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arxiv: 2604.19263 · v1 · submitted 2026-04-21 · 💻 cs.IT · math.IT

Uplink Signal Detection For Large-Scale MIMO-ISAC Systems

Jian Wang , Qiqiang Chen , Zheng Wang , Fan Liu , Yili Xia , Yongming Huang , Chau Yuen This is my paper

Pith reviewed 2026-05-10 01:39 UTC · model grok-4.3

classification 💻 cs.IT math.IT
keywords MIMO-ISACuplink detectionADMMmixed-integer least squaresdiversity orderneighborhood searchBERNMSE
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The pith

P-NS-ADMM achieves the same received diversity order as maximum likelihood detection in large-scale MIMO-ISAC uplink.

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

The paper models the uplink signal detection problem in large-scale MIMO-ISAC systems as a mixed-integer least squares problem. It proposes the projection-based neighborhood search-aided ADMM scheme (P-NS-ADMM) and proves through analysis that this scheme attains the same received diversity order as maximum likelihood detection. For lower complexity, it introduces an iteration-based variant (I-NS-ADMM) that removes the projection step and adds a flexible mechanism to tune ADMM iterations for better sensing signal estimates. Simulations confirm the new schemes improve both bit error rate and normalized mean square error relative to prior methods.

Core claim

By casting MIMO-ISAC uplink detection as a mixed-integer least squares problem, the authors develop P-NS-ADMM which, via neighborhood search and projection steps inside the ADMM framework, matches the diversity order of maximum likelihood detection; the companion I-NS-ADMM drops the projection for reduced complexity while using a flexible iteration count to maintain sensing accuracy.

What carries the argument

The projection-based neighborhood search-aided alternating direction method of multipliers (P-NS-ADMM) applied to the mixed-integer least squares model of the detection problem.

Load-bearing premise

The uplink MIMO-ISAC detection problem is accurately captured by the mixed-integer least squares model and the neighborhood search plus projection steps preserve the full diversity order without hidden parameter dependencies.

What would settle it

A high-SNR simulation or analysis in which the bit-error-rate slope of P-NS-ADMM is shallower than that of ML detection in a large-scale MIMO-ISAC setup would disprove the diversity-order claim.

Figures

Figures reproduced from arXiv: 2604.19263 by Chau Yuen, Fan Liu, Jian Wang, Qiqiang Chen, Yili Xia, Yongming Huang, Zheng Wang.

Figure 1
Figure 1. Figure 1: The uplink signal detection in MIMO-ISAC systems, where BS [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The flexible mechanism of the ADMM iterations. [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparisons of BER performance for 16-QAM in [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparisons of complexity in scenario 1 (32 × 8 × 2), scenario 2 (32 × 8 × 8), and scenario 3 (64 × 60 × 2). -3 -2 -1 0 1 2 3 4 5 6 10-6 10-5 10-4 10-3 10-2 10-1 [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparisons of BER performance for 16-QAM and 4-QAM in [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 9
Figure 9. Figure 9: Comparisons of NMSE performance for 16-QAM in [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 8
Figure 8. Figure 8: Comparisons of NMSE performance for 16-QAM in [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: Comparisons of NMSE performance for 16-QAM in [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
read the original abstract

Next-generation wireless communication systems are unifying large-scale multiple-input multiple-output (MIMO) and integrated sensing and communication (ISAC) to enhance sensing and communication performance. In this paper, the signal detection problem for MIMO-ISAC systems is modeled as a mixed-integer least squares (MILS) problem. To solve it efficiently, we propose a projection-based neighborhood search-aided alternating direction method of multipliers (P-NS-ADMM) detection scheme. By theoretical analysis, we demonstrate that P-NS-ADMM achieves the same received diversity order as maximum likelihood (ML) detection. For further complexity reduction, an iteration-based NS-ADMM (I-NS-ADMM) is proposed to remove the complex projection operation. Complexity analysis shows its complexity advantage compared with P-NS-ADMM. Moreover, to better estimate the sensing signals for I-NS-ADMM, a flexible mechanism of ADMM iterations is given. Finally, simulations demonstrate the proposed NS-aided ADMM detection schemes have significant performance advantages in terms of both BER and NMSE.

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.

Referee Report

1 major / 2 minor

Summary. The manuscript models the uplink signal detection problem in large-scale MIMO-ISAC systems as a mixed-integer least squares (MILS) problem. It proposes a projection-based neighborhood search-aided ADMM (P-NS-ADMM) scheme that is shown through theoretical analysis to achieve the same diversity order as maximum likelihood (ML) detection. An iteration-based variant (I-NS-ADMM) is introduced to reduce complexity by eliminating the projection step, along with a flexible ADMM iteration mechanism for sensing signal estimation. Complexity analysis and simulations demonstrating advantages in bit error rate (BER) and normalized mean square error (NMSE) are provided.

Significance. If the diversity-order claim holds, this work would offer a computationally efficient detection method for integrated sensing and communication systems that maintains near-optimal error performance, which is valuable for large-scale MIMO deployments in next-generation wireless networks. The provision of both theoretical guarantees and practical complexity reductions strengthens the contribution, though verification of the proof details and simulation parameters is needed to fully assess the impact.

major comments (1)
  1. [theoretical analysis section] The claim that P-NS-ADMM achieves the same received diversity order as ML detection requires an explicit bound demonstrating that the probability of the correct symbol lying outside the searched neighborhood or being modified by the projection operation decays at least as fast as the ML error probability at high SNR. The presence of sensing signals in the ISAC model may introduce correlations that could affect the independence assumptions in the diversity calculation, and this needs to be addressed to confirm the equivalence.
minor comments (2)
  1. [simulation results] The simulation results for BER and NMSE should include details on the exact system parameters, number of Monte Carlo runs, and error bars to allow reproducibility and assessment of statistical significance.
  2. [notation and definitions] Ensure consistent use of notation for the ADMM penalty parameter and other variables throughout the manuscript.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address the single major comment below and will revise the theoretical analysis section to provide the requested explicit bounds and clarifications.

read point-by-point responses

  1. Referee: [theoretical analysis section] The claim that P-NS-ADMM achieves the same received diversity order as ML detection requires an explicit bound demonstrating that the probability of the correct symbol lying outside the searched neighborhood or being modified by the projection operation decays at least as fast as the ML error probability at high SNR. The presence of sensing signals in the ISAC model may introduce correlations that could affect the independence assumptions in the diversity calculation, and this needs to be addressed to confirm the equivalence.

    Authors: We agree that an explicit bound would strengthen the presentation. In the revised manuscript we will insert a new lemma immediately following the existing diversity-order theorem. The lemma will bound the probability that the true symbol vector lies outside the neighborhood searched by P-NS-ADMM or is altered by the subsequent projection step; the bound will be shown to decay at least as fast as the ML pairwise error probability (i.e., exponentially with SNR). The proof proceeds by relating the neighborhood radius to the minimum distance of the constellation and using the fact that the ADMM iterates converge to a point whose distance to the ML solution is controlled by the noise variance. Regarding sensing signals, we will add a short paragraph clarifying that, under the uplink ISAC model, the sensing component is either known a priori or estimated separately before communication detection; the residual sensing interference appears as an additional deterministic term in the effective noise. Because this term is independent of the communication symbols and does not scale with SNR, it does not change the high-SNR slope of the error probability. Consequently the independence assumptions used in the diversity calculation remain valid conditionally on the estimated sensing parameters. These additions will be placed in the theoretical analysis section and will not alter the complexity or simulation results. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in diversity-order claim

full rationale

The paper models uplink MIMO-ISAC detection as a mixed-integer least-squares problem and introduces P-NS-ADMM, asserting via theoretical analysis that it matches the ML diversity order. No quoted derivation step reduces the diversity result to a fitted parameter, a self-definitional equivalence, or a load-bearing self-citation chain; the claim is framed as following from standard high-SNR error-probability analysis applied to the neighborhood-search and projection steps. The provided abstract and context contain no equations or citations that would make the output equivalent to the inputs by construction. This is the common non-circular outcome for algorithmic papers whose central result rests on external analytical techniques rather than internal redefinition.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The paper relies on standard convex optimization theory for ADMM convergence and conventional MIMO channel models; no new physical entities are introduced.

free parameters (1)
  • ADMM penalty parameter
    Typical algorithmic tuning parameter whose specific selection rule is not detailed in the abstract but affects convergence and performance.
axioms (1)
  • standard math ADMM converges to a stationary point for the formulated MILS problem under standard conditions on the penalty parameter and problem structure.
    Invoked implicitly in the design and theoretical analysis of both proposed schemes.

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