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Fundamental Trade-offs in Quantized Hybrid Radar Fusion: A CRB-Rate Perspective

Akhileswar Chowdary, Ahmad Bazzi, Vaibhav Kumar, Roberto Bomfin, Marwa Chafii

TL;DR

The paper addresses the fundamental CRB–rate trade-off in quantized hybrid radar fusion (HRF) systems under finite-resolution ADCs. It derives a Bussgang-based lower bound on the Fisher information matrix $\widehat{\mathbf{G}}_{\boldsymbol{\psi}}$ and a tractable uplink rate expression $R_k$, enabling a quantized CRB–rate framework. It then characterizes the trade-off via two constrained optimizations (sensing-centric and communication-centric) solved by semidefinite relaxation, revealing how ADC dynamic range and resolution shape the Pareto boundary. The results provide design guidelines for ADC architectures and operating regimes in future HRF-enabled ISAC systems.

Abstract

Hybrid radar fusion (HRF), which combines monostatic and bistatic sensing in a common spectrum, offers enhanced spatial diversity, but is particularly vulnerable to quantization error effects due to the large power imbalance between the direct and reflected uplink signals. Although finite-resolution analog-to-digital converters (ADCs) have been considered in the existing literature on integrated sensing and communication (ISAC), their role in HRF architectures has not yet been characterized. This paper develops a finite-resolution quantized sensing-communication framework for HRF systems by deriving a Cramer-Rao bound (CRB) and achievable uplink rate. Tight lower bounds on the Fisher information matrix and the communication rate are obtained, enabling a tractable characterization of finite-resolution quantized HRF. The fundamental sensing-communication trade-off is then characterized through two complementary constrained formulations: CRB minimization subject to per-user uplink rate requirements, and sum-rate maximization subject to a CRB constraint, whose solutions trace the CRB-rate trade-offs in HRF. Numerical results reveal how ADC resolution, dynamic range, and system configuration jointly shape this boundary and show that HRF performance can degrade sharply under coarse quantization due to the weak bistatic component, providing design guidelines for selecting ADC architectures and operating regimes in future HRF-enabled ISAC systems.

Fundamental Trade-offs in Quantized Hybrid Radar Fusion: A CRB-Rate Perspective

TL;DR

The paper addresses the fundamental CRB–rate trade-off in quantized hybrid radar fusion (HRF) systems under finite-resolution ADCs. It derives a Bussgang-based lower bound on the Fisher information matrix and a tractable uplink rate expression , enabling a quantized CRB–rate framework. It then characterizes the trade-off via two constrained optimizations (sensing-centric and communication-centric) solved by semidefinite relaxation, revealing how ADC dynamic range and resolution shape the Pareto boundary. The results provide design guidelines for ADC architectures and operating regimes in future HRF-enabled ISAC systems.

Abstract

Hybrid radar fusion (HRF), which combines monostatic and bistatic sensing in a common spectrum, offers enhanced spatial diversity, but is particularly vulnerable to quantization error effects due to the large power imbalance between the direct and reflected uplink signals. Although finite-resolution analog-to-digital converters (ADCs) have been considered in the existing literature on integrated sensing and communication (ISAC), their role in HRF architectures has not yet been characterized. This paper develops a finite-resolution quantized sensing-communication framework for HRF systems by deriving a Cramer-Rao bound (CRB) and achievable uplink rate. Tight lower bounds on the Fisher information matrix and the communication rate are obtained, enabling a tractable characterization of finite-resolution quantized HRF. The fundamental sensing-communication trade-off is then characterized through two complementary constrained formulations: CRB minimization subject to per-user uplink rate requirements, and sum-rate maximization subject to a CRB constraint, whose solutions trace the CRB-rate trade-offs in HRF. Numerical results reveal how ADC resolution, dynamic range, and system configuration jointly shape this boundary and show that HRF performance can degrade sharply under coarse quantization due to the weak bistatic component, providing design guidelines for selecting ADC architectures and operating regimes in future HRF-enabled ISAC systems.

Paper Structure

This paper contains 25 sections, 1 theorem, 76 equations, 11 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Transmit Signal Model at DFRC BS
  4. Transmit Signal Model at UE
  5. Received Signal at DFRC BS
  6. DT Domain Received Signal Model
  7. Quantization and Performance Analysis
  8. Quantizer Model
  9. Achievable Sum Rate
  10. Lower Bound on the FIM of HRF
  11. ADC Dynamic Range
  12. Optimization Framework for CRB-UL Rate Trade-off Characterization
  13. Sensing-Centric Design
  14. Communication-Centric Design
  15. Computational Complexity
  16. ...and 10 more sections

Key Result

Proposition 1

$\mathbf{R}_{\Tilde{\mathbf{w}}_{\mathrm{q}}^{(\ell)}\Tilde{\mathbf{w}}_{\mathrm{q}}^{(\ell)}}[m]$ can be approximated as

Figures (11)

  • Figure 1: HRF system model consisting of a DFRC BS operating in monostatic mode, receiving echo from $P$ radar targets, and UL signals from $K$ UEs.
  • Figure 2: Illustration of the dependence of the resolvability of $x_{\mathrm{w}}$ in the presence of $x_{\mathrm{s}}$ on the ADC resolution.
  • Figure 3: The impact of the ADC DR given in \ref{['eq:bit_bound']} on the HRF system from the perspective of CRB-rate Pareto boundary obtained through \ref{['eq:P0_2']}.
  • Figure 4: The impact of the ADC DR given in \ref{['eq:bit_bound']} on the HRF system from the perspective of CRB-rate Pareto boundary obtained through \ref{['eq:P1_1']}.
  • Figure 5: CRB-rate trade-off computed using optimization problem in \ref{['eq:P0_2']} for three different receive antenna configurations.
  • ...and 6 more figures

Theorems & Definitions (2)

  • Proposition 1
  • Remark 1