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MSE-Based Training and Transmission Optimization for MIMO ISAC Systems

Zhenyao He, Wei Xu, Hong Shen, Yonina C. Eldar, Xiaohu You

TL;DR

This work addresses joint training and transmission design for MIMO ISAC systems by formulating weighted MSE minimization objectives for both data communication and radar TRM estimation. It develops two main schemes: a sequential design using instantaneous CSI feedback and a joint design based on channel statistics, each optimized via majorization-minimization, semidefinite programming, geometric programming, and alternating optimization. The authors provide structured solutions under special cases and extend the framework to MI-based design, accompanied by extensive simulations showing radar performance gains and clear communication-sensing tradeoffs. The results demonstrate that leveraging training signals for sensing, together with robust and statistics-based designs, yields significant improvements in radar accuracy while maintaining competitive communication performance, with practical low-cost options for real-world deployments.

Abstract

In this paper, we investigate a multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) system under typical block-fading channels. As a non-trivial extension to most existing works on ISAC, both the training and transmission signals sent by the ISAC transmitter are exploited for sensing. Specifically, we develop two training and transmission design schemes to minimize a weighted sum of the mean-squared errors (MSEs) of data transmission and radar target response matrix (TRM) estimation. For the former, we first optimize the training signal for simultaneous communication channel and radar TRM estimation. Then, based on the estimated instantaneous channel state information (CSI), we propose an efficient majorization-minimization (MM)-based robust ISAC transmission design, where a semi-closed form solution is obtained in each iteration. For the second scheme, the ISAC transmitter is assumed to have statistical CSI only for reducing the feedback overhead. With CSI statistics available, we integrate the training and transmission design into one single problem and propose an MM-based alternating algorithm to find a high-quality solution. In addition, we provide alternative structured and low-complexity solutions for both schemes under certain special cases. Finally, simulation results demonstrate that the radar performance is significantly improved compared to the existing scheme that integrates sensing into the transmission stage only. Moreover, it is verified that the investigated two schemes have advantages in terms of communication and sensing performances, respectively.

MSE-Based Training and Transmission Optimization for MIMO ISAC Systems

TL;DR

This work addresses joint training and transmission design for MIMO ISAC systems by formulating weighted MSE minimization objectives for both data communication and radar TRM estimation. It develops two main schemes: a sequential design using instantaneous CSI feedback and a joint design based on channel statistics, each optimized via majorization-minimization, semidefinite programming, geometric programming, and alternating optimization. The authors provide structured solutions under special cases and extend the framework to MI-based design, accompanied by extensive simulations showing radar performance gains and clear communication-sensing tradeoffs. The results demonstrate that leveraging training signals for sensing, together with robust and statistics-based designs, yields significant improvements in radar accuracy while maintaining competitive communication performance, with practical low-cost options for real-world deployments.

Abstract

In this paper, we investigate a multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) system under typical block-fading channels. As a non-trivial extension to most existing works on ISAC, both the training and transmission signals sent by the ISAC transmitter are exploited for sensing. Specifically, we develop two training and transmission design schemes to minimize a weighted sum of the mean-squared errors (MSEs) of data transmission and radar target response matrix (TRM) estimation. For the former, we first optimize the training signal for simultaneous communication channel and radar TRM estimation. Then, based on the estimated instantaneous channel state information (CSI), we propose an efficient majorization-minimization (MM)-based robust ISAC transmission design, where a semi-closed form solution is obtained in each iteration. For the second scheme, the ISAC transmitter is assumed to have statistical CSI only for reducing the feedback overhead. With CSI statistics available, we integrate the training and transmission design into one single problem and propose an MM-based alternating algorithm to find a high-quality solution. In addition, we provide alternative structured and low-complexity solutions for both schemes under certain special cases. Finally, simulation results demonstrate that the radar performance is significantly improved compared to the existing scheme that integrates sensing into the transmission stage only. Moreover, it is verified that the investigated two schemes have advantages in terms of communication and sensing performances, respectively.
Paper Structure (33 sections, 6 theorems, 59 equations, 8 figures, 3 tables, 3 algorithms)

This paper contains 33 sections, 6 theorems, 59 equations, 8 figures, 3 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. Communication Model
  4. Channel Estimation
  5. Data Transmission With Instantaneous CSI Feedback
  6. Data Transmission With Statistical CSI Feedback
  7. Sensing Model
  8. Sequential Design With Instantaneous CSI Feedback
  9. Problem Formulation
  10. Solution for ISAC Training
  11. Solution for ISAC Robust Transmission
  12. Joint Training and Transmission Design
  13. Problem Formulation
  14. Optimization With Respect to the Training Signal
  15. Optimization With Respect to the Transmit Beamforming
  16. ...and 18 more sections

Key Result

Proposition 1

For $(\mathcal{P}_2)$, a surrogate problem used in each iteration of the MM algorithm is given by where the calculations of $\mathbf \Psi \succeq \mathbf 0$, $\lambda > 0$, and $\mathbf \Pi$ are based on the solution of $\mathbf W$ obtained in the previous iteration and their specific definitions are shown in (def:Psi), (def:lambda), and (def:Pi), respectively, in Appendix proof:MM_P2.

Figures (8)

  • Figure 1: Diagram of the considered MIMO ISAC system.
  • Figure 2: Frame structure over a channel fading block: (a) communication system; (b) considered ISAC system.
  • Figure 3: Objective value versus computing time for Algorithms 2 and 3.
  • Figure 4: Accurate and approximated sensing MSEs comparison versus the length of data symbol $L^\text{DT}$.
  • Figure 5: MSE performances versus $\gamma^\text{DT}$ with instantaneous CSI feedback.
  • ...and 3 more figures

Theorems & Definitions (6)

  • Proposition 1
  • Theorem 1
  • Proposition 2
  • Proposition 3
  • Theorem 2
  • Lemma 1: M.BigueshTSP2006Training-based