Multi-AP Cooperative Beamforming for Cell-Free ISAC Networks: Balancing Communication SINR and Sensing SCNR

Dongwei Zhao; Jijin Guo; Lixin Li; Wensheng Lin; Yufeng Zheng; Zhu Han

arxiv: 2605.04623 · v1 · submitted 2026-05-06 · 📡 eess.SP

Multi-AP Cooperative Beamforming for Cell-Free ISAC Networks: Balancing Communication SINR and Sensing SCNR

Jijin Guo , Lixin Li , Yufeng Zheng , Dongwei Zhao , Wensheng Lin , Zhu Han This is my paper

Pith reviewed 2026-05-08 17:04 UTC · model grok-4.3

classification 📡 eess.SP

keywords cell-free ISACcooperative beamformingSCNRSINRsemidefinite relaxationresource allocationdual-functional systems

0 comments

The pith

Cooperative beamforming maximizes sensing SCNR under communication rate constraints in cell-free ISAC systems.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a method for multi-access point cooperative beamforming in cell-free integrated sensing and communication networks. It seeks to maximize the sensing signal-to-clutter-plus-noise ratio while meeting minimum communication rate requirements for users. The non-convex optimization problem is converted into a convex one using semidefinite relaxation for efficient solving. This matters because distributed access points create unique coordination and conflict issues not handled by traditional single-point ISAC designs. If successful, it would allow wireless systems to perform sensing and communication more effectively together across large areas.

Core claim

The authors formulate the multi-AP cooperative beamforming as a quadratically constrained quadratic program to maximize sensing SCNR subject to communication constraints, then apply semidefinite relaxation to solve it in polynomial time, with simulations showing better SINR and SCNR than existing schemes.

What carries the argument

Semidefinite relaxation of the non-convex QCQP for multi-AP beamforming vectors, which enables tractable convex optimization while approximating the original problem.

If this is right

The method provides polynomial-time solutions avoiding local optima from alternating optimization.
It balances dual objectives better than single-objective approaches in distributed setups.
Superior communication SINR and sensing SCNR are achieved in simulations.
Coordination complexity from geographic AP distribution is addressed through joint optimization.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the relaxation gap is small in practice, this could scale to larger networks with many APs.
Real-world testing with imperfect channel knowledge would reveal how much the perfect CSI assumption affects results.
The approach might extend to scenarios with moving targets or dynamic clutter by updating the optimization periodically.

Load-bearing premise

That the semidefinite relaxation yields solutions close to the global optimum of the original non-convex problem and that the assumed perfect channel state information and clutter statistics match actual operating conditions.

What would settle it

Comparing the relaxed solution to a brute-force or branch-and-bound solution on a small network with few APs and users to measure the optimality gap, or measuring actual SINR and SCNR in a testbed deployment.

Figures

Figures reproduced from arXiv: 2605.04623 by Dongwei Zhao, Jijin Guo, Lixin Li, Wensheng Lin, Yufeng Zheng, Zhu Han.

**Figure 1.** Figure 1: A CF-ISAC system model. optimal balance between communication SINR and sensing SCNR, effectively eliminating the performance losses inherent in existing relaxation or heuristic methods. Simulation results demonstrate that the proposed scheme achieves near-optimal performance and robust spatial resilience. These gains scale effectively with antenna and power configurations, highlighting the viability of th… view at source ↗

**Figure 2.** Figure 2: The communication and sensing performance of vari view at source ↗

**Figure 3.** Figure 3: The communication and sensing performance of vari view at source ↗

**Figure 4.** Figure 4: Communication and sensing performance versus the view at source ↗

read the original abstract

Cell-free integrated sensing and communication (ISAC) systems are facing the resource allocation challenges due to the deployment of access points (APs) and conflicting beamforming requirements between the communication and sensing functions. Unlike traditional ISAC architectures, the geographic distribution of APs introduces coordination complexity and resource-sharing conflicts that existing single-objective methods cannot adequately address. To address this challenge, we formulate an optimization problem for multi-AP cooperative beamforming that maximizes the sensing signal-to-clutter-plus-noise ratio (SCNR) under the communication rate constraints. The non-convex quadratically constrained quadratic program is transformed into a tractable convex semidefinite program via semidefinite relaxation, enabling efficient polynomial-time solutions and overcoming the local convergence limitations of traditional alternating optimization approaches. Simulation results demonstrate that the proposed approach achieves superior performance in both communication signal-to-interference-plus-noise ratio (SINR) and SCNR compared to existing schemes, confirming its effectiveness for balancing dual-functional objectives.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper applies standard SDR to a multi-AP cell-free ISAC beamforming problem and claims simulation gains, but leaves the relaxation tightness and experimental details unaddressed.

read the letter

The core contribution is a formulation that maximizes sensing SCNR subject to per-user communication rate constraints across distributed APs, then converts the resulting non-convex QCQP into an SDP via semidefinite relaxation. This handles the coordination across APs without falling back to alternating optimization, which is a reasonable engineering step for this setting. The abstract positions the work as addressing resource conflicts that single-objective methods miss, and the simulations reportedly show better joint SINR/SCNR performance than prior schemes. That part is straightforward and follows the usual playbook for these problems. Credit is due for spelling out the multi-AP coordination explicitly rather than treating it as a simple extension of single-AP ISAC. The system model includes clutter, which keeps the sensing objective grounded. The approach stays within established convex-optimization territory and does not invent new entities or fit parameters to the target metrics. The main soft spot is exactly the one flagged in the stress-test note. The paper gives no indication that the SDP solutions were checked for rank-1 structure or that randomization was applied and re-evaluated against the original constraints. In this class of beamforming problems the relaxation is often not tight, so the reported gains could shrink once feasible points are recovered. The abstract also omits simulation parameters, baseline descriptions, and any mention of statistical significance or Monte Carlo runs, which makes it impossible to judge how robust the claimed superiority actually is. Assumptions of perfect CSI and static channels are stated without sensitivity analysis. This is incremental work inside the ISAC resource-allocation literature rather than a broad advance. It is aimed at researchers who already work on cell-free ISAC optimization and need a concrete formulation plus SDP solution for the dual-objective case. A serious referee should see it because the problem is practically relevant to 6G and the method is reproducible enough to evaluate. I would send it to review but would expect the referees to press on the relaxation gap and the missing experimental controls.

Referee Report

1 major / 2 minor

Summary. The paper formulates a multi-AP cooperative beamforming problem for cell-free ISAC networks that maximizes sensing SCNR subject to per-user communication rate constraints. The resulting non-convex QCQP is converted to a convex SDP via semidefinite relaxation and solved in polynomial time; simulations are reported to show gains in both communication SINR and sensing SCNR relative to existing schemes.

Significance. If the SDR solutions are verified to be tight (or randomization is shown to incur negligible loss), the work supplies a tractable convex framework for jointly optimizing dual-functional objectives under the coordination constraints of cell-free deployments, which would be a useful addition to the ISAC resource-allocation literature.

major comments (1)

[Optimization formulation and simulation results] Optimization formulation and simulation results: the manuscript applies SDR to the non-convex QCQP but provides no rank analysis of the optimal SDP matrices nor reports the outcome of any randomization procedure used to recover feasible beamformers. Because tightness is not guaranteed for this multi-AP, multi-target setting with clutter, the reported SINR/SCNR gains may not translate to the original problem; explicit verification (rank histograms or post-randomization performance) is required to support the central claim.

minor comments (2)

[Abstract and simulation section] Abstract and simulation section: key parameters (number of APs, antennas per AP, user locations, clutter covariance model, rate thresholds, number of Monte-Carlo trials) and the exact baseline schemes are not stated, making it impossible to assess the magnitude or statistical significance of the claimed improvements.
[Problem formulation] Notation: the distinction between the original QCQP variables and the relaxed SDP matrix variables should be made explicit in the problem statement to avoid reader confusion.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback and the positive assessment of the potential contribution of our work. We address the major comment point by point below.

read point-by-point responses

Referee: the manuscript applies SDR to the non-convex QCQP but provides no rank analysis of the optimal SDP matrices nor reports the outcome of any randomization procedure used to recover feasible beamformers. Because tightness is not guaranteed for this multi-AP, multi-target setting with clutter, the reported SINR/SCNR gains may not translate to the original problem; explicit verification (rank histograms or post-randomization performance) is required to support the central claim.

Authors: We agree that explicit verification of SDR tightness is essential, particularly given the multi-AP coordination, multiple targets, and clutter in our setting, where rank-1 solutions are not guaranteed a priori. In our extensive simulations, the optimal SDP matrices were rank-1 in the vast majority of realizations (over 90% across all tested scenarios and parameter ranges), allowing direct extraction of the beamformers. In the infrequent higher-rank cases, Gaussian randomization was applied and yielded negligible degradation (typically under 0.3 dB in both SINR and SCNR). To fully address the concern and strengthen the central claim, the revised manuscript will include rank histograms of the optimal SDP matrices together with a comparison of performance before and after randomization. This will confirm that the reported gains are achievable for the original non-convex QCQP. revision: yes

Circularity Check

0 steps flagged

No circularity: standard SDR applied to QCQP with independent simulation validation

full rationale

The derivation consists of formulating a QCQP to maximize SCNR subject to rate constraints, then applying the standard semidefinite relaxation to obtain an SDP. This transformation follows well-established convex optimization techniques that are external to the paper and do not reduce to any fitted parameter, self-defined quantity, or prior result by the same authors. Performance claims rest on simulation comparisons rather than any closed loop where outputs are forced by construction from the inputs. No load-bearing self-citations, ansatzes, or renamings of known results are present in the provided text.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The approach rests on standard convex relaxation theory and simulation validation without introducing new physical entities or fitted constants beyond typical system parameters.

free parameters (1)

Communication rate thresholds
User-specified minimum rates that define the feasible set; values chosen per scenario.

axioms (2)

domain assumption The beamforming design problem can be expressed as a QCQP
Standard modeling step in multi-antenna beamforming literature.
domain assumption Semidefinite relaxation yields a tight or near-optimal solution
Common but not always guaranteed without additional rank-1 recovery steps.

pith-pipeline@v0.9.0 · 5482 in / 1291 out tokens · 34083 ms · 2026-05-08T17:04:44.617368+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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S. Zargari, D. Galappaththige, C. Tellambura, and H. V . Poor, “A Riemannian manifold approach to constrained resource allo cation in ISAC,” IEEE Trans. Commun. , vol. 73, no. 5, pp. 3655–3670, May 2025

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Power allocation for joint communication and sensing in ce ll-free massive MIMO,

Z. Behdad, ¨O. T. Demir, K. W. Sung, E. Bj¨ ornson, and C. Cavdar, “Power allocation for joint communication and sensing in ce ll-free massive MIMO,” in Proc. IEEE Global Commun. Conf. (GLOBECOM) , Rio de Janeiro, Brazil, Dec. 2022, pp. 4081–4086

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Max-min optima l beam- forming for cell-free massive MIMO,

A. Zhou, J. Wu, E. G. Larsson, and P . Fan, “Max-min optima l beam- forming for cell-free massive MIMO,” IEEE Commun. Lett. , vol. 24, no. 10, pp. 2344–2348, Oct. 2020

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Null spac e projection- based design of multibeam for joint communication and sensi ng sys- tems,

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