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1-bit Quantized Continuous Aperture Arrays

Kuranage Roche Rayan Ranasinghe, Getuar Rexhepi, Zhaolin Wang, Giuseppe Thadeu Freitas de Abreu

Abstract

Continuous aperture arrays (CAPAs) have emerged as a promising physical-layer paradigm for sixth generation (6G) systems, offering spatial degrees of freedom beyond those of conventional discrete antenna arrays. This paper investigates the interaction between the CAPA receive architecture and low-cost 1-bit analog-to-digital converters (ADCs), which impose a severe nonlinear distortion penalty in conventional discrete systems. For Rayleigh fading, we derive a moment matching approximation (MMA)-based closed-form symbol error probability (SEP) approximation based on Gamma moment-matching of the spatial eigenvalue distribution, and show that CAPAs incur a diversity-order penalty governed by Jensen's inequality on the mode eigenvalues. For line-of-sight (LoS) propagation, we prove that CAPA achieves exactly the unquantized additive white Gaussian noise (AWGN) performance bound under perfect spatial and phase alignment, completely eliminating the 1-bit penalty that forces discrete systems to double their antenna count. Monte Carlo simulations under Rayleigh, Rician, and LoS conditions validate all analytical results.

1-bit Quantized Continuous Aperture Arrays

Abstract

Continuous aperture arrays (CAPAs) have emerged as a promising physical-layer paradigm for sixth generation (6G) systems, offering spatial degrees of freedom beyond those of conventional discrete antenna arrays. This paper investigates the interaction between the CAPA receive architecture and low-cost 1-bit analog-to-digital converters (ADCs), which impose a severe nonlinear distortion penalty in conventional discrete systems. For Rayleigh fading, we derive a moment matching approximation (MMA)-based closed-form symbol error probability (SEP) approximation based on Gamma moment-matching of the spatial eigenvalue distribution, and show that CAPAs incur a diversity-order penalty governed by Jensen's inequality on the mode eigenvalues. For line-of-sight (LoS) propagation, we prove that CAPA achieves exactly the unquantized additive white Gaussian noise (AWGN) performance bound under perfect spatial and phase alignment, completely eliminating the 1-bit penalty that forces discrete systems to double their antenna count. Monte Carlo simulations under Rayleigh, Rician, and LoS conditions validate all analytical results.

Paper Structure

This paper contains 16 sections, 1 theorem, 18 equations, 1 figure.

Table of Contents

  1. Introduction
  2. System Model
  3. SIMO System Model
  4. CAPA System Model
  5. Channel Model
  6. Analog Beamforming and Detection
  7. SEP Analysis
  8. 1-bit Quantized SIMO Baseline
  9. 1-bit Quantized CAPA Analysis
  10. MMA-based Bounding for Rayleigh Channels
  11. Analytical Expression for Line-of-Sight
  12. Architectural Implications of the Analytical Results
  13. Performance Analysis
  14. Rayleigh Fading
  15. Rician Fading
  16. ...and 1 more sections

Key Result

Proposition 1

In a pure LoS environment ($K \to \infty$), assuming uniform plane-wave incidence at broadside -- where all antenna elements experience identical deterministic channel gains and zero relative phase shifts -- the exact SEP of the 1-bit quantized discrete SIMO architecture is where $P_{e,R} = \sum_{\ell=\lfloor\frac{N}{2}\rfloor + 1}^N \binom{N}{\ell} p_0^\ell (1-p_0)^{N-\ell} + \frac{1}{2} \mathbb

Figures (1)

  • Figure 1: Comparison of SEP for CAPA and SIMO systems under various channel conditions.

Theorems & Definitions (3)

  • Remark 1: Channel Energy Normalization
  • Remark 2: Spatial Decorrelation and Mode Variance
  • Proposition 1