Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Optimal ISAC Beamforming Structure and Efficient Algorithms for Sum Rate and CRLB Balancing

Tianyu Fang, Mengyuan Ma, Markku Juntti, Nir Shlezinger, A. Lee Swindlehurst, Nhan Thanh Nguyen

TL;DR

This work tackles the joint optimization of communications and sensing in ISAC by balancing sum rate and CRLB under a transmit power constraint. It introduces a two‑layer successive convex approximation (SCA) framework and derives an optimal beamforming structure (OBS) to reveal low‑dimensional, scalable solutions. A low‑dimensional reformulation further reduces the optimization variables, with convergence guarantees and rigorous complexity analysis. Numerical results show the proposed method achieves competitive SR/CRLB performance at much lower computational cost than SDR/FP baselines, and the OBS enables effective design regardless of large antenna counts. The approach offers practical pathways for deploying ISAC in large MIMO settings and provides a foundation for future extensions to RIS and near‑field configurations.

Abstract

Integrated sensing and communications (ISAC) has emerged as a promising paradigm to unify wireless communications and radar sensing, enabling efficient spectrum and hardware utilization. A core challenge with realizing the gains of ISAC stems from the unique challenges of dual purpose beamforming design due to the highly non-convex nature of key performance metrics such as sum rate for communications and the Cramer-Rao lower bound (CRLB) for sensing. In this paper, we propose a low-complexity structured approach to ISAC beamforming optimization to simultaneously enhance spectral efficiency and estimation accuracy. Specifically, we develop a successive convex approximation (SCA) based algorithm which transforms the original non-convex problem into a sequence of convex subproblems ensuring convergence to a locally optimal solution. Furthermore, leveraging the proposed SCA framework and the Lagrange duality, we derive the optimal beamforming structure for CRLB optimization in ISAC systems. Our findings characterize the reduction in radar streams one can employ without affecting performance. This enables a dimensionality reduction that enhances computational efficiency. Numerical simulations validate that our approach achieves comparable or superior performance to the considered benchmarks while requiring much lower computational costs.

Optimal ISAC Beamforming Structure and Efficient Algorithms for Sum Rate and CRLB Balancing

TL;DR

This work tackles the joint optimization of communications and sensing in ISAC by balancing sum rate and CRLB under a transmit power constraint. It introduces a two‑layer successive convex approximation (SCA) framework and derives an optimal beamforming structure (OBS) to reveal low‑dimensional, scalable solutions. A low‑dimensional reformulation further reduces the optimization variables, with convergence guarantees and rigorous complexity analysis. Numerical results show the proposed method achieves competitive SR/CRLB performance at much lower computational cost than SDR/FP baselines, and the OBS enables effective design regardless of large antenna counts. The approach offers practical pathways for deploying ISAC in large MIMO settings and provides a foundation for future extensions to RIS and near‑field configurations.

Abstract

Integrated sensing and communications (ISAC) has emerged as a promising paradigm to unify wireless communications and radar sensing, enabling efficient spectrum and hardware utilization. A core challenge with realizing the gains of ISAC stems from the unique challenges of dual purpose beamforming design due to the highly non-convex nature of key performance metrics such as sum rate for communications and the Cramer-Rao lower bound (CRLB) for sensing. In this paper, we propose a low-complexity structured approach to ISAC beamforming optimization to simultaneously enhance spectral efficiency and estimation accuracy. Specifically, we develop a successive convex approximation (SCA) based algorithm which transforms the original non-convex problem into a sequence of convex subproblems ensuring convergence to a locally optimal solution. Furthermore, leveraging the proposed SCA framework and the Lagrange duality, we derive the optimal beamforming structure for CRLB optimization in ISAC systems. Our findings characterize the reduction in radar streams one can employ without affecting performance. This enables a dimensionality reduction that enhances computational efficiency. Numerical simulations validate that our approach achieves comparable or superior performance to the considered benchmarks while requiring much lower computational costs.

Paper Structure

This paper contains 32 sections, 11 theorems, 71 equations, 7 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Contributions
  4. Preliminaries
  5. Signal Model
  6. Transmitted Signal Model
  7. Communications Model
  8. Radar Model
  9. Problem Formulation
  10. ISAC Beamforming Optimization via SCA
  11. First-Layer SCA
  12. Second-Layer SCA
  13. Overall Optimization Framework for Problem \ref{['P1']}
  14. Convergence Analysis
  15. Computational Complexity Analysis
  16. ...and 17 more sections

Key Result

Lemma 1

The FIM for estimating the parameters in $\bm\omega$ is given by the block matrix whose block entries are given by FIM:blocks, shown at the top of the next page, where $\mathbf R_x =\mathbf W_ \mathrm{c} \mathbf W_ \mathrm{c} ^{\mathsf{H}}+\mathbf W_ \mathrm{s} \mathbf W_ \mathrm{s} ^{\mathsf{H}}$, $\odot$ denotes the Hadamard product, and

Figures (7)

  • Figure 1: Illustration of the system model.
  • Figure 2: Convergence behavior of the proposed algorithm with various weight coefficients.
  • Figure 3: Tradeoff region between communications and sensing.
  • Figure 4: Objective value versus the number of sensing streams.
  • Figure 5: Average CPU Time vs. the number of transmit antennas.
  • ...and 2 more figures

Theorems & Definitions (15)

  • Lemma 1
  • Proposition 1
  • Lemma 2: fang2023optimal
  • Lemma 3: sun2017major
  • Remark 1
  • Proposition 2
  • Lemma 4: fang2024beamforming
  • Remark 2
  • Proposition 3
  • Proposition 4
  • ...and 5 more