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Hierarchical Functionality Prioritization in Multicast ISAC: Optimal Admission Control and Discrete-Phase Beamforming

Luis F. Abanto-Leon, Setareh Maghsudi

TL;DR

This work tackles joint admission control and discrete-phase multicast beamforming for hierarchical ISAC, where communications is prioritized over sensing. It develops an exact MILP reformulation that replaces the nonconvex MINLP with a tractable, globally optimal MILP by introducing a rank-one matrix variable $W=ww^H$ and binary phase-encoding constructs, along with a robust angular-sampling formulation for sensing. The objective combines the number of admitted users and a sensing-threshold term, weighted so that the integer part (communications) dominates, yielding a hierarchical resource allocation. Simulation results demonstrate that the proposed OPT approach substantially outperforms three baselines, achieving larger communication-operating regions while maintaining robust sensing under angular uncertainty, with gains up to approximately 60% in the tested scenarios.

Abstract

We investigate the joint admission control and discrete-phase multicast beamforming design for integrated sensing and communications (ISAC) systems, where sensing and communications functionalities have different hierarchies. Specifically, the ISAC system first allocates resources to the higher-hierarchy functionality and opportunistically uses the remaining resources to support the lower-hierarchy one. This resource allocation problem is a nonconvex mixed-integer nonlinear program (MINLP). We propose an exact mixed-integer linear program (MILP) reformulation, leading to a globally optimal solution. In addition, we implemented three baselines for comparison, which our proposed method outperforms by more than 39%.

Hierarchical Functionality Prioritization in Multicast ISAC: Optimal Admission Control and Discrete-Phase Beamforming

TL;DR

This work tackles joint admission control and discrete-phase multicast beamforming for hierarchical ISAC, where communications is prioritized over sensing. It develops an exact MILP reformulation that replaces the nonconvex MINLP with a tractable, globally optimal MILP by introducing a rank-one matrix variable and binary phase-encoding constructs, along with a robust angular-sampling formulation for sensing. The objective combines the number of admitted users and a sensing-threshold term, weighted so that the integer part (communications) dominates, yielding a hierarchical resource allocation. Simulation results demonstrate that the proposed OPT approach substantially outperforms three baselines, achieving larger communication-operating regions while maintaining robust sensing under angular uncertainty, with gains up to approximately 60% in the tested scenarios.

Abstract

We investigate the joint admission control and discrete-phase multicast beamforming design for integrated sensing and communications (ISAC) systems, where sensing and communications functionalities have different hierarchies. Specifically, the ISAC system first allocates resources to the higher-hierarchy functionality and opportunistically uses the remaining resources to support the lower-hierarchy one. This resource allocation problem is a nonconvex mixed-integer nonlinear program (MINLP). We propose an exact mixed-integer linear program (MILP) reformulation, leading to a globally optimal solution. In addition, we implemented three baselines for comparison, which our proposed method outperforms by more than 39%.
Paper Structure (5 sections, 6 theorems, 11 equations, 5 figures, 1 table)

This paper contains 5 sections, 6 theorems, 11 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. Proposed Optimal Approach
  4. Simulation Results
  5. Conclusions

Key Result

Lemma 1

A set of weights ensuring that communications has higher hierarchy is given by $\rho_\mathrm{com} = 1$ and $\rho_\mathrm{sen} = \tfrac{\sigma_\mathrm{sen}^2}{2 \alpha N P_\mathrm{tx} }$.

Figures (5)

  • Figure 1: Multicast ISAC system with many users and a target.
  • Figure 2: Impact of the number of antennas, transmit power, and phase resolution on the sensing performance.
  • Figure 3: Impact of SNR threshold and target's angle uncertainty on sensing and communications.
  • Figure 4: Impact of SNR threshold on the beampattern.
  • Figure 5: Performance comparison of four different approaches.

Theorems & Definitions (13)

  • Lemma 1
  • proof
  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Proposition 3
  • proof
  • Proposition 4
  • proof
  • ...and 3 more