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Integrated Sensing and Communications in Downlink FDD MIMO without CSI Feedback

T0 review · 4 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read FDD MIMO-ISAC precoding can run with zero downlink CSI feedback: reconstruct each user's channel from uplink training, estimate the reconstruction error's covariance from the uplink signal, and let RSMA manage the resulting interference.

desk verdict Solid integration of zero-feedback FDD channel reconstruction with RSMA and NEPv for ISAC, but the error covariance estimate omits the non-reciprocal DL gain term and may overstate the claimed robustness. read the letter →

arxiv 2412.12590 v3 pith:EAJAIOAQ submitted 2024-12-17 cs.IT eess.SPmath.IT

Namhyun Kim , Juntaek Han , Jinseok Choi , Ahmed Alkhateeb , Chan-Byoung Chae , Jeonghun Park This is my paper · ORCID
classification cs.ITeess.SPmath.IT
keywords integratedsensingandcommunication(ISAC)frequencydivisionduplex(FDD)zero-feedbackCSIacquisitionpartialchannelreciprocityerrorcovarianceestimationobservedFisherinformationrate-splittingmultipleaccess(RSMA)nonlineareigenvalueproblem(NEPv)
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 claims that an FDD MIMO base station can run integrated sensing and communication without any downlink CSI feedback. The idea is to reconstruct each user's downlink channel from uplink training signals using partial reciprocity, estimate the covariance of the reconstruction error from observed Fisher information, and then design an RSMA precoder that maximizes ergodic sum spectral efficiency while keeping the sensing beam pattern within a target mean-squared error. If the error-covariance estimate is accurate, the scheme removes feedback latency and overhead while still managing the interference that imperfect CSI and radar symbols create. The payoff is a practical low-latency route to joint communication and sensing in FDD bands, a regime where feedback cost usually dominates.

What carries the argument

The load-bearing object is the estimated error covariance matrix $\hat{\boldsymbol{\Sigma}}_k$, obtained as the diagonal of $Q_k^H(f)\,I^{-1}(\hat{P}_k)\,Q_k(f)$, where $I(\hat{P}_k)$ is the observed Fisher information of the uplink channel parameters and $Q_k(f)$ is the Jacobian mapping uplink parameter errors to downlink channel errors. This matrix converts unknown CSI imperfection into a concrete quadratic penalty inside each user's SINR, making the imperfect-CSI precoding problem tractable. Two further mechanisms carry the optimization: rate-splitting multiple access (RSMA), whose common stream is decoded by every user and helps mitigate the interference caused by imperfect CSI and radar symbols, and the nonlinear-eigenvalue reformulation, which turns the KKT stationarity condition $L(\bar{p},\nu)\bar{p} = \zeta(\bar{p},\nu) R(\bar{p},\nu)\bar{p}$ into a fixed-point iteration for the leading eigenvector of $R^{-1}L$. The Lagrange multiplier $\nu$ acts as a dial between communication and sensing: small $\nu$ favors sum SE, large $\nu$ enforces the beam-pattern MSE constraint.

What would settle it

Take a measured FDD channel with strong spatial correlation and a larger UL-DL frequency gap, reconstruct the downlink channel with 2D-NOMP, and compare the true per-antenna error covariance against the diagonal $\hat{\boldsymbol{\Sigma}}_k$ from Eq. (63); if off-diagonal entries are non-negligible or the trace systematically misses the realized MSE, the RSMA precoder will misallocate power and the claimed SE gains should shrink in the corresponding simulations.

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Extended reading notes

Core claim

The central claim is that missing downlink channel error statistics—normally unavailable without feedback—can be synthesized from uplink observations alone. Because the 2D-NOMP uplink parameter estimator operates near the Cramér-Rao bound, the paper evaluates the negative Hessian of the uplink log-likelihood at the estimated parameters (the observed Fisher information), maps its inverse through the Jacobian to the downlink channel, and uses only its diagonal as the error covariance matrix $\hat{\boldsymbol{\Sigma}}_k$. Feeding this covariance into the SINR expressions turns the RSMA precoding problem into a nonlinear eigenvalue problem with eigenvector dependency; the proposed generalized power iteration updates the precoder and the Lagrange multiplier alternately, with the multiplier controlling how strictly the beam-pattern MSE constraint is enforced. The paper reports that this zero-feedback design achieves higher ergodic sum SE than the ISAC baselines across target MSE levels and SNRs, while matching or improving the achieved sensing beam-pattern MSE and sidelobe suppression.

Load-bearing premise

The whole scheme rests on the assumption that the base station can accurately guess how wrong its downlink channel reconstruction is—and that the guess needs no off-diagonal terms—using only the uplink training signal.

Editorial extensions

If this is right

  • Downlink CSI feedback can be dropped entirely in FDD MIMO-ISAC, removing the multi-millisecond feedback loop and the overhead that scales with antenna and user count.
  • The sensing beam pattern remains controllable to a prescribed MSE even though the precoder is built from reconstructed, imperfect CSI, and users see less sensing-induced interference than with the SDMA or SDR baselines.
  • The same optimization machinery extends to other sensing metrics: the paper formulates an SCNR-constrained variant and shows the beam pattern steers toward targets and away from clutter.
  • Precoder updates are a generalized power iteration, so per-iteration complexity scales as $O(N^3(K+M))$ rather than the semidefinite-programming cost of earlier ISAC designs.
  • The relative SE advantage narrows as the number of antennas grows because channel vectors become more orthogonal, but the zero-feedback RSMA design still outperforms the GPI-ISAC baseline at 128 antennas.

Reading between the lines

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

  • If the observed-Fisher-information estimate proves as faithful in hardware as in simulation, the same recipe could attach to any uplink estimator that operates near its Cramér-Rao bound, making it a general zero-feedback ISAC design pattern rather than a 2D-NOMP-specific fix.
  • The diagonal-only covariance assumption is the most fragile piece: in spatially correlated channels, off-diagonal error terms could leak through the SINR bounds, and an extension to full covariance or a diagonal inflation factor would be a natural fix.
  • The stated partial-reciprocity condition is tied to moderate UL-DL frequency separation; sweeping the frequency gap and locating where the SE advantage over feedback-based baselines disappears would map the method's operational range.
  • A hybrid design could add a low-rate feedback link that only corrects the common-stream rate allocation, using the error-covariance estimate to decide when such correction is needed.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The paper proposes a zero-feedback precoding framework for FDD MIMO-ISAC systems. The downlink channel is reconstructed from uplink training via 2D-NOMP, and an error covariance matrix (ECM) is estimated from the observed Fisher information of the uplink parameter estimates. This ECM is used in an RSMA-based precoder that maximizes a lower bound on the ergodic sum spectral efficiency under a beam-pattern MSE constraint. The precoder is obtained by a generalized power iteration derived from a nonlinear eigenvalue problem with eigenvector dependency (NEPv). The numerical results claim that the method provides precise beam pattern control, high SE, and a favorable sensing-communication trade-off without CSI feedback.

Significance. If the results are correct, the paper offers a meaningful advance: it removes CSI feedback overhead in FDD ISAC, which is a major practical barrier, and it combines RSMA with a Fisher-information-based error covariance estimate in a scalable NEPv framework. The paper gives a self-contained KKT derivation, a complexity analysis, and extensive simulations including detection probability, SCNR extension, and large-antenna regimes. However, the central component—the ECM estimation—has a modeling gap: the estimator in Eq. (63) omits the independent non-reciprocal DL gain component in Eq. (4). Because the RSMA precoder relies on this covariance to allocate power and whiten interference, the reported SE and trade-off improvements are not established for the stated channel model. The validation of the ECM refers to the authors' prior work [24], which does not cover the generalized non-reciprocal gain model.

major comments (4)
  1. [Section IV, Eq. (63)] The estimated ECM in Eq. (63) is biased low because it omits the independent non-reciprocal DL gain component β in Eq. (4). The reconstruction in Eq. (9) sets `\hat{α}^dl = η \hat{α}^ul`, but the true DL gain is η α^ul + sqrt(1−η²) β. The observed Fisher information I(\hat{P}_k) in Eq. (58) is computed from the UL likelihood and has no sensitivity to β, which is independent of α^ul and not observed from UL training. The Jacobian Q_k in Eq. (61) can only propagate the covariance of the UL parameter estimation errors; it cannot account for the variance of β. Consequently, Eq. (63) omits a contribution with per-path variance (1−η²)σ_path². Since the simulations set η=0.9, this is a non-negligible systematic under-estimate. Because the RSMA SINR expressions in Eqs. (40)–(43) and the precoder updates in Eqs. (66)–(73) depend directly on \Σhat, the SE gains shown in Figs. 3–4 and the claimed sensing–communication trade-off are not reliable for the model in Eq. (4). The validation via [24, Fig. 1] does not cover this generalized model.
  2. [Section IV, Eq. (63)] The diagonal approximation in Eq. (63) is inconsistent with the sparse geometric channel model. Even if the β components are independent across paths, after multiplication by the array response u(τ,θ) the antenna-domain error covariance has off-diagonal entries proportional to (1−η²)σ_path². The justification by reference to a 'rich scattering' environment [34] does not apply to the 2D-NOMP reconstruction error in Eqs. (1)–(10), which is based on a deterministic multipath model. Since the off-diagonal terms enter the RSMA interference terms through \Σhat in Eqs. (40)–(43), discarding them can systematically misallocate common/private power and distort the reported SE.
  3. [Section IV, Eq. (61)] The Jacobian matrix Q_k(f) is not derived; the paper only states that 'its derivation is straightforward' and refers to [22]. This step is load-bearing because the Jacobian must map the four UL parameters (real/imaginary gain, delay, angle) to the DL channel vector and must incorporate the partial-reciprocity scaling in Eq. (9). Without the explicit expression or a derivation, the reader cannot verify that the inverse observed Fisher information is transformed correctly, and the error propagation argument in Eq. (61) remains incomplete. Please provide the explicit form of Q_k(f) or a detailed derivation.
  4. [Section V, Proposition 1 and Algorithm 1] The convergence argument in Eqs. (74)–(81) is a perturbative analysis around a fixed point and assumes \bar{p}^{(t−1)} is already close to \bar{p}†. The paper does not provide a global convergence guarantee, and the initialization of \bar{p}^{(0)} is unspecified. In addition, the outer-loop condition in Algorithm 1 ('while |ν^{(n)}−ν^{(n−1)}|≥ε_ν or n≤n_max') appears to be a typo: with 'or' the loop always runs to n_max, making the first condition irrelevant. Please correct this condition and state precisely what convergence result is claimed.
minor comments (6)
  1. [Algorithm 1] The algorithm states 'Construct matrix L(\bar{p}^{(t−1)},ν^{(n)}) with (33); Construct matrix R(...) with (34);' but equations (33) and (34) are the MSE constraint and the norm constraint, not the matrix definitions. The intended references are likely Eqs. (67) and (68). Also, the variable \zeta_mse is not defined before it is used in the MSE feasibility check.
  2. [Notation] The symbol η is overloaded: in Eq. (4) it denotes the partial-reciprocity gain coefficient, while in Eq. (44) it is the LogSumExp smoothing parameter. Please rename one of them to avoid confusion.
  3. [Fig. 3 caption] The figure caption orders the subplots as '(a) Achieved MSE and (b) Ergodic sum SE', but the text refers to Fig. 3-(a) as the ergodic sum SE and Fig. 3-(b) as the achieved MSE. The caption and text should be made consistent.
  4. [Eq. (11)] In Eq. (10) and the following line, the reconstructed DL channel uses \hat{\phi}^{ul}_{k,ℓ,s}, which appears to be a typo: it should be \hat{\phi}^{dl}_{k,ℓ,s} or a notation that makes the DL frequency dependence explicit.
  5. [Simulation setup] The values of the LogSumExp smoothing parameter η and the bisection bounds (ν_min, ν_max) are not reported. Since these are user-specified free parameters, please provide their values and, ideally, a brief sensitivity study.
  6. [Remark 6] The complexity analysis refers to a matrix \Omega(\bar{p}) that is never defined. The statement should refer to the matrix inverted in the algorithm, presumably R(\bar{p},ν) or the matrix K(\bar{p},ν).

Circularity Check

1 steps flagged · score 4.0 of 10

Partial circularity: the central ECM-accuracy premise is imported from the authors' prior work [24] rather than validated under this paper's generalized channel model.

  1. self citation load bearing [Section IV (Error Covariance Matrix Estimation), after Eq. (62), around Eq. (63)]
    "We note that the robustness of our ECM estimation method can be found in our prior work [24]. As shown in Fig. 1 of [24], the estimated ECM closely matches the actual MSE and outperforms the CRLB."

    The precoder's claimed robustness under imperfect zero-feedback DL CSI—and the SE gains in Figs. 3–4—depend on the error covariance matrix 𝚺̂_k entering (40)–(43) being an accurate estimate of E[e_k e_k^H]. The only validation offered for this load-bearing estimate is Fig. 1 of [24], a prior paper whose first author (N. Kim) and advisor (J. Park) are authors of the present work. That prior result is not machine-checked, not reproduced in this paper, and is not shown to cover the generalized gain model (4) with η_kℓ=0.9 used in all simulations. The key support for the proposed method therefore reduces to a self-citation rather than to evidence generated independently in this paper.

full rationale

The main optimization pipeline—RSMA rate bounds in (20)–(27), the NEPv stationarity condition in Lemma 1, the GPI update in (73), and the Lagrange-multiplier search in Algorithm 1—is derived and simulated in this paper, and the SE/MSE curves are computed from independently generated channels rather than fitted to the outputs. Thus the central numerical claims are not circular in the sense of fitting a parameter and then predicting that same parameter. However, the most load-bearing component of the framework, the error covariance matrix 𝚺̂_k that shapes the SINR denominators in (40)–(43), is asserted to be accurate solely by reference to Fig. 1 of the authors' own prior paper [24]. That self-citation is the only support for the claim that Eq. (63) captures the realized DL reconstruction error, and the present paper contains no in-paper comparison of (63) with the true DL error under its own channel model (4). I also flag, as a non-circular correctness risk rather than a circularity, that Eq. (63) omits the statistically independent non-reciprocal gain term √(1−η²)β introduced in Eq. (4); this mismatch makes the estimator inconsistent with the stated model but does not by itself make the simulated SE values equal to the inputs. On balance, the derivation has substantial independent content, so the score reflects one load-bearing self-citation rather than a fully self-referential argument.

Assumptions & free parameters 2 free parameters · 8 assumptions · 0 invented entities

The central claim rests on partial reciprocity and near-CRLB 2D-NOMP, inherited from prior measurement-based work; the observed-Fisher ECM is validated in the authors' own [24], not independently; the diagonal covariance is a strong simplifying assumption. No new physical entities are introduced.

free parameters (2)
  • LogSumExp smoothing parameter eta = not specified
    Introduced in Eq. (44) to approximate the min function; the paper says larger eta gives tighter approximation but no simulation value is given, and it affects the SE objective and convergence.
  • Bisection bounds for Lagrange multiplier nu (nu_min, nu_max) = not specified
    Algorithm 1 requires nu_min and nu_max for the binary tree search over the sensing constraint multiplier; these are not specified, affecting reproducibility.
assumptions (8)
  • domain assumption Partial reciprocity: UL and DL share propagation delay, angle, and path count (tau, theta, L).
    Section II.A and Remark 1; required for DL reconstruction from UL training.
  • domain assumption DL channel gain obeys alpha_dl = eta alpha_ul + sqrt(1-eta^2) beta with eta != 1 allowed.
    Eq. (4); models non-reciprocal gains; eta is assumed known (0.9 in simulations).
  • domain assumption 2D-NOMP achieves near-CRLB estimation of UL parameters.
    Section IV; justifies replacing true Fisher information with observed Fisher information at the estimate.
  • standard math Inverse observed Fisher information provides optimal squared-error covariance estimate.
    Section IV and Eq. (61), citing Efron and Hinkley [37]; standard statistical result.
  • domain assumption DL CSI error covariance is diagonal (uncorrelated across antennas).
    Eq. (63)-(64); justified by rich scattering [34], but the channel model is sparse multipath ULA, where correlation may exist.
  • domain assumption Residual terms from imperfect CSI and sensing are treated as independent Gaussian noise.
    Eq. (17)-(21); yields lower bound on SE; standard worst-case assumption.
  • standard math Jensen's inequality gives valid lower bounds on ergodic rates.
    Eq. (20), (23); standard.
  • domain assumption Sparse multipath environment with path count less than product of antennas and subcarriers.
    Remark 5; required for 2D-NOMP to work.

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Cite this review

Pith. "Pith review of Integrated Sensing and Communications in Downlink FDD MIMO without CSI Feedback." pith.science (2026). https://pith.science/paper/EAJAIOAQ

@misc{pith2026241212590,
  author       = {Pith},
  title        = {Pith review of: Integrated Sensing and Communications in Downlink FDD MIMO without CSI Feedback},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EAJAIOAQ}},
  note         = {Machine review of arXiv:2412.12590}
}
read the original abstract

In this paper, we propose a precoding framework for frequency division duplex (FDD) integrated sensing and communication (ISAC) systems with multiple-input multiple-output (MIMO). Specifically, we aim to maximize ergodic sum spectral efficiency (SE) while satisfying a sensing beam pattern constraint defined by the mean squared error (MSE). Our method reconstructs downlink (DL) channel state information (CSI) from uplink (UL) training signals using partial reciprocity, eliminating the need for CSI feedback. To obtain the error covariance matrix of the reconstructed DL CSI, we devise an observed Fisher information-based estimation technique. Leveraging this, to mitigate interference caused by imperfect DL CSI reconstruction and sensing operations, we propose a rate-splitting multiple access (RSMA) aided precoder optimization method. This method jointly updates the precoding vector and Lagrange multipliers by solving the nonlinear eigenvalue problem with eigenvector dependency to maximize SE. The numerical results show that the proposed design achieves precise beam pattern control, maximizes SE, and significantly improves the sensing-communication trade-off compared to the state-of-the-art methods in FDD ISAC scenarios.

Figures

Figures reproduced from arXiv: 2412.12590 by the authors.

Figure 1
Figure 1. TDD ISAC may require modified time slot allocation for signal separation [14]; otherwise, interference between reflected sensing and UL communication signals may occur. In contrast, FDD ISAC leverages separate DL and UL frequency bands to achieve signal separation using established protocols. this approach does not assume designated radar symbols, making it sub-optimal compared to considering respective symbols for … view at source ↗
Figure 2
Figure 2. Normalized beam patterns and corresponding sidelobe [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. (a) Achieved MSE and (b) Ergodic sum SE with [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figures from the paper (4 more)
Figure 5
Figure 5. Figure 5: Average detection probability with 𝑁 = 8, 𝐾 = 4, 𝑀 = 4, and 𝜂𝑘,ℓ = 0.9 ∀(𝑘, ℓ). RS) outperforms the SDR-based algorithm with rank-1 ap￾proximation (SDR-Rank1) and regularized zero-forcing (RZF) in SE for 𝑇mse = −11 dB, while closely satisfying the MSE constraint, as de…
Figure 6
Figure 6. Figure 6: Convergence behavior of the proposed GPI-ISAC-RS [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]
Figure 7
Figure 7. Figure 7: Ergodic sum SE and sensing beam pattern when con [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]
Figure 8
Figure 8. Figure 8: Ergodic sum SE and sensing beam pattern in large [PITH_FULL_IMAGE:figures/full_fig_p015_8.png]

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.