating refinement to balance global and local components, and it demonstrates up to 2.8× (AERPAW) and 10.4× (RIS) MSE reductions, along with a 12.65% mean uplink goodput gain under a fixed budget. These results highlight SPARK’s potential to reduce CSI overhead while maintaining high-fidelity, hardware-aware beam management, and its applicability to open RAN ecosystems via compact, reusable pattern primitives.

Abstract

Channel state information (CSI) acquisition and feedback overhead grows with the number of antennas, users, and reported subbands. This growth becomes a bottleneck for many antenna and reconfigurable intelligent surface (RIS) systems as arrays and user densities scale. Practical CSI feedback and beam management rely on codebooks, where beams are selected via indices rather than explicitly transmitting radiation patterns. Hardware-aware operation requires an explicit representation of the measured antenna/RIS response, yet high-fidelity measured patterns are high-dimensional and costly to handle. We present SPARK (Sparse Parametric Antenna Representation using Kernels), a training-free compression model that decomposes patterns into a smooth global base and sparse localized lobes. For 3D patterns, SPARK uses low-order spherical harmonics for global directivity and anisotropic Gaussian kernels for localized features. For RIS 1D azimuth cuts, it uses a Fourier-series base with 1D Gaussians. On patterns from the AERPAW testbed and a public RIS dataset, SPARK achieves up to 2.8 and 10.4 reductions in reconstruction MSE over baselines, respectively. Simulation shows that amortizing a compact pattern description and reporting sparse path descriptors can produce 12.65% mean uplink goodput gain under a fixed uplink budget. Overall, SPARK turns dense patterns into compact, parametric models for scalable, hardware-aware beam management.
Paper Structure (33 sections, 14 equations, 4 figures, 5 tables, 1 algorithm)

This paper contains 33 sections, 14 equations, 4 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Antenna Metrology and Global-Basis Pattern Models
  4. Localized and Sparse Directional Bases
  5. CSI Feedback Compression and Overhead Reduction
  6. RIS Modeling and Measurement-Driven Characterization
  7. Programmable RAN Context
  8. Hybrid Spherical Harmonic-Gaussian Model
  9. Theoretical Foundation
  10. Data Preprocessing and Normalization
  11. Antenna Pattern Structure
  12. Basis Selection
  13. Additive Model Rationale
  14. Hybrid Fitting Methodology
  15. Stage 1: Spherical Harmonic Base Fit
  16. ...and 18 more sections

Figures (4)

  • Figure 1: Conceptual illustration of SPARK. A measured radiation pattern is represented as the sum of a smooth global base (low-order spherical harmonics) and a sparse set of localized lobes (anisotropic Gaussian kernels) that capture sharp features.
  • Figure 2: Visual comparison for the SA-1400-5900 antenna at 3.5 GHz. The top row shows original measured pattern, SPARK (joint refinement), SH-only ($L_{\max}{=}5$), and sequential hybrid (no joint refinement). The bottom row shows the magnified sidelobe region. SPARK better preserves fine sidelobe structure compared to the ablated models.
  • Figure 3: Analysis of SPARK on a representative RIS pattern ($\theta_t{=}20^\circ$, configuration $0^\circ;-30^\circ$). (a) Component decomposition showing the reconstruction is expressed as a smooth global Fourier component plus localized Gaussian components. (b) Ablation study comparing low-order Fourier-only, sequential hybrid (no alternating refinement), and the proposed alternating refinement. (c) Absolute error for each model, showing the error reduction achieved by alternating refinement.
  • Figure 4: Uplink resource allocation showing the system-level benefit of SPARK. Stacked bars show the fraction of a fixed 10-slot uplink budget consumed by CSI feedback payload versus remaining data goodput for a 5G NR-style baseline and the SPARK-enabled scheme. At 50 users, SPARK reduces mean feedback from 11.00 kb to 7.21 kb (34.5%), corresponding to 2.69 vs. 1.76 uplink slots of overhead (0.93 slots saved), which translates to a 12.65% mean goodput gain.