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Beamforming Design for Max-Min Fairness Performance Balancing in ISAC Systems

Tianyu Fang, Nhan Thanh Nguyen, Markku Juntti

TL;DR

This work addresses downlink monostatic ISAC beamforming to balance fairness among multiple communications users and sensing targets under a per-antenna power budget. It formulates the objective as maximizing a weighted sum of the minimum user SINR $\min_k\gamma_{\mathrm{c}k}$ and the minimum SCNR $\min_m\gamma_{\mathrm{s}m}$, and proposes two frameworks: a fractional-programming based AO method that solves convex subproblems via CVX, and a low-complexity AO method that yields closed-form beamformers through log-sum-exp smoothing and auxiliary variables. The FP approach delivers strong performance but incurs high computational cost, while the low-complexity design reduces complexity with a modest performance trade-off. Numerical results demonstrate effective fairness across users and targets and show substantial run-time savings for the proposed low-complexity method, underscoring its practicality for scalable ISAC deployments, with room for further performance enhancements in future work.

Abstract

Integrated sensing and communications (ISAC) is envisioned as a key technology for future wireless communications. In this paper, we consider a downlink monostatic ISAC system wherein the base station serves multiple communications users and sensing targets at the same time in the presence of clutter. We aim at both guaranteeing fairness among the communications users while simultaneously balancing the performances of communications and sensing functionalities. Therefore, we optimize the transmit and receive beamformers to maximize the weighted minimum signal-to-interference and clutter-plus-noise ratios. The design problem is highly challenging due to the non-smooth and non-convex objective function and strongly coupled variables. We propose two efficient methods to solve the problem. First, we rely on fractional programming and transform the original problem into convex sub-problems, which can be solved with standard convex optimization tools. To further reduce the complexity and dependence on numerical tools, we develop a novel approach to address the inherent non-smoothness of the formulated problem. Finally, the efficiencies of the proposed designs are demonstrated by numerical results.

Beamforming Design for Max-Min Fairness Performance Balancing in ISAC Systems

TL;DR

This work addresses downlink monostatic ISAC beamforming to balance fairness among multiple communications users and sensing targets under a per-antenna power budget. It formulates the objective as maximizing a weighted sum of the minimum user SINR and the minimum SCNR , and proposes two frameworks: a fractional-programming based AO method that solves convex subproblems via CVX, and a low-complexity AO method that yields closed-form beamformers through log-sum-exp smoothing and auxiliary variables. The FP approach delivers strong performance but incurs high computational cost, while the low-complexity design reduces complexity with a modest performance trade-off. Numerical results demonstrate effective fairness across users and targets and show substantial run-time savings for the proposed low-complexity method, underscoring its practicality for scalable ISAC deployments, with room for further performance enhancements in future work.

Abstract

Integrated sensing and communications (ISAC) is envisioned as a key technology for future wireless communications. In this paper, we consider a downlink monostatic ISAC system wherein the base station serves multiple communications users and sensing targets at the same time in the presence of clutter. We aim at both guaranteeing fairness among the communications users while simultaneously balancing the performances of communications and sensing functionalities. Therefore, we optimize the transmit and receive beamformers to maximize the weighted minimum signal-to-interference and clutter-plus-noise ratios. The design problem is highly challenging due to the non-smooth and non-convex objective function and strongly coupled variables. We propose two efficient methods to solve the problem. First, we rely on fractional programming and transform the original problem into convex sub-problems, which can be solved with standard convex optimization tools. To further reduce the complexity and dependence on numerical tools, we develop a novel approach to address the inherent non-smoothness of the formulated problem. Finally, the efficiencies of the proposed designs are demonstrated by numerical results.
Paper Structure (17 sections, 1 theorem, 19 equations, 3 figures, 2 tables, 1 algorithm)

This paper contains 17 sections, 1 theorem, 19 equations, 3 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. Signal Model
  4. Communications Model
  5. Sensing Model
  6. Problem Formulation
  7. Proposed Optimization Frameworks
  8. Fractional Programming Approach
  9. Proposed Low-Complexity Design
  10. Problem Reformulation
  11. AO Method for Solving \ref{['P2t2']}
  12. Update $\mathbf z_c, \mathbf z_{\mathrm{s}}$
  13. Update $\bm\xi,\bm\Theta,\mathbf F$
  14. Update $\mathbf W$
  15. Convergence and Complexity Analysis
  16. ...and 2 more sections

Key Result

Lemma 1

For any given positive semi-definite Hermitian matrix $\mathbf A \in\mathbb{C}^{L_{\mathrm{t}}\times L_{\mathrm{t}}}$, we have where $\mathbf P\in\mathbb C^{L_{\mathrm{t}}\times K}$ is an auxiliary matrix, and the equality is achieved if and only if $\mathbf W=\mathbf P$.

Figures (3)

  • Figure 1: Convergence of the proposed FP scheme and Algorithm \ref{['al1']} with various $\mu$.
  • Figure 2: Tradeoff between the minimum SINR and SCNR of the FP scheme and Algorithm \ref{['al1']}.
  • Figure 3: Performance comparison of the proposed FP scheme and Algorithm \ref{['al1']} for $K\in \{2,4,\ldots,12\}$.

Theorems & Definitions (2)

  • Lemma 1
  • proof