Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Integrated Sensing and Communication Exploiting Prior Information: How Many Sensing Beams are Needed?

Chan Xu, Shuowen Zhang

TL;DR

This work addresses ISAC beamforming when the target angle is unknown but has a known prior by introducing a periodic PCRB for the mean-cyclic error and using SDR to jointly design communication and sensing beams. The proposed approach reveals that enhancing sensing flexibility with dedicated sensing beams trades off against communication performance, and it proves that at most one dedicated sensing beam is needed. The main contributions are the periodic PCRB derivation, the SDR-based optimal transmit design, and the analytical proof of the single-sensing-beam requirement in the mid-rate regime, all validated by numerical results. The findings provide practical guidelines for ISAC system design under probabilistic target information, enabling efficient joint sensing and communication with guaranteed performance bounds.

Abstract

This paper studies an integrated sensing and communication (ISAC) system where a multi-antenna base station (BS) aims to communicate with a single-antenna user in the downlink and sense the unknown and random angle parameter of a target via exploiting its prior distribution information. We consider a general transmit beamforming structure where the BS sends one communication beam and potentially one or multiple dedicated sensing beam(s). Firstly, motivated by the periodic feature of the angle parameter, we derive the periodic posterior Cramér-Rao bound (PCRB) for quantifying a lower bound of the mean-cyclic error (MCE), which is more accurate than the conventional PCRB for bounding the mean-squared error (MSE). Then, note that more sensing beams enable higher flexibility in enhancing the sensing performance, while also generating extra interference to the communication user. To resolve this trade-off, we formulate the transmit beamforming optimization problem to minimize the periodic PCRB subject to a communication rate requirement for the user. Despite the non-convexity of this problem, we derive the optimal solution by leveraging the semi-definite relaxation (SDR) technique and Lagrange duality theory. Moreover, we analytically prove that at most one dedicated sensing beam is needed. Numerical results validate our analysis and the advantage of having a dedicated sensing beam.

Integrated Sensing and Communication Exploiting Prior Information: How Many Sensing Beams are Needed?

TL;DR

This work addresses ISAC beamforming when the target angle is unknown but has a known prior by introducing a periodic PCRB for the mean-cyclic error and using SDR to jointly design communication and sensing beams. The proposed approach reveals that enhancing sensing flexibility with dedicated sensing beams trades off against communication performance, and it proves that at most one dedicated sensing beam is needed. The main contributions are the periodic PCRB derivation, the SDR-based optimal transmit design, and the analytical proof of the single-sensing-beam requirement in the mid-rate regime, all validated by numerical results. The findings provide practical guidelines for ISAC system design under probabilistic target information, enabling efficient joint sensing and communication with guaranteed performance bounds.

Abstract

This paper studies an integrated sensing and communication (ISAC) system where a multi-antenna base station (BS) aims to communicate with a single-antenna user in the downlink and sense the unknown and random angle parameter of a target via exploiting its prior distribution information. We consider a general transmit beamforming structure where the BS sends one communication beam and potentially one or multiple dedicated sensing beam(s). Firstly, motivated by the periodic feature of the angle parameter, we derive the periodic posterior Cramér-Rao bound (PCRB) for quantifying a lower bound of the mean-cyclic error (MCE), which is more accurate than the conventional PCRB for bounding the mean-squared error (MSE). Then, note that more sensing beams enable higher flexibility in enhancing the sensing performance, while also generating extra interference to the communication user. To resolve this trade-off, we formulate the transmit beamforming optimization problem to minimize the periodic PCRB subject to a communication rate requirement for the user. Despite the non-convexity of this problem, we derive the optimal solution by leveraging the semi-definite relaxation (SDR) technique and Lagrange duality theory. Moreover, we analytically prove that at most one dedicated sensing beam is needed. Numerical results validate our analysis and the advantage of having a dedicated sensing beam.
Paper Structure (14 sections, 2 theorems, 33 equations, 2 figures)

This paper contains 14 sections, 2 theorems, 33 equations, 2 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Communication Model and Performance
  4. Sensing Model
  5. Sensing Performance Characterization Based on Periodic PCRB
  6. Problem Formulation
  7. Optimal Solution to Problem (P1)
  8. Problem Transformation
  9. Properties of the Optimal Solution to Problem (P2-R)
  10. Summary of the Optimal Solution to Problem (P1)
  11. Numerical Results
  12. Conclusions
  13. Proof of Proposition \ref{['prop_PCRB']}
  14. Proof of Proposition \ref{['prop_case3']}

Key Result

Proposition 1

The periodic PCRB for the MCE in estimating $\theta$ is given by where $\hat{p}_\Theta(\theta) = {p}_\Theta(\theta-2\pi\lfloor\frac{\theta+\pi}{2\pi}\rfloor),\theta\in \mathbb{R}$, $\bm{A}_1\!\!=\!\! \int_{-\pi}^\pi \!\left(\!\|\dot{\bm{b}}(\phi,\!\theta)\|^2\bm{a}(\phi,\!\theta)\bm{a}^H\!(\phi,\!\theta)\!+\!N_r\dot{\bm{a}}(\phi,\!\theta)\dot{\bm{a}}^H\!(\phi,\!

Figures (2)

  • Figure 1: Illustration of an ISAC system with dedicated sensing beam(s) for sensing the unknown and random angle parameter of a target.
  • Figure 2: Sensing periodic PCRB versus communication rate target.

Theorems & Definitions (3)

  • Proposition 1
  • Remark 1
  • Proposition 2