Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Optimal Transmit Beamforming for MIMO ISAC with Unknown Target and User Locations

Yizhuo Wang, Shuowen Zhang

TL;DR

This work tackles the problem of designing transmit beamforming for MIMO ISAC when both target and user locations are unknown but described by PDFs. It develops a PCRB-based framework to quantify sensing accuracy and couples it with an expected-rate constraint to optimize the transmit covariance $\mathbf{W}$, deriving a rank bound $\mathrm{rank}(\mathbf{W}^*) \le \sum_{k=1}^K \mathrm{rank}(\mathbf{H}(\theta_{\mathrm{U},k}))$ and proving that a static beamforming strategy is optimal. The paper extends to temporal flexibility and shows that time-varying covariances do not improve average performance under the rate constraint, while numerical results confirm that ISAC performance improves as target and user location PDFs become more similar and that distribution-aware association strategies can further enhance network performance. Overall, the PCRB-based design provides practical guidance for joint sensing and communication resource allocation and BS association in realistic ISAC deployments.

Abstract

This paper studies a challenging scenario in a multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) system where the locations of the sensing target and the communication user are both unknown and random, while only their probability distribution information is known. In this case, how to fully utilize the spatial resources by designing the transmit beamforming such that both sensing and communication can achieve satisfactory performance statistically is a difficult problem, which motivates the study in this paper. Moreover, we aim to reveal if it is desirable to have similar probability distributions for the target and user locations in terms of the ISAC performance. Firstly, based on only probability distribution information, we establish communication and sensing performance metrics via deriving the expected rate or posterior Cramér-Rao bound (PCRB). Then, we formulate the transmit beamforming optimization problem to minimize the PCRB subject to the expected rate constraint, for which the optimal solution is derived. It is unveiled that the rank of the optimal transmit covariance matrix is upper bounded by the summation of MIMO communication channel matrices for all possible user locations. Furthermore, due to the need to cater to multiple target/user locations, we investigate whether dynamically employing different beamforming designs over different time slots improves the performance. It is proven that using a static beamforming strategy is sufficient for achieving the optimal performance. Numerical results validate our analysis, show that ISAC performance improves as the target/user location distributions become similar, and provide useful insights on the BS-user/-target association strategy.

Optimal Transmit Beamforming for MIMO ISAC with Unknown Target and User Locations

TL;DR

This work tackles the problem of designing transmit beamforming for MIMO ISAC when both target and user locations are unknown but described by PDFs. It develops a PCRB-based framework to quantify sensing accuracy and couples it with an expected-rate constraint to optimize the transmit covariance , deriving a rank bound and proving that a static beamforming strategy is optimal. The paper extends to temporal flexibility and shows that time-varying covariances do not improve average performance under the rate constraint, while numerical results confirm that ISAC performance improves as target and user location PDFs become more similar and that distribution-aware association strategies can further enhance network performance. Overall, the PCRB-based design provides practical guidance for joint sensing and communication resource allocation and BS association in realistic ISAC deployments.

Abstract

This paper studies a challenging scenario in a multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) system where the locations of the sensing target and the communication user are both unknown and random, while only their probability distribution information is known. In this case, how to fully utilize the spatial resources by designing the transmit beamforming such that both sensing and communication can achieve satisfactory performance statistically is a difficult problem, which motivates the study in this paper. Moreover, we aim to reveal if it is desirable to have similar probability distributions for the target and user locations in terms of the ISAC performance. Firstly, based on only probability distribution information, we establish communication and sensing performance metrics via deriving the expected rate or posterior Cramér-Rao bound (PCRB). Then, we formulate the transmit beamforming optimization problem to minimize the PCRB subject to the expected rate constraint, for which the optimal solution is derived. It is unveiled that the rank of the optimal transmit covariance matrix is upper bounded by the summation of MIMO communication channel matrices for all possible user locations. Furthermore, due to the need to cater to multiple target/user locations, we investigate whether dynamically employing different beamforming designs over different time slots improves the performance. It is proven that using a static beamforming strategy is sufficient for achieving the optimal performance. Numerical results validate our analysis, show that ISAC performance improves as the target/user location distributions become similar, and provide useful insights on the BS-user/-target association strategy.
Paper Structure (15 sections, 4 theorems, 12 equations, 5 figures)

This paper contains 15 sections, 4 theorems, 12 equations, 5 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Communication Model and Performance
  4. Sensing Model
  5. Characterization of Sensing Performance Exploiting Prior Information
  6. Transmit Beamforming Optimization with Unknown Target and User Locations
  7. Problem Formulation
  8. Optimal Solution Structure of Problem (P1)
  9. Case I: Inactive expected rate constraint
  10. Case II: Active expected rate constraint
  11. Impact of Temporal Flexibility
  12. System Model with Temporal Flexibility
  13. Beamforming Optimization with Temporal Flexibility for MIMO ISAC
  14. Numerical Results
  15. Conclusions

Key Result

Lemma 1

To guarantee a bounded optimal value of Problem (P1-I), $\mu^{\star}$ should satisfy $\mu^{\star}>\lambda_1$ with $\lambda_1$ denoting the largest eigenvalue of the matrix $\bm{A}_1$.

Figures (5)

  • Figure 1: A MIMO ISAC system with unknown target and user locations.
  • Figure 2: PCRB versus communication rate target.
  • Figure 3: MSE/PCRB versus KLD for Gaussian distribution.
  • Figure 4: PCRB versus KLD with/without temporal flexibility.
  • Figure 5: PCRB performance with different BS-user/-target association.

Theorems & Definitions (4)

  • Lemma 1
  • Proposition 1
  • Proposition 2
  • Proposition 3