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arxiv: 2605.25018 · v1 · pith:VIWR2UKAnew · submitted 2026-05-24 · 📡 eess.SP

A Unified KLD Framework for Duplexity and Deployment Paradigms in Cell-Free mMIMO-ISAC

Yousef Kloob , Mohammad Al-Jarrah , Emad Alsusa This is my paper

Pith reviewed 2026-06-29 23:50 UTC · model grok-4.3

classification 📡 eess.SP
keywords cell-free mMIMOISACKullback-Leibler divergencefull-duplexhalf-duplexdeployment paradigmsself-interferenceradar detection
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The pith

KLD serves as a unified scale to compare HD/FD operation and shared/separated deployments in cell-free mMIMO-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 an analytical framework that applies Kullback-Leibler divergence to measure both communication and radar performance on one scale across four cell-free massive MIMO ISAC configurations. These are separated or shared access-point deployments under half-duplex or full-duplex operation, each including residual self-interference, imperfect cancellation, and clutter. Closed-form expressions derived via a generalised likelihood ratio test connect KLD values directly to radar detection probability. The results indicate that full-duplex yields gains over half-duplex when interference suppression meets stated thresholds and that shared deployments enlarge the effective aperture for sensing while tightening the communication-radar trade-off.

Core claim

Kullback-Leibler divergence functions as a common metric that places communication rates and radar detection on identical footing, allowing direct quantitative comparison of the four duplex-deployment combinations; the generalised likelihood ratio test supplies closed-form relations between these KLD values and detection probability under the listed impairments, and Monte Carlo verification confirms that full-duplex outperforms half-duplex once self-interference and cancellation quality are adequate while shared deployment improves radar performance through a larger aperture at the expense of stronger coupling between the two functions.

What carries the argument

Kullback-Leibler divergence (KLD) applied as a unified performance measure for communication and radar tasks, paired with a generalised likelihood ratio test (GLRT) that yields closed-form expressions linking KLD to detection probability.

If this is right

  • FD operation achieves substantial gains over HD when sufficient SI suppression and IC quality are maintained while radar detection remains strong.
  • Shared deployment enhances radar performance through a larger effective aperture.
  • Shared deployment exhibits tighter communication-radar coupling than separated deployment.
  • Monte Carlo simulations confirm the closed-form KLD-to-detection expressions.

Where Pith is reading between the lines

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

  • The derived thresholds on self-interference suppression could be used to set hardware specifications for future ISAC access points.
  • Comparing KLD across more than four configurations might expose additional optima when user density or target velocity varies.
  • The same KLD expressions could be reused to evaluate energy efficiency by treating power consumption as an additional divergence term.
  • Real-time adaptation of duplex mode based on instantaneous KLD estimates would require only the closed-form relations already derived.

Load-bearing premise

KLD is a valid unified measure that permits direct comparison of communication and radar performance on a common scale.

What would settle it

A set of measured communication rates and radar detection probabilities whose ordering or scaling disagrees with the ordering or scaling of the corresponding KLD values under the modeled impairments would falsify the framework.

Figures

Figures reproduced from arXiv: 2605.25018 by Emad Alsusa, Mohammad Al-Jarrah, Yousef Kloob.

Figure 1
Figure 1. Figure 1: System model Illustration for ISAC CF-mMIMO system for both duplexities. (a) Separated deployment; (b) Shared deployment. freedom. Accordingly, the transmitted signal vector sent by the CPU during the DL (radar transmission) phase of each snapshot l to the radar APs can be represented as, xl = Wr,l Pr Φ, (5) where Φ = [ϕ1, ϕ2, · · · , ϕT ] T is a set of T orthonormal baseband waveforms [39], Pr = diagp Pr,… view at source ↗
Figure 2
Figure 2. Figure 2: SE-ISAC performance under varying IC qualities. a) KLD(UL) c and SER(UL) vs Pr/N0. b) KLDr and PD vs Pr/N0. Fig.2 presents SE-ISAC performance under varying IC qualities σ 2 IC ∈ {10−6 , 10−3 , 10−1 } with fixed (Pc, Pr, Pu) = (0.8, 0.1, 0.1) and β AP = β R = 10−3 . Fig.2.a illustrates the UL communication performance in terms of KLD(UL) c and SER(UL) versus Pr/N0. FD operation with a high￾quality IC demon… view at source ↗
Figure 3
Figure 3. Figure 3: SE-ISAC performance under varying SI leakage levels. a) KLD(UL) c and SER(UL) vs Pr/N0. b) KLDr and PD vs Pr/N0. Fig.3 examines SE-ISAC performance under varying SI leakage β ∈ {10−5 , 10−3 , 10−1 }, quantifying residual Tx– Rx coupling after cancellation, with fixed (Pc, Pr, Pu) = (0.8, 0.1, 0.1) and σ 2 IC = 10−4 . Fig.3.a shows UL commu￾nication performance, where FD advantage is evident: at Pr/N0 = 10 … view at source ↗
Figure 6
Figure 6. Figure 6: SH-ISAC performance under varying SI leakage levels. a) KLD(UL) c and SER(UL) vs Pr/N0. b) KLDr and PD vs Pr/N0. Fig.6 evaluates SH-ISAC sensitivity to SI leakage β with (Pc, Pr, Pu) = (0.8, 0.1, 0.1) and σ 2 IC = 10−4 . Fig.6.a shows that FD maintains substantial advantages for low leak￾age. At Pr/N0 = 10 dB, the SER(UL) values are {4.9 × 10−3 , 1.1 × 10−4 , 1.1 × 10−4 } for HD, FD with β = 10−5 , and β =… view at source ↗
Figure 5
Figure 5. Figure 5: SH-ISAC performance under varying IC qualities. a) KLD(UL) c and SER(UL) vs Pr/N0. b) KLDr and PD vs Pr/N0. Fig.5 reports SH-ISAC performance under varying IC quality with (Pc, Pr, Pu) = (0.8, 0.1, 0.1) and β AP = β R = 10−3 . Although SH couples radar and communication more tightly (all M = 40 APs support both functions), significant FD advantages remain. Fig.5.a shows the UL communication performance. At… view at source ↗
Figure 7
Figure 7. Figure 7: SH-ISAC performance under varying power allocation. a) KLD(DL) c and SER(DL) vs Pr/N0. b) KLD(UL) c and SER(UL) vs Pr/N0. c) KLDr and PD vs Pr/N0. Fig.7 presents SH-ISAC performance under different power allocations. The FD case uses β AP = β R = 10−4 and an IC-error variance σ 2 IC = 10−3 . Fig.7.a shows sig￾nificant DL performance advantages for FD. At Pr/N0 = 10 dB with Pc = 0.8, the SER(DL) values are … view at source ↗
read the original abstract

This paper develops a unifying analytical framework for comparing deployment and duplexing paradigms in distributed cell-free massive multiple-input multiple-output (CF-mMIMO) integrated sensing and communication (ISAC) systems. The system comprises distributed access points (APs) serving multiple downlink and uplink users while simultaneously detecting radar targets. Four configurations are analysed - separated and shared AP deployment under half-duplex (HD) and full-duplex (FD) operation, each incorporating realistic impairments: residual self-interference (SI) from transmit-receive leakage, imperfect interference cancellation due to channel estimation errors, and clutter. Kullback-Leibler divergence (KLD) is applied to serve as a unified measure, enabling direct comparison of communication and radar performance on a common scale. A generalised likelihood ratio test (GLRT) framework is developed to produce closed-form expressions linking KLD to detection probability. Monte Carlo simulations are used to verify our expressions, which demonstrate that FD operation achieves substantial gains over HD, provided sufficient SI suppression and IC quality are maintained, while preserving strong radar detection. It is also shown that shared deployment enhances radar performance via a larger effective aperture but exhibits tighter communication-radar coupling than separated deployment. These results establish deployment guidelines and quantitative design thresholds for next-generation CF-mMIMO ISAC systems.

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 / 0 minor

Summary. The paper develops a unifying analytical framework for comparing four deployment and duplexing paradigms (separated/shared AP deployment under HD/FD) in cell-free mMIMO-ISAC systems. It employs KLD as a common scalar metric for communication and radar performance, derives closed-form expressions linking KLD to detection probability via a GLRT framework that incorporates residual SI, IC errors, and clutter, verifies the expressions via Monte Carlo simulation, and concludes that FD yields substantial gains over HD when SI suppression and IC quality are adequate while shared deployment improves radar via larger aperture at the cost of tighter comm-radar coupling.

Significance. If the derivations are rigorous, the work supplies a practical analytical tool for quantitative comparison of ISAC paradigms and explicit design thresholds, with the Monte Carlo verification and explicit impairment modeling as strengths. The KLD unification, if shown to remain exact, would enable direct cross-paradigm trade-off analysis not commonly available in the literature.

major comments (1)
  1. [Abstract / GLRT framework] Abstract and GLRT framework: the central claim that the GLRT construction yields closed-form Pd expressions governed exactly by the KLD must be demonstrated after insertion of residual SI, channel-estimation errors, and clutter into the likelihoods. If these terms render the conditional densities non-Gaussian or introduce statistical dependence between SI and target returns, the mapping from KLD (an expectation) to the exact tail probability Pd is no longer guaranteed to be closed-form; the manuscript must either supply the explicit derivation showing the mapping remains exact or state any required approximations.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the thorough review and valuable feedback on our manuscript. We address the major comment point by point below and will revise the paper to incorporate the requested clarifications.

read point-by-point responses

  1. Referee: [Abstract / GLRT framework] Abstract and GLRT framework: the central claim that the GLRT construction yields closed-form Pd expressions governed exactly by the KLD must be demonstrated after insertion of residual SI, channel-estimation errors, and clutter into the likelihoods. If these terms render the conditional densities non-Gaussian or introduce statistical dependence between SI and target returns, the mapping from KLD (an expectation) to the exact tail probability Pd is no longer guaranteed to be closed-form; the manuscript must either supply the explicit derivation showing the mapping remains exact or state any required approximations.

    Authors: We appreciate the referee pointing out the need for explicit verification of the closed-form mapping. In our model, residual SI, channel estimation errors, and clutter are each represented as additive zero-mean complex Gaussian terms independent of the target returns. This keeps the conditional densities under both hypotheses exactly Gaussian (with modified covariance matrices that absorb the impairment powers), so the GLRT statistic is a monotonic function of the KLD and the detection probability retains its closed-form expression in terms of the KLD. No statistical dependence between SI and target returns is introduced under the stated assumptions. To make this fully transparent, the revised manuscript will add an appendix that derives the likelihood functions step-by-step after substitution of the impairment terms and shows that the KLD-to-Pd mapping remains exact without further approximation. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation presented as independent analytical construction

full rationale

The provided abstract and description contain no equations, self-citations, or parameter-fitting steps that reduce any claimed result to its own inputs by construction. KLD is introduced as an applied measure and GLRT as a developed framework yielding closed-form links, with Monte Carlo verification stated separately. No load-bearing premise is justified solely by prior author work or by renaming a fitted quantity as a prediction. The framework is therefore self-contained against external benchmarks within the given text.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The framework rests on domain assumptions about the applicability of KLD to both communication and radar metrics and the accuracy of impairment models; no new physical entities are postulated. Free parameters include the levels of SI suppression and IC quality that control the reported FD gains.

free parameters (2)
  • SI suppression level
    The amount of residual self-interference suppression is a key control parameter that determines whether FD achieves the claimed gains over HD.
  • IC quality
    The quality of interference cancellation, affected by channel estimation errors, is modeled as a variable that must be sufficient for the FD advantages to hold.
axioms (2)
  • domain assumption KLD serves as a unified measure for communication and radar performance on a common scale
    Invoked directly in the abstract as the basis for the unifying framework.
  • domain assumption The GLRT framework produces closed-form expressions linking KLD to detection probability
    Developed in the paper to connect the performance metrics.

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