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Hybrid Radar Fusion with Quantization: CRB-Rate Trade-offs and ADC Dynamic Range

Akhileswar Chowdary, Ahmad Bazzi, Marwa Chafii

TL;DR

This work addresses how finite-resolution ADCs and their dynamic range constrain hybrid radar fusion (HRF) in uplink scenarios where direct and reflected paths share the same band. It develops a quantized CRB framework for AoA estimation and derives a lower bound on the FIM via the Bussgang decomposition, complemented by a low-SNR simplification, and proposes two optimization problems to map the CRB-rate boundary under ADC DR constraints. Through convex-relaxation-based solutions and extensive simulations, it demonstrates that HRF performance improves with higher ADC resolution but experiences diminishing returns in uplink rate beyond a certain point, while excessive dynamic range can render HRF infeasible. The results offer practical insights for selecting ADC resolution and beamforming strategies in HRF-enabled ISAC systems, guiding hardware design and signaling strategies to balance sensing accuracy and uplink throughput.

Abstract

Recent advancements have underscored the relevance of low-resolution analog-to-digital converters (ADCs) in integrated sensing and communication (ISAC) systems. Nevertheless, their specific impact on hybrid radar fusion (HRF) remains largely unexplored. In HRF systems, where uplink (UL) paths carry direct and reflected signals in the same frequency band, the reflected signal is often significantly weaker, making HRF performance particularly sensitive to ADC resolution. To study this effect, we use the quantized Cramér-Rao bound (CRB) to measure sensing accuracy. This work derives an upper bound on the quantized CRB for angle of arrival (AoA) estimation and explores CRB-rate trade-offs through two formulated optimization problems. Simulation results indicate that HRF becomes infeasible when the dynamic range of the received signal exceeds the dynamic range supported by the ADC, which is inherently limited by its resolution. Furthermore, the UL communication rate does not increase significantly when the ADC resolution is raised beyond a certain threshold. These observations highlight a fundamental trade-off between sensing and communication performance: while HRF performance benefits from higher ADC resolutions, the corresponding gains in communication rate plateau. This trade-off is effectively characterized using CRB-rate boundaries derived through simulation.

Hybrid Radar Fusion with Quantization: CRB-Rate Trade-offs and ADC Dynamic Range

TL;DR

This work addresses how finite-resolution ADCs and their dynamic range constrain hybrid radar fusion (HRF) in uplink scenarios where direct and reflected paths share the same band. It develops a quantized CRB framework for AoA estimation and derives a lower bound on the FIM via the Bussgang decomposition, complemented by a low-SNR simplification, and proposes two optimization problems to map the CRB-rate boundary under ADC DR constraints. Through convex-relaxation-based solutions and extensive simulations, it demonstrates that HRF performance improves with higher ADC resolution but experiences diminishing returns in uplink rate beyond a certain point, while excessive dynamic range can render HRF infeasible. The results offer practical insights for selecting ADC resolution and beamforming strategies in HRF-enabled ISAC systems, guiding hardware design and signaling strategies to balance sensing accuracy and uplink throughput.

Abstract

Recent advancements have underscored the relevance of low-resolution analog-to-digital converters (ADCs) in integrated sensing and communication (ISAC) systems. Nevertheless, their specific impact on hybrid radar fusion (HRF) remains largely unexplored. In HRF systems, where uplink (UL) paths carry direct and reflected signals in the same frequency band, the reflected signal is often significantly weaker, making HRF performance particularly sensitive to ADC resolution. To study this effect, we use the quantized Cramér-Rao bound (CRB) to measure sensing accuracy. This work derives an upper bound on the quantized CRB for angle of arrival (AoA) estimation and explores CRB-rate trade-offs through two formulated optimization problems. Simulation results indicate that HRF becomes infeasible when the dynamic range of the received signal exceeds the dynamic range supported by the ADC, which is inherently limited by its resolution. Furthermore, the UL communication rate does not increase significantly when the ADC resolution is raised beyond a certain threshold. These observations highlight a fundamental trade-off between sensing and communication performance: while HRF performance benefits from higher ADC resolutions, the corresponding gains in communication rate plateau. This trade-off is effectively characterized using CRB-rate boundaries derived through simulation.
Paper Structure (13 sections, 23 equations, 4 figures)

This paper contains 13 sections, 23 equations, 4 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Quantized CRB and lower bound on FIM
  4. Lower Bound on Rate and 1-bit Quantization
  5. Optimization framework for CRB-UL Rate trade-off characterization
  6. Sensing-Centric Design
  7. Communication-Centric Design
  8. Lower bound on FIM of AoA and Numerical Results
  9. Numerical Results
  10. CRB-Rate Trade-off with ADC DR
  11. Impact of Target Distance on CRB-Rate Trade-off
  12. Minimum Bits for ADC
  13. Conclusion and Future Work

Figures (4)

  • Figure 1: HRF system consisting of a DFRC BS operating in monostatic mode, receiving echoes from $P$ radar targets, and uplink signals from $K$ users.
  • Figure 2: CRB vs UL rate for K = 1 and P = 1 varying the ADC resolution and fixing the user and target at a distance of 100 m from the DFRC BS.
  • Figure 3: CRB vs. UL rate for K = 1 and P = 1, fixing the user and varying the distance of the target from the DFRC BS.
  • Figure 4: DR of the UL signal vs. the minimum required ADC resolution to differentiate the reflection and the direct path for K = 1 and P = 1.