Extended AB Algorithms for Bistatic Integrated Sensing and Communications Systems

Tian Jiao; Yanlin Geng; Zai Yang; Zhiqiang Wei

REVIEW 4 major objections 4 minor 16 references

Extended AB Algorithms for Bistatic Integrated Sensing and Communications Systems

T0 review · 4 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A classical alternating-maximization method, extended by replacing each estimator with a free auxiliary variable, computes the capacity-distortion tradeoff of bistatic integrated sensing and communication systems for both squared-error and

desk verdict A useful AB-style extension for bistatic ISAC rate-distortion, but the headline claim of computing C(D) goes beyond the proved convergence; worth a revision, not a desk reject. read the letter →

arxiv 2508.07567 v1 pith:2DLPVLVZ submitted 2025-08-11 cs.IT math.IT

Tian Jiao , Yanlin Geng , Zhiqiang Wei , Zai Yang This is my paper · ORCID

classification cs.ITmath.IT MSC 94A1594A1794A3490C26

keywords integratedsensingandcommunicationbistaticISACrate-distortionfunctioncapacity-distortionABalgorithmnon-convexconstraintssquared-errordistortionlogarithmicloss

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

Bistatic integrated sensing and communication (ISAC) systems face a fundamental tradeoff: the more a codeword tells the communication receiver, the less accurately a separated sensing receiver can estimate the environment from the same transmission. The optimal tradeoff is the capacity-distortion function, but the optimization problems defining it carry distortion constraints that are non-convex in the input distribution, which blocks the standard AB algorithm. The paper's central move is to replace the estimator in the distortion term with a free auxiliary variable ($c(u,z)$ for squared error, $f(s,u,z)$ for log-loss), which makes the constraint linear while provably preserving the optimum. On that reformulation, the paper constructs extended AB algorithms with closed-form updates, proves the objective is monotonically non-decreasing along iterations, and shows numerical rate-distortion curves that match known values or exceed known lower bounds. A sympathetic reader takes away a practical method for drawing the full rate-distortion curve of bistatic ISAC channels instead of relying on theoretical bounds alone.

What carries the argument

The auxiliary-variable linearization of the distortion constraint. For squared error, the estimator $\hat{S}(U,Z)$ is pulled out of the constraint and treated as an independent function $c(u,z)$, so the constraint becomes a sum of terms $p(u,x)(s-c(u,z))^2$; for log-loss, the conditional estimator $p(s|u,z)$ is replaced by a free soft function $f(s,u,z)$. The AB surrogate $\tilde{F}(p,q)$ then separates the variables, and the Lagrange multiplier $\lambda$, found by solving the one-dimensional equation $G(\lambda)=0$, pins the iterate to the distortion boundary. Each block update ($q$, then $p$, then $c$ or $f$) has a closed form.

What would settle it

Take a small finite-alphabet instance, enumerate or globally optimize over all input distributions $p(u,x)$, and compare the true optimal value with the value Algorithm 1 returns from many random initializations. Any run that stops at a strictly smaller value while satisfying the distortion constraint, or two initializations that settle at different values, would falsify the claim that the algorithm calculates the rate-distortion tradeoff.

Watch

Extended reading notes

Core claim

The paper claims that the capacity-distortion optimization of a bistatic ISAC system can be solved by an extended AB algorithm. Its pivotal result (Theorem 1) equates the optimum of the original non-convex problem (1), with squared-error distortion and objective $I(X;Y|U,S)+I(U;Z)$, to the optimum of a reformulated problem in which the distortion constraint is linear because the estimator $\hat{S}(U,Z)$ is replaced by a free variable $c(u,z)$. At the optimum, $c(u,z)$ recovers exactly the conditional mean $\hat{S}(u,z)$, so the reformulation's feasible set collapses back to the original one and the two optima coincide. The same equivalence is developed for log-loss distortion with a free sof

Load-bearing premise

The algorithm's alternating updates are assumed to reach the global maximum of the auxiliary objective, so that the value at the stopping point really is the capacity-distortion function; the paper proves only that the objective never goes down.

Editorial extensions

If this is right

The non-convex distortion constraint can be replaced by a linear one without changing the optimum, so the original problem becomes tractable by alternating maximization.
Both the squared-error and log-loss versions admit closed-form updates for $p$, $q$, and the auxiliary estimator, avoiding the multiplier traversal of classical AB rate-distortion computation.
The same framework extends directly to Gaussian channels with a power constraint by adding a second Lagrange multiplier, yielding rate-distortion curves for practical bistatic channels.
The monotone convergence proof guarantees that any stopping point of the iteration is at least a local optimum of the surrogate, making the algorithm a stable numerical tool for capacity-distortion evaluation.

Reading between the lines

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

If the auxiliary-variable linearization is as general as the proof suggests, it should also apply to other bounded distortion measures whose optimal estimator has a closed form, such as absolute error or Hamming loss under discrete alphabets; the paper does not test this.
The global-convergence question is left open by Theorem 2; a natural extension is a formal proof that every limit point of the iterates satisfies the KKT conditions and that the surrogate has no spurious local maxima, or a counterexample if it does.
For the second log-loss Gaussian regime the computed curve sits above the known lower bound; if that bound is not tight, the algorithm may be providing the first numerical evidence of a larger rate-distortion region than theory currently certifies.
The same reformulation appears portable to monostatic ISAC or multi-antenna settings where the distortion constraint is non-convex, although the paper restricts itself to the bistatic model.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

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

This paper extends Arimoto-Blahut algorithms to compute the rate-distortion trade-off in bistatic ISAC systems with squared-error and log-loss distortion. The new idea is introducing an auxiliary variable to convert the non-convex distortion constraint into a linear constraint, then alternating maximization of an AB surrogate. The reformulation in Theorem 1 is algebraically correct (once you assume the state is independent of the input), and the closed-form updates are a genuine extension of AB to a problem class it didn't previously handle. The numerical results match known theory in the cases shown, and the comparison against [12] is appropriate.

The main soft spot is the gap between what the algorithm provably does and what the abstract claims. Theorem 2 proves only monotone non-decrease of the surrogate; it does not establish global convergence of the alternating scheme. Since the objective I(X;Y|U,S)+I(U;Z) is generally not concave in p(u,x), the iterates could converge to a stationary point below C(D). So the claim that the algorithm 'calculates the rate-distortion trade-off' is not proven. This is the load-bearing issue. It's fixable: a duality/concavity argument, a global-convergence proof, or a carefully worded statement that the algorithm provides a lower bound would close the gap.

Two smaller issues. First, the proof of Theorem 1 assumes the distortion constraint is active (λ > 0) without stating that condition; the argument can be patched (the monotonicity of C(D) helps), but as written it's incomplete. Second, the log-loss section omits the actual update details and convergence analysis ("omitted due to space limitations"), and the Gaussian numerical section never explains how the continuous alphabet is discretized. These omissions make the log-loss results hard to reproduce.

The core idea is sound, the extension is real, and the citation pattern is honest. The paper deserves a serious referee, but not in its current form. I'd recommend sending it to peer review with a request for a global-convergence analysis (or a sharpened claim), plus the missing details for log-loss and the Gaussian discretization.

Referee Report

4 major / 4 minor

Summary. The paper develops Arimoto-Blahut-type algorithms for computing the capacity-distortion function C(D) of a bistatic ISAC system under squared-error and log-loss distortions. The original non-convex optimization problems (1) and (2) are reformulated by introducing auxiliary estimator variables c(u,z) and f(u,s,z), which turn the distortion constraints into linear constraints. The authors prove a formal equivalence (Theorem 1), derive closed-form alternating updates for p(u,x), q, and c/f, prove monotone non-decrease of the surrogate function (Theorem 2), and report numerical comparisons for Gaussian channels. The central claim is that Algorithm 1 calculates the rate-distortion trade-off.

Significance. If the global-convergence gap can be closed, this is a useful extension of the AB method to non-convex rate-distortion problems and would make the information-theoretic limits of bistatic ISAC computable in practice. The reformulation is natural, the updates are closed-form, and the monotonicity theorem is a useful partial result. The numerical agreement with known theoretical values in the log-loss case is encouraging. However, the central claim is currently only partially supported: monotone convergence of the surrogate does not by itself establish that the limit equals C(D), and the continuous-alphabet implementation is unspecified. These issues are load-bearing and require revision.

major comments (4)

[Section III-C, Theorem 2] The proof of Theorem 2 establishes only \tilde{F}(p_{n-1},q_{n-1}) ≤ \tilde{F}(p_{n-1},q_n) ≤ \tilde{F}(p_n,q_n), i.e., monotone non-decrease and boundedness of the surrogate. Since \tilde{F} is biconcave but not jointly concave, and since F(p) in (1) is not concave (I(U;Z) contains -H(Z|U)), coordinate ascent can converge to a stationary point or saddle with value strictly below max_p F(p). The p-update (9) maximizes the surrogate for fixed q, not F itself; the q-update (6) makes the surrogate tight only at the current p. No global-convergence, strong-duality, or KKT-sufficiency argument is supplied. Thus the abstract's claim that Algorithm 1 'calculate[s] the rate-distortion trade-off' is not established. Please add a global optimality proof under stated conditions, or revise the claims to convergence to a local/stationary point and support the computation claim with additional argumen
[Section III-A, Theorem 1] In the proof of Theorem 1, the KKT stationarity condition L'_c(p*,c*)=0 yields c*=\hat{s} only when the multiplier λ is strictly positive, i.e., when the distortion constraint is active. If λ=0, the stationarity condition is vacuous and the argument fails. The monotonicity assertion later in Section III-A implies activity only for D below the unconstrained-achievable distortion, a condition not stated in Theorem 1. Moreover, the algorithm's Step 3, G(λ)=0, assumes equality in the constraint; for D larger than the distortion achieved by the unconstrained maximizer, no λ≥0 solves G(λ)=0. The equivalence can be repaired by observing that c enters only through the constraint and can be replaced by the conditional-mean estimator \hat{s}(p) without changing feasibility or objective, but the manuscript should state and prove this and handle the inactive-constraint case explicitly.
[Section IV and Remark 1] Algorithm 1 is formulated for finite alphabets with sums over p(u,x), p(y,s,z|x), etc. The numerical section applies it to continuous Gaussian channels with a power constraint, but no discretization, grid size, initialization, stopping criterion, or numerical method for solving the multiplier equations (λ, μ) is provided. Consequently, the validation in Figs. 1 and 2 cannot be reproduced or fully assessed, and the extension of the discrete-alphabet AB updates to continuous alphabets is not justified. Please provide full implementation details or a separate derivation for the Gaussian case.
[Section III-B] The log-loss variant is presented only as a set of update formulas; the pseudocode, the derivation of the p-update, and any convergence analysis are omitted ('details are omitted due to space limitations'). Since log-loss is one of the two distortion metrics advertised in the abstract and is used in Fig. 2, this is a substantive omission. Please include the full algorithm and at least a monotonicity/convergence statement analogous to Theorem 2, or clearly state that no convergence guarantee is claimed.

minor comments (4)

[Section III-A, text after Eq. (4)] The displayed expression for F(p) - \tilde{F}(p,q) writes the first KL term as D(p(x,y|u,s) || q(x,y|u,s)); since q has no y component, this should be D(p(x|u,y,s) || q(x|u,y,s)), and the second term should be D(p(u|z) || q(u|z)).
[Algorithm 1] No stopping criterion is given; please specify one (e.g., tolerance on function values or on p, or a maximum iteration count).
[Section IV, Fig. 2] The labels '1/σ2=1' and '1/σ2=3' are ambiguous; specify whether these refer to σ_1^2, σ_2^2, or their inverses, and state the other parameters used for each curve.
[Section III-A, Remark 1] The statement that Step 3 is replaced by solving a set of equations for λ and μ is too terse: no uniqueness, monotonicity, or solution method is given for the two-multiplier case.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the paper's inputs are prior capacity-distortion characterizations; the auxiliary-variable reformulation and AB updates are derived rather than fitted to the target rate-distortion curve.

full rationale

The derivation chain is self-contained with respect to the paper's own claims. Lemma 1 and Lemma 2, which define the capacity-distortion optimization problems (1) and (2), are quoted from prior work [11] and [12]; Lemma 1 is a self-citation, but it is a parameter-free information-theoretic characterization with stated assumptions and is not the quantity the algorithm is supposed to predict, so it does not constitute a circular reduction. Theorem 1 establishes equivalence between the original problem and the linearly constrained reformulation by comparing feasible sets and using KKT stationarity with respect to the auxiliary c(u,z); this does not assume the target rate-distortion value. The surrogate function \tilde{F} in (4) is a standard lower bound that becomes tight at q(x|u,y,s)=p(x|u,y,s) and q(u|z)=p(u|z), and the updates (6), (7), (9) are obtained by closed-form stationarity of that surrogate, not by fitting the final C(D). Numerical comparison in Fig. 2 uses the theoretical value and lower bound from the external reference [12]. The main gaps—Theorem 2 only proves monotone boundedness of \tilde{F}, not global optimality for the non-concave objective, and the log-loss proof is omitted—are correctness/convergence concerns rather than circularity: nothing in the paper reduces its 'prediction' to a fitted parameter or to a self-referential uniqueness claim.

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

The auxiliary variables c(u,z) and f(u,s,z) are mathematical slack variables introduced to linearize constraints; they are not physical entities and carry no independent-evidence requirement. The algorithm has no free parameters fitted to data: lambda and (in the power-constrained case) mu are Lagrange multipliers solved to enforce constraints. Initial p0 and c0 are algorithmic starting points, not fitted parameters.

assumptions (5)

domain assumption The capacity-distortion function is given by Lemma 1 [11, Theorem 6] for SE distortion and Lemma 2 [12, Corollary 2] for log-loss.
The paper builds on these prior characterizations of C(D) for the bistatic ISAC model; if they are wrong or have narrower scope, the algorithm solves the wrong problem.
domain assumption The state S is independent of the transmitted codeword X (and of U), so that H(X|U,S)=H(X|U) and the objective expression in (3) equals I(X;Y|U,S)+I(U;Z).
The text states S^n is i.i.d. from P_S and the codeword carries W, but never explicitly writes p(s|x)=p(s); the equivalence in Theorem 1 relies on the log-form identity that requires this independence.
domain assumption The capacity-distortion function C(D) is monotonically non-decreasing in D, so the distortion constraint can be assumed active (lambda>0) at the optimum.
Used to justify the equality-form constraint and the unique root of G(lambda)=0; cited to [11, Lemma 1].
ad hoc to paper The alternating maximization of the surrogate F_tilde over p and q converges to the global maximum of F, not merely to a local optimum.
No concavity or global-convergence proof is given. Theorem 2 only establishes monotone non-decrease of F_tilde along iterates; the claim that the algorithm 'calculates the rate-distortion trade-off' assumes this premise.
ad hoc to paper Discrete-alphabet AB updates remain valid for the continuous Gaussian channels used in the numerical section, either through discretization or a parametric restriction that the paper does not specify.
Algorithm 1 is stated for pmf p(u,x); Section IV applies it to Gaussian Y=S+X+N1, Z=S+X+N2 without explaining how sums become integrals or how U and X are parametrized.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Extended AB Algorithms for Bistatic Integrated Sensing and Communications Systems." pith.science (2026). https://pith.science/paper/2DLPVLVZ

@misc{pith2026250807567,
  author       = {Pith},
  title        = {Pith review of: Extended AB Algorithms for Bistatic Integrated Sensing and Communications Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2DLPVLVZ}},
  note         = {Machine review of arXiv:2508.07567}
}

read the original abstract

Integrated sensing and communication (ISAC) is pivotal for next-generation wireless networks, rendering the computation of rate-distortion trade-off in ISAC systems critically important. In this paper, we propose the extended Arimoto-Blahut (AB) algorithms to calculate the rate-distortion trade-off in bistatic ISAC systems, which overcome the limitation of existing AB algorithms in handling non-convex constraints. Specifically, we introduce auxiliary variables to transform non-convex distortion constraints into linear constraints, prove that the reformulated linearly-constrained optimization problem maintains the same optimal solution as the original problem, and develop extended AB algorithms for both squared error and logarithmic loss distortion metrics based on the framework of AB algorithm. Numerical results validate the effectiveness of the proposed algorithm.

Figures

Figures reproduced from arXiv: 2508.07567 by the authors.

**Figure 2.** Rate-distortion function of the bistatic ISAC syste [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

16 extracted references · 2 linked inside Pith

[12]

On the fundamental limits of integrated sensing and communicatio ns under logarithmic loss,

J. Chen, L. Y u, Y . Li, W. Shi, Y . Ge, and W. Tong, “On the fundamental limits of integrated sensing and communicatio ns under logarithmic loss,” arXiv preprint arXiv:2502.08502 , 2025

arXiv 2025
[1]

Waveform design and performance ana ly- sis for full-duplex integrated sensing and communication,

Z. Xiao and Y . Zeng, “Waveform design and performance ana ly- sis for full-duplex integrated sensing and communication, ” IEEE J. Sel. Areas Commun. , vol. 40, no. 6, pp. 1823–1837, 2022

2022
[2]

On t he effectiveness of OTFS for joint radar parameter estimation and communication,

L. Gaudio, M. Kobayashi, G. Caire, and G. Colavolpe, “On t he effectiveness of OTFS for joint radar parameter estimation and communication,” IEEE Trans. Wireless Commun. , vol. 19, no. 9, pp. 5951–5965, 2020

2020
[3]

Integrated sensing and communication with mmwave massive MIMO: A compressed sampling perspective,

Z. Gao, Z. Wan, D. Zheng, S. Tan, C. Masouros, D. W. K. Ng, and S. Chen, “Integrated sensing and communication with mmwave massive MIMO: A compressed sampling perspective,” IEEE Trans. Wireless Commun. , vol. 22, no. 3, pp. 1745–1762, 2023

2023
[4]

The rise of intelligent reﬂecting surfaces in integrated s ensing and communications paradigms,

A. M. Elbir, K. V . Mishra, M. B. Shankar, and S. Chatzinota s, “The rise of intelligent reﬂecting surfaces in integrated s ensing and communications paradigms,” IEEE Netw., vol. 37, no. 6, pp. 224–231, 2022

2022
[5]

Beamforming in in- tegrated sensing and communication systems with reconﬁgur able intelligent surfaces,

R. P . Sankar, S. P . Chepuri, and Y . C. Eldar, “Beamforming in in- tegrated sensing and communication systems with reconﬁgur able intelligent surfaces,” IEEE Trans. Wireless Commun. , vol. 23, no. 5, pp. 4017–4031, 2024

2024
[6]

An information-theoretic approach to joint sensing and commu nica- tion,

M. Ahmadipour, M. Kobayashi, M. Wigger, and G. Caire, “An information-theoretic approach to joint sensing and commu nica- tion,” IEEE Trans. Inf. Theory , vol. 70, no. 2, pp. 1124–1146, 2022

2022
[7]

O n the fundamental tradeoff of integrated sensing and communi ca- tions under Gaussian channels,

Y . Xiong, F. Liu, Y . Cui, W. Y uan, T. X. Han, and G. Caire, “O n the fundamental tradeoff of integrated sensing and communi ca- tions under Gaussian channels,” IEEE Trans. Inf. Theory , vol. 69, no. 9, pp. 5723–5751, 2023

2023

Show all 16 references

[8]

Deterministic-random tradeoff of integrated sensing and com- munications in Gaussian channels: A rate-distortion persp ective,

F. Liu, Y . Xiong, K. Wan, T. X. Han, and G. Caire, “Deterministic-random tradeoff of integrated sensing and com- munications in Gaussian channels: A rate-distortion persp ective,” in Proc. IEEE Int. Symp. Inf. Theory (ISIT) , 2023

2023
[9]

Information-th eoretic limits of integrated sensing and communication with correl ated sensing and channel states for vehicular networks,

Y . Liu, M. Li, A. Liu, J. Lu, and T. X. Han, “Information-th eoretic limits of integrated sensing and communication with correl ated sensing and channel states for vehicular networks,” IEEE Trans. V eh. Technol., vol. 71, no. 9, pp. 10 161–10 166, 2022

2022
[10]

Strong conver ses for memoryless bi-static ISAC,

M. Ahmadipour, M. Wigger, and S. Shamai, “Strong conver ses for memoryless bi-static ISAC,” in Proc. IEEE Int. Symp. Inf. Theory (ISIT) . IEEE, 2023, pp. 1818–1823

2023
[11]

Information-theoretic limits of bistatic integrated sen sing and communication,

T. Jiao, K. Wan, Z. Wei, Y . Geng, Y . Li, Z. Y ang, and G. Cair e, “Information-theoretic limits of bistatic integrated sen sing and communication,” arXiv preprint arXiv:2306.06648 , 2025

2025 arXiv
[13]

An algorithm for computing the capacity of arbitrary discrete memoryless channels,

S. Arimoto, “An algorithm for computing the capacity of arbitrary discrete memoryless channels,” IEEE Trans. Inf. Theory , vol. 18, no. 1, pp. 14–20, 1972

1972
[14]

Computation of channel capacity and rate-d istortion functions,

R. Blahut, “Computation of channel capacity and rate-d istortion functions,” IEEE Trans. Inf. Theory , vol. 18, no. 4, pp. 460–473, 1972

1972
[15]

Toward computing the capac ity region of degraded broadcast channel,

K. Y asui and T. Matsushima, “Toward computing the capac ity region of degraded broadcast channel,” in Proc. IEEE Int. Symp. Inf. Theory (ISIT) , 2010

2010
[16]

Blahut-Arimoto algorithms for comp uting capacity bounds of broadcast channels,

Y . Liu and Y . Geng, “Blahut-Arimoto algorithms for comp uting capacity bounds of broadcast channels,” in Proc. IEEE Int. Symp. Inf. Theory (ISIT) , 2022

2022

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

[1] [12]

On the fundamental limits of integrated sensing and communicatio ns under logarithmic loss,

J. Chen, L. Y u, Y . Li, W. Shi, Y . Ge, and W. Tong, “On the fundamental limits of integrated sensing and communicatio ns under logarithmic loss,” arXiv preprint arXiv:2502.08502 , 2025

arXiv 2025

[2] [1]

Waveform design and performance ana ly- sis for full-duplex integrated sensing and communication,

Z. Xiao and Y . Zeng, “Waveform design and performance ana ly- sis for full-duplex integrated sensing and communication, ” IEEE J. Sel. Areas Commun. , vol. 40, no. 6, pp. 1823–1837, 2022

2022

[3] [2]

On t he effectiveness of OTFS for joint radar parameter estimation and communication,

L. Gaudio, M. Kobayashi, G. Caire, and G. Colavolpe, “On t he effectiveness of OTFS for joint radar parameter estimation and communication,” IEEE Trans. Wireless Commun. , vol. 19, no. 9, pp. 5951–5965, 2020

2020

[4] [3]

Integrated sensing and communication with mmwave massive MIMO: A compressed sampling perspective,

Z. Gao, Z. Wan, D. Zheng, S. Tan, C. Masouros, D. W. K. Ng, and S. Chen, “Integrated sensing and communication with mmwave massive MIMO: A compressed sampling perspective,” IEEE Trans. Wireless Commun. , vol. 22, no. 3, pp. 1745–1762, 2023

2023

[5] [4]

The rise of intelligent reﬂecting surfaces in integrated s ensing and communications paradigms,

A. M. Elbir, K. V . Mishra, M. B. Shankar, and S. Chatzinota s, “The rise of intelligent reﬂecting surfaces in integrated s ensing and communications paradigms,” IEEE Netw., vol. 37, no. 6, pp. 224–231, 2022

2022

[6] [5]

Beamforming in in- tegrated sensing and communication systems with reconﬁgur able intelligent surfaces,

R. P . Sankar, S. P . Chepuri, and Y . C. Eldar, “Beamforming in in- tegrated sensing and communication systems with reconﬁgur able intelligent surfaces,” IEEE Trans. Wireless Commun. , vol. 23, no. 5, pp. 4017–4031, 2024

2024

[7] [6]

An information-theoretic approach to joint sensing and commu nica- tion,

M. Ahmadipour, M. Kobayashi, M. Wigger, and G. Caire, “An information-theoretic approach to joint sensing and commu nica- tion,” IEEE Trans. Inf. Theory , vol. 70, no. 2, pp. 1124–1146, 2022

2022

[8] [7]

O n the fundamental tradeoff of integrated sensing and communi ca- tions under Gaussian channels,

Y . Xiong, F. Liu, Y . Cui, W. Y uan, T. X. Han, and G. Caire, “O n the fundamental tradeoff of integrated sensing and communi ca- tions under Gaussian channels,” IEEE Trans. Inf. Theory , vol. 69, no. 9, pp. 5723–5751, 2023

2023