Unified Interference-Aware Water-Filling for QoS-Constrained Communication, Sensing, and JRC

Ahmed Naeem; Anastassia Gharib; H\"useyin Arslan

REVIEW 4 major objections 4 minor 12 references

Unified Interference-Aware Water-Filling for QoS-Constrained Communication, Sensing, and JRC

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Water-filling can jointly serve communication, sensing, and JRC users in one QoS-constrained power allocation.

desk verdict A timely problem formulation whose central KKT derivations fail in two of three updates: the algorithm as written is not derived, even though the framing is worth engaging. read the letter →

arxiv 2506.01400 v1 pith:PVA6YMVV submitted 2025-06-02 eess.SP

Ahmed Naeem , Anastassia Gharib , Hüseyin Arslan This is my paper

classification eess.SP

keywords 6GMIMOwater-fillingpowerallocationjointradarandcommunicationsensingQoSconstraintsmulti-userinterference

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish that water-filling, the classic MIMO scheme for distributing power across sub-channels, can be generalized to a downlink where some users need communication, some need sensing, and some need both. The proposal is an iterative algorithm that freezes the interference seen by each user, solves the resulting QoS-constrained problem with KKT-based closed-form updates, and updates dual variables to satisfy per-user rate and signal-to-clutter-plus-noise requirements. Simulation results are used to argue that this unified procedure beats traditional communication-only water-filling and equal-power allocation in capacity, probability of detection, and QoS satisfaction. If the claim holds, network designers would need only one power-allocation routine rather than separate designs for each service type, which matters as 6G networks mix phones, sensors, and vehicles.

What carries the argument

The central object is the frozen-interference iteration: at each step the algorithm computes $I_{k,i} = \sum_{j\neq k} P_{j,i}|H_k w_{j,i}|^2$ using current powers, holds that value constant, and maximizes a per-user concave surrogate whose KKT conditions give the closed-form power updates (8), (10), and (12). The formulas have the classic water-filling shape: power is poured into a sub-channel up to a level set by the water level $1/\mu$, after subtracting the noise-plus-interference floor divided by the channel gain. The QoS multipliers $\nu$ and $\eta$ act as extra water levels that raise the allocation to users whose rate or sensing constraint is violated, and the bisection on $\mu$ enforces the total power budget. This machinery is what converts the coupled nonconvex problem (5) into a practical fixed-point algorithm.

What would settle it

Take a single channel realization with at least one sensing or JRC user, run the algorithm to convergence, and evaluate $\partial L/\partial P_{S,k,i}$ from (9) at the power value returned by (10). The derivative in (9) does not depend on $P_{S,k,i}$, so a nonzero value means the returned power is not a KKT point; the same check can be run for equations (11) and (12).

Watch

Extended reading notes

Core claim

The paper's central claim is that the nonconvex, interference-coupled problem of allocating power to heterogeneous users can be approximated by a sequence of convex subproblems, one per user and sub-channel, with the cross-user interference term $I_{k,i}$ held fixed from the previous iteration. For communication-only users the KKT analysis yields the water-filling update $P_{C,k,i} = [B(1+\nu_{k,i})/(\mu \ln 2) - (N_{0,k}+I_{k,i})/\lambda_{k,i}]^+$; for sensing-only users it yields $P_{S,k,i} = [(1+\eta_{k,i})\lambda_{k,i}/(\mu(N_{0,k}+C_{0,k}+I_{k,i}))]^+$; and for joint radar-communication users it yields a combined update that mixes both rates. The power budget multiplier $\mu$ is found by bisection, the QoS multipliers $\nu$ and $\eta$ by subgradient steps, and the loop repeats until the power vector stops changing. The paper reports that this converges within about 50 iterations and, in simulation, gives higher capacity, faster growth of detection probability, and better QoS satisfaction than traditional water-filling and equal-power allocation.

Load-bearing premise

Everything rests on the assumption that freezing each user's interference for one iteration turns the coupled nonconvex problem into independent convex subproblems whose KKT equations the closed-form updates actually solve, and that iterating this surrogate converges to a local optimum of the original problem.

Editorial extensions

If this is right

One power-allocation routine can serve a cell whose users have different service types, replacing separate communication and sensing resource managers.
Rate and sensing QoS constraints can be enforced by tuning dual variables, giving a concrete fairness mechanism among heterogeneous users.
The per-iteration complexity is polynomial in the number of users and sub-channels, on the order of $O(T(K^2r^2 + Kr\log(1/\epsilon)))$ with $T\approx 50$ in the simulations, suggesting the method is implementable.
In the reported experiments the proposed scheme raises capacity by about 2.7 Mbps over traditional WF and 5.5 Mbps over equal-power WF at SNR 20 dB, reaches detection probability near 1 at lower SNR, and exceeds 90\% QoS satisfaction at high SNR.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The same fixed-interference surrogate could be applied to other user-centric QoS metrics, such as delay or reliability, by swapping the objective and re-deriving the KKT update.
Because the interference term is updated from current powers, the algorithm has a natural fixed-point interpretation; a direct comparison with crosstalk-channel water-filling fixed points in the communication-only case would test whether the generalization is faithful.
Sensing performance is measured here by SCNR, so a next natural check is whether the allocations also improve end-to-end detection or tracking metrics such as Cramér-Rao bounds or track loss rates.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Two things to know. The problem framing is timely and the unified three-class formulation is genuinely new, but the central derivation is broken: the sensing update (10) does not follow from (9), and the JRC update (12) does not solve (11). I checked both; the stress-test note is right. Since these are the exact formulas Algorithm 1 executes, the Section V gains come from an algorithm the paper did not actually derive.

Credit where due. The three-class UE model—communication-only, sensing-only, JRC—with per-user QoS thresholds and service weights is a useful way to pose the heterogeneous 6G power-allocation problem, and I don't see that exact combination in the water-filling literature they cite. The paper is clearly written, it benchmarks against external baselines rather than only its own variants, and the communication-only update (8) is the standard correct water-filling.

The soft spots are load-bearing, not cosmetic. For sensing, SCNR is linear in P_{S,k,i}, so the derivative in (9) contains no power variable; setting it to zero pins down μ, not P, so (10) is an invented water-filling-looking expression. The deeper conceptual point: a linear sensing utility is not a water-filling problem at all—its true optimum is corner allocation, all power to the strongest subchannel—unless the objective is reformulated (log-SCNR would restore water-filling structure). For JRC, solving (11) gives P = [(α+ν)B/ln2] / [μ/λ − (1−α+η)/(N0+C0+I)] − (N0+I)/λ, which is not the additive expression in (12). The convergence argument in IV-C inherits all this: it cites Razaviyayn's SCA conditions without verifying the surrogate property, and since the iterates are not even stationary for the fixed-interference subproblem, the citation can't carry the argument. A small symptom of the same confusion: the paper says fairness comes from the 'logarithmic utility functions implicit in C_k and SCNR_k,' but SCNR has no logarithm.

Who this is for: researchers in JCAS/6G resource allocation might cite the formulation as a statement of the heterogeneous QoS problem, but nobody should build on the algorithm as written.

Recommendation: not acceptable in current form. I would still send it to a serious referee rather than desk-reject: the formulation is novel, and the errors are specific enough that a report can hand the authors a genuine repair path—reformulate the sensing objective, redo the JRC algebra, prove the convergence claim. If those come back correct, it becomes a defensible methods contribution.

Referee Report

4 major / 4 minor

Summary. This paper proposes an iterative water-filling algorithm for downlink power allocation in a multi-user MIMO system with three classes of user equipment: communication-only, sensing-only, and joint radar-communication (JRC). The authors formulate a weighted utility maximization with total power, nonnegativity, and QoS constraints (Eq. (5)), then fix the multi-user interference per iteration to obtain convex subproblems. They derive closed-form KKT power updates for the three user classes (Eqs. (8), (10), (12)), update Lagrange multipliers via bisection and subgradient rules, and claim convergence by successive convex approximation. Simulations compare the proposed algorithm with traditional water-filling and equal-power allocation in terms of capacity, detection probability, QoS satisfaction rate, and runtime.

Significance. The problem addressed is relevant to 6G systems that must serve heterogeneous communication and sensing users, and the paper provides a clear system model plus simulation comparisons against standard baselines. The communication-only update (8) is a correct KKT solution, and the overall complexity analysis is plausible. However, the paper's central claim rests on the sensing and JRC closed-form updates, and these are not derived from the stated KKT conditions. Because Algorithm 1 is the main contribution, the incorrect derivations invalidate the claimed optimality and the simulation results do not validate the proposed method.

major comments (4)

[IV-A, Eqs. (9)-(10)] The stationarity equation (9) contains P_{S,k,i} only through the fixed interference term I_{k,i}; as a function of P_{S,k,i}, the left-hand side is a constant. Setting it to zero with gamma_{k,i}=0 therefore yields only the multiplier feasibility condition mu = (1+eta_{k,i}) lambda_{k,i}/(N0_{k}+C0_{k}+I_{k,i}), not a power update. Formula (10) is consequently not the root of (9), and the sensing branch of Algorithm 1 is not a KKT-based water-filling update.
[IV-A, Eqs. (11)-(12)] Solving (11) for P_{JRC,k,i} with gamma_{k,i}=0 gives P_{JRC,k,i} = [B(alpha_{k,i}+nu_{k,i})/(ln 2)] / [mu - (1-alpha_{k,i}+eta_{k,i}) lambda_{k,i}/(N0_{k}+C0_{k}+I_{k,i})] - (N0_{k}+I_{k,i})/lambda_{k,i}, after applying the nonnegativity projection. This rational form differs from the additive expression in (12). Substituting (12) into (11) does not generally satisfy the equation, so the JRC update is not the KKT solution claimed.
[IV-C] The convergence argument asserts that the algorithm maximizes a concave surrogate f~(P|I^(t)) in each iteration and cites the block successive minimization theory of [12]. However, since (10) and (12) are not stationary points of the fixed-interference subproblem, the paper has not shown that the iterates maximize any surrogate. The conditions of [12] are therefore not verified, and the claimed convergence to a local optimum is unsupported.
[V] The simulation results in Figures 2 and 3 evaluate Algorithm 1, whose sensing and JRC branches use formulas (10) and (12). Because those formulas do not solve the KKT conditions of the optimization problem in (5), the numerical comparisons do not substantiate the paper's conclusion that the proposed QoS-constrained water-filling algorithm outperforms the baselines in capacity, detection, and fairness.

minor comments (4)

[III, Eq. (5)] The statement that the binary beta_{k,i} factor eliminates low-gain subchannels 'without loss of optimality' is not justified; no argument is given that a priori discarding a subchannel is optimal for the nonconvex problem.
[III] The notation C_{k,i} and SCNR_{k,i} is used in (5) but only the UE-level sums C_k and SCNR_k are defined in (2) and (3); the per-subchannel counterparts should be defined explicitly.
[V] The simulation setup omits several parameters needed for reproducibility, including the QoS thresholds C_{k,i,min} and S_{k,i,min}, the priority weights alpha_k, the subgradient step size delta, the convergence thresholds, and the channel or waveform model behind Figures 2 and 3.
[Algorithm 1] The initialization on line 2 sets P^{(0)}_{k,i} to P_total / sum_k r_k, but this ignores beta_{k,i} and may not correspond to a feasible starting point for the QoS constraints; the bisection search for mu is also described without explicit termination tolerances beyond epsilon_mu.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the KKT derivation is self-contained and simulations use external baselines; possible algebra errors are a correctness issue, not circularity.

full rationale

The paper's central derivation is a Lagrangian/KKT analysis of its own optimization problem (5), and no fitted parameter or precomputed result is renamed as a prediction. The sensing and JRC closed forms (10) and (12) are claimed to follow from the stationarity equations (9) and (11), and while those algebraic steps may be incorrect, incorrectness is not circularity. The convergence argument relies on the external SCA framework of reference [12] (Razaviyayn et al.), not on a self-citation, and even if the invoked conditions are unverified, invoking an external theorem is an evidence source rather than a circular reduction. References [1] and [2] are author self-citations, but they appear only as background motivation for 6G heterogeneous services and do not carry the load of the algorithm's derivation or performance claims. The simulation comparisons are against traditional water-filling and equal-power allocation baselines, which are independent of the paper's own fitted values. No step in the paper reduces by definition to its inputs, and no 'prediction' is statistically forced by a fitted parameter. Therefore the circularity score is 0; any serious concerns about the stationarity-algebra mismatch or the unverified SCA conditions belong to the correctness pass, not the circularity pass.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central algorithm rests on a fixed-interference convex approximation and standard KKT machinery. No new physical entities are introduced. The paper's free parameters are service weights, QoS thresholds, subgradient step sizes, and tolerances, most of which are not reported in the simulation section, making the exact experimental configuration under-specified.

free parameters (5)

alpha_{k,i} service priority weight
Balances communication and sensing in the JRC utility (Eq. 4); set to 1 for comm UEs, 0 for sensing UEs, and between 0 and 1 for JRC UEs. The simulation values are not reported.
beta_{k,i} subchannel quality factor
Binary factor introduced after Eq. (5) to eliminate low-gain subchannels. The threshold for declaring a subchannel low-gain is not specified.
C_{k,i,min} and S_{k,i,min} QoS thresholds
Communication and sensing QoS constraints in Eq. (5). The values used in the simulation, including for Fig. 2(c), are not reported.
Subgradient step size delta
Step size in the dual updates in Eq. (13). Its value is not reported in the simulation setup.
Convergence tolerances epsilon and epsilon_mu
Stopping criteria in Algorithm 1 and the bisection search for mu. Their values are not reported.

assumptions (6)

standard math KKT conditions characterize the global optimum of each fixed-interference convex subproblem.
Invoked in Section IV-A to derive equations (8), (10), and (12). This requires the fixed-I surrogate to be convex, which holds for the log and linear terms, but the resulting formulas are not computed correctly.
ad hoc to paper The interference term I_{k,i} can be treated as a fixed constant within each iteration while optimizing P.
Stated in Section IV: the interference term is assigned to the sum over j not equal to k in (2), (3), and (4). This approximation transforms (5) into convex subproblems but is the core simplification on which the whole algorithm rests.
domain assumption Successive convex approximation with a fixed-interference surrogate converges under bounded channel gains.
Section IV-C appeals to [12] for convergence. The required surrogate lower-bound property is not verified, so this is a load-bearing assumption, not an established fact for this algorithm.
domain assumption Zero-forcing precoding leaves only residual multi-user interference of the form sum_{j != k} P_{j,i} |H_k w_{j,i}|^2.
Used in Section III, equations (2) and (4), to model the communication and JRC capacities under ZF precoding.
domain assumption Matched precoding for sensing UEs yields an SCNR with denominator N0 + C0 plus interference.
Used in Section III, equation (3), for the sensing utility. The SCNR is linear in the allocated power, which is why the water-filling update cannot be derived as written.
ad hoc to paper The binary beta_{k,i} factor removes low-gain subchannels without loss of optimality.
Introduced after Eq. (5) to eliminate low-gain sub-channels and reduce interference. The optimality impact of this hard thresholding is not analyzed.

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Cite this review

Pith. "Pith review of Unified Interference-Aware Water-Filling for QoS-Constrained Communication, Sensing, and JRC." pith.science (2026). https://pith.science/paper/PVA6YMVV

@misc{pith2026250601400,
  author       = {Pith},
  title        = {Pith review of: Unified Interference-Aware Water-Filling for QoS-Constrained Communication, Sensing, and JRC},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PVA6YMVV}},
  note         = {Machine review of arXiv:2506.01400}
}

read the original abstract

Water-filling (WF) algorithms are pivotal in maximizing capacity and spectral efficiency in multiple-input and multiple-output (MIMO) systems. However, traditional WF approaches cater solely to communication requirements, neglecting the emerging heterogeneity of 6G, including sensing and joint radar-communication (JRC). As these diverse demands grow in importance and have different Quality of Service (QoS) constraints, traditional WF becomes inadequate. Therefore, in this paper, we propose a unified interference-aware and QoS-constrained WF algorithm for systems with communication, sensing, and JRC. The proposed algorithm enables power allocation for multi-user MIMO systems, effectively addressing interference and balancing the support for heterogeneous user requirements.

Figures

Figures reproduced from arXiv: 2506.01400 by the authors.

**Figure 1.** Proposed MU MIMO system architecture. where sC,k ∈ C Nr,k , sS,k ∈ C Nr,k , and sJRC,k ∈ C Nr,k are the communication, sensing, and JRC dual function radar communication (DFRC) signals, respectively. The corresponding beamforming matrices and PA for sub-channel i are WC,k ∈ C Nt×Nr,k , WS,k ∈ C Nt×Nr,k , WJRC,k ∈ C Nt×Nr,k and PC,k,i, PS,k,i, PJRC,k,i, respectively. The received signal at the k-th UE is therefore g… view at source ↗

**Figure 2.** Comparison between the proposed iterative unified WF (i.e., Prop), traditional WF (i.e., Trad), and equal PA WF (i.e., Equal) algorithms: (a) average [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Average runtime for equal PA, proposed WF and traditional WF. [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

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Reference graph

Works this paper leans on

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [12]

A unified convergence analysis of block succes- sive minimization methods for nonsmooth optimization,

M. Razaviyaynet al., “A unified convergence analysis of block succes- sive minimization methods for nonsmooth optimization,”SIAM Journal on Optimization, vol. 23, no. 2, pp. 1126–1153, 2013

work page 2013

[2] [1]

Polarization-based multiplexing: Enabling spectrum efficient joint radar and communication,

A. Naeemet al., “Polarization-based multiplexing: Enabling spectrum efficient joint radar and communication,”IEEE Wireless Communica- tions Letters, vol. 13, no. 5, pp. 1414–1418, 2024

work page 2024

[3] [2]

Heterogeneous cluster-based information- centric sensor networks with user security satisfaction,

A. Gharib and M. Ibnkahla, “Heterogeneous cluster-based information- centric sensor networks with user security satisfaction,”IEEE Internet of Things Journal, vol. 10, no. 9, pp. 8123–8139, 2023

work page 2023

[4] [3]

Implementation of water- filling algorithm for optimal power allocation in the wireless channel of a MIMO 2x2 system over SDR,

M. A. C. Castro and J. L. A. Cusicuna, “Implementation of water- filling algorithm for optimal power allocation in the wireless channel of a MIMO 2x2 system over SDR,” inIEEE Colombian Caribbean Conference, 2023, pp. 1–6

work page 2023

[5] [4]

Physically-consistent multi-band massive MIMO systems: A radio resource management model,

N. Balasuriya, A. Mezghani, and E. Hossain, “Physically-consistent multi-band massive MIMO systems: A radio resource management model,”IEEE Transactions on Wireless Communications, pp. 1–1, 2025

work page 2025

[6] [5]

Resource allocation in multi-user MIMO-OFDMA VLC systems over low-pass LED channels,

Y . Donget al., “Resource allocation in multi-user MIMO-OFDMA VLC systems over low-pass LED channels,”IEEE Photonics Technology Letters, vol. 37, no. 11, pp. 633–636, 2025

work page 2025

[7] [6]

Multiuser water-filling in the presence of crosstalk,

W. Yu, “Multiuser water-filling in the presence of crosstalk,” in2007 Information Theory and Applications Workshop, 2007, pp. 414–420

work page 2007

[8] [7]

Simultaneous water filling in mutually interfering systems,

O. Popescu, D. C. Popescu, and C. Rose, “Simultaneous water filling in mutually interfering systems,”IEEE Transactions on Wireless Com- munications, vol. 6, no. 3, pp. 1102–1113, 2007

work page 2007