Harnessing the Freedom of Non-Uniformity in Monostatic ISAC with Antenna Flexibility

Emil Bj\"ornson; Mahmoud Zaher; Vitaly Petrov; Zhe Wang

arxiv: 2604.27571 · v1 · submitted 2026-04-30 · 💻 cs.IT · eess.SP· math.IT

Harnessing the Freedom of Non-Uniformity in Monostatic ISAC with Antenna Flexibility

Zhe Wang , Mahmoud Zaher , Vitaly Petrov , Emil Bj\"ornson This is my paper

Pith reviewed 2026-05-07 08:46 UTC · model grok-4.3

classification 💻 cs.IT eess.SPmath.IT

keywords monostatic ISACnon-uniform arrayantenna mode assignmentsum-rate maximizationflexible array designbeamforming optimizationintegrated sensing and communication

0 comments

The pith

Non-uniform antenna arrays formed by flexible transmit-receive-inactive assignments deliver higher ISAC sum rates than uniform arrays while using substantially fewer active elements.

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

The paper examines a base-station antenna pool in monostatic ISAC where each element can be assigned to transmit, receive, or inactive mode, allowing the effective array geometry to become non-uniform and to be designed jointly with the precoding. The central task is to maximize the sum communication rate subject to sensing performance, total power, and mode constraints. An alternating optimization procedure solves the joint problem by cycling between weighted minimum mean square error beamforming updates and successive convex approximation of the relaxed mode-assignment variables. Numerical comparisons indicate that the resulting non-uniform configurations outperform fixed uniform arrays, with the largest gains appearing when only a small number of antennas are activated, and can reach or exceed uniform-array performance with markedly fewer active elements.

Core claim

By allowing each candidate antenna to be set dynamically to transmit, receive, or inactive, a non-uniform effective array is formed and optimized together with the ISAC beamforming vectors. The resulting designs achieve higher sum communication rates than uniform-array baselines under identical sensing, power, and mode constraints, and can match or surpass the performance of those baselines while activating substantially fewer antennas.

What carries the argument

Alternating optimization that alternates weighted minimum mean square error beamforming with continuous-relaxation penalty and successive convex approximation of the discrete antenna-mode assignment variables.

If this is right

Gains from non-uniform geometry are largest when the number of activated antennas is small.
Equivalent communication performance can be reached with a smaller active subset than required by uniform designs.
Joint mode-assignment and beamforming optimization provides a practical route to geometry-aware rather than brute-force array scaling.
The framework respects sensing quality, power budgets, and mode exclusivity in the evaluated scenarios.

Where Pith is reading between the lines

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

If the same flexibility is applied to multi-cell or bistatic ISAC, the geometry degrees of freedom could further relax the usual trade-off between sensing resolution and communication throughput.
Hardware implementations could test whether the predicted rate advantage survives phase noise, mutual coupling, and imperfect channel estimates.
The ability to deactivate antennas suggests a path to dynamic power scaling that tracks instantaneous sensing and communication demands.
Extending the mode set to include different polarization states or subarray groupings could yield additional performance margins without increasing total element count.

Load-bearing premise

The continuous relaxation of the antenna mode variables, when solved by successive convex approximation, yields assignments that remain close to the true discrete optimum and satisfy all original constraints.

What would settle it

In a Monte Carlo trial with a fixed small number of active antennas and identical sensing and power limits, the sum rate of the optimized non-uniform array falls below the rate of a uniform array using the same number of elements.

Figures

Figures reproduced from arXiv: 2604.27571 by Emil Bj\"ornson, Mahmoud Zaher, Vitaly Petrov, Zhe Wang.

**Figure 1.** Figure 1: Average sum-rate for different array schemes versus view at source ↗

**Figure 2.** Figure 2: Average sum-rate for different array schemes with va view at source ↗

**Figure 3.** Figure 3: Average sum-rate for different array schemes versus view at source ↗

read the original abstract

This paper studies flexible non-uniform array design for monostatic integrated sensing and communication (ISAC) systems. An antenna pool is considered at the base station, where each candidate antenna can be dynamically assigned to transmit, receive, or inactive modes, such that a non-uniform effective array is jointly constructed with the ISAC precoding design. We formulate a sum communication rate maximization problem by jointly optimizing the ISAC beamforming schemes and antenna-mode assignment under sensing, power, and antenna mode constraints. We develop an alternating-optimization-based solution framework mainly with the aid of weighted minimum mean square error, continuous relaxation-based penalty, and successive convex approximation. Numerical results show that the proposed non-uniform array achieves higher sum-rates than the uniform-array baselines, with particularly large gains when the number of activated antennas is small. Moreover, the proposed non-uniform array can achieve, and in some cases exceed, the performance of uniform array baselines with substantially fewer activated antennas, highlighting geometry-aware non-uniform array design as a compelling alternative to brute-force antenna scaling-based array design.

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

Non-uniform ISAC arrays show simulated gains over uniform ones especially at low activation counts, but the alternating optimization with relaxation needs tighter checks on whether it actually delivers feasible discrete assignments.

read the letter

The main point is that allowing each antenna in the pool to switch between transmit, receive, or inactive modes lets you build a non-uniform effective array that improves sum rates in monostatic ISAC compared with fixed uniform layouts, and the gains are largest when few antennas are active. In some cases the non-uniform design matches or beats the uniform baseline while using substantially fewer active elements overall. That is the practical hook for hardware-constrained 6G setups. The paper does a clean job of setting up the joint problem: sum-rate maximization subject to sensing, power, and mode constraints, then solving it by alternating between WMMSE for the precoders and a penalty-relaxed SCA loop for the mode variables. The numerical comparisons to uniform-array baselines are presented directly and the advantage appears consistent across the tested regimes. The soft spot is exactly where the stress-test flagged it. The continuous relaxation plus penalty and SCA steps are standard, but the abstract and method give no numbers on how close the relaxed variables end up to {0,1}, what rounding rule is applied, or whether the final discrete solution still satisfies the sensing constraints at the reported performance level. If the relaxation is loose, the claimed superiority is between two differently approximated problems rather than the intended discrete designs. That does not kill the idea, but it does mean the numerical evidence is not yet conclusive. This is for people working on ISAC array geometry and hardware flexibility. It deserves a serious referee because the formulation is systematic and the core claim is testable once the optimization details are filled in. I would send it to review and ask specifically for convergence plots on the mode variables and post-rounding performance.

Referee Report

1 major / 2 minor

Summary. The paper studies monostatic ISAC systems with a flexible antenna pool at the BS, where each candidate antenna can be dynamically assigned to transmit, receive, or inactive modes to form a non-uniform effective array. The central contribution is a joint optimization of antenna-mode assignments and ISAC beamforming to maximize the sum communication rate subject to sensing, power, and mode constraints. The authors develop an alternating-optimization framework that employs WMMSE for the rate objective, a penalty-based continuous relaxation for the discrete mode variables, and successive convex approximation to handle the resulting non-convex problem. Numerical results are presented showing that the non-uniform designs achieve higher sum rates than uniform-array baselines, with the largest gains occurring at small numbers of activated antennas, and that they can match or exceed uniform-array performance while using substantially fewer active elements.

Significance. If the reported numerical gains are shown to arise from feasible discrete antenna assignments, the work would demonstrate that geometry-aware non-uniform array design can be a more efficient alternative to brute-force scaling of uniform arrays in ISAC systems. This could reduce hardware complexity while preserving or improving joint communication-sensing performance. The approach builds on standard tools (WMMSE, SCA, penalty relaxation) but applies them to a joint geometry-and-precoding problem that has not been extensively explored in the monostatic ISAC literature.

major comments (1)

[method section (alternating optimization framework)] The alternating-optimization framework (described in the method section) relies on continuous relaxation of the binary mode-assignment variables together with a penalty term and SCA. No analysis or numerical diagnostics are provided on how close the relaxed variables converge to {0,1} values, nor is any post-processing rounding or projection procedure specified that guarantees satisfaction of the discrete sensing and power constraints after relaxation. Because the central performance claims rest entirely on the numerical results obtained from this procedure, the absence of feasibility verification is load-bearing for the validity of the reported sum-rate gains versus uniform baselines.

minor comments (2)

[abstract and introduction] The abstract and introduction would benefit from a brief statement of the assumed channel models (e.g., whether far-field or near-field, LoS/NLoS components) and the precise definition of the sensing constraint (e.g., beampattern matching or CRLB).
[system model] Notation for the mode-assignment variables and the effective array response vectors should be introduced with an explicit table or diagram to improve readability when the joint optimization is first presented.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback and the positive evaluation of the work's significance. We address the major comment on the alternating optimization framework point by point below.

read point-by-point responses

Referee: The alternating-optimization framework (described in the method section) relies on continuous relaxation of the binary mode-assignment variables together with a penalty term and SCA. No analysis or numerical diagnostics are provided on how close the relaxed variables converge to {0,1} values, nor is any post-processing rounding or projection procedure specified that guarantees satisfaction of the discrete sensing and power constraints after relaxation. Because the central performance claims rest entirely on the numerical results obtained from this procedure, the absence of feasibility verification is load-bearing for the validity of the reported sum-rate gains versus uniform baselines.

Authors: We agree that the current manuscript does not include explicit diagnostics on the convergence of the relaxed mode-assignment variables to binary values or a specified post-processing procedure to enforce discrete feasibility. In the revised manuscript we will add a dedicated subsection to the method section that reports: (i) numerical statistics (mean and maximum deviation from {0,1} across Monte-Carlo trials) confirming that the penalty term drives the relaxed variables sufficiently close to binary; (ii) the exact rounding rule (threshold at 0.5 followed by a greedy projection that restores the prescribed numbers of transmit and receive antennas) together with a lightweight feasibility-recovery step that re-optimizes the beamformer under the now-fixed discrete mode assignment to satisfy the sensing and power constraints exactly. We will also tabulate the fraction of trials that remain feasible after projection and the associated rate loss, thereby ensuring all reported gains correspond to feasible discrete solutions. revision: yes

Circularity Check

0 steps flagged

No circularity in optimization framework or numerical claims

full rationale

The paper formulates a sum-rate maximization problem for joint ISAC precoding and discrete antenna-mode assignment, then applies an alternating optimization solver using WMMSE, penalty-based continuous relaxation, and SCA. Performance claims rest on numerical simulations comparing the resulting non-uniform designs against uniform-array baselines. No derivation step reduces to its own inputs by construction, no fitted parameters are relabeled as predictions, and no load-bearing self-citations or uniqueness theorems appear in the provided text. The results are obtained by solving the stated non-convex problem against external benchmarks, satisfying the self-contained criterion for a score of 0.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The approach assumes standard mathematical tools for non-convex optimization and relies on simulation-based validation rather than theoretical proofs or external benchmarks.

free parameters (1)

Penalty parameters for relaxation
Used in the continuous relaxation-based penalty method to enforce discrete mode constraints, likely tuned for convergence.

axioms (1)

domain assumption The non-convex joint optimization problem can be effectively solved using alternating optimization, WMMSE, continuous relaxation, and successive convex approximation.
Invoked in the solution framework description in the abstract.

pith-pipeline@v0.9.0 · 5493 in / 1328 out tokens · 44689 ms · 2026-05-07T08:46:08.280803+00:00 · methodology

discussion (0)

Reference graph

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K. Chen, C. Qi et al. , “Simultaneous beam training and target sensing in ISAC systems with RIS,” IEEE Trans. Wireless Commun. , vol. 23, no. 4, pp. 2696–2710, Apr. 2024

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Q. Shi, M. Razaviyayn et al., “An iteratively weighted MMSE approach to distributed sum-utility maximization for a MIMO interfe ring broad- cast channel,” IEEE Trans. Signal Process. , vol. 59, no. 9, pp. 4331– 4340, Apr. 2011

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A. Sabharwal, P . Schniter et al. , “In-band full-duplex wireless: Chal- lenges and opportunities,” IEEE J. Sel. Areas Commun. , vol. 32, no. 9, pp. 1637–1652, Sep. 2014

2014