Pith. sign in

REVIEW 4 major objections 4 minor 1 cited by

On Pareto-Optimal Estimation-Information Performance Limits of MIMO Integrated Sensing and Communications Systems

T0 review · 4 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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

Pith's one-line read The paper characterizes the MIMO ISAC performance limit as a Pareto boundary and proves that the SISO boundary is unreachable except at its endpoints.

desk verdict Serious ISAC limits paper with real new results, but the central convergence proof has a sign mismatch and the compound-signaling gain is optimistic; worth refereeing, not taking at face value. read the letter →

arxiv 2501.01053 v3 pith:QATDUN7J submitted 2025-01-02 eess.SP

Zi-Jie Wang , Xudong Wang , Giuseppe Caire This is my paper · ORCID
classification eess.SP
keywords integratedsensingandcommunicationMIMOMMSE-ratetradeoffParetooptimalityBlahut-Arimotoalgorithmwater-fillingwaveformuncertaintychannelestimation
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

The paper aims to pin down the fundamental sensing-communication limit of a MIMO integrated sensing and communication (ISAC) system, where one random waveform has to estimate a sensing channel and transmit data at the same time. It defines the limit as the Pareto boundary of all achievable pairs of a modified MMSE sensing metric and an ergodic coherent rate, and derives variational conditions that any boundary-achieving input and output distribution must satisfy. For a fast-fading SISO channel, it proves that every interior point of this boundary is unattainable, so the limit is a supremum that practical signals can approach but cannot reach, except at the sensing-only and communication-only endpoints. It then contributes a provably convergent alternating-maximization algorithm for computing boundary points, closed-form endpoint waveforms that exhibit a water-filling tradeoff and a waveform-uncertainty tradeoff, and a compound signaling scheme for coincided sensing and communication channels. If these arguments hold, the MMSE-Rate limit becomes a computable benchmark rather than an abstract multi-objective optimization, and system designers know both what is achievable and which purported bounds are loose.

What carries the argument

The object that carries the argument is the MMSE-Rate limit set (11) together with the variational equation (13) that characterizes its boundary. Equation (13) is the statement that the Gaussian-blurred logarithm of the optimal output density must equal a sensing-dependent term plus Lagrange-multiplier terms; it converts the functional Pareto optimization into a solvability condition for $p_Y^\star$. The computational machinery is an alternating-maximization algorithm over the input density $p_X$ and an auxiliary backward channel $\phi$, with a Newton-Raphson update for the Lagrange multiplier that enforces the average power constraint and a proof that the objective is concave, so the iterates converge to the supremum. At the two endpoints the machinery reduces to standard water-filling: sensing optimality forces a deterministic sample correlation matrix and an isometry waveform, while communication optimality forces a Gaussian waveform whose covariance water-fills the channel.

What would settle it

Run a Monte Carlo simulation of the compound signaling scheme of Section III-D in which the data precoder is built from the actual MMSE estimate $\hat{\mathbf{H}}$ obtained from the sensing phase, rather than from the true channel, and compare the achieved rate with $\breve{R}$ in (53). If the achieved rate lies persistently below $\breve{R}$ by a gap that does not vanish as $T'$ grows, the perfect-estimate premise is false. Alternatively, for the SISO case, a square-integrable $\log p_y^\star(y,\alpha)$ satisfying (13) for any $\alpha\in(0,1)$ would contradict Theorem 2.

Watch

Extended reading notes

Core claim

On its own terms, the paper's central claim is that the MMSE-Rate limit, i.e. the boundary of the set in (11), is characterized by Theorem 1: for each weight $\alpha\in(0,1]$, any optimal output distribution $p_Y^\star(\mathbf{Y},\alpha)$ must solve the convolutional equation $\int p_{\mathbf{Z}_c}(\mathbf{Y}-\mathbf{H}\mathbf{X})\log p_Y^\star(\mathbf{Y},\alpha)\,d\mathbf{Y} = T(1-1/\alpha)\operatorname{Tr}\!\big[(\bar{\Sigma}_g^{-1}+\sigma_s^{-2} \mathbf{I}_{N_s}\otimes\mathbf{X}\mathbf{X}^\dagger)^{-1}\big]+\mu_1(\alpha)+\mu_2(\alpha)\operatorname{Tr}(\mathbf{X}\mathbf{X}^\dagger)$. For $\alpha=0$, a deterministic sample correlation matrix is sufficient. Theorem 2 then shows that in the fast-fading SISO case no square-integrable output density solves the equation for $\alpha\in(0,1)$, so interior points of the limit curve are not achievable; only the Gaussian communication-optimal endpoint and the binary sensing-optimal endpoint are. Algorithm 1, a constrained alternating-maximization algorithm of Blahut-Arimoto type, is proven to converge to the supremum and is used to plot the boundary numerically. The paper also derives closed-form endpoint waveforms: an isometry waveform with water-filling over the sensing channel statistics at the sensing-optimal point, and a Gaussian waveform with water-filling over the communication channel realization at the communication-optimal point. For coincided channels it proposes a compound signal that first sends the sensing-optimal waveform for channel estimation and then the communication-optimal waveform for data, claiming a rate improvement over non-coherent capacity.

Load-bearing premise

The compound-signaling rate calculation in Section III-D uses the channel estimate $\hat{\mathbf{H}}$ as if it were the true channel when evaluating the coherent data rate, so residual estimation error and its effect on the water-filling precoder are not modelled.

Editorial extensions

If this is right

  • Any candidate ISAC waveform can be checked against (13): if its output density fails the variational condition, that waveform cannot lie on the MMSE-Rate limit for that weight $\alpha$.
  • For fast-fading SISO channels, interior points of the limit curve are a supremum, not achievable operating points; a practical SISO ISAC system must either time-share between the sensing-optimal and communication-optimal endpoints or operate strictly inside the region.
  • Algorithm 1 supplies a numerical benchmark that converges with a proven guarantee, so comparisons against the true limit no longer have to rely on loose Gaussian/isometry outer and inner bounds.
  • The closed-form endpoint waveforms make the two tradeoffs explicit: power is divided between sensing water-filling and communication water-filling, and randomness is divided between a predictable isometry signal and an entropy-maximizing Gaussian signal.
  • For coincided channels, the compound scheme implies that investing a short sensing-optimal pilot phase can raise the achievable rate above the non-coherent capacity, quantifying the integration gain of ISAC at finite coherence time.

Reading between the lines

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

  • Inference: The SISO unattainability result hints that for general MIMO the boundary may also be an unattainable supremum; if that is proved, the design target shifts from operating on the frontier to approaching the frontier from inside the region.
  • Inference: The perfect-estimate simplification could be relaxed by modelling $\hat{\mathbf{H}}$ as a noisy version of $\mathbf{H}$; re-deriving the data-phase rate with the induced estimation error would likely reduce the claimed gain over non-coherent capacity at small $T'$.
  • Inference: The same variational-plus-alternating-maximization template applies to other sensing metrics that the paper mentions, such as the modified Cramér-Rao bound or the estimation rate, yielding analogous Pareto frontiers.
  • Inference: The numerical finding that $\breve{R}_c$ saturates once $T'=N$ suggests a simple design rule for pilot length in this scheme: use $N$ symbols to estimate an $N$-column channel, because additional pilots cost rate without improving the data-phase rate.
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.

Referee Report

4 major / 4 minor

Summary. The paper studies fundamental estimation-information performance limits of MIMO ISAC systems with random dual-functional waveforms. It defines an MMSE-Rate region whose boundary is the MMSE-Rate limit, derives variational conditions for optimal input/output distributions (Theorem 1), proves non-achievability of the limit for fast-fading SISO channels except at the SAC-optimal endpoints (Theorem 2), proposes a Blahut-Arimoto-type algorithm for computing the limit (Algorithm 1), derives closed-form sensing- and communication-optimal waveforms (Theorems 3-6), and proposes a compound signaling strategy for coincided SAC channels (Section III-D). Numerical examples illustrate the MMSE-Rate region, the two tradeoffs (water-filling and waveform uncertainty), and gains of the compound strategy.

Significance. If the results are fully established, the paper would be a substantial contribution: it gives a variational characterization of a genuine ISAC performance limit with random waveforms, closed-form SAC-optimal strategies, an explicit non-achievability result for SISO channels, and a signaling strategy exploiting integrated sensing for channel acquisition. The derivations are largely self-contained, and prior work including [7] is cited with attribution. The paper makes falsifiable numerical predictions and does not disguise fitted parameters as predictions. However, the central computational claim rests on a convergence proof that, as written, does not match the implemented update and lacks the required functional-analytic hypotheses; the compound-signaling rate is evaluated under a perfect-channel-estimate assumption. These issues are load-bearing for the paper's main claims.

major comments (4)
  1. [Appendix C, Eq. (C.6) and Algorithm 1] The update rule derived in Appendix C, Eq. (C.6), contains exp[+(1/alpha - 1)T Phi_tilde(X)] in the p_X exponent, whereas Algorithm 1 step 13 and the inner Newton update in line 7 use exp[-(1/alpha - 1)T Phi_tilde(X)]. Re-solving the first-order condition of (C.2a) gives the sensing-penalty term as -(1-alpha)Phi, i.e., an exponent of -(1/alpha - 1)T Phi_tilde(X), so the algorithm's sign is the correct one and Eq. (C.6) is not. Since Appendix C is the only proof that Algorithm 1 converges to the MMSE-Rate limit, this inconsistency must be fixed by re-deriving Eq. (C.6) consistently with the implemented iteration.
  2. [Appendix C-B] The convergence proof establishes only concavity of the functional J-tilde and cites [24, Theorem 9.5]. It does not verify the compactness and continuity conditions needed for alternating maximization over infinite-dimensional distribution spaces, does not account for the effect of the inner Newton iteration for the Lagrange multiplier, and provides no error bound connecting convergence of J to the returned p_X and the claimed (epsilon, R) pair to tolerance epsilon_J. The algorithm is presented for continuous random matrices, yet the numerical implementation necessarily involves discretization, and no discretization-error analysis is supplied. Therefore the statement that Algorithm 1 converges 'rigorously' to the limit 'to any desired level of precision' is not supported.
  3. [Section III-D, Eq. (53)] The compound signaling scheme evaluates the data-phase rate as R_c(X_c) with the coherent capacity expression (41) in which H is replaced by the estimate H-hat. This assumes the estimation phase yields a perfect channel estimate for the data phase. Residual estimation error from the finite-length pilot phase (T' symbols) is not propagated into the rate expression, and the water-filling precoder computed from H-hat is not necessarily optimal for the true H. Thus (53) and the rate improvements shown in Fig. 10 are optimistic upper bounds, not established achievable rates. The paper should either provide an achievable rate that accounts for channel estimation error or explicitly label the compound-signaling comparison as a genie-aided upper bound.
  4. [Appendix B, Theorem 2] The non-existence proof for alpha in (0,1) rests on the Hermite expansion of log p_y and the claim that the right-hand side of (B.1) cannot be a Gaussian convolution because the Cauchy term is not a Gaussian convolution. As written, this is not fully rigorous: the left-hand side of (B.1) is analytic in x for densities with Gaussian tails, while 1/(sigma_g^{-2}+sigma_s^{-2}x^2) has poles at x = ± i sigma_s/sigma_g, and the role of the additional mu_2 x^2 term is not addressed. Since Theorem 2 is a central theoretical claim, the proof should be stated cleanly, e.g., via Fourier transforms or a rigorous analyticity argument, rather than relying on a cited example that concerns only the pure Cauchy term.
minor comments (4)
  1. [Theorem 2, Eq. (17)] In the expression for p_y^*(y,1), the exponent is written with x^2 instead of y^2; this is a typo.
  2. [Section III-C3] The text contains an unresolved cross-reference 'Section ??'; the reference to the limit-achieving conditions should be fixed.
  3. [Eq. (44b)] The notation 'E {Phi [I ⊗ R*_X(alpha)]}' is ambiguous because R*_X(alpha) is a deterministic matrix; the expectation operator should be removed or clarified.
  4. [Section IV-B3] The legend and axis labels in Fig. 10 are difficult to parse; please clarify which curves correspond to the compound signal components and which to the non-coherent baseline.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation; the central MMSE-Rate limit, SISO unattainability, and Algorithm 1 are derived from first principles, with only a minor supporting self-citation to [7].

full rationale

The paper's central chain is self-contained: (10) formulates a stochastic functional optimization; Theorem 1 derives variational necessary conditions via standard calculus of variations (references [35], [29]); Theorem 2 solves the SISO specialization and shows non-existence of limit-achieving distributions for alpha in (0,1) by Hermite/power-series arguments; Algorithm 1 is a Blahut-Arimoto-type alternation on that same objective; Theorems 4 and 6 derive the endpoint waveforms using convexity and the classical MIMO water-filling capacity result. None of these steps takes the desired MMSE-Rate pair as an input, and no fitted parameter is relabeled as a prediction: the algorithm's output is evaluated in the same objective J that defines the limit, not calibrated to any precomputed curve. The only self-citation is Theorem 5, whose proof points to '[19] and [7, Theorem 1]' with G. Caire an author of both [7] and the present paper; this supplies a supporting high-SNR sensing-limited-rate formula used for inner bounds and numerical comparisons, but it is not used to establish the central variational conditions, the SISO unattainability result, the convergence claim, or the compound-signaling conclusion, and it is an attributed external published result. A separate correctness concern exists in Appendix C: the derived exponent in (C.6) has the opposite sign of the Phi-tilde term relative to Algorithm 1, and the convergence argument invokes [24, Thm 9.5] without verifying compactness over the infinite-dimensional distribution spaces; these are proof-quality issues, not circular reductions, so they do not change the circularity score.

Assumptions & free parameters 0 free parameters · 7 assumptions · 0 invented entities

The central claims rest on standard Gaussian channel assumptions, known covariance models, and several mathematical regularity conditions. No free parameters are fitted to data; water-filling levels are determined by power constraints. No new physical entities are postulated.

assumptions (7)
  • domain assumption Sensing channel g is zero-mean circular Gaussian with known full-rank covariance \bar\Sigma_g (assumption A1, and A1* block-diagonal for Theorem 4).
    Model assumption standard in sensing literature; its validity is not tested.
  • domain assumption Communication channel H has i.i.d. Gaussian entries and is known at the transmitter (assumption A2).
    Enables coherent water-filling capacity; later relaxed for the coincided channel case.
  • domain assumption Block fading: both G and H are constant for T symbols and change i.i.d. (assumption A3).
    Defines the coherence time and makes the ergodic rate and average MMSE meaningful.
  • domain assumption The random ISAC signal X is known at sensing receivers and unknown at communication receivers (assumption A6).
    Basis for treating X as a nuisance parameter in sensing and as data in communication.
  • standard math The variational reformulation via [35, Corollary 1] and the Hermite series arguments (Appendices A-B) require existence and regularity of the optimal output distribution.
    Theorem 2 itself shows this regularity fails for SISO with alpha in (0,1), so the necessary condition may be vacuous in some cases.
  • standard math The convergence of the B-A algorithm uses concavity of the functional J and [24, Theorem 9.5] (Appendix C).
    Assumes the infinite-dimensional alternating maximization converges to the supremum; practical discretization is not analyzed.
  • ad hoc to paper The compound signaling rate (53) assumes the channel estimate \hat{H} is effectively perfect for the data phase.
    This is the load-bearing simplification behind the claimed ISAC gain; residual estimation error is not modeled.

how reviews work

0 comments
Cite this review

Pith. "Pith review of On Pareto-Optimal Estimation-Information Performance Limits of MIMO Integrated Sensing and Communications Systems." pith.science (2026). https://pith.science/paper/QATDUN7J

@misc{pith2026250101053,
  author       = {Pith},
  title        = {Pith review of: On Pareto-Optimal Estimation-Information Performance Limits of MIMO Integrated Sensing and Communications Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QATDUN7J}},
  note         = {Machine review of arXiv:2501.01053}
}
read the original abstract

In this paper, we investigate the joint estimation-information performance limits of MIMO integrated sensing and communications systems.

Figures

Figures reproduced from arXiv: 2501.01053 by the authors.

Figure 1
Figure 1. ISAC system model considered in this paper. Plotted is bi-static sensing for demonstration purposes. The sensing receiver(s) can be [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. The ISAC MMSE-Rate region: an illustrative plot. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. The optimal input and output distributions for the SISO ISAC channel ( [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: ISAC signaling strategy for the case of coincided SAC channel. [PITH_FULL_IMAGE:figures/full_fig_p020_4.png]
Figure 5
Figure 5. Figure 5: The MMSE-Rate performance limit for fast-fading SISO ISAC channels ( [PITH_FULL_IMAGE:figures/full_fig_p022_5.png]
Figure 6
Figure 6. Figure 6: The MMSE-Rate limit and other loose bounds for MIMO ISAC channels. [PITH_FULL_IMAGE:figures/full_fig_p023_6.png]
Figure 7
Figure 7. Figure 7: Sensing- and communication-optimal power allocation ( [PITH_FULL_IMAGE:figures/full_fig_p023_7.png]
Figure 8
Figure 8. Figure 8: Effects of transmit SNR. 5 10 15 20 25 30 14 16 18 20 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 Normalized MMSE Rate R [bit/s/channel] Rc Rs ǫc ǫs (numerical) ǫs (analytical) [PITH_FULL_IMAGE:figures/full_fig_p024_8.png]
Figure 9
Figure 9. Figure 9: Effects of sensing channel dimensionality (number of widely-distributed sensing receivers) [PITH_FULL_IMAGE:figures/full_fig_p024_9.png]
Figure 10
Figure 10. Figure 10: Communication and sensing performance for different signaling strategies for coincided SAC channel ( [PITH_FULL_IMAGE:figures/full_fig_p025_10.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Data-Aided Target Localization in Multistatic ISAC Systems With Communication Constraints

    eess.SP 2026-07 accept novelty 6.0 of 10

    Data-aided multistatic ISAC localization bounds and algorithms show that marginalized or decoded OFDM data symbols improve SPEB under ergodic-rate constraints via joint pilot-fraction and covariance design.

Reference graph

Works this paper leans on

38 extracted references · 27 canonical work pages · cited by 1 Pith paper

  1. [7]

    On the fundamental tradeoff of integrated sensing and communications under Gaussian channels,

    Y . Xiong, F. Liu, Y . Cui, W. Yuan, T. X. Han, and G. Caire, “On the fundamental tradeoff of integrated sensing and communications under Gaussian channels,” IEEE Trans. Inf. Theory , vol. 69, no. 9, pp. 5723–5751, 2023

    work page 2023

  2. [1]

    Iterative sensing-assisted beam alignment for THz communications: Theory and method,

    Z. Wang, A. Tang, and X. Wang, “Iterative sensing-assisted beam alignment for THz communications: Theory and method,” in Proc. IEEE GLOBECOM, 2023, pp. 3916–3921

    work page 2023

  3. [2]

    Integrated sensing and communications: Toward dual-functional wireless networks for 6G and beyond,

    F. Liu, Y . Cui, C. Masouros, J. Xu, T. X. Han, Y . C. Eldar, and S. Buzzi, “Integrated sensing and communications: Toward dual-functional wireless networks for 6G and beyond,” IEEE J. Sel. Areas Commun. , vol. 40, no. 6, pp. 1728–1767, 2022

    2022

  4. [3]

    A survey on fundamental limits of integrated sensing and communication,

    A. Liu, Z. Huang, M. Li, Y . Wan, W. Li, T. X. Han, C. Liu, R. Du, D. K. P. Tan, J. Lu, Y . Shen, F. Colone, and K. Chetty, “A survey on fundamental limits of integrated sensing and communication,” IEEE Commun. Surveys Tuts. , vol. 24, no. 2, pp. 994–1034, 2022

    work page 2022

  5. [4]

    An overview of signal processing techniques for joint communication and radar sensing,

    J. A. Zhang, F. Liu, C. Masouros, R. W. Heath, Z. Feng, L. Zheng, and A. Petropulu, “An overview of signal processing techniques for joint communication and radar sensing,” IEEE J. Sel. Topics Signal Process. , vol. 15, no. 6, pp. 1295–1315, 2021

    2021

  6. [5]

    MIMO integrated sensing and communication: CRB-rate tradeoff,

    H. Hua, T. X. Han, and J. Xu, “MIMO integrated sensing and communication: CRB-rate tradeoff,” IEEE Trans. Wireless Commun., vol. 23, no. 4, pp. 2839–2854, 2024

    work page 2024

  7. [6]

    Fundamental CRB-rate tradeoff in multi-antenna ISAC systems with information multicasting and multi-target sensing,

    Z. Ren, Y . Peng, X. Song, Y . Fang, L. Qiu, L. Liu, D. W. K. Ng, and J. Xu, “Fundamental CRB-rate tradeoff in multi-antenna ISAC systems with information multicasting and multi-target sensing,” IEEE Trans. Wireless Commun. , vol. 23, no. 4, pp. 3870–3885, 2024

    work page 2024

  8. [8]

    MIMO radar waveform design based on mutual information and minimum mean-square error estimation,

    Y . Yang and R. S. Blum, “MIMO radar waveform design based on mutual information and minimum mean-square error estimation,” IEEE Trans. Aerosp. Electron. Syst. , vol. 43, no. 1, pp. 330–343, 2007

    2007

Show all 38 references
  1. [9]

    A modified Cram ´er-Rao bound and its applications (corresp.),

    R. Miller and C. Chang, “A modified Cram ´er-Rao bound and its applications (corresp.),” IEEE Trans. Inf. Theory , vol. 24, no. 3, pp. 398–400, 1978

    1978

  2. [10]

    On the true and the modified Cram ´er-Rao bounds for the estimation of a scalar parameter in the presence of nuisance parameters,

    M. Moeneclaey, “On the true and the modified Cram ´er-Rao bounds for the estimation of a scalar parameter in the presence of nuisance parameters,” IEEE Trans. Commun. , vol. 46, no. 11, pp. 1536–1544, 1998

    1998

  3. [11]

    Tse and P

    D. Tse and P. Viswanath, Fundamentals of wireless communication . Cambridge university press, 2005

    2005

  4. [12]

    Computation of channel capacity and rate-distortion functions,

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

    1972

  5. [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

  6. [14]

    Capacity of a mobile multiple-antenna communication link in Rayleigh flat fading,

    T. Marzetta and B. Hochwald, “Capacity of a mobile multiple-antenna communication link in Rayleigh flat fading,” IEEE Trans. Inf. Theory, vol. 45, no. 1, pp. 139–157, 1999

    1999

  7. [15]

    MIMO radar waveform design in colored noise based on information theory,

    B. Tang, J. Tang, and Y . Peng, “MIMO radar waveform design in colored noise based on information theory,” IEEE Trans. Signal Process., vol. 58, no. 9, pp. 4684–4697, 2010

    2010

  8. [16]

    Cram ´er-Rao bound optimization for joint radar-communication beamforming,

    F. Liu, Y .-F. Liu, A. Li, C. Masouros, and Y . C. Eldar, “Cram ´er-Rao bound optimization for joint radar-communication beamforming,” IEEE Trans. Signal Process. , vol. 70, pp. 240–253, 2022

    2022

  9. [17]

    Spectrally constrained MIMO radar waveform design based on mutual information,

    B. Tang and J. Li, “Spectrally constrained MIMO radar waveform design based on mutual information,” IEEE Trans. Signal Process. , vol. 67, no. 3, pp. 821–834, 2019

    2019

  10. [18]

    Goldsmith, Wireless Communications

    A. Goldsmith, Wireless Communications. Cambridge University Press, 2005

    2005

  11. [19]

    Communication on the Grassmann manifold: a geometric approach to the noncoherent multiple-antenna channel,

    L. Zheng and D. Tse, “Communication on the Grassmann manifold: a geometric approach to the noncoherent multiple-antenna channel,” IEEE Trans. Inf. Theory , vol. 48, no. 2, pp. 359–383, 2002

    2002

  12. [20]

    An information-theoretic approach to joint sensing and communication,

    M. Ahmadipour, M. Kobayashi, M. Wigger, and G. Caire, “An information-theoretic approach to joint sensing and communication,” IEEE Trans. Inf. Theory, vol. 70, no. 2, pp. 1124–1146, 2024

    2024

  13. [21]

    S. M. Kay, Fundamentals of statistical signal processing: estimation theory . Prentice-Hall, Inc., 1993

    1993

  14. [22]

    Salvendy, Handbook of Industrial Engineering: Technology and Pperations Management , 3rd ed

    G. Salvendy, Handbook of Industrial Engineering: Technology and Pperations Management , 3rd ed. John Wiley & Sons, 2001

    2001

  15. [23]

    The sample average approximation method for stochastic discrete optimization,

    A. J. Kleywegt, A. Shapiro, and T. Homem-de Mello, “The sample average approximation method for stochastic discrete optimization,” SIAM Journal on Optimization , vol. 12, no. 2, pp. 479–502, 2002

    2002

  16. [24]

    R. W. Yeung, Information theory and network coding . Springer Science & Business Media, 2008. SUMBITTED TO THE IEEE TRANSACTIONS ON INFORMATION THEORY 35

    2008

  17. [25]

    S. P. Boyd and L. Vandenberghe, Convex optimization. Cambridge university press, 2004

    2004

  18. [26]

    MIMO radar with widely separated antennas,

    A. M. Haimovich, R. S. Blum, and L. J. Cimini, “MIMO radar with widely separated antennas,” IEEE Signal Process. Mag. , vol. 25, no. 1, pp. 116–129, 2008

    2008

  19. [27]

    Target velocity estimation and antenna placement for MIMO radar with widely separated antennas,

    Q. He, R. S. Blum, H. Godrich, and A. M. Haimovich, “Target velocity estimation and antenna placement for MIMO radar with widely separated antennas,” IEEE J. Sel. Topics Signal Process. , vol. 4, no. 1, pp. 79–100, 2010

    2010

  20. [28]

    Generalized Cram ´er-Rao bound for joint estimation of target position and velocity for active and passive radar networks,

    Q. He, J. Hu, R. S. Blum, and Y . Wu, “Generalized Cram ´er-Rao bound for joint estimation of target position and velocity for active and passive radar networks,” IEEE Trans. Signal Process. , vol. 64, no. 8, pp. 2078–2089, 2016

    2016

  21. [29]

    T. M. Cover, Elements of information theory . John Wiley & Sons, 1999

    1999

  22. [30]

    Conflict and trade-off of waveform uncertainty in joint communication and sensing systems,

    H. Li, “Conflict and trade-off of waveform uncertainty in joint communication and sensing systems,” in Proc. IEEE ICC , 2022, pp. 5561–5566

    2022

  23. [31]

    Mutual information and minimum mean-square error in Gaussian channels,

    D. Guo, S. Shamai, and S. Verdu, “Mutual information and minimum mean-square error in Gaussian channels,” IEEE Trans. Inf. Theory , vol. 51, no. 4, pp. 1261–1282, 2005

    2005

  24. [32]

    CVX: Matlab software for disciplined convex programming, version 2.0,

    CVX Research, Inc., “CVX: Matlab software for disciplined convex programming, version 2.0,” https://cvxr.com/cvx, Aug. 2012

    2012

  25. [33]

    Optimal signaling schemes and capacities of non-coherent correlated MISO channels under per-antenna power constraints,

    M. N. Vu, N. H. Tran, H. D. Tuan, T. V . Nguyen, and D. H. N. Nguyen, “Optimal signaling schemes and capacities of non-coherent correlated MISO channels under per-antenna power constraints,” IEEE Trans. Commun. , vol. 67, no. 1, pp. 190–204, 2019

    2019

  26. [34]

    Target localization accuracy gain in MIMO radar-based systems,

    H. Godrich, A. M. Haimovich, and R. S. Blum, “Target localization accuracy gain in MIMO radar-based systems,” IEEE Trans. Inf. Theory, vol. 56, no. 6, pp. 2783–2803, 2010

    2010

  27. [35]

    A unifying variational perspective on some fundamental information theoretic inequalities,

    S. Park, E. Serpedin, and K. Qaraqe, “A unifying variational perspective on some fundamental information theoretic inequalities,” IEEE Trans. Inf. Theory, vol. 59, no. 11, pp. 7132–7148, 2013

    2013

  28. [36]

    Using Hermite bases in studying capacity-achieving distributions over AWGN channels,

    J. J. Fahs and I. C. Abou-Faycal, “Using Hermite bases in studying capacity-achieving distributions over AWGN channels,” IEEE Trans. Inf. Theory, vol. 58, no. 8, pp. 5302–5322, 2012

    2012

  29. [37]

    Distributions which are Gaussian convolutions,

    A. DasGupta, “Distributions which are Gaussian convolutions,” in Statistical Decision Theory and Related Topics V , S. S. Gupta and J. O. Berger, Eds. New York, NY: Springer New York, 1994, pp. 391–400

    1994

  30. [38]

    Capacity of multi-antenna Gaussian channels,

    E. Telatar, “Capacity of multi-antenna Gaussian channels,” European Trans. Telecommun., vol. 10, no. 6, pp. 585–595, 1999

    1999

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.