Optimal User and Target Scheduling, User-Target Pairing, and Low-Resolution Phase-Only Beamforming for ISAC Systems

TL;DR

The paper addresses ISAC downlink resource allocation with a fixed number of RF chains and low-resolution phase control. It casts joint scheduling, user-target pairing, and phase-only beamforming as a nonconvex MINLP and derives an exact MILP reformulation to obtain a global optimum. The authors provide a sequence of equivalent reformulations that transform the problem into a convex MILP $\mathcal{Q}$, enabling global optimization and establishing substantial performance gains over heuristic baselines in simulations. The study demonstrates the practical value of a unified design for ISAC, showing robust improvements across scenario variations and highlighting the role of phase discretization in achievable sensing and communication performance.

Abstract

We investigate the joint user and target scheduling, user-target pairing, and low-resolution phase-only beamforming design for integrated sensing and communications (ISAC). Scheduling determines which users and targets are served, while pairing specifies which users and targets are grouped into pairs. Additionally, the beamformers are designed using few-bit constant-modulus phase shifts. This resource allocation problem is a nonconvex mixed-integer nonlinear program (MINLP) and challenging to solve. To address it, we propose an exact mixed-integer linear program (MILP) reformulation, which leads to a globally optimal solution. Our results demonstrate the superiority of an optimal joint design compared to heuristic stage-wise approaches, which are highly sensitive to scenario characteristics.

Figures (5)

• Figure 1: ISAC system consisting of a BS and multiple users and targets. "Allocation #1" shows a favorable resource allocation strategy, featuring well-separated pairs and strong alignment between users and targets within each pair. This ensures high directivity, benefiting both users and targets. The sufficient spacing between scheduled users ($\mathsf{U}_1$, $\mathsf{U}_3$, $\mathsf{U}_5$) minimizes inter-user interference, while the adequate separation between targets ($\mathsf{T}_1$, $\mathsf{T}_3$) reduces cross-interference. In contrast, "Allocation #2" is less optimal due to closer pairs spread over a wider angular range, resulting in weaker alignment and reduced directivity. The angular proximity of users ($\mathsf{U}_2$, $\mathsf{U}_3$, $\mathsf{U}_4$) increases inter-user interference, and the limited separation between targets ($\mathsf{T}_1$, $\mathsf{T}_2$) heightens cross-correlation. While this scenario highlights the importance of alignment, a more comprehensive resource allocation approach is needed. Factors such as user channel conditions, target characteristics, and phase resolution significantly influence performance, necessitating a unified optimization strategy beyond fixed pairing and scheduling criteria.
• Figure 2: Performance as a function of transmit power.
• Figure 3: Performance as a function of SINR threshold in correlated channels.
• Figure 4: Performance as a function of SINR threshold in uncorrelated channels.
• Figure 5: Beampatterns for scheduled and paired users and targets.

Theorems & Definitions (20)

• Proposition 1
• Proposition 2
• Proposition 3
• Proposition 4
• Proposition 5
• Proposition 6
• Proposition 7
• Proposition 8
• Remark 1
• proof : Proof of Proposition 1